Abstract:
In a stabilized laser system, a an output signal is to be generated having a desired central wavelength. At least one laser, which, while emitting light and having a preselected portion thereof fed back thereto, causes the output signal of the laser to be shifted in wavelength in a first direction which is spaced apart from the center wavelength of the fed back signal. A feedback generating arrangement processes a first portion of the output signal from each laser and generates a feedback signal having a spectral response peaking at a wavelength shifted in an opposite direction to the first direction generated by each laser. The feedback signal each laser to provide an output signal at the output of the stabilized laser system having a spectral response that peaks essentially at the desired wavelength.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is related to U.S. Ser. No. 10/776,810, which is entitled “Single And Multiple Wavelength Reflector And Transmission Filter Arrangements” (Optovia 7), and U.S. Ser. No. 10/776,809, which is entitled “Stable High Efficiency Multiple Wavelength Laser Sources” (Optovia 8), both having a common assignee and some common inventors with the present application, and being filed concurrently with the present application. 
   FIELD OF THE INVENTION 
   The present invention relates to a method and apparatus intended primarily, although not so limited, for providing a high efficiency stabilized wavelength laser system for irradiating (pumping) particular portions of an optical fiber used as part of an optical fiber transmission line to form such portions into optical amplifiers. These amplifiers serve to overcome transmission losses occurring in other portions of the optical fiber. Such apparatus generally is described as a pump laser. 
   BACKGROUND OF THE INVENTION 
   Pump lasers are generally found in the form of Fabry Perot (FP) cavity lasers whose multimode spectrums are broadband and extremely sensitive to temperature and laser drive current. Such lasers, therefore, require wavelength stabilization for most applications, such as, for example, with optical amplifiers. Different methods have been proposed in the past to stabilize such pump lasers. 
   In a first prior art laser stabilization method, a laser source is coupled at its output to a reflection filter that selectively reflects back a part of the output of the laser sources toward the laser to stabilize the laser source&#39;s spectrum and power. The reflection filter sets both the wavelength and the amount of reflection used to feed back a signal to the laser source as found in, for example, Fiber Bragg Gratings (FBG) stabilized lasers. In such FBG system, the pump laser is connected to the FBG via a Polarization Maintaining (PM) optical fiber. The FBG provides the required reflection for stabilization of the FP laser chip. This method has been extensively used to stabilize a single laser source. Some multiple wavelength applications have also used this method to stabilize multiple laser sources using individual FBG for each laser source followed by a wavelength Division Multiplexer (WDM) to combine stabilized laser source signals. 
   Referring now to  FIG. 1 , there is shown a stabilized laser system  10  illustrating a second prior art laser stabilization method. The system  10  comprises a laser source  11  whose output/input facet  12  is coupled to an input/output port  13  of a laser stabilization system  14  (shown within a dashed line rectangle) comprising a transmission filter  15  and a reflector  16 . The transmission filter  15  is coupled at an output/input port  17  thereof to an input/output port  18  of the reflector  16 . An output port  19  of the reflector  16  provides an output signal from the stabilized laser system  10 . The transmission filter  15  sets the wavelength (hereinafter also designated “w”), and the reflector  16  sets the amount of signal reflection provided back through the transmission filter  15  to the laser source  11 . 
   For the system  10  of  FIG. 1 , an overall Forward filter spectral response for the transmission filter  15  is defined as F o (w) as the transmission filter spectral response between the output/input facet  12  of the laser source  11  and the output port  19  from the reflector  16 . A Feedback filter spectral response for the transmission filter  15  is defined as F f (w) as the overall transmission filter spectral response between the forward and backward (feedback) signals found at the output/input facet  12  of the laser source  11 . In operation, an output signal of the laser source  11  at its output/input facet  12  is filtered by the transmission filter  15 , F(w), to provide a signal f o (w) in the path between output/input port  17  and input/output port  18 , and is partially reflected back by the reflector  16 . A main portion of the signal received by the reflector at its input/output port  18  is transmitted through the reflector  16  to the output port  19  of the system  10 . Therefore, the output signal, F o (w), at output port  19  of the laser stabilization system  10  is defined as:
 
 F   o ( w )= f   o ( w )/ f   i ( w )= F ( w )  (1)
 
The reflected or feedback signal, f f (w), from the reflector  16  is filtered by the transmission filter  15  for a second time to generate a signal f f (w) that is fed back into the output/input facet  12  of the laser source  11 . Therefore, the Feedback filter spectral response is defined as F f (w) that is further defined as:
 
 F   f ( w )= f   f ( w )/ f   i ( w )= F ( w )· F ( w )  (2)
 
   Referring now to  FIG. 2 , there is shown a graph of wavelength on the X-axis versus amplitude on the Y-axis for a curve  20  showing an exemplary forward filter spectral response and a curve  22  (shown as a dashed line) for a feedback filter spectral response obtainable in the laser stabilization system  10  shown in  FIG. 1  for the transmission filter  15 . If the stabilized laser system  10  uses a transmission filter  15  followed by a broadband reflector  16  in the manner shown in  FIG. 1  for a single laser system  10 , a red shift (a shift to a longer wavelength) in the signal center wavelength  24  from the laser  12  (shown by curve  22 ) can cause significant excess loss (filtering loss) depending upon the filter transmission bandwidth and the wavelength shift. As a laser drive current increases, the signal center wavelength shifts from a peak wavelength of the transmission filter F(w)  20  to a longer wavelength and suffers a higher insertion loss as shown by exemplary point  26  on the curve  20 . 
   In operation, the output signal (not shown in  FIG. 2 ) generated by laser source  11  is filtered by the transmission filter  15  having a spectral response curve as is shown by curve  20  to provide a desired output signal from the system  10  where the power peaks at a center wavelength corresponding to the peak of curve  20 . When a portion of this filtered signal is reflected by reflector  16 , it is again filtered by the transmission filter  15  resulting in the narrower dashed line curve  22  and returned to the input of the laser sources  11 . It is found that the laser source, in response to a feedback signal, produces a wavelength shift relative to the center wavelength of feedback signal and now generates an output signal that now has a center wavelength shown by line  24  which is separated by an amount δw from the peak of curve  20  as is shown in  FIG. 2 . This results in an excess loss of power in the output signal of the system  10  from the desired output signal that has a center wavelength at the peak of curve  20 . The above description indicates that the laser source  11  produces a red shift in response to a reflected feedback signal. The occurrence of a red directional shift (in a first direction) shown in  FIG. 2  is mostly true for semiconductor diodes lasers. However, there are other types of lasers that actually produce a blue shift (to a shorter wavelength) in response to the reception of a feedback signal that also causes a similar excess loss. 
   This second laser source stabilization method shown in  FIG. 1  is not really effective for a single laser source system, but it can be used effectively in stabilizing a multiple wavelength laser source system (not shown). In such multiple wavelength laser source system, multiple laser signals from a multiple laser source are multiplexed using a transmission filter/multiplexer coupled at an output thereof to a broadband reflector. The spectral response of the combination of the broadband reflector and the transmission filter/multiplexer for the demultiplexed laser signals returning to corresponding lasers of the multiple laser source of the system, stabilizes each laser at a predetermined center wavelength. 
   In an FBG stabilized laser system, the FBG is a reflection filter and, therefore, the signal outside of the reflection spectral band is not subjected to any additional loss (excess loss or filtering loss). As a result, this red shift does not impose significant limitations on the operation of the FBG stabilized laser if the particular application can tolerate a wavelength shift of up to 1 nanometer depending on both the FBG reflection bandwidth and the laser drive current and power. 
   It is desirable to provide a more efficient single or multiple laser source system that reduces loss for a single or multiple laser source stabilization system based on the use of a transmission filter of various technologies. 
   SUMMARY OF THE INVENTION 
   The present invention relates to method and apparatus for providing high efficiency stabilized single or multiple wavelength laser source systems by reducing losses using one or more red or blue shifted (shift towards a longer or shorter wavelength, respectively) feedback signals in systems that are based on a transmission filter of various technologies. 
   From a first apparatus aspect, the present invention relates to a stabilized laser system comprising at least one laser, a main transmission filter and a feedback transmission filter, and a feedback arrangement. Each of the transmission filter comprises first and second ports with the first ports of both transmission filters being coupled to the at least one laser. Still further, each of the transmission filters comprises a different spectral wavelength response as a function of wavelength. The second port of the main transmission filter is coupled to an output of the stabilized laser system. The feedback arrangement comprises one of a group consisting of a reflector coupled to the second port of the feedback transmission filter, and a loop coupled between the second ports of the main and feedback transmission filters. 
   From a second apparatus aspect, the present invention relates to a stabilized laser system for generating a signal at an output thereof having a desired central wavelength comprising at least one laser, and means coupled to the at least one laser for generating, from a portion of a signal generated thereby, a feedback signal having a wavelength that is different from the desired wavelength and feeding the feedback signal back to the laser for stabilizing the laser system at the desired central wavelength. 
   From a third apparatus aspect, the present invention relates to a stabilized laser system for generating a signal at an output thereof having a desired center wavelength comprising at least one laser, and feedback signal generating means. The at least one laser, which, while emitting light and having a preselected portion thereof fed back thereto, causes the output signal of the at least one laser source to be shifted in wavelength in a first direction which is spaced apart from the center wavelength of the fed back signal. The feedback signal generating means is coupled to the at least one laser for generating a feedback signal having a spectral response peaking at a wavelength shifted in an opposite direction to the first direction generated by at least one laser in response to the feedback signal so as to provide an output signal at the output of the stabilized laser system having a spectral response that peaks essentially at the desired wavelength. 
   From a fourth apparatus aspect, the present invention relates to a stabilized laser system for generating a signal at an output thereof having a desired central wavelength comprising at least one laser, and a first and a second transmission filter. Each laser of the at least one laser, which, while emitting light at the desired central wavelength and having a preselected portion thereof fed back thereto, causes the output signal of the at least one laser source to be shifted in wavelength in a first direction which is spaced apart from the center wavelength of the fed back signal. Each of the first and second transmission filters comprises a different wavelength spectral response and a first and second port. The output signal from the laser is coupled to the input of the first transmission filter such that at least a first portion of any signal emitted by the laser is transmitted to the first port of the first transmission filter. The second port of the first transmission filter is coupled to an output of the stabilized laser system. The output of the laser is coupled to the first port of the second transmission filter such that at least a second portion of any signal emitted by the laser is transmitted to the first port of the second transmission filter. The second port of the second transmission filter is coupled to the output of the laser such that any signal generated at the second port of the second transmission filter, whose spectral response peaks at a wavelength shifted in an opposite direction to that generated by the at least one laser in response to a feedback signal, is fed back to the laser so as to provide at the output of the stabilized laser system an output signal having a spectral response that peaks at the desired central wavelength. 
   From a fifth apparatus aspect, the present invention relates to a stabilized laser system for generating a signal at an output thereof having a desired central wavelength comprising a plurality of n lasers, and a multiplexer/filter arrangement. Each of the plurality of n lasers, which, while emitting light at the desired central wavelength and having a preselected portion thereof fed back thereto, causes the output signal of the laser source to be shifted in wavelength in a first direction which is spaced apart from the central wavelength of the fed back signal. The multiplexer/filter arrangement comprises a forward multiplexer/filter section and a feedback multiplexer/filter section. Each of the forward and feedback multiplexer/filter sections comprises a different wavelength spectral response as a function of wavelength, a plurality of n first ports, and a second port. The output signal from each of the lasers is coupled to a corresponding one of the plurality of n first ports of the forward multiplexer/filter section such that at least a first portion of the output signal emitted by each of the lasers is transmitted to a corresponding one of the first ports of the forward multiplexer/filter section. Still further, the second port of the forward multiplexer/filter section is coupled to an output of the stabilized laser system. The output signal from the second port of the forward multiplexer/filter section is further coupled to the second port of the feedback multiplexer/filter section wherein the received signal is demultiplexed and delivered to the plurality of n first ports of the feedback multiplexer/filter section. Still further, each of the plurality of n first ports of the feedback multiplexer/filter section is coupled to one of a group consisting of (a) a corresponding one of a plurality of n reflectors for returning a received signal back through the forward and feedback multiplexer/filter sections to the corresponding one of the plurality of n lasers, and (b) a second feedback multiplexer/filter subsection comprising a plurality of n first ports, and a second port, where each one of the plurality of n first ports thereof is coupled to a corresponding one of the plurality of n first ports of the first feedback multiplexer/filter subsection. The second port of the second feedback multiplexer/filter subsection is coupled to one of a group consisting of a reflector, and a loop for returning the feedback signal through the forward multiplexer/filter to the output of the plurality of n lasers such that any signal generated at the second port of the second multiplexer/filter subsection has a spectral response that peaks at a wavelength shifted in an opposite direction to that generated by each of the plurality of n lasers in response to a feedback signal so as to provide at the output of the stabilized laser system an output signal comprising a spectral response that peaks at the desired central wavelength. 
   From a first method aspect, the present invention relates to a method of stabilizing a laser system to generate an output signal comprising a desired wavelength. In the method, a laser is biased so as to generate a light signal at a desired central wavelength at an input/output thereof. The laser, which, while emitting light and having a preselected portion thereof fed back thereto, the output signal of laser source is shifted in wavelength in a first direction which is spaced apart from the center wavelength of fed back signal. The signal from the laser is divided into first and a second portions where the first portion is coupled to an output of the laser system. The second portion of the signal is processed such that the wavelength is shifted in an opposite direction to the first direction. The processed second portion of the signal is fed back to the input/output of the laser such that the output signal of the laser system is at essentially the desired wavelength. 
   From a second method aspect, the present invention relates to a method of stabilizing a laser system to generate an output signal comprising a desired wavelength. Each of a plurality of n laser sources is biased so as to generate a light signal at a desired central wavelength at an input/output thereof. Each laser source, which, while emitting light and having a preselected portion thereof fed back thereto, the output signal of laser source is shifted in wavelength in a first direction which is spaced apart from the center wavelength of fed back signal. In the method, the signal from the plurality of n laser sources is divided into a first and a second portions thereof, the first portion being multiplexed before being coupled to an output of the laser system. Each of the second portions of the output signals from the plurality of n laser sources is processed such that the wavelength thereof is shifted in an opposite direction to the first direction. Each of the processed second portions of the signals is fed back to the input/output of a corresponding one of the plurality of n laser sources such that the output signal of the laser system is at essentially the desired wavelength. 
   The invention will be better understood from the following more detailed description taken with the accompanying drawings and claims. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
       FIG. 1  shows a schematic diagram of a prior art stabilized laser system; 
       FIG. 2  shows a graph of a forward and feedback filter spectral response in the prior art laser system of  FIG. 1 ; 
       FIG. 3  shows a schematic diagram of a stabilized laser system illustrating the basic concept for the blue shift stabilizing of a single radiation source in accordance with the present invention; 
       FIG. 4  shows a graph of wavelength on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward and feedback spectral responses that might be found in the system of  FIG. 3 ; 
       FIG. 5  shows a schematic diagram of a stabilized laser system illustrating the basic concept for the blue shift stabilizing of multiple radiation sources in accordance with the present invention; 
       FIG. 6  shows a graph of wavelength on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward and feedback spectral responses that might be found in the system of  FIG. 5 ; 
       FIG. 7  shows a schematic diagram of an arrangement for a single radiation source in accordance with a first embodiment of the present invention; 
       FIG. 8  shows a schematic diagram of a system for multiple radiation sources in accordance with the first embodiment of the present invention; 
       FIG. 9  shows a schematic diagram of a system for a single radiation source in accordance with a second embodiment of the present invention; 
       FIG. 10  is a graph of wavelength on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward and feedback spectral responses that might be found in the system of  FIG. 9 ; 
       FIG. 11  shows schematic diagram of a system for multiple radiation sources in accordance with the second embodiment of the present invention; 
       FIG. 12  shows a graph of wavelength on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward and feedback spectral responses that might be found in the system of  FIG. 11 ; 
       FIG. 13  shows a schematic diagram of a system for multiple laser sources similar to the system shown in  FIG. 11  in accordance with the second embodiment of the present invention; 
       FIG. 14  shows a schematic diagram of a system for multiple laser sources similar to the system shown in  FIG. 11  in accordance with the second embodiment of the present invention; 
       FIG. 15  shows a schematic diagram of a system for a single radiation source in accordance with a third embodiment of the present invention; 
       FIG. 16  shows a schematic diagram of a system for multiple laser sources similar to the feedback stabilization system of  FIG. 15  in accordance with the third embodiment of the present invention; 
       FIG. 17  shows a schematic diagram of a system, which is less complex than the feedback stabilization system of  FIG. 15 , for a single radiation source in accordance with the third embodiment of the present invention; 
       FIG. 18  shows a graph of wavelength on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward and feedback spectral responses that might be found in the system of  FIG. 17 ; 
       FIG. 19  shows a schematic diagram of a system, which is less complex than the feedback stabilization system of  FIG. 16 , that illustrates a blue shift stabilizing arrangement for multiple radiation sources in accordance with the third embodiment of the present invention; 
       FIG. 20  shows a graph of wavelength on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward and feedback spectral responses that might be found in the system of  FIG. 19 ; 
       FIG. 21  shows a schematic diagram of a system, which is an alternative to the system of  FIG. 19  and illustrates a blue shift stabilizing arrangement for multiple radiation sources in accordance with the third embodiment of the present invention; 
       FIG. 22  shows a schematic diagram of a system, which is similar to the system of  FIG. 19 , and illustrates a blue shift stabilizing arrangement for multiple radiation sources in accordance with the third embodiment of the present invention; 
       FIG. 23  shows a schematic diagram of a system illustrating a blue shift stabilizing arrangement similar to that shown in  FIG. 11  for multiple radiation sources in accordance with a fourth embodiment of the present invention; 
       FIG. 24  shows a schematic diagram of a system similar to the system shown in  FIG. 14  for multiple laser sources in accordance with the fourth embodiment of the present invention; 
       FIG. 25  shows a schematic diagram of a system for multiple laser sources similar to the system shown in  FIG. 13  in accordance with the fourth embodiment of the present invention; 
       FIG. 26  shows a schematic diagram of a system for multiple laser sources similar to the system shown in  FIG. 13  in accordance with the fourth embodiment of the present invention; 
       FIG. 27  shows a schematic diagram of a system for multiple laser sources in accordance with the fourth embodiment of the present invention; 
       FIG. 28  shows a schematic diagram of a system for multiple laser sources in accordance with the fourth embodiment of the present invention; 
       FIG. 29  shows a schematic diagram of a system for multiple laser sources in accordance with the fourth embodiment of the present invention; 
       FIG. 30  shows a schematic diagram of a system for multiple laser sources in accordance with the fourth embodiment of the present invention; 
       FIG. 31  shows a schematic diagram of a system for multiple laser sources in accordance with the fourth embodiment of the present invention; 
       FIG. 32  shows a schematic of a system for blue shift feedback stabilizing a single radiation source in accordance with the third embodiment of the present invention; 
       FIG. 33  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with the third embodiment of the present invention; 
       FIG. 34  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with a third embodiment of the present invention; 
       FIG. 35  shows a schematic of a system for blue shift feedback stabilizing a single radiation sources in accordance with the third embodiment of the present invention; 
       FIG. 36  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with the third embodiment of the present invention; 
       FIG. 37  shows a schematic of a system for blue shift feedback stabilizing a single radiation source in accordance with a fifth embodiment of the present invention; 
       FIG. 38  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with fifth embodiment of the present invention; 
       FIG. 39  shows a schematic of a system for blue shift feedback stabilizing a single radiation source in accordance with fifth embodiment of the present invention; 
       FIG. 40  shows a schematic of a system for blue shift feedback stabilizing a single radiation source in accordance with fifth embodiment of the present invention; 
       FIG. 41  shows a schematic of a system that modifies the system of  FIG. 39  for blue shift feedback stabilizing multiple radiation sources in accordance with fifth embodiment of the present invention; 
       FIG. 42  shows a schematic of a system for blue shift feedback stabilizing a single radiation source in accordance with fifth embodiment of the present invention; 
       FIG. 43  shows a schematic of a system that implements the system of  FIG. 42  for blue shift feedback stabilizing multiple radiation sources in accordance with fifth embodiment of the present invention; 
       FIG. 44  shows a schematic of a system that implements the system of  FIG. 42  for blue shift feedback stabilizing multiple radiation sources in accordance with the fifth embodiment of the present invention; 
       FIG. 45  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with the fifth embodiment of the present invention; 
       FIG. 46  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with the fifth embodiment of the present invention; 
       FIG. 47  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with the fifth embodiment of the present invention; 
       FIG. 48  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with the fifth embodiment of the present invention; 
       FIG. 49  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with the fifth embodiment of the present invention; 
       FIG. 50  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with the fifth embodiment of the present invention; and 
       FIG. 51  shows a schematic of a system for blue shift feedback stabilizing multiple radiation sources in accordance with the fifth embodiment of the present invention; 
   

   The drawings are not necessarily to scale. 
   DETAILED DESCRIPTION OF THE INVENTION 
   As was described for the prior art second apparatus aspect, in a stabilized laser system one or multiple laser sources each generate a separate predetermined output signal at an output port thereof that is centered at a desired wavelength. Each of the one or multiple laser sources is caused to be shifted in response to a feedback signal in a first predetermined direction, depending on the laser source used, to a non-desired center wavelength, and thereby produces an excess loss in power of the output signal from the system. In accordance with the present invention, a feedback signal is generated from a portion of the output signal from each of the one or multiple laser sources having a center wavelength that is shifted in an opposite second direction from an expected output signal shift in the first direction normally produced by each of the one or more laser sources in response to receiving a feedback signal. This shifted feedback signal is transmitted back to the output port of each of the one or multiple laser sources such that the laser source output signal, when shifted in the first direction by a feedback signal, peaks, and is stabilized, at the desired center wavelength to substantially avoid the excess power loss found in the prior art. 
   Referring now to  FIG. 3 , there is shown a schematic diagram of a stabilized laser system  30  illustrating the basic concept of blue-shift stabilizing a single radiation source (LASER SOURCE)  31  in accordance with the present invention. The system  30  comprises the single radiation source  31 , and a blue shift feedback stabilizing arrangement  34 . The laser source  31  comprises a front facet  32  (output/input port) that is coupled to an input/output port  33  of the arrangement  34 . The arrangement  34  also comprises an output port  35  that provides an output signal from the feedback stabilization system  30 . The arrangement  34  can comprise one or multiple components (not shown, but as will described hereinafter in accordance with various embodiments of the present invention) to perform the desired blue shift stabilizing of the laser source  31  in different technology arrangements such as planar waveguide technology [e.g., planar waveguide circuits on different material platforms such as Silica on Silicon, Indium Phosphide (InP), Silicon, glass, etc.), free space optics, guided optics (e.g., optical fibers), etc]. 
   In a stabilized external cavity feedback laser (e.g., laser source  31 ), the laser is basically operating as an amplifier whose output is used to provide a feedback signal from an external reflecting means back into a front facet of the laser. The output signal from the laser is the amplified signal obtained by the round trip travel through the laser gain medium between the laser front and back facets. The laser front facet (designated  32 ) is normally coated with an anti-reflection (AR) coating (not shown), and the laser back facet is normally coated with a high reflection (HR) coating (not shown). Laser diodes, in general, demonstrate significantly different gain profiles for orthogonal Transverse Electric (TE) and Transverse Magnetic (TM) polarizations. These laser diodes generally emit signals in the horizontal (TE) polarization due to higher TE gain. Therefore, for a stable operation of a stabilized external cavity feedback laser, the entire optical path in which the feedback signal is propagating must preserve the polarization state due to signal and environmental conditions. 
   Assuming that f i (w) is the input signal from the laser source  31  received by the feedback stabilizing arrangement  34  at input/output port  33  as a function of wavelength, f o (w) is the output signal from the feedback stabilizing arrangement  34  appearing at output port  35  as a function of wavelength (w), and f f (w) is the reflected feedback signal propagating back toward the laser source  31  from the input/output port  33  of the feedback stabilizing arrangement  34  as a function of wavelength. The forward filter and feedback filter spectral responses in the feedback stabilization system  30  are then defined as F o (w)=f o (w)/f i (w) and F f (w)=f f (w)/f i (w), respectively. The reflected signal, f f (w), comprises one or multiple components that arrive at the front facet  32  of the laser source  31  with different time delays and amplitudes. In terms of time delay, there are cases where (a) all components arrive with the same time delay, (b) some components arrive with the same time delay and the rest with different time delays, and (c) all components have different time delays. In terms of amplitude there are cases where (a) all components arrive with the same amplitude, (b) some components arrive with the same amplitude and the rest with different amplitudes, and (c) all components have different amplitudes. 
   Referring now to  FIG. 4 , there is shown a graph of wavelength (w) on the X-axis versus amplitude (dB) on the Y-axis for illustrating an exemplary forward filter spectral response curve  36 , F o (w), and a dashed line feedback filter spectral response curve  37 , F f (w), as might be found in the stabilized laser system  30  of  FIG. 3 . In accordance with the present invention, the system  30  is designed such that the center wavelength of a feedback filter spectral response, F f (w), in the feedback stabilizing arrangement  34  is shifted toward a shorter wavelength (blue shift) by an amount δw to compensate for a red shift of the laser center wavelength. The blue shift design moves the center wavelength  38  of the stabilized laser source  31  closer to the center wavelength  38  of the forward filter spectral response  36 , F o (w). The blue shift δw minimizes the excess loss shown in  FIG. 2  that is associated with the conventional stabilized laser system  10  of  FIG. 1  using a transmission filter  15 . 
   Referring now to  FIG. 5 , there is shown a schematic diagram of a feedback stabilization system  40  illustrating the basic concept for a blue shift stabilizing of a plurality of n radiation sources (LASERS SOURCE)  41   a – 41   n  (only laser sources  41   a  and  41   n  are shown) in accordance with the present invention. The basic feedback stabilization system  40  comprises the plurality of n laser sources  41   a – 41   n , and a multi-wavelength blue shifted feedback stabilizing arrangement  44 . Each of the laser sources  41   a – 41   n  have a front facet  42   a – 42   n  (output/input port), respectively, that is coupled to a separate respective one of a plurality of n input/output ports  43   a – 43   n  of the blue shift feedback stabilizing arrangement  44 . The blue shift feedback stabilizing arrangement  44  comprises an output port  45  that provides a multiplexed output signal from the feedback stabilization system  40  generated by the plurality of n laser sources  41   a – 41   n . The blue shift feedback stabilizing arrangement  44  functions to multiplex all of the input signals, in the wavelength and polarization domain, received at the input/output port  43   a – 43   n  from the laser sources  41   a – 41   n . The feedback stabilizing arrangement  44  can comprise one or multiple components (not shown, but as will be described hereinafter in accordance with various embodiments of the present invention) to perform the desired blue shift stabilizing of the plurality of n laser sources  41   a – 41   n  in different technology arrangements such as planar waveguide technology [e.g., planar waveguide circuits on different material platforms such as Silica on Silicon, Indium Phosphide (InP), Silicon, glass, etc.), free space optics, guided optics (e.g., optical fibers), etc]. The multiplexing in the wavelength and polarization domain of the input signals to the blue shift feedback stabilizing arrangement  44  can be accomplished using an Arrayed Waveguide grating (AWG), Eschelle grating, Mach-Zehnder interferometer, bulk grating, thin film filters, optical fiber filters, etc. Similar to that stated for the system  30  of  FIG. 3 , the entire optical paths in which feedback signals are propagating in the feedback stabilization system  40  must preserve the polarization state (polarization maintaining, PM). 
   Assuming that f i   j (w) is the jth input signal received by the feedback stabilizing arrangement  44  from a laser source  41   j  (not shown) at its input/output port  43   j  (not shown) as a function of wavelength, f o (w) is the multiplexed output signal from the feedback stabilizing arrangement  44  appearing at output port  45  as a function of wavelength, and f f   j (w) is the reflected feedback signal propagating toward the jth laser source  41   j  out of the input/output port  43   j  of the feedback stabilizing arrangement  44  as a function of wavelength (w). The forward and feedback filter spectral responses for the jth laser source  41   j  in the feedback stabilization system  40  are defined as F o   j (w)=f o (w)/f i   j (w) and F f (w)=f f   j (w)/f i   j (w), respectively. The reflected signal, f f   j (w), comprises one or multiple components that arrive at the front facet  42   j  of the laser source  41   j  with different time delays and amplitudes. In terms of time delay, there are cases where (a) all components arrive with the same time delay, (b) some components arrive with the same time delay and the rest with different time delays, and (c) all components have different time delays. In terms of amplitude there are cases where (a) all components arrive with the same amplitude, (b) some components arrive with the same amplitude and the rest with different amplitudes, and (c) all components have different amplitudes. 
   Referring now to  FIG. 6 , there is shown a graph of wavelength (w) on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward filter spectral response curves  46   a – 46   n  (only curves  46   a  and  46   n  are shown), and dashed line feedback filter spectral response curves  47   a – 47   n  (only curves  47   a  and  47   n  are shown) as might be found in the multi-wavelength blue shift feedback stabilization system  40  of  FIG. 5 . In accordance with the present invention, the blue shifted feedback stabilization system  40  is designed such that, for the laser source  41   j  channel and wavelength, the center wavelength of a feedback filter spectral response, F f   j (w) in the feedback stabilizing arrangement  44  is shifted toward a shorter wavelength (blue shift) by an amount δw j  to compensate for the red shift of the laser center wavelength of laser source  41   j . The blue shift design moves the center wavelength  48   j  of the stabilized laser source  41   j  close to the center wavelength of the forward filter spectral response  46   j , F o   j (w). The same operation occurs for each of the laser sources  41   a – 41   n  as shown for the laser sources  41   a  and  41   n  by the curves  46   a  and  47   a , and  46   n  and  47   n , respectively. The blue shift for the feedback signal for each of the laser sources  41   a – 41   n  minimizes the excess loss for each of the laser sources  41   a – 41   n  that is shown in  FIG. 2  and associated with the conventional stabilized laser system  10  of  FIG. 1  using a transmission filter  15 . 
   Referring now to  FIG. 7 , there is shown a schematic diagram of a stabilized laser system  50  illustrating a blue shift stabilizing arrangement  54  (shown within a dashed line area) for a single radiation source (LASER SOURCE)  51  in accordance with a first embodiment of the present invention. The blue shift stabilizing arrangement  54  comprises a first 2×2 power splitter  55 , a main transmission filter  56  (f 1 (w)), a first feedback transmission filter (f 2 (w))  57 , a second feedback transmission filter (f 3 (w))  58 , a first optional reflector  59 , a second 2×2 power splitter  60 , a third feedback transmission filter (f 4 (w))  61 , and a second optional reflector  62 . The laser source  51  is coupled to a first input/output port  55   a  of the first 2×2 power splitter  55  via an optical path A, a second input/output port  55   b  of the first 2×2 power splitter  55  is coupled to an input/output port  56   a  of the main transmission filter  56  via an optical path B, a third input/output port  55   c  of the first 2×2 power splitter  55  is coupled to a first input/output port  57   a  of the first feedback transmission filter  57  via an optical path F, and a fourth input/output port  55   d  of the first 2×2 power splitter  55  is coupled to a first input/output port  58   a  of the second feedback transmission filter  58  via an optical path G. A second input/output port  58   b  of the second feedback transmission filter  58  is coupled to an input/output port of the first reflector  59  via an optical path H. A second input/output port  56   b  of the main transmission filter  56  is coupled to a first input/output port  60   a  of the second 2×2 power splitter  60  via an optical path C. A second output port  60   b  of the second 2×2 power splitter  60  provides an output signal from the system  50  to any predetermined downstream device via optical path D, a third input/output port  60   c  of the second 2×2 power splitter  60  is coupled to a second input/output port  57   b  of the first feedback transmission filter  57  via an optical path E, and a fourth input/output port  60   d  of the second 2×2 power splitter  60  is coupled to a first input/output port  61   a  of the third feedback transmission filter  61  via an optical path I. A second input/output port  61   b  of the third feedback transmission filter  61  is coupled to an input/output port of the second optional reflector  62  via an optical path J. 
   The main concept of the system  50  is to tap off a portion of the signal propagating through a main optical signal path comprising optical paths A→B→C→D via the first 2×2 power splitter  55 , the first main transmission filter  56 , f 1 (w), and the second 2×2 power splitter  60  in a forward direction. The signal tapped off by the second power splitter  60  at input/output port  60   c  is directed back to the laser source  51  via the first feedback transmission filter  57 , f 2 (w), and the first 2×2 power splitter  55  via optical paths E→F→A. 
   In operation, the output power of the laser source  51  is tapped by the first 2×2 power splitter  55  at its third input/output port  55   c , and the tapped laser output power is routed to the first feedback transmission filter  57 , f 2 (w), via optical path F. The second input/output port  55   b  of the first 2×2 power splitter  55  directs most of the laser signal power to the first input/output port  56   a  of the main transmission filter  56 , f 1 (w), via optical path B. The input signal received by the main transmission filter  56 , f 1 (w), is filtered and routed to the first input/output port  60   a  of the second 2×2 power splitter  60  via optical path C. The function of the second 2×2 power splitter  60  is to tap a portion of the signal received from the optical path C, and to send the tapped signal via it third input/output port  60   c  to the first feedback transmission filter  57 , f 2 (w), via optical path E, and direct a main portion of the received signal from optical path C to the second output port  60   b  as the output signal from the system  50  to a downstream device via optical path D. Therefore, the optical path for the main component of the output signal from the system  50  comprises the laser source  51 , the 2×2 first power splitter  55 , the main transmission filter, f 1 (w),  56 , and the second 2×2 power splitter  60  including optical paths A→B→C→D. 
   The output signal from the system  50  has other components due to the presence of two cavities in the blue shift stabilizing arrangement  54 . A first cavity is disposed between the second reflector  62  and the first reflector  59  via optical paths J→I→E→F→G→H. Each round trip of the signal in this first cavity adds two components to the output signal from the system  50  in optical path D. The second cavity comprises a loop from and back to the first optional reflector  59  using the optical path of H→G→B→C→E→F→G→H. Each round trip of the signal in this second cavity also adds one component to the output signal from the system  50  in optical path D. 
   The feedback signal has two main components. The optical path for the first main component is the laser source  51 , the first 2×2 power splitter  55 , the main transmission filter, f 1 (w),  56 , the second 2×2 power splitter  60 , the first feedback transmission filter, f 2 (w),  57 , the first 2×2 power splitter  55 , and back to a front facet of the laser source  51  via optical paths A→B→C→E→F→A. The optical path for the second main component is the laser source  51 , the first 2×2 power splitter  55 , the first feedback transmission filter, f 2 (w),  57 , the second 2×2 power splitter  60 , the main transmission filter, f 1 (w),  56 , the first 2×2 power splitter  55 , and back to the front facet of the laser source  51  via optical paths A→F→E→C→B→A. A signal round trip in the first cavity of optical paths A→B→C→E→F→A adds two components, and in the second cavity of optical paths A→F→E→C→B→A adds one component to the feedback signal to the laser source  51 . 
   The desired spectral response properties for the forward, F o (w), and feedback, F f (w), filters are such as filter bandwidth and a center wavelength that can be achieved by the proper choice of the f 1 (w), f 2 (w), f 3 (w), f 4 (w), coupling ratios, and cavity length for the transmission filters  56 ,  57 ,  58 , and  61 , respectively. The spectral responses for the forward and feedback filters for the system  50  correspond to the curves  36  and  37  shown in  FIG. 4  and described for the general feedback stabilization system  30  of  FIG. 3 . As described hereinbefore for the system  30  of  FIG. 3 , the entire optical path in which a feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except at the second output port  60   b  of the second 2×2 power splitter  60  is maintaining the polarization state. The broadband power splitter functions of each of the first and second 2×2 power splitters  55  and  60  can be achieved by different methods in different technology platforms such as planar waveguide technology using a directional coupler (DC), multimode interference (MMI) coupler, asymmetric Y junctions, Mach-Zehnder interferometer, etc, and free space optics using thin film, etc. 
   Referring now to  FIG. 8 , there is shown a schematic diagram of an alternative stabilized laser system  70  illustrating a blue shift stabilizing arrangement  74  (shown within a dashed line area) for a plurality of n radiation sources (LASER SOURCE)  71   a – 71   n  (of which only laser sources  71   a  and  71   n  are shown) in accordance with the first embodiment of the present invention. The blue shift stabilizing arrangement  74  comprises a plurality of n 2×2 power splitters  75   a – 75   n  (of which only power splitter  75   a  and  75   n  are shown), a forward multiplexer  76 , f 1   j (w), a first feedback multiplexer  77 , f 2   j (w), a second feedback multiplexer  78 , f 3   j (w), a first optional broadband reflector  79 , a broadband power splitter  80 , a third feedback multiplexer  81 , f 4   j (w), a plurality of n second optional reflectors  82   a – 82   n  (of which only reflectors  82   a  and  82   n  are shown), and an optional loop arrangement  83   a  (shown as a dashed line block) comprising a broadband power splitter  84  and an optional delay line  85 . Each of the plurality of n laser sources  71   a – 71   n  is coupled to a first input/output port  73   a  of a separate respective one of the plurality of n 2×2 power splitters  75   a – 75   n  via a separate optical path A. A second input/output port  73   b  of each one of the plurality of n first 2×2 power splitters  75   a – 75   n  is coupled to a separate corresponding one of a plurality of n input/output ports  76   a  of the forward multiplexer  76  via an optical path B. A third input/output port  73   c  of each one of the plurality of n 2×2 power splitters  75   a – 75   n  is coupled to a corresponding one of a plurality of n first input/output ports  77   a  of the first feedback multiplexer  77  via an optical path F. A fourth input/output port  73   d  of each one of the plurality of n 2×2 power splitter  75   a – 75   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  78   a  of the second feedback multiplexer  78  via an optical path G. A second input/output port  78   b  of the second feedback multiplexer  78  is coupled to an only input/output port of the first reflector  79  via an optical path H. A second input/output port  76   b  of the forward multiplexer  76  is coupled to a first input/output port  80   a  of the broadband power splitter  80  via an optical path C. A second output port  80   b  of the broadband power splitter  80  provides an output signal from the feedback stabilization system  70  to any predetermined downstream device via optical path D. A third input/output port  80   c  of the broadband power splitter  80  is coupled via first and second ports of the broadband power splitter  84  of the optional loop arrangement  83   a  to a second input/output port  77   b  of the first feedback multiplexer  77  via an optical path E, and a fourth input/output port  80   d  of the broadband power splitter  80  is coupled to a first input/output port  81   a  of the third feedback multiplexer  81  via an optical path I. Each one of a plurality of n second input/output ports  81   b  of the third feedback multiplexer  81  is coupled to an input/output port of a separate corresponding one of the plurality of n second optional reflectors  82   a – 82   n  via an optical path J. 
   The system  70  shows an implementation of the configuration of the system  50  of  FIG. 7  for a plurality of n laser sources  71   a – 71   n . For the system  70 , the single channel main transmission filter  56  (f 1 (w)), and the single channel feedback transmission filters  57  (f 2 (w)),  58  (f 3 (w)), and  61  (f 4 (w)) of  FIG. 7  are replaced with a multiple channel forward multiplexer  76  (f 1   j (w)), and multiple channel multiplexers  77  (f 2   j (w)),  78  (f 3   j (w)), and  81  (f 4   j (w)), respectively. The spectral response of the forward multiplexer  76  between the jth input/output port  76   a  (not shown) and the input/output port  76   b  is represented with f 1   j (w), the spectral response of the first feedback multiplexer  77  between the jth input/output port  77   a  (not shown) and the input/output port  77   b  is represented with f 2   j (w), the spectral response of the second feedback multiplexer  78  between the jth input/output port  78   a  (not shown) and the input/output port  78   b  is represented with f 3   j (w), and the spectral response of the third feedback multiplexer  81  between the jth input/output port  81   b  (not shown) and the input/output port  81   a  is represented with f 4   j (w). The forward filter F o (w) and feedback filter F f (w) spectral responses for the system  70  correspond to the curves  46   a – 46   n  and  47   a – 47   n  shown in  FIG. 6  as was described for the general multiple laser source system  40  of  FIG. 5 . 
   Where an incoherent feedback signal is desired for the laser sources  71   a – 71   n , a single optical delay line (not shown) can be positioned in, for example, the single optical path E to take care of all of laser sources  71   a – 71   n . Although possible, it is not desirable to place delay lines, when required, in optical paths A, B, or C because the main signal to optical path D is propagating through this route. Alternatively, a separate optional delay line (not shown) can be placed in each one of, for example, the n optical paths F for the laser sources  71   a – 71   n  requiring an incoherent feedback signal, but such arrangement requires many more delay lines than just placing an optional single delay line in, for example, optical path E and/or H. Depending on the technology platform, the multiplexers  76 ,  77 ,  78 , and  81  can be implemented using different devices such as an Array Waveguide grating (AWG), Eschelle grating, Mach-Zehnder interferometer, bulk grating, thin film filters, fiber filters, etc. 
   An alternative arrangement for the loop arrangement  83   a  is shown as a cavity arrangement  83   b  (shown within a dashed line area). The cavity arrangement  83   b  comprises a broadband power splitter  86  having four input/output ports (comparable to power splitter  84  in the loop arrangement  83   a ), a first optional delay line  87   a  and a first broadband reflector  88   a  coupled in series to the third input/output port of the broadband power splitter  86 , and a second optional delay line  87   b  and a second broadband reflector  88   b  coupled in series to the fourth input/output port of the broadband power splitter  86 . The presence of an additional loop arrangement  83   a  or  83   b  in the feedback signal path is to tap a portion of the signal traveling through the feedback signal path E and generate additional components for the feedback signal. The purpose of selectively adding multiple components into a feedback signal is to provide the conditions that cause each of the plurality of lasers  71   a – 71   n  to enter into coherence collapse mode of operation and the laser output signal to become very stable. 
   Referring now to  FIG. 9 , the there is shown a schematic diagram of a stabilized laser system  90  illustrating a blue shift stabilizing arrangement  94  (shown within a dashed line rectangle) for a single radiation source  91  in accordance with a second embodiment of the present invention. The system  90  shows a simplified implementation of the system  50  of  FIG. 7  for a single laser source system. The blue shift stabilizing arrangement  94  comprises a first power splitter  95 , a main transmission filter, f 1 (w),  96 , a second power splitter  97 , and a feedback transmission filter, f 2 (w),  98 . The laser source  91  is coupled at a front facet (output port)  91   a  thereof to a first input/output port  95   a  of the first power splitter  95  via an optical path A. A second input/output port  95   b  of the first power splitter  95  is coupled to a first input/output port  96   a  of the main transmission filter  96  via an optical path B. A second input/output port  96   b  of the main transmission filter  96  is coupled to a first input/output port  97   a  of the second power splitter  97  via an optical path C. A second output port  97   b  of the second power splitter  97  provides an output signal from the system  90  via an optical path D to any remote downstream device (not shown) using the output signal, and a third input/output port  97   c  is coupled to a first input/output port  98   a  of the feedback transmission filter  98  via an optical path E. A second input/output port  98   b  of the feedback transmission filter  98  is coupled to a third input/output port  95   c  of the first power splitter  95 . 
   A main output signal from the system  90  propagates through the first power splitter  95 , the main transmission filter, f 1 (w),  96 , and the second power splitter  97  via optical paths A→B→C→D. The feedback signal at the laser front facet  91   a  comprises two components. The optical path of one feedback signal component comprises the laser source  91 , the first power splitter  95 , the main transmission filter  96  [f 1 (w)], the second power splitter  97 , the feedback transmission filter  98  [f 2 (w)], the first power splitter  95 , and the front facet  91   a  of the laser source  91  via the paths A→B→C→E→F→A. The optical path for the other signal feedback component comprises the laser source  91 , the first power splitter  95 , the feedback transmission filter  98 , the second power splitter  97 , the main transmission filter  96 , the first power splitter  95 , and the front facet  91   a  of the laser source  91  via the paths A→F→E→C→B→A. Since the two optical feedback paths are exactly the same, the feedback components therefrom are in-phase with equal amplitude. The stabilized output signal at output terminal  97   b  of the second power splitter  97  is filtered only by the main transmission filter  96 , f 1 (w), and, therefore, the forward filter spectral response is F o (w)=f 1 (w). The feedback signal, however, is passed through both the feedback transmission filter  98  [f 2 (w)] and the main transmission filter  96  [f 1 (w)] and, therefore, the feedback spectral response is F f (w)=f 1 (w)·f 2 (w). 
   Referring now to  FIG. 10 , there is shown a graph of wavelength (w) on the X-axis versus amplitude (dB) on the Y-axis for illustrating an exemplary forward filter spectral response F o (w) curve  100  where F o (w)=f 1 (w), a feedback transmission filter spectral response curve  101  of f 2 (w) (shown as a dashed line curve) found in the feedback transmission filter  98 , and a feedback filter spectral response F f (w) curve  102  (shown as a dashed and dotted line curve) where F f (w)=f 1 (w)·f 2 (w), that might be found in the blue shift system  90  of  FIG. 9 . The main transmission filter  96  and feedback transmission filter  98  must be designed such that the forward and feedback filters spectral responses  100  and  102  of f 1 (w) and f 2 (w), respectively, provide the desired center wavelengths, bandwidths and the blue wavelength shift (δw) shown by curve  102  between the F o (w) and F f (w) curves  100  and  102 . 
   As described hereinbefore for systems  30  and  50 , for a stable operation of a stabilized external cavity feedback laser, the entire optical path in which the feedback signal is propagating must preserve the polarization state due to signal and environmental conditions. This means that all components and interconnects, except at the second output port  97   b  of the second 2×2 power splitter  97 , maintain the polarization state. Still further, one or multiple optional delay lines (not shown) can be added between any two components in the feedback optical signal path of ABCEFA when an incoherent feedback signal is required for the laser source  91 . 
   Referring now to  FIG. 11 , there is shown a schematic diagram of a stabilized laser system  110  illustrating a blue shift stabilizing arrangement  114  (shown within a dashed line area) for a plurality of n radiation sources (LASER SOURCE)  111   a – 111   n  (of which only laser sources  111   a  and  111   n  are shown) in accordance with the second embodiment of the present invention. The system  110  shows a simplified implementation of the system  70  of  FIG. 8  for a plurality of n laser source  111   a – 111   n . The blue shift stabilizing arrangement  114  comprises a plurality of n first power splitters  115   a – 115   n  (of which only power splitters  115   a  and  115   n  are shown), a forward multiplexer, f 1   j (w),  116 , a second power splitter  117 , and a feedback multiplexer, f 2   j (w),  118 . Each of the plurality of n laser sources  111   a – 111   n  is coupled at a front facet (output port)  112   a – 112   n  thereof to a first n input/output port  113   a – 113   n  of a separate corresponding one of the plurality of n first power splitters  115   a – 115   n  via an optical path A. A second input/output port  113   b  of each of the first power splitters  115   a – 115   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  116   a  of the forward multiplexer  116  via an optical path B. A second input/output port  116   b  of the forward multiplexer  116  is coupled to a first input/output port  117   a  of the second power splitter  117  via an optical path C. A second output port  117   b  of the second power splitter  117  provides an output signal from the system  110  via an optical path D to any remote downstream device (not shown) using the output signal, and a third input/output port  117   c  is coupled to a first input/output port  118   a  of the feedback multiplexer  118  via an optical path E. A second input/output port  118   b  of the feedback multiplexer  118  is coupled to a third input/output port  113   c  of a separate corresponding one of the plurality of n first power splitter  115   a – 115   n  via an optical path F. 
   In the configuration of the system  110 , the single channel main transmission filter, f 1 (w),  96  and the single channel feedback transmission filter, f 2 (w),  98  shown in  FIG. 9  are replaced with the forward multiplexer  116  and feedback multiplexer  118 , respectively. The spectral response between the jth input port  116   j  (not shown) and output port  116   b  of the forward multiplexer  116  is represented by f 1   j (w), and the spectral response between the jth input port  118   j  (not shown) and the output port  118   a  of the feedback multiplexer  118  is represented by f 2   j (w). Depending on the technology platform used, the multiplexers  116  and  118  can be implemented using different techniques such as Arrayed Waveguide Gratings (AWG), Eschelle gratings, Mach-Zehnder interferometers, bulk gratings, thin film filters, optical fiber filters, etc. 
   A main output signal [e.g., wavelength  1  (w 1 )] from, for example, the laser source  111   a  is propagating a single trip from laser source  111   a  to the output optical path D through the first and second power splitter  115   a  and  117  and the forward multiplexer  116 , f 1   j (w), via optical paths A→B→C→D. Concurrently, this signal (w 1 ) is being multiplexed with the other input signals (e.g., w 2 –w n ) from the lasers  111   b – 111   n  in the forward multiplexer  116 . The feedback signal at the front facets  112   a  of the laser sources  111   a – 111   n  comprises two components. The optical path providing one of the feedback signal components comprises the laser sources  111   a – 111   n , the first power splitters  115   a – 115   n , the forward multiplexer  116 , f 1   j (w), the second power splitter  117 , the feedback multiplexer  118 , f 2   j (w), the first power splitters  115   a – 115   n , and the front facets  112   a  of the lasers sources  111   a – 111   n  including the optical paths A→B→C→E→F→A. The optical path providing the other one of the feedback signal components comprises the laser sources  111   a – 111   n , the feedback multiplexer  118 , f 2   j (w), the second power splitter  117 , the forward multiplexer  116 , f 1   j (w), the first power splitters  115   a – 115   n , and the front facets  112   a  of the lasers sources  111   a – 111   n  including the optical paths A→F→E→C→B→A. Since the two optical paths are exactly the same, feedback components are in-phase with equal amplitudes. As indicated hereinbefore, the stabilized output signal appearing at the output port  117   b  of the second power splitter  117  is filtered only by the forward multiplexer  116 , f 1   j (w), and, therefore, the forward filter spectral response for the jth port is F o   j (w)=f 1   j (w). The feedback signal for the jth port, however, is passed through both the feedback multiplexer  118 , f 2   j (w), and the forward multiplexer  116 , f 1   j (w), resulting in a feedback spectral response for the jth port of F f   j (w)=f 1   j (w)·f 2   j (w). 
   Referring now to  FIG. 12 , there is shown a graph of wavelength (w) on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward multiplexer spectral response curves  120   a – 120   n  (each being shown by a solid curve), feedback multiplexer spectral response curves  121   a – 121   n  (shown by dashed line curves of which only curves  120   a ,  120   n ,  121   a , and  121   n  are shown), and feedback filter spectral response curves  122   a – 122   n  (shown as dashed and dotted curves of which only curves  122   a  and  122   n  are shown) that might be found in the blue shift system of  FIG. 11 . The forward and feedback multiplexers  116  and  118  must be designed such that the forward and feedback spectral responses, F o   j (w) and F fj (w), for port  112   a  of the laser source  111   j  (not shown) provide the desired center wavelengths, bandwidths, and wavelength shift (δw) between the responses F o   j (w) and F f   j (w). As described hereinbefore for systems  30  and  50 , for a stable operation of a stabilized external cavity feedback laser, the entire optical path in which the feedback signal is propagating must preserve the polarization state due to signal and environmental conditions. This means that the components and interconnects except the output port  112   b  is maintaining the polarization state from the laser sources  111   a – 111   n . Still further, one or multiple optional delay lines (not shown) can be added between any two components in the feedback optical signal path of A→B→C→E→F→A when an incoherent feedback signal is required for the laser sources  111   a – 111   n.    
   Referring now to  FIG. 13 , there is shown a schematic diagram of a stabilized laser system  130  (shown within a dashed line rectangle) for a plurality of n laser sources  131   a – 131   n  (of which only lasers sources  131   a  and  131   n  are shown) which is modified from the system  110  of  FIG. 11 . The system  130  comprises the laser sources  131   a – 131   n , a blue shift feedback stabilizing arrangement  134  (shown within a dashed line rectangle) comprising a forward and feedback multiplexer  135  and a power splitter  136 . Front facets  132   a – 132   n  of the plurality of n laser sources  131   a – 131   n , respectively, are coupled to a respective separate one of first input/output ports  135   a  of the forward and feedback multiplexer  135  via optical paths A. A second input/output port  135   b  of the forward and feedback multiplexer  135  is coupled to a first input/output port  136   a  of the power splitter  136  via an optical path B, while a third input/output port  135   c  of the forward and feedback multiplexer  135  is coupled to a third input/output port  136   c  of the power splitter  136  via an optical path D. A second output port  136   b  of the power splitter  136  provides an output signal from the system  130  via an optical path C to any desired downstream device or system (not shown). Depending on the technology platform, the forward and feedback multiplexer  135  can be implemented using different devices such as an Array Waveguide Grating (AWG), Eschelle grating, Mach-Zehnder interferometer, bulk grating, thin film filters, fiber filters, etc. 
   In the system  130 , the main output signal (e.g., for wavelength  1 –n (w 1 –w n )) propagates for a single trip from the laser sources  131   a – 131   n  through the forward and feedback multiplexer  135  and the power splitter  136  to its output port  136   b  via optical paths A→B→C. In a forward direction, the forward multiplexer  135 , having a spectral response of f 1   j (w), receives the output signals from the laser sources  131   a – 131   n  at the associated input/output ports  135   a , and multiplexes these laser source input signals to generate a multiplexed output signal at input/output port  135   b  onto optical path B for transmission to input/output port  136   a  of the power splitter  136 . In the power splitter  136 , a portion of the multiplexed output signal from the forward and feedback multiplexer  135  is tapped at input/output port  136   c  and sent to input/output port  135   c  of the forward and feedback multiplexer  135  via optical path D. This tapped signal is demultiplexed and filtered by the feedback multiplexer  135 , having a spectral response f 2   j (w), and the demultiplexed and filtered output signal from input/output ports  135   a  provide the associated separate feedback signals to the associated front facets  132   a – 132   n  of the respective laser sources  131   a – 131   n , respectively, via optical paths A. 
   If the multiplexer  135  is designed such that it provides both functions of forward multiplexing and feedback demultiplexing for all input ports  135   a ,  135   b , and  135   c , then forward and feedback multiplexers  116  and  118  of  FIG. 11  can be merged into one component as shown in  FIG. 13 . The multiplexer  135  has two output ports  135   b  and  135   c , the output port  135   b  being for transmitting the main forward signal via input port  136   a  of the power splitter  136  to optical path D which is similar to output port  116   b  of  FIG. 11 . The second output port  135   c  of the multiplexer  135  delivers a feedback signal that is blue shifted with respect to the output port  135   b  of the multiplexer  135  and is similar to port  118   a  in  FIG. 11 . 
   The feedback signal at the front facets  132   a – 132   n  of the laser sources  131   a – 131   n , respectively, comprise two components. The optical path of one feedback signal component for a jth laser source comprises the laser source  131   j  (not shown), the forward section, f 1   j (w), of the multiplexer  135 , power splitter  136 , the feedback section, f 2   j (w), of the multiplexer  135 , and the laser front facet  132   j  using the optical paths A→B→D→A. The optical path of the second feedback signal component for a jth laser source comprises the laser source  131   j , the feedback section, f 2   j (w), of the multiplexer  135 , power splitter  136 , the forward section, f 1   j (w), of the multiplexer  135 , and the laser front facet  132   j  using the optical paths A→D→B→A. Since the two optical paths are exactly the same, feedback components are in-phase with equal amplitude. The stabilized output signal from the laser sources  131   a – 131   n  found at output port  136  of the power splitter  136  is filtered only by the forward section of the multiplexer  135 , f 1   j (w), and, therefore, the forward filter spectral response (F o   j ) for the jth port is F o   j =f 1   j (w). The feedback signal for the jth port, however, is passed through both the feedback section of the multiplexer  135 , f 2   j (w), and the forward section of the multiplexer  135 , f 1 j(w). Therefore, the feedback filter spectral response for the jth port is F f j(w)=f 1 j(w)·f 2 j(w). The forward and feedback multiplexer sections must be designed such that the forward, F o j(w), and feedback, F f j(w), filter spectral responses for the port j provide desired wavelengths, bandwidths, and wavelength shift (δw) between the spectral responses F o   j (w) and F f   j (w). The spectral response curves  120   a – 120   n  (Forward filter, F o   j (w)),  121   a – 121   n  (feedback multiplexer, f 2   j (w)), and  122   a – 122   n  (Feedback filter, F f   j (w)) shown in  FIG. 12  correspond to spectral response curves obtainable in the system  130 , where, for a jth port  135   a  (not shown) of the multiplexer  135 , the curves  120   a – 120   n  show the forward filter spectral response of F o   j (w)=f o   j (w), curves  121   a – 121   n  show the feedback multiplexer spectral response f 2   j (w), and curves  122   a – 122   n  show the feedback filter spectral response F f   j (w)=f 1   j (w)·f 2   j (w). 
   As indicated hereinbefore for other systems (e.g., system  30 ), the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects except the output port  136   b  of the power splitter  136  is maintaining the polarization state. Still further, where incoherent feedback signals are desired for the laser sources  131   a – 131   n , optional delay lines can be added between any two components in the optical paths A→B→D→A of feedback signal. 
   Referring now to  FIG. 14 , there is shown a schematic diagram of an alternative stabilized laser system  140  for a plurality of n laser sources  141   a – 141   n  using a combination of components shown in the systems  110  and  130  shown in  FIGS. 11 and 13 , respectively, in accordance with the second embodiment of the present invention. The feed back stabilization system  140  comprises a plurality of n laser sources  141   a – 141   n , and a blue shift feedback stabilizing arrangement  144  (shown within a dashed line rectangle) comprising a plurality of n first power splitters  145   a – 145   n , a forward and feedback multiplexer  146 , and a second power splitter  148 . The plurality of N laser sources  141   a – 141   n  are each coupled at the respective one of forward facets  142   a – 142   n  thereof, respectively, via optical paths A to a first input/output port  143   a  of a separate corresponding one the plurality on n first power splitters  145   a – 145   n . A second input/output port  143   b  of each of the first power splitter  145   a – 145   n  is coupled via an optical path B to a separate corresponding one of a plurality of n first input/output ports  146   a  of the forward and feedback multiplexer  146 . A second input/output port  146   b  of the forward and feedback multiplexer  146  is coupled via an optical path C to a first input/output port  148   a  of the second power splitter  148 . A second output port  148   b  of the second power splitter  148  is coupled to an optical path D to provide an output signal from the system  140 , and a third input/output port  148   c  of the second power splitter  148  is coupled via optical path E to a third input/output port  146   c  of the forward and feedback multiplexer  146 . Each of a plurality of n fourth input/output ports  146   d  of the forward and feedback multiplexer  146  is coupled via an optical path F to a third input/output port  143   c  of a separate corresponding one of the plurality of n first power splitters  145   a – 145   n  for providing a predetermined blue shifted wavelength feedback signal to its associated one of the laser sources  141   a – 141   n.    
   The plurality of n laser sources  141   a – 141   n , the plurality of n first power splitters  145   a – 145   n , and forward and feedback multiplexer  146  correspond to, and are connected and function as described hereinbefore for, the n laser sources  111   a – 111   n  and the first power splitters  115   a – 115   n , and forward multiplexer  116  and feedback multiplexer  118 , respectively, of  FIG. 11 . Therefore, a description of the operation of the laser sources  141   a – 141   n , the first power splitters  145   a – 145   n , the forward and feedback multiplexer  146 , and the second power splitter  148  is essentially the same as described for the corresponding components in  FIG. 11  and will not be repeated here. As was described for the systems  110  and  130 , the entire optical path in the system  140  in which the feedback signal is traveling must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects except the output port  148   b  of the second power splitter  148  is maintaining the polarization state. Still further, where incoherent feedback signals are desired for the laser sources  141   a – 141   n , optional delay lines can be added between any two components in the optical paths A→B→C→E→F→A of the feedback signals. The spectral response curves  120   a – 120   n  (Forward filter, F o   j (w)),  121   a – 121   n  (feedback multiplexer, f 2   j (w)) and  122   a – 122   n  (Feedback filter, F f   j (w)) shown in  FIG. 12  correspond to spectral response curves obtainable in the system  140 , where, for a jth channel, the curves  120   a – 120   n  show the forward filter spectral response of F o   j (w)=f 1   j (w), curves  121   a – 121   n  show the feedback section multiplexer spectral response f 2   j (w), and curves  122   a – 122   n  show the feedback filter spectral response F f   j (w)=f 1   j (w)·f 2   j (w). 
   Referring now to  FIG. 15 , there is shown a schematic diagram of a system  150  illustrating a blue shift feedback stabilizing arrangement  152  (shown within a dashed line area) for a single radiation source  151  in accordance with a third embodiment of the present invention. The stabilizing arrangement  152  comprises a 2×2 power splitter  153 , a main transmission filter (f 1 (w))  154 , a first feedback transmission filter (f 2 (w))  155 , a second feedback transmission filter (f 3 (w)  156 , a first reflector  157 , and a second reflector  158 . The laser source  151  is coupled at a front facet  151   a  thereof to a first input/output port  153   a  of the power splitter  153  via an optical path A. A second input/output port  153   b  of the power splitter  153  is coupled to a first input/output port  154   a  of the main transmission filter  154  via an optical path B, a third input/output port  153   c  is coupled to a first input/output port  155   a  of the first feedback transmission filter  155  via an optical path D, and a fourth input/output port  153   d  is coupled to a first input/output port  156   a  of the second feedback transmission filter  156  via an optical path F. A second output port  154   b  of the main transmission filter  154  is coupled via an optical path C to provide an output signal from the system  150  to any downstream device (not shown). A second input/output port  155   b  of the first feedback transmission filter  155  is coupled to an input/output port  157   a  of the first reflector  157  via an optical path E. A second input/output port  156   b  of the second feedback transmission filter  156  is coupled to an input/output port  158   a  of the second reflector  158  via an optical path G. In any third embodiment in accordance with the present invention, a blue shift feedback stabilizing arrangement (e.g., arrangement  152 ), the output signal from the system (e.g., system  150 ) is obtained directly from a component (e.g., main transmission filter  154 ) that only provides such output signal, and not from a component that is providing both the output signal and a tapped off portion of the output signal to be used as a feedback signal for at least one laser source. 
   In the system  150 , a portion of the signal propagating through the main signal path (optical paths A→B→C) is tapped off in the forward direction at input/output port  153   c  of the 2×2 power splitter  153  between the laser source  151  and the main transmission filter, f 1 (w),  154 . This tapped off signal is filtered using the first feedback transmission filter, f 2 (w),  155 , and is reflected by the first reflector  157  back into the laser source  151 . The remainder of the signal in the forward direction is filtered by the main transmission filter, f 1 (w),  154 , and routed to output port  154   b  and onto optical path C as the output signal from the system  150 . The output signal has other components due to the presence of a cavity created between the first and second reflectors  157  and  158 , respectively, via optical paths E→D→F→G. Each signal round trip in the cavity (in optical paths E→D→F→G→F→D→E) contributes a delayed component to the output signal whose properties are set by the cavity length, the first feedback transmission filter, f 2 (w),  155 , the second feedback transmission filter, f 3 (w),  156 , the power splitter  153 , and the first and second reflectors  157  and  158 . A first component of the feedback signal propagates from the laser source  151  through the power splitter  153 , the first feedback transmission filter  155 , f 2 (w), reflector  157  and back again through the same reverse path (optical path A→D→E→D→A). The feedback signal has other components due to the presence of the cavity between the first and second reflectors  157  and  158 . Each signal round trip via optical paths F→G→F→D→E→D→F in the cavity contributes a delayed component whose properties are set by the cavity length, the first feedback transmission filter, f 2 (w),  155 , the second feedback transmission filter, f 3 (w),  156 , the power splitter  153 , and the first and second reflectors  157  and  158 . 
   The spectral responses that are obtainable in the system  150  for each of the forward filter spectral response, F o (w), and the feedback filter spectral response, F f (w), correspond to the curves  36  and  37 , respectively, shown in  FIG. 4 . The spectral responses for the forward and feedback filters whose properties such as filter bandwidth, and wavelength shift (δw) between the forward and feedback spectral responses can be achieved by a proper choice of f 1 (w), f 2 (w), and f 3 (w), the coupling ratio, and the cavity length. As described for each of the prior systems of the present invention, the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the main transmission filter, f 1 (w),  154  and its input/output ports  154   a  and  154   b  are maintaining the polarization state of the laser source  151 . Depending on the technology platform, the 2×2 power splitter  153  can be achieved by different methods such as planar waveguide technology using a directional coupler (DC), multimode interference (MMI) coupler, asymmetric Y junctions, Mach-Zehnder interferometer, etc, and free space optics using thin film, etc. Still further, one or multiple optional delay lines (not shown) can be added between any two components in the feedback optical signal path of A→D→E when an incoherent feedback signal is required for the laser source  151 . 
   Referring now to  FIG. 16 , there is shown a schematic diagram of a stabilized laser system  160  similar to the system  150  of  FIG. 15  illustrating a blue shift stabilizing arrangement  162  (shown within a dashed line area) for a plurality of radiation sources  161   a – 161   n  (of which only laser sources  161   a  and  161   n  are shown) in accordance with the third embodiment of the present invention. The system  160  comprises the plurality of n laser sources  161   a – 161   n , and a blue shift feedback stabilizing arrangement  162  (shown within a dashed line area). The blue shift feedback stabilizing arrangement  162  comprises a plurality of n 2×2 power splitters  163   a – 163   n  (of which only power splitters  163   a  and  163   n  are shown), a forward multiplexer, f 1   j (w),  164 , a first feedback multiplexer, f 2   j (w),  165 , a second multiplexer, f 3   j (w),  166 , a first broadband reflector  167 , and a second broadband reflector  168 . Each of the laser sources  161   a – 161   n  is coupled from a front facet  161   a  thereof to first input/output port  163   p  of a separate corresponding one of the plurality of n power splitters  163   a – 163   n  via an optical path A. A second input/output port  163   q  of each of the first power splitters  163   a – 163   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  164   a  of the forward multiplexer  164  via an optical path B. A second output port  164   b  of the forward multiplexer  164  provides an output signal from the system  160  via an optical path C to any remote downstream device (not shown). A third input/output port  163   r  of each of the plurality of n power splitters  163   a – 163   n  is coupled to a separate corresponding one of a plurality of first input/output port  165   a – 165   n  of the first feedback multiplexer  165  via a separate optical path D, while a fourth input/output port  160   s  of each of the plurality of n power splitters  163   a – 163   n  is coupled to a separate corresponding one of a plurality of first input/output port  166   a  of the second feedback multiplexer  166  via a separate optical path F. A second input/output port  165   b  of the first feedback multiplexer  165  is coupled to an input/output port  167   a  of the first broadband reflector  167  via an optical path E, and a second input/output port  166   b  of the second feedback multiplexer  166  is coupled to an input/output port  168   a  of the second broadband reflector  168  via an optical path G. In the system  160 , the single power splitter  153 , the single channel main transmission filter, f 1 (w),  154 , and the first and second feedback transmission filters, f 2 (w) and f 3 (w),  155  and  156  in the system  150  of  FIG. 15  are replaced by a plurality of n power splitter  163   a – 163   n , a multiple channel forward multiplexer, f 1   j (w),  164 , and multiple channel first and second feedback multiplexers, f 2   j (w) and f 3   j (w),  165  and  166 , respectively. 
   The spectral response between the jth first input/output port  164   j  (not shown) and the second output port  164   b  of the forward multiplexer  164  is represented by f 1   j (w), the spectral response between the jth first input/output port  165   a  (not shown) and the second input/output port  165   b  of the first feedback multiplexer  165  is represented by f 2   j (w), and the spectral response between the jth first input/output port  166   a  (not shown) and the second input/output port  166   b  of the second feedback multiplexer  166  is represented by f 3   j (w). The description of the operation for the single laser source  151  and the blue shift feedback stabilizing arrangement  152  of  FIG. 15  is applicable to the operation of each of the multiple laser sources  161   a – 161   n  and the blue shift stabilization feedback arrangement  162  of  FIG. 16  except that each of the forward multiplexer  164  and the first and second feedback multiplexers  165  and  166  perform multiplexing and demultiplexing functions for the concurrent multiple signal received. 
   Depending on the technology platform, the multiplexers  164 ,  165 , and  166  can be implemented using different devices such as an Array Waveguide grating (AWG), Eschelle grating, Mach-Zehnder interferometer, bulk grating, thin film filters, fiber filters, etc. Still further, one or multiple optional delay lines (not shown) can be added between any two components in any one of the optical feedback signal paths of A, D, E, F, or G when incoherent feedback signals are required for the laser sources  161   a – 161   n . The spectral responses that are obtainable in the system  160  for each of the forward filter spectral response, F o (w), and the feedback filter spectral response, F f (w), correspond to the. curves  46   a – 46   n  and  47   a – 47   n , respectively, shown in  FIG. 6 . As described for each of the prior systems (e.g., systems  30 ,  110 ,  130 ) of the present invention, the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the forward multiplexer, f 1 (w),  164  and its input/output ports  164   a  and  164   b  are maintaining the polarization state of the laser sources  161   a – 161   n.    
   Referring now to  FIG. 17 , there is shown a schematic diagram of a stabilized laser system  170  illustrating a blue shift stabilizing arrangement  172  (shown within a dashed line area) for a single radiation source (Laser Source, (w 1 ),  171  in accordance with the third embodiment of the present invention. The arrangement  172  is a reduced version of the arrangement  152  of  FIG. 15  in that the arrangement  172  eliminates the use of the second feedback transmission filter  156  and the second reflector  158  shown in the arrangement  152 . The arrangement  172  comprises a power splitter  173 , a main transmission filter (f 1 (w))  174 , a feedback transmission filter (f 2 (w))  175 , and a reflector  177 . The laser source  171  is coupled at a front facet  171   a  thereof to a first input/output port  173   a  of the power splitter  173  via an optical path A. A second input/output port  173   b  of the power splitter  173  is coupled to a first input/output port  174   a  of the main transmission filter  174  via an optical path B, and a third input/output port  173   c  is coupled to a first input/output port  175   a  of the feedback transmission filter  175  via an optical path D. A second output port  174   b  of the main transmission filter  174  is coupled to an optical path C that provides an output signal from the system  170  to any downstream device (not shown) using such output signal. A second input/output port  175   b  of the feedback transmission filter  175  is coupled to an input/output port  177   a  of the reflector  177  via an optical path E. As described hereinbefore for, for example, the system  30  of  FIG. 3 , the entire optical path in which a feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except at the first and second output ports  174   a  and  174   b  of the main transmission filter  174  is maintaining the polarization state. Still further, one or multiple optional delay lines (not shown) can be added between any two components in the feedback optical signal path of A→D→E→D→A when an incoherent feedback signal is required for the laser source  171 . 
   The main output signal propagates for a single trip from the laser source  171  through the power splitter  173 , the main transmission filter, f 2 (w),  174 , to its output port  174   b  and the optical path C. The signal on the main optical paths A→B→C is tapped off by the power splitter  173  at its third input/output port  173   c  before reaching the main transmission filter, f 1 (w), to be processed as the feedback signal. The feedback signal at the front facet  171   a  of the laser source  171  comprises one component. The optical path for the feedback signal comprises the laser source  171 , the power splitter  173 , the feedback filter, f 2 (w),  175 , the reflector  177 , and back through the same optical paths for a complete feedback optical path of A→D→E→D→A. Therefore, the forward filter spectral response is F o (w)=f 1 (w) since the main output signal only passes through the main transmission filter, f 1 (w),  174 . The feedback is filtered twice in going through and back in the feedback transmission filter, f 2 (w),  175 , and, therefore, the feedback filter spectral response is F f (w)=f 2 (w)·f 2 (w). In the implementation of the system  170 , the two filter spectral responses F o (w) and F f (w) are independent of each other. 
   Referring now to  FIG. 18 , there is shown a graph of wavelength (w) on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward and feedback spectral responses that might be found in the system  170  of  FIG. 17 . The main transmission filter, f 1 (w),  174  and the feedback transmission filter, f 2 (w),  175  must be designed such that the forward and feedback filter spectral responses, F o (w) and F f (w), provide desired center wavelengths, bandwidths of the forward and feedback spectral responses, and wavelength shift (δw) between the spectral responses F o (w) and F f (w). The curve  180  shows an exemplary forward filter spectral response F o (w)=f 1 (w), the curve  181  shows an exemplary feedback transmission filter spectral response f 2 (w), and curve  182  shows an exemplary feedback filter spectral response F f (w)=f 2 (w)·f 2 (w) for the system  170 . 
   Referring now to  FIG. 19 , there is shown a schematic diagram of a stabilized laser system  190  that is a reduced version of the system  160  of  FIG. 16  and illustrates a blue shift stabilizing arrangement  192  (shown within a dashed line area) for a plurality of n radiation sources (Laser Source)  191   a – 191   n  (of which only laser sources  191   a  and  191   n  are shown) in accordance with the third embodiment of the present invention. The arrangement  192  comprises a plurality of n power splitters  193   a – 193   n  (of which only power splitters  193   a  and  193   n  are shown), a forward multiplexer  194 , a feedback multiplexer  195 , and a reflector  197 . Each of the laser sources  191   a – 191   n  is coupled from a front facet (output port)  191   p  thereof to first input/output port  193   p  of a separate corresponding one of the plurality of n power splitters  193   a – 193   n  via an optical path A. A second input/output port  193   q  of each of the first power splitters  193   a – 193   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  194   a  of the forward multiplexer  194  via an optical path B. A second output port  194   b  of the forward multiplexer  194  provides an output signal from the system  190  via an optical path C to any remote downstream device (not shown). A third input/output port  193   r  of each of the plurality of n power splitters  193   a – 193   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  195   a  of the feedback multiplexer  195  via a separate optical path D. A second input/output port  195   b  of the feedback multiplexer  195  is coupled to an input/output port  197   a  of the reflector  197  via an optical path E. In this configuration, the single channel main transmission filter, f 1 (w),  174  and the single channel feedback transmission filter, f 2 (w),  175  in the blue shift stabilizing arrangement  172  of  FIG. 17  are replaced by a multiple channel forward multiplexer  194  and a multiple channel feedback multiplexer  195  in the blue shift stabilizing arrangement  192 . The spectral response between a jth input port  194   a  and the input/output port  194   b  of the forward multiplexer  194  is represented by f 1   j (w), and the spectral response between a jth input port  195   a  and the input/output port  195   b  of the feedback multiplexer  195  is represented by f 2   j (w). Depending on the technology platform, the multiplexers  194  and  195  can be implemented using different devices such as an Array Waveguide grating (AWG), Eschelle grating, Mach-Zehnder interferometer, bulk grating, thin film filters, fiber filters, etc. 
   In operation, the main output signal (e.g., for w 1  for laser source  191   a ) is propagating a single trip from the laser source  191   a  through the power splitter  193   a  and the forward multiplexer  194 , f 1   j (w), to the output port  194   b  of the forward multiplexer  194 . This signal is being multiplexed in the forward multiplexer  194  with the other input signals provided to the forward multiplexer  194  from the other laser sources  191   b – 191   n  via the associated power splitters  193   b – 193   n , respectively. A feedback signal at the front facet  191   p  of each of the laser sources  191   a – 191   n  comprises one component. The optical path of the feedback signal component for each of the laser sources  191   a – 191   n  comprises the laser source (e.g.,  191   a ) itself, the associated one of the power splitters  193   a – 193   n , the feedback multiplexer  195 , f 2   j (w), the reflector  177 , and back again via the same optical path to the front facet  191   p  of each of the laser sources  191   a – 191   n . Therefore, the overall feedback optical path includes the serial optical paths of A→D→E→D→A. As was described for each of the prior systems (e.g., systems  30 ,  110 ,  130 ) of the present invention, the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the forward multiplexer, f 1   j (w),  194  and its input/output ports  194   a  and  194   b  are maintaining the polarization state of the laser sources  191   a – 191   n . Still further, one or multiple optional delay lines (not shown) can be added between any two components in any one of the optical feedback signal paths of A, D, or E, when incoherent feedback signals are required for the laser sources  191   a – 191   n.    
   Referring now to  FIG. 20 , there is shown a graph of wavelength (w) on the X-axis versus amplitude (dB) on the Y-axis for illustrating exemplary forward and feedback spectral responses  200   a – 200   n  and  202   a – 202   n  (of which only spectral response curves  200   a  and  200   n , and  202   a  and  202   n  are shown) that might be found in the system of  FIG. 19 . In the system  190 , a stabilized output signal at output port  194   b  of the forward multiplexer, f 1   j (w),  194  is filtered only by the forward multiplexer  194 , and, therefore, the forward filter spectral response for the jth port (not shown)  194   a  is F o   j (w)=f 1   j (w) as shown by the solid curves  200   a – 200   n . The spectral response of the feedback multiplexer, f 2   j (w),  195  is shown by the dashed and dotted line curves  201   a – 201   n . The feedback signal, however, is passed twice through the feedback multiplexer, f 2   j (w), and, therefore the feedback filter spectral response for the jth port is F f   j (w)=f 2   j (w)·f 2   j (w) and is shown by the dashed line curves  202   a – 202   n . The forward multiplexer  194  and the feedback multiplexer  195  must be designed such that the forward and feedback filter spectral responses for port j, F o   j (w) and F f   j (w), provide desired center wavelengths  204   j  and  205   j , bandwidths, and wavelength shift (δw j ) between F o   j (w) and F f   j (w). 
   Referring now to  FIG. 21 , there is shown a schematic diagram of a stabilized laser system  210  that is less complex than the system  190  of  FIG. 19  and illustrates a blue shift stabilizing arrangement  212  (shown within a dashed line area) for a plurality of n radiation sources (Laser Source)  211   a – 211   n  in accordance with the third embodiment of the present invention. The blue shift stabilizing arrangement  212  comprises a forward and feedback multiplexer  214 , and a reflector  216 . Each of the plurality of n laser sources  211   a – 211   n  is coupled at a front facet  211   p  thereof to a separate one of a plurality of n first input/output ports  214   a  of the forward and feedback multiplexer  214  via a separate optical path A. A second output port  214   b  of the forward and feedback multiplexer  214  provides an output signal from the system  210  via an optical path B to any predetermined downstream device (not shown). A third input/output port  214   c  of the forward and feedback multiplexer  214  is coupled to an input/output port  216   a  of the reflector  216  via an optical path C. In the blue shift stabilizing arrangement  212 , the second output port  214   b  of the multiplexer  214  is the main output port of the system  210  (similar to port  194   b  in  FIG. 19 ), and the third input/output port  214   c  of the multiplexer  214  taps off a portion of the total multiplexed signal generated by the multiplexer  214  that is blue shifted with relation to the multiplexed output signal obtained at the main second output port  214   b . The spectral responses shown in  FIG. 20  of the Forward Filter spectral response F o   j (w) (shown by curves  200   a – 200   n ), the feedback multiplexer spectral response f 2   j (w) (shown by curves  201   a – 201   n ), and the feedback filter spectral response F f   j (w)=f 2   j (2)·f 2   j (w) (shown by curves  202   a – 202   n ) also apply to corresponding spectral responses obtained in the system  210 . 
   In operation, the main output signal for, for example, the jth laser source  211   j  (not shown) is propagating a single trip from the laser source  211   j  through the forward and feedback multiplexer  214  where it is multiplexed with the other output signals from the laser sources  211   a – 211   n  and provided to the main output port  214   b  of the forward and feedback multiplexer  214  via optical paths A→B. Concurrently, the output signal from laser source  211   j  is routed through the forward and feedback multiplexer  214  where it is multiplexed with the other output signals from the laser sources  211   a – 211   n  and provided to the third input/output port  214   c  and transmitted to reflector  216  and then fed back to the laser source  211   j  via optical paths A→C→A. The feedback signal at the front facet  211   p  of the each of the laser sources  211   a – 211   n  comprises one component. The components in the optical path of the feedback signal for, for example, the jth laser source  211   j  comprise the laser source  211   j , the forward and feedback multiplexer  214 , f 2   j (w), via its ports  214   a  and  214   c , the reflector  216 , the forward and feedback multiplexer  214 , f 2   j (w), via its ports  214   c  and  214   a , and back to the front facet  211   p  of the laser source  211   j . The stabilized output signal found in optical path B is filtered only once by the forward and feedback multiplexer  214  and, therefore, the forward filter spectral response for the jth port  214   a  (not shown) is F o   j (w)=f 1   j (w). The feedback signal, however, is passed twice through the forward and feedback multiplexer  214  and, therefore, the feedback spectral response for the jth port  214   a  (not shown) is F f   j (w)=f 2   j (w)·f 2   j (w). The forward and feedback multiplexer  214  must be designed such that the forward filter spectral response F o   j (w) and the feedback spectral response F f   j (w) provide the desired center wavelengths, bandwidths, and wavelength shift (δw) between the forward and the feedback spectral responses. The forward and feedback multiplexer  214  is also designed such that it provides both functions of forward and feedback multiplexing for all input ports  214   a . This implementation merges the separate functions of power splitter  193 , the individual forward multiplexer  194 , and the feedback multiplexer  195  in the blue shift stabilizing arrangement  192  of  FIG. 19  into one component  214 . 
   As described for each of the prior systems of the present invention, the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the forward multiplexing portion of the forward and feedback multiplexer, f 1   j (w),  214  and its input/output ports  214   a  and  214   b  are maintaining the polarization state of the laser sources  211   a – 211   n . Still further, one or multiple optional delay lines (not shown) can be added between any two components in the feedback optical signal path of A→C→A when an incoherent feedback signal is required for the laser sources  211   a – 211   n.    
   Referring now to  FIG. 22 , there is shown a schematic diagram of a stabilized laser system  220  that is similar to the system  190  of  FIG. 19  illustrating a blue shift feedback stabilizing arrangement  222  (shown within a dashed line area) for a plurality of n radiation sources (Laser Source)  221   a – 221   n  in accordance with the third embodiment of the present invention. The blue shift stabilizing arrangement  222  comprises a plurality of n power splitters  223   a – 223   n , a forward and feedback multiplexer  224 , and a reflector  226 . Each of the plurality of n laser sources  221   a – 221   n  is coupled at a front facet  221   p  thereof to a first input/output port  223   p  of a separate corresponding one of the plurality of n power splitters  223   a – 223   n  via an optical path A. A second input/output port  223   q  of each of the power splitters  223   a – 223   n  is coupled via an optical path B to a separate corresponding one of a plurality of n first input/output ports  224   a  of the forward and feedback multiplexer  224 . A third input/output port  223   r  of each of the power splitters  223   a – 223   n  is coupled via an optical path D to a separate corresponding one of a plurality of n third input/output ports  224   c  of the forward and feedback multiplexer  224 . A second output port  224   b  of the forward and feedback multiplexer  224  provides an output signal from the system  220  via an optical path C to any predetermined downstream device (not shown). A fourth input/output port  224   d  of the forward and feedback multiplexer  224  is coupled to an input/output port  226   a  of the reflector  226  via an optical path E. In the blue shift stabilizing arrangement  222 , the second output port  224   b  of the multiplexer  214  is the main output port of the system  220  (similar to output port  194   b  in  FIG. 20 ), and the third input/output ports  224   c  of the multiplexer  224  receive a tapped off portion of laser signals concurrently appearing at the input/output ports  223   r  of the power splitters  223   a – 223   n  to generate a multiplexed signal by the multiplexer  224  that is blue shifted with relation to the multiplexed output signal at the main second output port  224   b . The spectral responses shown in  FIG. 20  of the Forward Filter spectral response F o   j (w) (shown by curves  200   a – 200   n ), the feedback multiplexer spectral response f 2   j (w) (shown by curves  201   a – 201   n ), and the feedback filter spectral response F f   j (w)=f 2   j (2)·f 2   j (w) (shown by curves  202   a – 202   n ) also apply to corresponding spectral responses obtained in the system  220 . 
   In operation, the main output signal for, for example, the jth laser source  211   j  (not shown) is propagating a single trip from the laser source  221   j  through the power splitter  223   j  (not shown), and the forward and feedback multiplexer  224  where it is multiplexed with the other output signals from the laser sources  221   a – 221   n , and a multiplexed output signal is provided to the main output port  224   b  of the forward and feedback multiplexer  224  via optical paths A→B→C. Concurrently, the output signal from laser source  211   j  is routed through the jth power splitter  223   j  to the third input/output port  224   c  of forward and feedback multiplexer  214  where it is multiplexed with the other output signals from the laser sources  221   a – 221   n  and power splitters  223   a – 223   n  and provided to the fourth input/output port  224   d  of the forward and feedback multiplexer  224  and transmitted to reflector  226  and fed back to the laser source  221   j  via optical paths A→D→E→D→A. 
   The feedback signal at the front facet  221   p  of the each of the laser sources  221   a – 221   n  comprises one component. The components in the optical path of the feedback signal for, for example, the jth laser source  221   j  comprise the laser source  221   j , the power splitter  223   j , the forward and feedback multiplexer  224 , f 2   j (w), via its ports  224   c  and  224   d , the reflector  226 , the forward and feedback multiplexer  224 , f 2   j (w), via its ports  224   d  and  224   c , the power splitter  224   j , and back to the front facet  221   p  of the laser source  221   j . The stabilized output signal found in optical path C is filtered only once by the forward and feedback multiplexer  224  and, therefore, the forward filter spectral response for the jth port  224   a  (not shown) is F o   j (w)=f 1   j (w). The feedback signal, however, is passed twice through the forward and feedback multiplexer  224  and, therefore, the feedback spectral response for the jth port  224   c  (not shown) is F f   j (w)=f 2   j (w)·f 2   j (w). The forward and feedback multiplexer  224  must be designed such that the forward filter spectral response F o   j (w) and the feedback spectral response F f   j (w) provide the desired center wavelengths  204   a  and  205   a  shown in  FIG. 20 , bandwidths of the forward and feedback spectral responses, and wavelength shift (δw) between the forward and the feedback spectral responses. The forward and feedback multiplexer  224  is also designed such that it provides both functions of forward and feedback multiplexing for all input ports  224   a  and  224   c . This implementation merges the separate functions the individual forward multiplexer  194 , and the feedback multiplexer  195  in the blue shift stabilizing arrangement  192  of  FIG. 19  into one component  224  but provide separate paths through the forward and feedback multiplexer  224  for each function. 
   As described for each of the prior systems of the present invention, the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the forward multiplexing portion of the forward and feedback multiplexer, f 1   j (w),  224  and its input/output ports  224   a  and  224   b  are maintaining the polarization state of the laser sources  221   a – 221   n . Still further, one or multiple optional delay lines (not shown) can be added between any two components in the feedback optical signal path of A→D→E→D→A when an incoherent feedback signal is required for the laser sources  221   a – 221   n.    
   Referring now to  FIG. 23 , there is shown a schematic diagram of a high-efficiency multi-wavelength pump source stabilized laser system  230  illustrating a blue shift feedback stabilizing arrangement  232  (shown within a dashed line rectangle) similar to that shown in  FIG. 11  for a plurality of n radiation sources (LASER)  231   a – 231   n  with a plurality of n optional polarization rotators (PR)  233   a – 233   n  in accordance with a fourth embodiment of the present invention. The blue shift feedback stabilizing arrangement  232  comprises a plurality of n power splitters  234   a – 234   n  (of which only power splitters  234   a  and  234   n  are shown), a first Arrayed Waveguide Grating (AWG) multiplexer  235 , a second AWG multiplexer  236 , a broadband power splitter  237 , and an optional delay line  238 . Each of the laser sources  231   a – 231   n  is coupled from a front facet (output port)  231   p  thereof via an optical path A to a first input/output port  233   p  of a separate corresponding one of the plurality of n optional polarization rotators  233   a – 233   n . A second input/output port  233   q  of each of the polarization rotators  233   a – 233   n  is coupled to a first input/output port  234   p  of a separate corresponding one of the plurality of n power splitters  234   a – 234   n  via an optical path B. A second input/output port  234   q  of each of the power splitters  234   a – 234   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  235   a  of the first AWG multiplexer  235  via an optical path C. A second input/output port  235   b  of the first AWG multiplexer  235  is coupled to a first input/output port  237   a  of the broadband power splitter  237  via an optical path D. A second output port of the broadband power splitter  237  provides an output signal from the system  230  via an optical path E to any remote downstream device (not shown). A third input/output port  234   r  of each of the plurality of n power splitters  234   a – 234   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  236   a  of the second AWG multiplexer  236  via a separate optical path H. A second input/output port  236   b  of the second AWG multiplexer  236  is coupled to a first input/output port  238   a  of the optional delay line  238  via an optical path G. A second input/output port  238   b  of the optional delay line  238  is coupled to a third input/output port  237   c  of the broadband power splitter  237  via an optical path F. 
   The optional polarization rotators  233   a – 233   n  are included between the laser sources  231   a – 231   n , respectively, and the respective input/outputs  235   a  and  236   a  of the first and second AWG multiplexers  235  and  236 , respectively, (via power splitters  234   a – 234   n ) in case the laser output state of polarization (TE to TM, or vice versa) is to be rotated. Depending on the application and the number of polarization rotators used, the input signals to the first and second AWG multiplexers  235  and  236  may have the same polarization state (all TE or all TM) or different states of polarizations. For some applications such as Raman amplification, the polarization states of the adjacent input/output ports  235   a  and  236   a  (in the wavelength domain) of the first and second AWG multiplexers  235  and  236 , respectively, must be orthogonal (TE and TM polarizations) to reduce the degree of polarization (DoP) and, therefore, reduce or eliminate the Raman amplification polarization dependent gain (PDG). For such implementation, there are an even number of lasers sources  231   a – 231   n  that are grouped in pairs. The system  230  can be designed such that the resulting stabilization wavelengths of each pair of the laser sources  231   a – 231   n  with orthogonal polarizations are exactly the same, or there is a slight shift between the two wavelengths. 
   The Arrayed Waveguide Gratings (AWGs)  235  and  236  can function in one of three modes. In a first mode, the AWGs  235  and  236  can each function as a wavelength multiplexer where all inputs at the associated input/output ports  235   a  and  236   a  have the same polarization (TE or TM), and the AWGs  235  and  236  are designed such that all signals are multiplexed in the wavelength domain to the main output port  235   b  and  236   b , respectively. In a second mode, the AWGs  235  and  236  can each function as a multi-wavelength polarization multiplexer where the AWG  235  and  236  combine multiple pairs of laser source signals with orthogonal polarizations, and each pair of laser signals with the orthogonal polarizations is stabilized at the same wavelength. In a third mode, the AWGs  235  and  236  can each function as a polarization and wavelength multiplexer where each of the AWG  235  and  236  multiplexes signals with different wavelength and polarizations and routes the multiplexed signal to the main output port  235   b  and  236   b , and each signal pair with orthogonal polarizations may have different wavelengths. The first AWG  235  comprises a first Free Propagating Region (FPR)  235   e , a second FPR  235   f , and a plurality of waveguides  235   g  interconnecting the first and second FPRs  235   e  and  235   f  as is well know in the art. The second AWG  236  similarly comprises a first Free Propagating Region (FPR)  236   e , a second FPR  236   f , and a plurality of waveguides  236   g  interconnecting the first and second FPRs  236   e  and  236   f  as is well know in the art. Although AWG multiplexers  235  and  236  are shown and described for use in the feedback stabilizing arrangement  232 , an Eschelle grating can replace each of the AWG multiplexers  235  and  236  and provide the same function. 
   In operation, the optical signal from, for example, the laser source  231   j  (not shown) goes through an optional polarization rotator  233   j  (not shown) to rotate the received signal state of polarization. In the power splitter  234   j  (not shown), a major first portion of the received optical signal from the polarization rotator  233   j  is tapped and transmitted from its input/output port  234   q  to its associated input/output port  235   a  of the first AWG multiplexer  235 , while a remaining second portion of the received optical signal is concurrently transmitted via its input/output port  234   r  to its associated input/output port  236   a  of the second AWG multiplexer  236 . In the AWG multiplexer  235 , the input signals concurrently received at each of the plurality of n input/output ports  235   a  are filtered and multiplexed and a resultant multiplexed output signal is provided at input/output port  235   b  and is sent via optical path D to the input/output port  237   a  of the broadband power splitter  237 . In the broadband power splitter  237 , a first major portion of the received multiplexed signal is tapped off and routed to its input/output port  237   b  to provide an output signal of the system  230 , and the second remaining portion is routed to its input/output port  237   c  and to the second input/output port  238   b  of the optional delay line  238 . When the delay is used, the received multiplexed signal portion is delayed by a predetermined amount and routed via optical path G to the input/output port  236   b  of the second AWG multiplexer  236 . In the AWG multiplexer  236 , the received delayed multiplexed signal is filtered, demultiplexed, and routed by input/output ports  236   a  and via optical paths H to their corresponding input/output ports  234   r  of the plurality of n power splitter  234   a – 234   n . Each filtered and demultiplexed signal is routed by the associated one of the power splitter  234   a – 234   n  to its input/output port  234   p  and back through the associated one of the optional polarization rotators  233   a – 233   n  to the associated one of the laser sources  231   a – 231   n.    
   The filter spectral response between the input/output ports  235   a  and  235   b  of the first multiplexer  235  is F o   1 =f 1   j (w), and the first AWG multiplexer  235  is designed such that the spectral response f 1   j (w) provides the desired center wavelength and bandwidth for a jth input/output port  235   a  (not shown). The filter spectral response of the second AWG multiplexer  236  between the input/output ports  236   a  and  236   b  for the jth port of the AWG multiplexer  236  is f 2   j (w), and corresponds to each of the dashed line spectral response curves  121   a – 121   n  shown in  FIG. 12  for the n input/output ports  236   a  of the second AWG multiplexer  236 . The first and second AWG multiplexers  235  and  236  are designed such that a center wavelength of the feedback transmission filter, f 2   j (w), for the jth port is slightly shifted towards a shorter wavelength in relation to a center wavelength of the forward transmission filter, f 1   j (w), of the first AWG multiplexer  235  for input/output port j. The wavelength shift (blue shift) between the filters f 1   j (w) and f 2   j (w), and their respective bandwidth, can be controlled by the design of the AWG multiplexers  235  and  236 . Since the feedback signal is filtered by both filters f 1   j (w) and f 2   j (w), the result is a total feedback spectral response of F f   j (w)=f 1   j (w)·f 2   j (w) for the jth port and is shown by the dashed and dotted spectral response curves  122   a – 122   n  in  FIG. 12 . The forward filter spectral response for a jth port  235   a  is F o   j (w)=f 1   j (w) since the main output signal from the laser source  231   j  to the output port  237   b  of the broadband power splitter  237  only passes once through the first AWG multiplexer  235 , f 1   j (w), and corresponds to the solid spectral response curves  120   a – 120   n  shown in  FIG. 12 . 
   The feedback signal at the front facet  231   p  of each of the lasers  231   a – 231   n  comprises two in-phase components with equal amplitudes. One component travels through the associated one of the polarization rotators  233   a – 233   n , the power splitters  234   a – 234   n , the first AWG multiplexer  235 , the broadband power splitter  237 , the optional delay line  238 , the second AWG multiplexer  236 , and the associated one of the power splitter  234   a – 234   n  and the polarization rotators  233   a – 233   n  via the optical path A→B→C→D→F→G→H→B→A. The other component travels through the associated one of the polarization rotators  233   a – 233   n  and power splitters  234   a – 234   n , the second AWG multiplexer  236 , the optional delay  238 , the broadband power splitter  237 , the first AWG multiplexer  235 , and the associated one of the power splitters  234   a – 234   n  and polarization rotators  233   a – 233   n  via optical path A→B→H→G→F→D→C→B→A. One or more optional delay lines (not shown), other than the optional delay line  237 , can be added between any two components on the feedback optical path of A→B→C→D→F→G→H→B→A. 
   Referring now to  FIG. 24 , there is shown a schematic diagram of a stabilized laser system  240  illustrating a blue shift feedback stabilizing arrangement  242  (shown within a dashed line rectangle) comparable to the blue shift feedback stabilizing arrangement  232  shown in  FIG. 23  for a plurality of n laser sources (LASER)  241   a – 241   n  with a plurality of n optional polarization rotators (PR)  243   a – 243   n  in accordance with the fourth embodiment of the present invention. The blue shift feedback stabilizing arrangement  242  comprises a plurality of n power splitters  244   a – 244   n  (of which only power splitters  244   a  and  244   n  are shown), an Arrayed Waveguide Grating (AWG) multiplexer  245  (shown within a dashed line rectangle), a broadband power splitter  247 , and an optional delay line  248 . Each of the laser sources  241   a – 241   n  is coupled from a front facet (output port)  241   p  thereof via an optical path A to a first input/output port  243   p  of a separate corresponding one of the plurality of n optional polarization rotators  243   a – 243   n . A second input/output port  243   q  of each of the polarization rotators  243   a – 243   n  is coupled to a first input/output port  244   p  of a separate corresponding one of the plurality of n power splitters  244   a – 244   n  via an optical path B. A second input/output port  244   q  of each of the power splitters  244   a – 244   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  245   a  of the AWG multiplexer  245  via an optical path C. A second input/output port  245   b  of the AWG multiplexer  245  is coupled to a first input/output port  247   a  of the broadband power splitter  247  via an optical path D. A second output port  247   b  of the broadband power splitter  247  provides an output signal from the system  240  via an optical path E to any remote downstream device (not shown). A third input/output port  244   r  of each of the plurality of n power splitters  244   a – 244   n  is coupled to a separate corresponding one of a plurality of n third input/output ports  245   c  of the AWG multiplexer  245  via a separate optical path H. A third input/output port  247   c  of the broadband power splitter  247  is coupled to a second input/output port  248   b  of the optional delay line  248 , and a first input/output port  248   a  of the delay line  248  is coupled to a fourth input/output port  245   d  of the AWG multiplexer  245  via an optical path G. The AWG  245  multiplexer comprises a first Free Propagating Region (FPR)  245   e , a second FPR  245   f , and a plurality of waveguides  245   g  interconnecting the first and second FPRs  245   e  and  245   f  as is well know in the art. 
   The optional polarization rotators  243   a – 243   n  are included between the laser sources  241   a – 241   n , respectively, and the respective input/outputs  245   a  of the AWG multiplexer  245  (via power splitters  244   a – 244   n ) in case the laser output state of polarization (TE to TM or vice versa) is to be rotated as was described hereinbefore for the polarization rotators  233   a – 233   n  of  FIG. 23 . The main difference between the blue shift feedback stabilizing arrangement  232  of  FIG. 23  and the present blue shift feedback stabilizing arrangement  242  is that the first and second AWG multiplexers  235  and  236  of  FIG. 23  have been implemented using a single AWG multiplexer  245 . All spectral responses and definitions remain the same as described for the components of  FIG. 23  and will not be repeated here. 
   In operation, the optical signal on optical path A from, for example, the laser source  241   j  (not shown) goes through an optional polarization rotator  243   j  (not shown) to rotate the received signal state of polarization which optical signal then is coupled into a first input/output port  234   p  of the associated power splitter  244   j  via an optical path B. In the power splitter  244   j  (not shown), a major first portion of the received optical signal from the polarization rotator  243   j  is tapped and transmitted from its input/output port  243   q  via an optical path C to its associated input/output port  245   a  of the AWG multiplexer  245 , while a remaining second portion of the received optical signal is concurrently transmitted via its input/output port  244   r  to its associated input/output port  245   c  of the AWG multiplexer  245 . In the AWG multiplexer  245 , the input signals concurrently received at each of the plurality of n input/output ports  235   a  are filtered and multiplexed, and a routed entirely to its second input/output port  245   b . The filter spectral response for the jth port between the input/output ports  245   a  and  245   b  is F o   j =f 1   j (w) which is correspond to what is shown by the curves  120   a – 120   n  shown in  FIG. 12 . The AWG multiplexer  245  is designed such that f 1   j (w) provides the desired wavelength and bandwidth for the jth input/output port  245   a . The multiplexed and filtered signal generated at input/output port  245   b  is sent via optical path D to the input/output port  247   a  of the broadband power splitter  247 . In the broadband power splitter  247 , a first major portion of the received multiplexed signal is tapped off and routed to its second output port  247   b  to provide an output signal of the system  240 , and the second remaining portion is routed to its input/output port  247   c  and to the second input/output port  248   b  of the optional delay line  248  via optical path F. When the delay line  248  is used, the received multiplexed signal portion is delayed by a predetermined amount and routed via optical path G to the input/output port  245   d  of the AWG multiplexer  245 . In the AWG multiplexer  245 , the received delayed multiplexed signal is filtered, demultiplexed, and routed via optical paths H to their corresponding input/output ports  244   r  of the plurality of n power splitters  244   a – 244   n . Each filtered and demultiplexed signal is routed by the associated one of the power splitter  244   a – 244   n  to its input/output port  244   p  and back through the associated one of the optional polarization rotators  243   a – 243   n  to the associated one of the laser sources  241   a – 241   n.    
   As indicated hereinabove, the filter spectral response between the input/output ports  245   a  and  245   b  of the AWG multiplexer  245  is F o   1 =f 1   1 (w). The filter spectral response of the AWG multiplexer  245  for the feedback transmission filter between the input/output ports  245   d  and  245   c  for the jth port of the AWG multiplexer  245  is f 2   j (w) corresponds to each of the dashed line spectral response curves  121   a – 121   n  shown in  FIG. 12  for the n input/output ports  245   c  of the AWG multiplexer  245 . The AWG multiplexers  245  is designed such that a center wavelength of the feedback transmission filter, f 2   j (w), for the jth port is slightly shifted towards the shorter wavelength in relation to the center wavelength of the forward transmission filter, f 1   j (w), for input/output port j. The wavelength shift (blue shift) between the filters f 1   j (w) and f 2   j (w) and their respective bandwidth can be controlled by the design of the AWG  245 . Since the feedback signal is filtered by both filters f 1   j (w) and f 2   j (w), the result is a total feedback spectral response of F f   j (w)=f 1   j (w)·f 2   j (w) for the jth port and is shown by the dashed and dotted spectral response curves  122   a – 122   n  in  FIG. 12 . The forward filter spectral response, as indicated hereinbefore, is F o   j (w)=f 1   j (w) for the port j since the main output signal from the laser source  241   j  to the output port  247   b  of the broadband power splitter  247  only passes through the AWG multiplexer  245 , f 1   j (w), once, and corresponds to the solid spectral response curves  120   a – 120   n  shown in  FIG. 12 . 
   The feedback signal at the front facet  241   p  of each of the lasers  241   a – 241   n  comprises two in-phase components with equal amplitudes. One component travels through the associated one of the polarization rotators  243   a – 243   n  and the power splitters  244   a – 244   n , the AWG multiplexer  245 , the broadband power splitter  247 , the optional delay line  248 , the AWG multiplexer  245 , and the associated one of the power splitters  244   a – 244   n  and the polarization rotators  243   a – 243   n  via the optical path A→B→C→D→F→G→H→B→A. The other component travels through the associated one of the polarization rotators  243   a – 243   n  and power splitters,  244   a – 244   n , the AWG multiplexer  245 , the optional delay  248 , the broadband power splitter  247 , the AWG multiplexer  245 , and the associated one of the power splitters  244   a – 244   n  and polarization rotators  243   a – 243   n  via optical path A→B→H→G→F→D→C→B→A. One or more optional delay lines (not shown), other than the optional delay line  247 , can be added between any two components on the feedback optical path A→B→C→D→F→G→H→B→A. As described for each of the prior systems of the present invention, the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that only the output port  247   b  after the broadband power splitter  247  may not be polarization maintaining. 
   Referring now to  FIG. 25 , there is shown a schematic diagram of a stabilized laser system  250  for a plurality of n laser sources (LASER)  251   a – 251   n  (of which only laser sources  251   a  and  251   n  are shown) similar to the system  130  shown in  FIG. 13  in accordance with the fourth embodiment of the present invention. The system  250  comprises the laser sources  251   a – 251   n , a plurality of n polarization rotators (PR)  253   a – 253   n  (of which only PR  253   a  and  253   n  are shown), and a blue shift feedback stabilizing arrangement  252  (shown within a dashed line rectangle). The blue shift feedback stabilizing arrangement  252  comprises an Arrayed Waveguide Grating (AWG) multiplexer  255  (shown within a dashed line rectangle), a broadband power splitter  257 , and an optional delay line  258 . Each of the laser sources  251   a – 251   n  is coupled from a front facet (output port)  251   p  thereof via an optical path A to an input/output port  253   p  of a separate corresponding one of the plurality of n optional polarization rotators  253   a – 253   n . A second input/output port  253   q  of each of the polarization rotators  253   a – 253   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  255   a  of the AWG multiplexer  255  via an optical path B. A second input/output port  255   b  of the AWG multiplexer  255  is coupled to a first input/output port  257   a  of the broadband power splitter  257  via an optical path C, while a second output port  257   b  of the broadband power splitter  257  provides an output signal from the system  250  via an optical path D to any remote downstream device (not shown). A third input/output port  257   c  of the broadband power splitter  257  is coupled to a second input/output port  258   b  of the optional delay line  258 , and a first input/output port  258   a  of the delay line  258  is coupled to a third input/output port  255   c  of the AWG multiplexer  255 . The AWG  255  multiplexer comprises a first Free Propagating Region (FPR)  255   e , a second FPR  255   f , and a plurality of waveguides  255   g  interconnecting the first and second FPRs  255   e  and  255   f  as is well know in the art. 
   The main difference between the blue shift feedback stabilizing arrangement  242  shown in  FIG. 24  and the present blue shift feedback stabilizing arrangement  252  is that the plurality of n power splitters  244   a – 244   n  in  FIG. 24  are not used in the present blue shift feedback stabilizing arrangement  252 . Therefore, the AWG multiplexer  255  is designed to provide both of the power splitting and multiplexing functions, and the feedback paths through each of the AWG multiplexer  245  of  FIG. 24  and the present AWG multiplexer  255  are different because of the elimination of the power splitters  244   a – 244   n . In the AWG multiplexer  255 , a first optical path is directed between the input/output ports  255   a  and  255   b , and a second optical path is directed between the input/output ports  255   c  and  255   a . Therefore, the functioning of the laser sources  251   a – 251   n , the polarization rotators  253   a – 253   n , the AWG multiplexer  255 , the broadband power splitter  257 , and the optional delay line  258  are essentially the same as that described for the laser sources  241   a – 241   n , the polarization rotators  243   a – 243   n , the AWG multiplexer  245 , the broadband power splitter  247 , and the optional delay line  248  shown in  FIG. 24  except for the revised feedback path between the input/output ports  255   c  and  255   a  in the AWG multiplexer  255 . This revised feedback path between the input/output ports  255   c  and  255   a  in the AWG multiplexer  255  and that shown for the AWG multiplexer  245  of  FIG. 24  is achieved by a slight design change in the AWG multiplexer  255 . Still further, the spectral responses found in the blue shift feedback stabilizing arrangement  252  are the same as those obtained in the blue shift feedback stabilizing arrangement  242  of  FIG. 24  and are shown by the curves  120   a – 120   n ,  121   a – 121   n , and  122   a – 122   n  in  FIG. 12 . Additionally, the entire optical path A→B→C→E→F→B→A in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that only the output port  257   b  after the broadband power splitter  257  may not be polarization maintaining. 
   Referring now to  FIG. 26 , there is shown a schematic diagram of a stabilized laser system  260  for a plurality of laser sources (LASER)  261   a – 261   n  (of which only laser sources  261   a  and  261   n  are shown) in accordance with the fourth embodiment of the present invention. The system  260  comprises the laser sources  261   a – 261   n , of which only  261   a  and  261   n  are shown, a plurality of n polarization rotators (PR)  263   a – 263   n  of which only PRs  263   a  and  263   n  are shown), and a blue shift feedback stabilizing arrangement  262  (shown within a dashed line area). The blue shift feedback stabilizing arrangement  262  comprises an Arrayed Waveguide Grating (AWG) multiplexer  265 , a broadband power splitter  267 , an optional delay line  268 , and a plurality of n reflectors  269   a – 269   n  of which only  269   a  and  269   n  are shown. Each of the laser sources  261   a – 261   n  is coupled from a front facet (output port)  261   p  thereof via optical path A to an input/output port  263   p  of a separate corresponding one of the plurality of n optional polarization rotators  263   a – 263   n . A second input/output port  263   q  of each of the polarization rotators  263   a – 263   n  is coupled to a separate corresponding one of a plurality of n first input/output ports  265   a  of the AWG multiplexer  265  via an optical path B. A second input/output port  265   b  of the AWG multiplexer  265  is coupled to a first input/output port  267   a  of the broadband power splitter  267  via an optical path C. A second output port  267   b  of the broadband power splitter  267  provides an output signal from the system  260  via an optical path D to any remote downstream device (not shown). A third input/output port  267   c  of the broadband power splitter  267  is coupled to a third input/output port  265   c  of the AWG multiplexer  265 . A fourth input/output port  267   d  of the broadband power splitter  267  is coupled to a second input/output port  268   b  of the optional delay line  268 , and a first input/output port  268   a  of the delay line  268  is coupled to a fourth input/output port  265   d  of the AWG multiplexer  265 . Each of a plurality of n fifth input/output ports  265   e  of the AWG multiplexer  265  is coupled to an input/output ports  269   p  of a separate corresponding one of the plurality of n reflectors  269   a – 269   n  via an optical path G. The AWG  265  multiplexer comprises a first Free Propagating Region (FPR)  265   k , a second FPR  265   f , and a plurality of waveguides  265   m  interconnecting the first and second FPRs  265   k  and  265   i  as is well know in the art. 
   The main difference between the blue shift feedback stabilizing arrangement  262  and the blue shift feedback stabilizing arrangement  252  of  FIG. 25  is that the optional delay line  268  has been removed from the optical path E and has been place in a new separate feedback path F coupling a fourth input/output port  267   d  of the broadband power splitter  267  and a fourth input/output port  265   d  of the AWG multiplexer  265 , and a plurality of n reflectors  269   a – 269   n  have been added which are coupled to a new plurality of fifth input/output ports  265   e  of the AWG multiplexer  265 . 
   In operation, the output signals from the laser sources  261   a – 261   n , after optional polarization rotation in polarization rotators  263   a – 263   n , are received via optical paths A and B at the plurality of n input/output ports  265   a  of the AWG multiplexer  265  wherein the received signals are filtered and multiplexed and provided at both the input/output port  265   b  for transmission to the first input/output port  267   a  of the broadband power splitter  267  via optical path C, and at a second input/output port  265   c  for transmission to the third input/output port  267   c  of the broadband power splitter  267  via optical path E. A main portion of the multiplexed signal is routed via the output port  267   b  onto optical path D for downstream transmission as the output signal from the system  260 . A smaller portion of the received multiplexed signal is routed via input/output port  267   c  of the broadband power splitter  267  to the input/output port  265   c  of the AWG multiplexer  265  via optical path E, where the received signal is filtered and demultiplexed in the AWG multiplexer  265  and transmitted back to the laser sources  261   a – 261   n  via the polarization rotators  263   a – 263   n  and optical paths B and A. 
   The AWG multiplexer  265  is designed such that the Forward spectral response between the jth input/output ports  265   a  (not shown) and  265   b , f 1   j (w), and provides a desired center wavelength and bandwidth as is shown in the solid curves  46   a – 46   n  in  FIG. 6 . The filter spectral response between input/output ports  265   c  and  265   a  is represented by f 2   j (w), and the AWG multiplexer  265  is designed such that the center wavelength of f 2   j (w) is slightly shifted toward a shorter wavelength with relationship to the center wavelength of f 1   j (w). The multiplexed output signal at input/output tap  265   c  is routed to the input/output port  267   c  of the broadband power splitter  267  whose function is to divide and route the received multiplexed signal to its two input/output ports  267   a  and  267   d . The signal at input/output port  267   a  is routed via optical path C to the input/output ports  265   b  of the AWG multiplexer  265  and is one of the two feedback signal components in the manner described hereinbefore for the other component for the feedback stabilizing arrangement  252  of  FIG. 25 . The signal appearing at input/output port  267   d  of the power splitter  267  is delayed by the optional delay line  268  and routed via optical path F to the input/output port  265   d  of the AWG multiplexer  265  to be filtered and demultiplexed at routed via input output ports  265   e  to the plurality of n reflectors  269   a – 269   n  via optical path G. The spectral response between input/output ports  265   d  and ports  265   e  of the AWG multiplexer  265  is represented by f 4   1 (w). The AWG multiplexer is designed such that it can function as a demultiplexer for input/output port  265   d  such that the demultiplexed signals are routed to different input/output ports  265   e  than used for the input/output ports  265   a  for the laser sources  261   a – 261   n . Each of the demultiplexed signal is reflected by the associated one of the reflectors  269   a – 269   n  and travels the same optical path G→F→E→B→A in an opposite direction back to the laser sources  261   a – 262   n.    
   While propagating back through the power splitter  267 , a portion of the signal at input/output port  267   d  is routed to the output port  267   b  adding an additional component to the output signal on optical path D. Therefore, the optical path for the additional component of the feedback signal is the output from the laser sources  261   a – 261   n , the polarization rotators  263   a – 263   n , the AWG multiplexer  265  to input/output port  265   c , f 2   1 (w), the broadband power splitter  267 , the optional delay line  268 , the AWG multiplexer  265  input/output port  265   e  as a demultiplexer, f 4   1 (w), the reflectors  269   a – 269   n , back through the AWG multiplexer  265 , f 4   1 (w), the delay line  268 , the power splitter  267 , the polarization rotators  263   a – 263   n , and back to the lasers  261   a – 261   n  via optical path A→B→E→F→G→F→E→B→A. The additional component of the output signal at output port  267   b  of the power splitter  267  goes through a filter with a spectral response f 2   1 (w)·f 4   1 (w)·f 4   1 (w). The additional component of the feedback signal to the laser sources  261   a – 261   n  goes through a filter with a spectral response f 2   1 (w)·f 2   1 (w)·f 4   1 (w)·f 4   1 (w). As described for each of the prior systems of the present invention, the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that only the output port  267   b  of the broadband power splitter  267  may not be made to be polarization maintaining. 
   Referring now to  FIG. 27 , there is shown a schematic diagram of a stabilized laser system  270  for a plurality of n laser sources (LASER)  271   a – 271   n  (of which only laser sources  271   a  and  271   n  are shown) in accordance with the fourth embodiment of the present invention. The system  270  comprises the plurality of n laser sources  271   a – 271   n , a plurality of n optional polarization rotators  273   a – 273   n  (of which only polarization rotators  273   a  and  273   n  are shown), and a blue shift feedback stabilizing arrangement  272  (shown within a dashed line area). The blue shift stabilizing arrangement  270  comprises a first AWG multiplexer  275  (shown within a dashed line rectangle), a second AWG multiplexer  276  (shown within a dashed line rectangle), a broadband power splitter  277 , an optional delay line  278 , and a broadband reflector  279 . Each of the plurality of n laser sources  271   a – 271   n  are coupled at a front facet  271   p  thereof to a first input/output port  273   p  of a separate corresponding one of the polarization rotators  273   a – 273   n  via an optical path A. A second input/output port  273   q  of each of the polarization rotators  273   a – 273   n  is coupled to an separate corresponding one of an input/output port  273   a  of the first AWG multiplexer  275  via an optical path B. A second input/output port  275   b  of the first AWG multiplexer  275  is coupled to a first input/output port  277   a  of the broadband power splitter  277  via an optical path C, while a second output port  277   b  of the broadband power splitter  277  provides an output signal from the system  270  via an optical path D to any remote downstream device (not shown). A third input/output port  277   c  of the broadband power splitter  277  is coupled to a third input/output port  275   c  of the first AWG multiplexer  275 . A fourth input/output port  277   d  of the broadband power splitter  277  is coupled to a first input/output port  278   a  of the optional delay line  278 , and a second input/output port  278   b  of the delay line  278  is coupled to a fourth input/output port  275   d  of the first AWG multiplexer  275 . Each of a plurality of n fifth input/output ports  275   e  of the first AWG multiplexer  275  is coupled to a corresponding one of a plurality of n input/output ports  276   a  of the second AWG multiplexer  276  via optical paths H. A second input/output port  276   b  of the second AWG multiplexer  276  is coupled to an input/output of the broadband reflector  279 . The first and second AWG multiplexer  275  and  276  comprises a first Free Propagating Region (FPR)  275   k  and  276   k , respectively, a second respective FPR  275   l  and  276   l , and a plurality of waveguides  275   m  and  276   m , respectively, interconnecting the respective first and second FPRs  275   k  and  275   l , and  276   k  and  276   l , as is well know in the art. 
   The implementation of the system  270  performs the same function as the system  260  of  FIG. 26  except that the plurality of n reflectors  269   a – 269   n  of  FIG. 26  have been replaced by a single broadband reflector  279 , and the demultiplexed signals obtained at input/output ports  265   e  of the AWG multiplexer  265  of  FIG. 26  that are transmitted to the plurality of n reflectors  269   a – 269   n  in  FIG. 26  are now multiplexed in the second AWG multiplexer  276  for transmission to the single broadband reflector  279 . The system  270  operates in a same manner as was described for the system  260  of  FIG. 26 . More particularly, the first AWG multiplexer  275  is designed such that the spectral response between input/output ports  275   a  and  275   b  is f 1   1 (w), and that for the jth  265   a  port (not shown) the spectral response is equal to f 1   j (w) and provides a desired center wavelength and bandwidth. The filter spectral response between input/output ports  275   c  and  275   a  is represented by f 2   j (w), and the AWG multiplexer  275  is designed such that the center wavelength of f 2   j (w) is slightly shifted toward a shorter wavelength with relation to the center wavelength of f 1   j (w). Still further, the spectral response between input/output ports  275   d  and ports  275   e  of the AWG multiplexer  275  is represented by f 4   1 (w). As was shown in for the feedback stabilizing arrangement  265  of  FIG. 26 , the additional component of the output signal at output port  277   b  of the power splitter  277  goes through a filter with a spectral response of f 2   1 (w)·f 4   1 (w)·f 4   1 (w). The additional component of the feedback signal to the laser sources  271   a – 271   n  goes through a filter with spectral response of f 2   1 (w)·f 2   1 (w)·f 4   1 (w)·f 4   1 (w). As was described for each of the prior systems of the present invention, the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that only the output port  277   b  of the broadband power splitter  277  may not be polarization maintaining. 
   Referring now to  FIG. 28 , there is shown a schematic diagram of a stabilized laser system  280  for a plurality of n laser sources (LASER)  281   a – 281   n  (of which only laser sources  281   a  and  281   n  are shown) in accordance with the fourth embodiment of the present invention. The system  280  comprises the plurality of n laser sources  281   a – 281   n , a plurality of n optional polarization rotators (PR)  283   a – 283   n  (of which only PR  283   a  and  283   n  are shown), and a blue shift feedback stabilizing arrangement  282  (shown within a dashed line rectangle). The feedback stabilizing arrangement  282  comprises an AWG multiplexer  285 , a broadband power splitter  286 , an optional delay line  287 , and a broadband reflector  288 . Each of the plurality of n laser sources  281   a – 281   n  is coupled at a front facet  281   p  thereof to a first input/output port  283   p  of a separate corresponding one of the plurality of n polarization rotators  283   a – 283   n  via an optical path A. A second input/output port  283   q  of each of the plurality of n polarization rotators  283   a – 283   n  is coupled via and optical path B to a separate corresponding one of a plurality of n input/output ports  285   a  of the AWG multiplexer  285 . A second input/output port  285   b  of the AWG multiplexer  285  is coupled to a first input/output port  286   a  of the broadband power splitter  286  via an optical path C. A second output port  286   b  of the broadband power splitter  286  provides an output signal from the system  280  via an optical path D to any remote downstream device (not shown). A third input/output port  286   c  of the broadband power splitter  286  is coupled to a third input/output port  285   c  of the AWG multiplexer  285  via an optical path E. A fourth input/output port  286   d  of the broadband power splitter  286  is coupled to a first input/output port  287   a  of the optional delay line  287 , and a second input/output port  287   b  of the delay line  287  is coupled to an input/output port  288   a  of the broadband reflector  288  via an optical path F. Basically the system  280  is a simplified configuration of the system  260  and  270  shown in  FIGS. 26 and 27 , respectively, due to the removal of the feedback multiplexing path G in the AWG multiplexer  265  of  FIG. 26 , and the second multiplexer  276  and the feedback path H to G in the first AWG multiplexer  275  in  FIG. 27 . 
   Effectively, the system  280  provides the same functioning as that found in the systems  260  and  270  of  FIGS. 26 and 27 , respectively. For example, since the signal being fed back to the laser sources  281   a – 281   n  from the broadband reflector  288  only pass once through the AWG multiplexer  285  f 2   j (w) via optical paths A→B→E→F→G→F before adding a component to the output signal at output port  286   b  of the broadband power splitter  286 , the additional component of the output signal goes through a filter with a spectral response of f 2 (w). The component of the feedback signal goes through a filter with a spectral response of f 2   j (w) f 2   j (w) since the feedback signal passes twice through the AWG multiplexer  285 . The forward filter spectral response, F o   j (w), and the feedback filter spectral response, F f   j (w), obtained in the system  280  is the same as those shown by the curves  46   a – 46   n  and  47   a – 47   n , respectively, in  FIG. 6 . 
   Referring now to  FIG. 29 , there is shown a schematic diagram of a stabilized laser system  290  for a plurality of n laser sources (LASER)  291   a – 291   n  (of which only laser sources  291   a  and  291   n  are shown) in accordance with the fourth embodiment of the present invention. The system  290  comprises the plurality of n laser sources  291   a – 291   n , a plurality of n optional polarization rotators (PR)  283   a – 283   n  (of which only PR  291   a  and  291   n  are shown), and a blue shift feedback stabilizing arrangement  292  (shown within a dashed line area). The blue shift feedback stabilizing arrangement  292  comprises a plurality of n power splitters  294   a – 294   n  (of which only power splitters  294   a  and  294   n  are shown), a first Arrayed Waveguide Grating (AWG) multiplexer  295  (shown within a dashed line rectangle), a second AWG multiplexer  296  (shown within a dashed line rectangle), an optional delay line  297 , and a broadband reflector  298 . The configuration of the system  290  is similar to the configuration of the system  190  shown in  FIG. 19  except that polarization rotators  293   a – 293   n  and the optional delay line  297  have been added, and the first and second AWG multiplexers  295  and  296  replace the forward multiplexer  194  and feedback multiplexer  195 , respectively. A front facet  291   p  of each of the plurality of n laser sources  291   a – 291   n  is coupled to a first input/output port  293   p  of a separate corresponding one of the polarization rotators  293   a – 293   n  via an optical path A. A second input/output port  293   q  of each of the polarization rotators  293   a – 293   n  is coupled to an first input/output port  294   p  of a separate corresponding one of the power splitters  294   a – 294   n  via an optical path B. A second input/output port  294   q  of each of the power splitters  294   a – 294   n  is coupled to a separate corresponding first input port  295   a  of the first AWG multiplexer  295  via an optical path C, while a third input/output port  294   r  of each of the power splitters  294   a – 294   n  is coupled to a separate corresponding one of a plurality of n first input ports  296   a  of the second AWG multiplexer  296  via an optical path E. A second output of the first AWG multiplexer  295  provides an output signal from the system  290  via an optical path D to any remote downstream device (not shown). A second input/output port  296   b  of the second AWG multiplexer  296  is coupled to a first input/output port  297   a  of the optional delay line  297  via an optical path F. A second input/output port  297   b  of the optional delay line  297  is coupled to an input/output port  298   a  of the broadband reflector  298  via an optical path G. 
   The functioning of the polarization rotators  293   a – 293   n  corresponds to that described hereinbefore for, for example, the polarization rotators  243   a – 243   n  of  FIG. 24 . Still further, the functioning of the system  290  is the same as that described for the feedback stabilization system  190  of  FIG. 19  where the first and second AWG multiplexers  295  and  296  provide the functions of the optical paths between ports  194   a  to  194   b , and ports  195   a  and  195   b , respectively, in the forward and feedback multiplexer  194  and  195  of  FIG. 19 . The spectral response curves obtained in the system  290  are the same as those obtained for the system  220  of  FIG. 22 . As described for each of the prior systems of the present invention, the entire optical path A→B→E→F→G in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the forward multiplexing portion provided by the first AWG multiplexer, f 1   j (w),  295  and its input/output ports  295   a  and  295   b  are maintaining the polarization state of the laser sources  291   a – 291   n . Still further, one or multiple optional delay lines (not shown) can be added between any two components in the feedback optical signal path of A, B, E, F, and G. 
   Referring now to  FIG. 30 , there is shown a schematic diagram of a stabilized laser system  300  for a plurality of n laser sources  301   a – 301   n  (of which only laser sources  301   a  and  301   n  are shown) in accordance with the fourth embodiment of the present invention. The system  300  comprises the plurality of n laser sources  301   a – 301   n , a plurality of n optional polarization rotators (PR)  303   a – 303   n  (of which only PR  303   a  and  303   n  are shown), and a blue shift feedback stabilizing arrangement  302  (shown within a dashed line area). The blue shift feedback stabilizing arrangement  302  comprises a plurality of n power splitters  304   a – 304   n  (of which only power splitters  304   a  and  304   n  are shown), an Arrayed Waveguide Grating (AWG) multiplexer  305  (shown within a dashed line rectangle), an optional delay line  307 , and a broadband reflector  308 . The system  300  is a modified version of the system  290  of  FIG. 29  in that the functioning of the first and second AWG multiplexers  295  and  296  of  FIG. 29  have been combined into a single AWG multiplexer  305 . A front facet  301   p  of each of the plurality of n laser sources  301   a – 301   n  is coupled to a first input/output port  303   p  of a separate corresponding one of the polarization rotators  303   a – 303   n  via an optical path A. A second input/output port  303   q  of each of the polarization rotators  303   a – 303   n  is coupled to an first input/output port  304   p  of a separate corresponding one of the power splitters  304   a – 304   n  via an optical path B. A second input/output port  304   q  of each of the power splitters  304   a – 304   n  is coupled to a separate corresponding one of a plurality of n first input ports  305   a  of the AWG multiplexer  305  via an optical path C, while a third input/output port  304   r  of each of the power splitters  304   a – 304   n  is coupled to a separate corresponding one of a plurality of n fourth input/output ports  305   d  of the AWG multiplexer  305  via an optical path G. A second output of the AWG multiplexer  305  provides an output signal from the system  300  via an optical path D to any downstream remote device (not shown). A third input/output port  305   c  of the AWG multiplexer  305  is coupled to a first input/output port  307   a  of the optional delay line  307  via an optical path E, while a second input/output port  307   b  of the optional delay line  307  is coupled to an input/output port  308   a  of the broadband reflector  308  via an optical path F. 
   The functioning of the polarization rotators  303   a – 303   n  corresponds to that described hereinbefore for, for example, the polarization rotators  243   a – 243   n  of  FIG. 24 . Still further, the functioning of the system  300  provides the same results as that described for the feedback stabilization system  210  of  FIGS. 21 , where the of the optical paths between ports  305   a  to  305   b , and ports  305   c  and  305   a  in the AWG multiplexer  305  provide the functions of the optical paths between ports  214   a  to  214   b , and ports  214   c  and  214   a , respectively, in the forward and feedback multiplexer  214  of  FIG. 22 . The spectral response curves obtained in the system  300  are the same as those obtained for the system  210  of  FIG. 21 . As described for each of the prior systems of the present invention, the entire optical path A→B→G→E→F in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the forward multiplexing portion provided by the AWG multiplexer, f 1   j (w),  305  and its input/output ports  305   a  and  305   b  are maintaining the polarization state of the laser sources  301   a – 301   n . Still further, one or multiple optional delay lines (not shown) can be added between any two components in the feedback optical signal path of A, B, E, F, and G. 
   Referring now to  FIG. 31 , there is shown a schematic diagram of a stabilized laser system  310  for a plurality of n laser sources (LASER)  311   a – 311   n  (of which only laser sources  311   a  and  311   n  are shown) in accordance with the fourth embodiment of the present invention. The system  310  comprises the plurality of n laser sources  311   a – 311   n , a plurality of n optional polarization rotators (PR)  313   a – 313   n  (of which only PRs  313   a  and  313   n  are shown), and a blue shift feedback stabilizing arrangement  312  (shown within a dashed line area). The blue shift feedback stabilizing arrangement  312  comprises an Arrayed Waveguide Grating (AWG) multiplexer  315  (shown within a dashed line rectangle), an optional delay line  317 , and a broadband reflector  318 . The system  310  is a modified version of the system  300  of  FIG. 30  in that the power splitters  304   a – 304   n  of  FIG. 30  are eliminated, and the design of the AWG multiplexer  305  of  FIG. 30  has been slightly modified to provide the AWG multiplexer  315  of  FIG. 31 . In the system  310 , a front facet  311   p  of each of the plurality of n laser sources  311   a – 311   n  is coupled to a first input/output port  313   p  of a separate corresponding one of the polarization rotators  313   a – 313   n  via an optical path A. A second input/output port  313   q  of each of the polarization rotators  313   a – 313   n  is coupled to a separate corresponding one of a plurality of n first input ports  315   a  of the AWG multiplexer  315  via an optical path B. A second output port  315   b  of the AWG multiplexer  315  provides an output signal from the system  310  via an optical path C to any downstream remote device (not shown). A third input/output port  315   c  of the AWG multiplexer  315  is coupled to a first input/output port  317   a  of the optional delay line  317  via an optical path D. A second input/output port  317   b  of the optional delay line  317  is coupled to an input/output port  318   a  of the broadband reflector  318  via an optical path E. 
   The functioning of the polarization rotators  313   a – 313   n  corresponds to that described hereinbefore for, for example, the polarization rotators  243   a – 243   n  of  FIG. 24 . Still further, the functioning of the system  310  provides the same results as that described for the feedback stabilization system  210  of  FIG. 21 , where the optical paths between ports  315   a  to  315   b , and ports  315   c  and  315   a  in the AWG multiplexer  315  provide the functions of the optical paths between ports  214   a  to  214   b , and ports  214   c  and  214   a , respectively, in the forward and feedback multiplexer  214  of  FIG. 21 . The spectral response curves obtained in the system  310  are the same as those obtained for the system  210  of  FIG. 21 . As described for each of the prior systems of the present invention, the entire optical path A→B→D→E in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the forward multiplexing portion provided by optical paths from plurality of n input/output ports  315   a  to the single input/output port  315   b  in the AWG multiplexer, f 1   j (w),  315 , and its input/output port  315   b  are maintaining the polarization state of the laser sources  301   a – 301   n . Still further, one or multiple optional delay lines (not shown) can be added between any two components in the feedback optical signal path of A, B, D, E, and F. 
   Referring now to  FIG. 32 , there is shown a schematic of a system  320  for blue shift feedback stabilizing a single radiation source (Laser Source)  321  in accordance with the third embodiment of the present invention. The system  320  comprises the laser source  321 , and a feedback stabilizing arrangement  322  (shown within a dashed line area) comprising a main transmission filter, f 1 (w),  323 , a 2×2 power splitter  324 , a first feedback transmission filter, f 2 (w),  325 , a second feedback transmission filter, f 3 (w),  326 , a first reflector  327 , and a second reflector  328 . The laser source  321  is coupled at a front facet  321   a  thereof to a first input/output port  323   a  of the main transmission filter  323  via an optical path A. A second input/output port  323   b  of the main transmission filter  323  is coupled to a first input/output port  324   a  of the power splitter  324  via an optical path B. A second output port  324   b  of the power splitter  324  provides an output signal from the feedback stabilizing arrangement  322  via an optical path C that was generated by the laser source  321  and is the system  320  output. A third input/output  324   c  of the power splitter  324  is coupled to a first input/output port  325   a  of the first feedback transmission filter  325  via an optical path D, and a fourth input/output  324   d  of the power splitter  324  is coupled to a first input/output port  326   a  of the second feedback transmission filter  326  via an optical path F. A second input/output port  325   b  of the first feedback transmission filter  325  is coupled to an input/output port  327   a  of the first reflector  327  via an optical path E. A second input/output port  326   b  of the second feedback transmission filter  326  is coupled to an input/output port  328   a  of the second reflector  328  via an optical path G. 
   In operation, an output signal from the laser source  321  is received by the main transmission filter  323  at a first input/output port  323   a  thereof via the optical path A. The received signal is filtered by the main transmission filter  323 , f 1 (w), and transmitted to a first input/output port  324   a  of the power splitter  324  via the optical path B. In the power splitter  324 , a first portion carrying most of the power of the filtered signal received at the first input/output port  324   a  is tapped and delivered to a second output port  324   b  thereof for transmission as an output signal from the system  320  via the optical path C. A second portion of the received filtered signal is tapped and routed by the power splitter  324  via a third input/output port  324   c  thereof to a first input/output port  325   a  of the first feedback transmission filter, f 2 (w), via the optical path D. A filtered signal from the first feedback transmission filter  325  is transmitted from a second input/output port  325   b  thereof to a an input/output port  327   a  of the first reflector via the optical path E, and is reflected back through the first feedback transmission filter, f 2 (w),  326  where it is filtered again and transmitted back to the third input/output port of the power splitter  323  via the optical path D. The returned feedback signal is split in the power splitter  324 , and a first portion is returned to the laser source  321  via the main transmission filter  323  and the optical paths B and A. A second portion of the returned feedback signal is transmitted via the input/output port  324   d  of the power splitter  324  to the second feedback transmission filter f 3 (w),  326  where it is filtered and the resultant filter signal is transmitted from the second input/output port  326   b  thereof to the input/output port  328   a  of the second reflector  328  via the optical path G. The signal received by the second reflector  328  is reflected and transmitted back through the second feedback transmission filter  326  to the fourth input/output port  324   d  of the power splitter  324 . The signal received at the fourth input/output port  324   d  is split and a first portion thereof adds a component to the output signal transmitted at the second output port  324   b , and a second portion is transmitted through the first feedback transmission filter, f 2 (w),  325  and then to the first reflector  327 , and fed back as described hereinabove. 
   The optical path for the main component of the output signal propagates from the laser source  321 , through the main transmission filter, f 1 (w),  323 , and through the power splitter  324  via optical paths ABC. However, the output signal propagating via optical path C has other components due to a cavity between the first and second reflectors  327  and  328  including the first feedback transmission filter  325 , f 2 (w), the second feedback transmission filter  326 , f 3 (w), and the power splitter  324  using optical paths DEDFGF. Each signal round trip in the cavity adds another component to the output signal propagating via optical path C. The feedback signal returning to the laser source  321  also has other components due to the cavity between the first and second reflectors  327  and  328 . Each signal round trip in the cavity adds another component to the feedback signal. The spectral responses obtained by the feedback stabilizing arrangement  322  is essentially the same as that shown in  FIG. 4 , where curve  36  represents the forward filter spectral response F o (w), and curve  37  represents the feedback filter spectral response F f (w). The desired blue shift (δw) is accomplished by the proper choice of the coupling ratio of power splitter  324 , and the spectral responses f 1 (w), f 2 (w), and f 3 (w) when designing the main transmission filter  324 , the first feedback transmission filter  325 , and the second feedback transmission filter  326 , respectively. 
   As described hereinbefore for the feedback stabilizing arrangement in each of the other systems, the entire optical path in which the feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the output port  324   b  of the power splitter  324 , maintains the polarization state. Still further one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 33 , there is shown a schematic of a system  330  for blue shift feedback stabilizing a plurality of n radiation sources (Laser Source)  331   a – 331   n  (of which only laser sources  331   a  and  331   n  are shown) in accordance with the third embodiment of the present invention. The system  330  comprises the plurality of n laser sources  331   a – 331   n , and a feedback stabilizing arrangement  332  (shown within a dashed line area) comprising a forward multiplexer, f 1   j (w),  333 , a broadband power splitter  334 , a first feedback multiplexer, f 2   j (w),  335 , a second feedback multiplexer, f 3   j (w),  336 , a plurality of n first reflectors  337   a – 337   n  (of which only first reflectors  337   a  and  337   n  are shown), and a plurality of n second reflectors  338   a – 338   n  (of which only second reflectors  338   a  and  338   n  are shown). Each of the laser sources  331   a – 331   n  is coupled at a front facet  331   p  thereof to a separate corresponding one of a plurality of n first input/output ports  333   a  of the forward multiplexer  333  via an optical path A. A second input/output port  333   b  of the main transmission filter  323  is coupled to a first input/output port  334   a  of the power splitter  334  via an optical path B. A second output port  334   b  of the power splitter  334  provides an output signal from the feedback stabilizing arrangement  332  via an optical path C that was generated by the laser source  321  and is an output of the system  330 . A third input/output  334   c  of the power splitter  334  is coupled to a first input/output port  335   a  of the first feedback multiplexer  335  via an optical path D, and a fourth input/output  334   d  of the power splitter  334  is coupled to a first input/output port  336   a  of the second feedback multiplexer  326  via an optical path F. Each of a plurality of n second input/output ports  335   b  of the first feedback multiplexer  335  is coupled to an input/output port  337   a  of a separate corresponding one of the plurality of n first reflectors  327  via an optical path E. Each of a plurality of n second input/output ports  336   b  of the second feedback multiplexer  326  is coupled to an input/output port  338   a  of a separate corresponding one of the plurality of n second reflectors  328  via an optical path G. 
   The operation of the feedback stabilizing arrangement  332  is essentially the same as that described for the feedback stabilizing arrangement  322  of  FIG. 32 . More particularly, the output wavelength signals from the plurality of n laser sources  331   a – 331   n  are multiplexed in the forward multiplexer  333  into a multiplexed output signal delivered to its input/output port  333   b . Similarly the multiplexed signals received at each of the input/output ports  335   a  and  336   a  of the first and second feedback multiplexers  335  and  336 , respectively, are demultiplexed and the plurality of n demultiplexed signals are transmitted to the corresponding one of the respective plurality of n first reflectors  337   a – 337   n  and the plurality of n second reflectors  338   a – 338   n , and vice versa. The signals propagating through the power splitter  334  to each of the input/output ports  334   a ,  334   b ,  334   c , and  334   d  function in the same manner as described hereinbefore for the power splitter  324  of  FIG. 32 . Therefore, the output signal at output port  334   b  of the power splitter  334  has components that are added as a result of the cavities between the corresponding ones of the plurality of first reflectors  337   a – 337   n  and the plurality of second reflectors  338   a – 338   n  in the manner described hereinabove for the cavity between the reflectors  327  and  328  of  FIG. 32 . Similarly, the cavities between the corresponding ones of the plurality of first reflectors  337   a – 337   n  and the plurality of second reflectors  338   a – 338   n  also adds a component to the feedback signal to the corresponding one of the laser sources  331   a – 331   n . The spectral responses obtained by the feedback stabilizing arrangement  332  is essentially the same as that shown in  FIG. 6 , where curves  46   a – 46   n  represent the forward filter spectral response F o (w), for each of the wavelengths generated by the corresponding one of the plurality of n laser sources  331   a – 331   n , and curves  47   a – 47   n  represent the feedback filter spectral response F f (w) for each of the wavelengths fed back to the corresponding one of the plurality of n laser sources  331   a – 331   n . The desired blue shift (δw) is accomplished by the proper choice of the coupling ratio of power splitter  334 , and the spectral responses f 1 (w), f 2 (w), and f 3 (w) when designing the forward multiplexer  333 , the first feedback multiplexer  335 , and the second feedback multiplexer  336 , respectively. 
   As described hereinbefore for the feedback stabilizing arrangement in each of the other prior systems of  FIGS. 3–32 , the entire optical path in which a feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the output port  334   b  of the power splitter  334 , maintains the polarization state. Still further one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 34 , there is shown a system  340  for the blue shift feedback stabilizing of a plurality of n radiation sources (Laser Sources w 1  to w n )  341   a – 341   n  (of which only lasers sources  341   a  and  341   n  are shown) that is an alternative system to that of system  330  of  FIG. 33  in accordance with the third embodiment of the present invention. The system  340  comprises the plurality of n laser sources  341   a – 341   n , and a blue shift feedback stabilizing arrangement  342  (shown within a dashed line area). The blue shift feedback stabilizing arrangement  342  comprises a forward multiplexer, f 1   j (w),  343 , a broadband power splitter  344 , a first feedback multiplexer, f 2   j (w),  345   a , a second feedback multiplexer, f 22   j (w),  345   b , a third feedback multiplexer, f 3   j (w),  346   a , a fourth feedback multiplexer, f 32   j (w),  346   b , a first broadband reflector  347 , and a second broadband reflector  348 . The blue shift feedback stabilizing arrangement  342  is essentially the same as the blue shift feedback stabilizing arrangement  332  of  FIG. 33 , except that the feedback multiplexers  335  and  336  of  FIG. 33  have been replaced by a pair of feedback multiplexers  345   a  and  345   b , and  346   a  and  346   b , respectively, and the plurality of reflectors  337   a – 337   n  and  338   a – 338   n  of  FIG. 33  have been replaced by individual reflectors  347  and  348 , respectively. The overall interconnections and operation of the blue shift feedback stabilizing arrangement  342  is essentially the same as the blue shift feedback stabilizing arrangement  332  of  FIG. 33  and will not be repeated here. The advantage of the blue shift feedback stabilizing arrangement  342  is that it saves the need for the many reflectors  337   a – 337   n  and  338   a – 338   n  of  FIG. 33  by demultiplexing the output signals from the first and third feedback multiplexers  345   a  and  346   a  using the second and fourth feedback multiplexers  345   b  and  346   b . The spectral responses f 2   j (w), f 22   j (w), f 3   j (w), f 32   j (w), of the first, second, third, and fourth feedback multiplexer  345   a ,  345   b ,  346   a , and  346   b , respectively, are designed to provide the same overall spectral responses f 2   j (w), f 3   j (w), provided by the first and second feedback multiplexers  335  and  336  of  FIG. 33 , respectively. As a result, the spectral responses obtained by the blue shift feedback stabilizing arrangement  342  is essentially the same as that shown in  FIG. 6  and obtained with the system  330  of  FIG. 33 . As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  344   b  of the power splitter  324 , maintains the polarization state. Still further one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 35 , there is shown a schematic of a system  350  for blue shift feedback stabilizing a single radiation source [Laser Source (w)]  351  that is a simplified version of the system of  320  of  FIG. 32  in accordance with the third embodiment of the present invention. The system  350  comprises the laser source  351 , and a blue shift feedback stabilizing arrangement  352  (shown within a dashed line area) comprising a main transmission filter, f 1 (w),  353 , a power splitter  354 , a feedback transmission filter, f 2 (w),  355 , and a reflector  356 . The laser source  351  is coupled at its front facet  351   a  to a first input/output port  353   a  of the main transmission filter  353  via an optical path A, while a second input/output port  353   b  of the main transmission filter  353  is coupled to a first input/output port  354   a  of the power splitter  354  via an optical path B. A second output port of the power splitter  354  provides an output signal from the system  350  to a predetermined downstream device via an optical path C, and a third input/output port  354   c  of the power splitter  354  is coupled to a first input/output port  355   a  of the feedback transmission filter, f 2 (w),  355  via an optical path D. A second input/output port  355   b  of the feedback transmission filter  355  is coupled to an input/output port  356   a  of the reflector  356  via an optical path E. In the configuration of feedback stabilizing arrangement  352 , the feedback transmission filter, f 3 (w),  326  and the second reflector  328  of the feedback stabilizing arrangement  322  of  FIG. 32  are removed and the 2×2 power splitter  324  of  FIG. 32  is replaced with a 1×2 power spitter  354 . 
   In operation, the main output signal propagates through the feedback stabilizing arrangement  352  only once from the laser source  351  to the second output port  354   b  of the power splitter  354 . The stabilized output signal from the laser source  351  is filtered only by the main transmission filter, f 1 (w),  353 , and, therefore, a forward filter spectral response for the feedback stabilizing arrangement  352  is F o (w)=f 1 (w). A feedback signal found at the front facet  351   a  comprises one component when propagating from laser source  351 , through the main transmission filter, f 1 (w),  353 , the power splitter  354 , the feedback transmission filter, f 2 (w),  355 , the reflector  356 , and back again through the same path via optical paths A→B→D→E→D→B→A. As a result, the feedback signal passes twice through the feedback transmission filter, f 2 (w),  355  and the main transmission filter, f 1 (w),  353  such that the Feedback filter spectral response is F f (w)=[f 1 (w)·f 2 (w)]2. Spectral response curves obtained with the system  350  correspond to the curves  100 – 102  shown in  FIG. 10 , where curve  100  represents the Forward Filter Spectral response F o (w)=f 1 (w), curve  101  represents the Feedback transmission filter spectral response f 2 (w), and curve  102  represents the Feedback filter spectral response F f (w)=[f 1 (w)·f 2 (w)] 2 . The transmission filter  353  [with the spectral response f 1 (w)] and the transmission filter  355  [with the spectral response f 2 (w)] must be designed such that the spectral responses F o (w) and F f (w) provide desired central wavelengths, bandwidths of forward and feedback spectral responses, and wavelength shift (δw) between the spectral responses F o (w) and F f (w). As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  344   b  of the power splitter  324 , maintains the polarization state. Still further one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 36 , there is shown a schematic of a system  360  for blue shift feedback stabilizing a plurality of n radiation sources [Laser Sources w 1  to w n )]  361   a – 361   n  (of which only laser sources  361   a  and  361   n  are shown) that is a simplified version of the system of  330  of  FIG. 33  in accordance with the third embodiment of the present invention. The system  360  comprises the plurality of n laser sources  361   a – 361   n , and a blue shift feedback stabilizing arrangement  362  (shown within a dashed line area) comprising a forward multiplexer, f 1   j (w),  363 , a power splitter  364 , a feedback multiplexer, f 2   j (w),  365 , and a plurality of reflectors  366   a  to  366   n  with only  366   a  and  366   n  being shown. Each of the plurality of n laser sources  361   a – 361   n  is coupled at its front facet  361   p  to a separate corresponding one of a plurality of n first input/output ports  363   a  of the forward multiplexer  363  via an optical path A, while a second input/output port  363   b  of the forward multiplexer  363  is coupled to a first input/output port  364   a  of the power splitter  364  via an optical path B. A second output port  364   b  of the power splitter  364  provides an output signal from the system  360  to a predetermined downstream device via an optical path C, and a third input/output port  364   c  of the power splitter  364  is coupled to a first input/output port  365   a  of the feedback multiplexer, f 2   j (w),  365  via an optical path D. Each of a plurality of n second input/output ports  365   b  of the feedback multiplexer  365  is coupled to an input/output port  366   p  of a separate corresponding one of the plurality of n reflectors  366   a – 366   n  via an optical path E. 
   In operation, the main output signal from each of the plurality of n laser sources  361   a – 361   n  propagates through the feedback stabilizing arrangement  362  only once to the second output port  364   b  of the power splitter  364 . The stabilized output signal from each of the plurality of n laser sources  361   a – 361   n  is filtered only by the forward multiplexer, f 1 (w),  363 , and, therefore, a forward filter spectral response for a jth port is F o   j (w)=f 1 (w). A feedback signal found at each of the front facets  361   p  of the laser sources  361   a – 361   n  comprises one component in propagating from the corresponding one of the laser sources  361   a – 361   n  [e.g., laser sources  361   j  (not shown)], through the forward multiplexer, f 1   j (w),  363 , the power splitter  364 , the feedback multiplexer, f 2   j (w),  365 , the corresponding one of the plurality of n reflectors  366   a – 366   n , and back again through the same path via optical paths A→B→D→E→D→B→A. As a result, the feedback signal passes twice through the feedback multiplexer, f 2   j (w),  365  and the forward multiplexer, f 1   j (w),  363  such that the resultant feedback filter spectral response is F f   j (w)=[f j (w)·f 2   j (w)] 2 . Spectral response curves obtained with the system  360  correspond to the curves  120   a – 120   n ,  121   a – 121   n , and  102   a – 102   n  shown in  FIG. 12 , where each of the curves  120   a – 120   n  represent the Forward multiplexer response F o (w)=f 1 (w) for each of the corresponding laser sources  361   a – 361   n , curves  121   a – 121   n  represent the spectral response f 2 (w) provided by the feedback multiplexer  365  for each of the feedback signals, and curves  122   a – 122   n  represent the Feedback filter spectral response F f (w)=[f 1 (w)·f 2 (w)] 2  for each of the laser sources  361   a – 361   n . The forward multiplexer  363  [with the spectral response f 1 (w)] and the feedback multiplexer  365  [with the spectral response f 2 (w)] must be designed such that the spectral responses F o (w) and F f (w) provide desired central wavelengths, bandwidths of forward and feedback spectral responses, and wavelength shift (δw) between the spectral responses F o (w) and F f (w). As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  364   b  of the power splitter  364 , maintains the polarization state. Still further one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 37 , there is shown a schematic of a system  370  for blue shift stabilizing a single radiation source [Laser Source (w)]  371  in accordance with a fifth embodiment of the present invention. The system  370  comprises the laser source  371 , and a blue shift feedback stabilizing arrangement  372  (shown within a dashed line rectangle) comprising a first power splitter  373 , a main transmission filter, f 1 (w),  374 , a first feedback transmission filter, f 2 (w),  375 , a second feedback transmission filter, f 3 (w),  376 , and a second power splitter  377 . The laser source  371  is coupled at its front facet  371   a  to a first input/output port  373   a  of the first power splitter  373  via an optical path A. For the first power splitter  373 , a second input/output port  373   b  thereof is coupled to a first input/output port  374   a  of the main transmission filter  374  via an optical path B, a third input/output port  373   c  thereof is coupled to a first input/output port  375   a  of the first feedback transmission filter  375  via an optical path E, and a fourth input/output port  373   d  thereof is coupled to a second input/output port  376   b  of the second feedback transmission filter  376  via and an optical path H. A second input/output port  374   b  of the main transmission filter  374  is coupled to a first input/output port  377   a  of the second power splitter  377  via an optical path C. For the second power splitter  377 , a second input/output port  377   b  thereof provides an output signal from the system  370  to a predetermined downstream device via an optical path D, a third input/output port  377   c  is coupled to a second input/output port  375   b  of the first feedback transmission filter  375  via an optical path F, and a fourth input/output port  377   d  thereof is coupled to a first input/output port  376   a  of the second feedback transmission filter  376  via an optical path G. 
   In operation, an output signal from the laser source  371  is tapped in the first power splitter  373 , and a first portion thereof carrying most of the laser signal power is transmitted via optical path B to the first input/output port  374   a  of the main transmission filter  374  while a second portion thereof is transmitted via the optical path E to the first input/output port  375   a  of the first feedback transmission filter  375 . The signal received by the main transmission filter  374 , f 1 (w), is filtered and transmitted via the optical path C to the first input/output port  377   a  of the second power splitter  377 . In the second power splitter  377 , the received signal is tapped and a first portion thereof carrying most of the received signal power is provided as an output signal from the system  370  via optical path D to any predetermined downstream device, while a second portion thereof is transmitted via optical path F to the second input/output port  375   b  of the first feedback transmission filter  375 . Therefore, the optical path (A→B→C→D) for the main component of the output signal from the system  370  involves the first power splitter  373 , the main transmission filter, f 1 (w),  374 , and the second power splitter  377 . The output signal has other components due to the presence of a cavity comprising a twisted loop configuration involving the optical paths F→E→H→G→F. Each signal round trip in this cavity adds one component to the output signal propagating on optical path D. A feedback signal to the laser source  371  has two main components. A first main component in the feedback signal involves a round trip from the laser source  371  through the optical paths A→B→C→F→E→A, while a second main component in the feedback signal involves a round trip from the laser source  371  through the optical paths A→E→F→C→B→A. Each signal round trip in this cavity adds one component to the feedback signal to the laser source  371 . 
   Spectral response curves obtained with the system  370  correspond to the spectral response curves  36  and  37  shown in  FIG. 4 , where curve  36  represents the Forward Filter Spectral response F o (w), and curve  37  represents the Feedback filter spectral response F f (w). The main transmission filter  373  [with the spectral response f 1 (w)] and the first and second feedback transmission filters  375  and  376 , respectively, [with the respective spectral response f 2 (w) and f 3 (w)] must be designed such that the desired forward and feedback spectral responses F o (w) and F f (w) are achieved by a proper choice of the individual spectral responses f 1 (w), f 2 (w), and f 3 (w), coupling ratios, and cavity length. As indicated for prior systems (e.g.,  90  of  FIG. 9 and 110  of  FIG. 11 ), all components and interconnects, except the output port  377   b  of the power splitter  377 , maintains the polarization state. Still further, one or more optional delay lines can be added between any two components in the path of the feedback signal. Additionally, the broadband power splitter function for the first and second power splitters  373  and  377  can be achieved in different technology platforms such as planar waveguide technology using directional couplers (DC), multimode interference (MMI) couplers, asymmetric Y junctions, Mach-Zehnder interferometers, etc., and free space optics using thin film, etc. 
   Referring now to  FIG. 38 , there is shown a schematic of a system  380  for blue shift stabilizing a plurality of n radiation sources [Laser Sources w 1  to w n )]  381   a – 381   n  with only  381   a  and  381   n  being shown in accordance with a fifth embodiment of the present invention. The system  380  comprises the plurality of n laser sources  381   a – 381   n , and a blue shift feedback stabilizing arrangement  382  (shown within a dashed line area) comprising a plurality of n 2×2 power splitters  383   a – 383   n , a forward multiplexer, f 1   j (w),  384 , a first feedback multiplexer, f 2   j (w),  385 , a second feedback multiplexer, f 3   j (w),  386 , and a broadband power splitter  387 . Each of the plurality of n laser sources  381   a – 381   n  is coupled at its front facet  381   p  to a first input/output port  383   p  of a separate corresponding one of the plurality of n 2×2 power splitters  383   a – 383   n  via an optical path A. For each of the 2×2 power splitters  383   a – 383   n , a second input/output port  383   q  thereof is coupled to a corresponding one of a plurality of n first input/output ports  384   a  of the forward multiplexer  384  via an optical path B, a third input/output port  384   r  thereof is coupled to a corresponding one of a plurality of n first input/output port  385   a  of the first feedback multiplexer  385  via an optical path F, and a fourth input/output port  383   s  thereof is coupled to a corresponding one of a plurality of n first input/output port  386   a  of the second feedback multiplexer  386  via and optical path G. A second input/output port  384   b  of the forward multiplexer  384  is coupled to a first input/output port  387   a  of the second power splitter  387  via an optical path C. For the broadband power splitter  387 , a second output port  387   b  thereof provides an output signal from the system  380  to a predetermined downstream device via an optical path D, a third input/output port  387   c  thereof is coupled to a second input/output port  385   b  of the first feedback multiplexer  385  via an optical path E, and a fourth input/output port  387   d  thereof is coupled to a second input/output port  386   b  of the second feedback multiplexer  386  via an optical path H. 
   The blue shift feedback stabilizing arrangement  382  is an implementation for a plurality of n laser sources  381   a – 381   n  similar to that described for the blue shift feedback stabilizing arrangement  372  of  FIG. 37  for a single laser source  371 . However, in the blue shift feedback stabilizing arrangement  382 , the single channel main transmission filter, f 1 (w),  374 , and the single channel first and second feedback transmission filters, f 2 (w) and f 3 (w),  375  and  376 , respectively, of  FIG. 37  have been replaced with a multiple channel forward multiplexer, f 1   j (w),  384 , and first and second feedback multiplexers, f 2   j (w) and f 3   j (w),  385  and  386 , respectively, where “j” represents a jth port. The overall operation of the blue shift feedback stabilizing arrangement  382  is essentially the same as that described hereinbefore for the blue shift feedback stabilizing arrangement  372  of  FIG. 37  except that the output signals from the plurality of n laser sources  381   a – 381   n  are selectively multiplexed or demultiplexed where a single multiplexed or a plurality of n demultiplexed output signals, respectively, are needed from each of the multiplexers  384 ,  385 , or  386 . 
   The spectral responses obtained by the blue shift feedback stabilizing arrangement  382  is essentially the same as that shown in  FIG. 6 , where curves  46   a – 46   n  represent the forward filter spectral response F o   j (w), for each of the wavelengths generated by the corresponding one of the plurality of n laser sources  381   a – 381   n , and curves  47   a – 47   n  represent the feedback filter spectral response F f   j (w) for each of the wavelengths fed back to the corresponding one of the plurality of n laser sources  381   a – 381   n . As was found in the blue shift feedback stabilizing arrangement  372  of  FIG. 37 , in the blue shift feedback stabilizing arrangement  382  the output signal in optical path D has components due to the presence of a cavity comprising a twisted loop configuration involving the optical paths E→F→G→H→E. Each signal round trip in this cavity adds one component to the output signal propagating on optical path D. A feedback signal to each of the plurality of n laser sources  381   a – 381   n  has two main components. A first main component in the feedback signal involves a round trip from a laser source (e.g.,  381   a ) through the optical paths A→B→C→E→F→A, while a second main component in the feedback signal involves a round trip from the laser source  381   a  through the optical paths A→F→E→C→B→A. Each signal round trip in this cavity adds one component to the feedback signal to each of the plurality of n laser sources  381   a – 381   n . The desired blue shift (δw) is accomplished by the proper choice of the spectral responses f 1   j (w), f 2   j w), and f 3   j (w) when designing the forward multiplexer  384 , the first feedback multiplexer  385 , and the second feedback multiplexer  386 , respectively. 
   As described hereinbefore for other feedback stabilizing arrangements, the entire optical path in which a feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the output port  387   b  of the second power splitter  387 , maintains the polarization state. Still further one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 39 , there is shown a schematic of a system  390  for a blue shift feedback stabilizing arrangement  392  (shown within a dashed line rectangle), similar to system  370  that is shown in  FIG. 37 , for a single radiation source [laser source (w)]  391  in accordance with the fifth embodiment of the present invention. The system  390  comprises the laser source  391 , and a blue shift feedback stabilizing arrangement  392  (shown within a dashed line rectangle) comprising a main transmission filter, f 1 (w),  393 , first power splitter  394 , a second power splitter  395 , a first feedback transmission filter, f 2 (w),  396 , and a second feedback transmission filter, f 3 (w),  397 . The laser source  391  is coupled at its front facet  391   a  to a first input/output port  393   a  of the main transmission filter, f 1 (w),  393  via an optical path A; and a second input/output port  393   b  of the main transmission filter  393  is coupled to a first input/output port  394   a  of the first power splitter  394  via an optical path B. For the first power splitter  394 , a second input/output port  394   b  thereof is coupled to a first input/output port  395   a  of the second power splitter  395  via an optical path C, a third input/output port  394   c  thereof is coupled to a first input/output port  396   a  of the first feedback transmission filter  396  via an optical path F, and a fourth input/output port  394   d  thereof is coupled to a first input/output port  397   a  of the second feedback transmission filter  397  via and optical path G. For the second power splitter  395 , a second input/output port  395   b  thereof provides an output signal from the system  390  to a predetermined downstream device via an optical path D, a third input/output port  395   c  is coupled to a second input/output port  396   b  of the first feedback transmission filter  396  via an optical path E, and a fourth input/output port  395   d  thereof is coupled to a second input/output port  397   b  of the second feedback transmission filter  397  via an optical path H. 
   In operation, an output signal from the laser source  391  is filtered by the main transmission filter  393  and a resultant output signal is transmitted to the first power splitter  394 . The filtered signal is tapped in the first power splitter  394 , and a first portion thereof, carrying most of the laser signal power, is transmitted via optical path C to the first input/output port  395   a  of the second power splitter  395 , while a second portion thereof is transmitted via optical path F to the first input/output port  396   a  of the first feedback transmission filter  396 . In the second power splitter  395 , the received signal is tapped and a first portion thereof carrying most of the received signal power is provided as an output signal from the system  390  via optical path D to any predetermined downstream device, while a second portion thereof is transmitted via optical path E to the second input/output port  396   b  of the first feedback transmission filter  396 . Therefore, the optical path (A→B→C→D) for the main component of the output signal from the system  390  involves the main transmission filter, f 1 (w),  393 , the first power splitter  394 , and the second power splitter  395 . The output signal has other components due to the presence of a cavity comprising a twisted loop configuration involving the optical paths F→E→H→G→F. Each signal round trip in this cavity adds one component to the output signal propagating on optical path D. A feedback signal to the laser source  391  has two main components. A first main component in the feedback signal involves a round trip from the laser source  391  through the optical paths A→B→C→E→F→A, while a second main component in the feedback signal involves a round trip from the laser source  391  through the optical paths A→B→F→E→C→B→A. Each signal round trip in this cavity adds one component to the feedback signal to the laser source  391 . An alternative arrangement to the feedback stabilizing arrangement  392  that provides a same result is to replace the second feedback transmission filter, f 3 (w),  347  with an optional delay line  347  (not shown). 
   Spectral response curves obtained with the system  390  correspond to the spectral response curves  36  and  37  shown in  FIG. 4 , where curve  36  represents the Forward Filter Spectral response F o (w), and curve  37  represents the Feedback filter spectral response F f (w). The main transmission filter  393  [with the spectral response f 1 (w)] and the first and second feedback transmission filters  396  and  397 , respectively, [with the respective spectral response f 2 (w) and f 3 (w)] must be designed such that the desired forward and feedback spectral responses F o (w) and F f (w) are achieved by a proper choice of the individual spectral responses f 1 (w), f 2 (w), and f 3 (w), coupling ratios, and cavity length. As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  395   b  of the second power splitter  395 , maintains the polarization state. Still further, one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 40 , there is shown a schematic of a system  400 , which is similar to the system  390  of  FIG. 39 , for blue shift stabilizing a plurality of n radiation sources [laser sources (w 1  to w n )]  401   a – 401   n  in accordance with the fifth embodiment of the present invention. The system  400  comprises the plurality of n laser sources  401   a – 401   n  (with only  401   a  and  401   n  being shown), and a blue shift feedback stabilizing arrangement  402  (shown within a dashed line rectangle) comprising a forward multiplexer, f 1   j (w),  403 , a first broadband power splitter  404 , a second broadband power splitter  405 , a first feedback multiplexer arrangement, f 2   j (w),  406  (shown within a dashed line rectangle), and a second feedback multiplexer arrangement, f 3   j (w),  407  (shown within a dashed line rectangle. The first feedback multiplexer arrangement, f 2   j (w),  406  comprises a cascaded feedback multiplexer  406   g and a feedback multiplexer  406   h ; and the second feedback multiplexer arrangement, f 3   j (w),  407  comprises cascaded feedback multiplexer  407   g  and feedback multiplexer  407   h . Each of the plurality of n laser sources  401   a – 401   n  is coupled at its front facet  401   p  to a corresponding one of first input/output ports  403   a  of the forward multiplexer, f 1   j (w),  403  via an optical path A; and a second input/output port  403   b  of the forward multiplexer  403  is coupled to a first input/output port  404   a  of the first broadband power splitter  404  via an optical path B. For the first power splitter  404 , a second input/output port  404   b  thereof is coupled to a first input/output port  405   a  of the second power splitter  405  via an optical path C, a third input/output port  404   c  thereof is coupled to a first input/output port  406   a  of the first feedback multiplexer arrangement  406  via an optical path F, and a fourth input/output port  404   d  thereof is coupled to a first input/output port  407   a  of the second feedback multiplexer arrangement  407  via and optical path G. For the second power splitter  405 , a second input/output port  405   b  thereof provides an output signal from the system  400  to a predetermined downstream device via an optical path D, a third input/output port  405   c  is coupled to a second input/output port  406   b  of the first feedback multiplexer arrangement  406  via an optical path E, and a fourth input/output port  405   d  thereof is coupled to a second input/output port  407   b  of the second feedback multiplexer arrangement  407  via an optical path H. 
   In the first feedback multiplexer arrangement  406 , a signal received at the first input/output port  406   a  is demultiplexed into a plurality of n demultiplexed signals by the first feedback multiplexer  406   g , and each demultiplexed signal is delivered to a corresponding one of a plurality of n input/output ports  406   c  thereof. Each of the plurality of n demultiplexed signals from the first feedback multiplexer  406   g  are received at a corresponding one of a plurality of n input/output ports  406   d  of the second feedback multiplexer  406   h , and the plurality of n received signals are multiplexed into a single output signal at input/output port  406   b  thereof. The operation of the first and second feedback multiplexers  407   g  and  407   h , respectively, in the second feedback multiplexer arrangement  407  are the same as that described for the operation of the in the first and second feedback multiplexers  406   g  and  406   h  in the first feedback multiplexer arrangement  406 . Still further, the operation in each of the first and second feedback multiplexer arrangements  406  and  407  for signals propagating in an opposite direction therein is exactly the reverse of that described hereinabove. The operation of the feedback stabilizing arrangement  402  is substantially the same as that described for the feedback stabilizing arrangement  392  of  FIG. 39  except that the output signals from the plurality of n laser sources  401   a – 401   n  are multiplexed into a filtered single multiplexed output signal from the forward multiplexer  403  before being similar processed by the remaining components  404 ,  405 ,  406 , and  407 . The advantage of providing a forward multiplexer  403  before the first broadband power splitter  404 , and a pair of cascaded feedback multiplexers  406   g and  406   h , and  407   g  and  407   h  in the first and second feedback multiplexer arrangements  406  and  407 , respectively, is to maintain a single multiplexed signal between the components  404 ,  405 ,  406  and  407  and avoid the necessity of a plurality of n same components to handle the separate demultiplexed signals. 
   The spectral responses obtained by the blue shift feedback stabilizing arrangement  402  is essentially the same as that shown in  FIG. 6 , where curves  46   a – 46   n  represent the forward filter spectral response F o (w), for each of the wavelengths generated by the corresponding one of the plurality of n laser sources  401   a – 401   n , and curves  47   a – 47   n  represent the feedback filter spectral response F f (w) for each of the wavelengths fed back to the corresponding one of the plurality of n laser sources  401   a – 401   n . As was found in the blue shift feedback stabilizing arrangement  372  of  FIG. 37 , in the blue shift feedback stabilizing arrangement  402  the output signal in optical path D has components due to the presence of a cavity comprising a twisted loop configuration involving the optical paths E→F→G→H→E. Each signal round trip in this cavity adds one component to the output signal propagating on optical path D. A feedback signal to each of the plurality of n laser sources  401   a – 401   n  has two main components. A first main component in the feedback signal involves a round trip from a laser source (e.g.,  401   a ) through the optical paths A→B→C→E→F→A, while a second main component in the feedback signal involves a round trip from the laser source  401   a  through the optical paths A→B→F→E→C→B→A. Each signal round trip in this cavity adds one component to the feedback signal to each of the plurality of n laser sources  401   a – 401   n . The desired blue shift (δw) is accomplished by the proper choice of the spectral responses f 1   j (w), f 2   j (w), and f 3   j (w) when designing the forward multiplexer  403 , the first feedback multiplexer arrangement  406 , and the second feedback multiplexer arrangement  407 , respectively. 
   As described hereinbefore for other feedback stabilizing arrangements, the entire optical path in which a feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the output port  405   b  of the second power splitter  405 , maintains the polarization state. Still further one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 41 , there is shown a schematic of a system  410  that modifies the system  400  of  FIG. 40  for feedback stabilizing a plurality of n radiation sources [laser sources w 1  to w n )]  411   a – 411   n  (of which only laser sources  411   a  and  411   n  are shown) in accordance with the fifth embodiment of the present invention. The system  410  comprises the plurality of n laser sources  411   a – 411   n , and a blue shift feedback stabilizing arrangement  412  (shown within a dashed line rectangle) comprising a forward multiplexer, f 1   j (w),  413 , a first broadband power splitter  414 , a second power splitter  415 , a feedback multiplexer arrangement, f 2   j (w),  416  (shown within a dashed line rectangle) comprising cascaded first and second feedback multiplexers  416   g  and  416   h , and an optional delay line  417 . Each of the plurality of n laser sources  411   a – 411   n  is coupled at a front facet  411   p  thereof to a corresponding one of a plurality of n first input/output ports  413   a  of the forward multiplexer, f 1   j (w),  413  via an optical path A; and a second input/output port  413   b  of the forward multiplexer  413  is coupled to a first input/output port  414   a  of the first broadband power splitter  414  via an optical path B. For the first broadband power splitter  414 , a second input/output port  414   b  thereof is coupled to a first input/output port  415   a  of the second broadband power splitter  415  via an optical path C, a third input/output port  414   c  thereof is coupled to a first input/output port  416   a  of the feedback multiplexer arrangement  416  via an optical path F, and a fourth input/output port  414   d  thereof is coupled to a first input/output port  417   a  of the optional delay line  417  via and optical path G. For the second broadband power splitter  415 , a second input/output port  415   b  thereof provides an output signal from the system  410  to a predetermined downstream device via an optical path D, a third input/output port  415   c  is coupled to a second input/output port  416   b  of the feedback multiplexer arrangement  416  via an optical path E, and a fourth input/output port  415   d  thereof is coupled to a second input/output port  417   b  of the optional delay line  417  via an optical path H. 
   The operation of the feedback stabilizing arrangement  412  is essentially the same as was described for the operation of the feedback stabilizing arrangement  402  of  FIG. 40  except that the optional delay line  417  of  FIG. 41  replaces second feedback multiplexer arrangement  407 . 
   The spectral responses obtained by the blue shift feedback stabilizing arrangement  410  is essentially the same as that shown in  FIG. 6 , where curves  46   a – 46   n  represent the forward filter spectral response F o   j (w), for each of the wavelengths generated by the corresponding one of the plurality of n laser sources  411   a – 411   n , and curves  47   a – 47   n  represent the feedback filter spectral response F f   j (w) for each of the wavelengths fed back to the corresponding one of the plurality of n laser sources  411   a – 411   n . As was found in the blue shift feedback stabilizing arrangement  372  of  FIG. 37 , in the blue shift feedback stabilizing arrangement  412  the output signal in optical path D has components due to the presence of a cavity comprising a twisted loop configuration involving the optical paths E→F→G→H→E. Each signal round trip in this cavity adds one component to the output signal propagating on optical path D. A feedback signal to each of the plurality of n laser sourced  411   a – 411   n  has two main components. A first main component in the feedback signal involves a round trip from a laser source (e.g.,  411   a ) through the optical paths A→B→C→E→F→B→A, while a second main component in the feedback signal involves a round trip from the laser source  411   a  through the optical paths A→B→F→E→C→B→A. Each signal round trip in this cavity adds one component to the feedback signal to each of the plurality of n laser sources  411   a – 411   n . The desired blue shift (δw) is accomplished by the proper choice of the spectral responses f 1   j (w), f 2   j (w), when designing the forward multiplexer  413 , the feedback multiplexer arrangement  416 , respectively, and the optional delay line  417 . 
   As described hereinbefore for other feedback stabilizing arrangements (e.g., arrangements  330  and  360 ), the entire optical path in which a feedback signal is propagating must preserve the polarization state (polarization maintaining, PM). This means that all components and interconnects, except the output port  415   b  of the second broadband power splitter  415 , maintains the polarization state. Still further one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 42 , there is shown a schematic of a system  420  for blue shift feedback stabilizing a single radiation source [Laser Source (w)]  421  in accordance with the fifth embodiment of the present invention. The system  420  comprises the laser source  421 , and a blue shift feedback stabilizing arrangement  422  shown within a dashed line enclosed area. The feedback stabilizing arrangement  422  comprises a main transmission filter, f 1 (w),  423 , a first feedback transmission filter, f 2 (w),  424 , a second feedback transmission filter, f 3 (w),  425 , a third feedback transmission filter, f 4 (w),  426 , a first 2×2 power splitter  427 , a second 2×2 power splitter  428 , a first reflector  429 , and a second reflector  430 . The laser source  421  is coupled from its front facet  421   a  to a first input/output port  423   a  of the main transmission filter  423  via an optical path A. A second input/output port  423   b  of the main transmission filter  423  is coupled to a first input/output port  427   a  of the first 2×2 power splitter  427  via an optical path B. In the first power splitter  427 , a second input/output port  427   b  thereof is coupled to a first input/output port  428   a  of the second 2×2 power splitter  428  via an optical path C, a third input/output port  427   c  is coupled to a first input/output port  424   a  of the first feedback transmission filter, f 2 (w),  424  via an optical path F, and a fourth input/output port  427   d  is coupled to a first input/output port  425   a  of the second feedback transmission filter, f 3 (w),  425  via an optical path G. In the second power splitter  428 , a second output port  428   b  thereof provides an output signal from the system  420  to any predetermined downstream device (not shown) via an optical path D, a third input/output port  428   c  thereof is coupled to a second input/output port  424   b  of the first feedback transmission filter, f 2 (w),  424  via an optical path E, and a fourth input/output port thereof is coupled to a first input/output port  426   a  of the third feedback transmission filter, f 4 (w),  426  via an optical path J. A second input/output port  425   b  of the second feedback transmission filter  425  is coupled to an input/output port  430   a  of the second reflector  430  via an optical path H. A second input/output port  426   b  of the third feedback transmission filter  426  is coupled to an input/output port  429   a  of the first reflector  429  via an optical path K. 
   In operation, the output signal from the laser source  421  is filtered by the main transmission filter, f 1 (w),  423  and a portion of the filtered signal is tapped and a first portion thereof, carrying most of the signal power, is transmitted to the second power splitter  428  via optical path C, and a second portion thereof is sent to the first input/output port  424   a  of the first feedback transmission filter  424  via optical path F. In the second power splitter  428 , a first portion of the received signal received at input/output port  428   a , carrying most of the received signal power, is transmitted as the output signal from the system  420  via optical path D, and a second portion is sent to the second input/output port  424   b  of the first feedback transmission filter  424  via optical path E. Therefore the optical path for the main component of the output signal on optical path D comprises the optical paths A→B→C→D. The output signal has other components due to the presence of two cavities in the blue shift feedback stabilizing arrangement  422 . A first cavity is between the first and second reflectors  429  and  430  an involves the optical paths of K→J→E→F→G→H. Each signal round trip in this cavity adds two components to the output signal on optical path D, where one component is added by the signal from reflector  429  being tapped in the second power splitter  428  and sent to optical path D, and the second component is added by the signal from reflector  430  being tapped in the first power splitter  427  and sent to optical path C and then to optical path D via the second power splitter  428 . The other cavity comprises the optical paths H→G→C→E→F→G→H. Each signal round trip in this other cavity adds one component to the output signal on optical path D. 
   The feedback signal to the laser source  421  has two main components. The optical path for the first main component involves the optical paths A→B→C→E→F→B→A. The optical path for the second main component involves the optical paths A→B→F→E→C→B→A. These two components are in-phase with equal amplitudes. A signal round trip between the first and second reflectors  429  and  430  involving optical paths K→J→E→F→G→H adds two components to the feedback signal, and a signal round trip in the cavity with the second reflector  430  involving optical paths H→G→C→E→F→G→H adds one component to the feedback signal. 
   Spectral response curves obtained with the system  420 . correspond to the spectral response curves  36  and  37  shown in  FIG. 4 , where curve  36  represents the Forward Filter Spectral response F o (w), and curve  37  represents the Feedback filter spectral response F f (w). The main transmission filter  423  [with the spectral response f 1 (w)] and the first, second, and third feedback transmission filters  424 ,  425 , and  426 , respectively, [with the respective spectral response f 2 (w), f 3 (w), and f 4 (w)] must be designed such that the desired forward and feedback spectral responses F o (w) and F f (w) are achieved by a proper choice of the individual spectral responses f 1 (w), f 2 (w), f 3 (w), and f 4 (w) coupling ratios, and cavity length. As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  428   b  of the second power splitter  428 , maintains the polarization state. Still further, one or more optional delay lines can be added between any two components in the path of the feedback signal. Additionally, the power splitter function for the first and second power splitters  427  and  428  can be achieved in different technology platforms such as planar waveguide technology using directional couplers (DC), multimode interference (MMI) couplers, asymmetric Y junctions, Mach-Zehnder interferometers, etc., and free space optics using thin film, etc. A same spectral response effect can be achieved in the blue shift feedback stabilizing arrangement  422  when one or both of the second and third feedback transmission filters  425  and  426  are replaced with Delay Lines  425  and  426  (not shown). 
   Referring now to  FIG. 43 , there is shown a schematic of a system  440  that implements the system  420  of  FIG. 42  for feedback stabilizing a plurality of n radiation sources [Laser Sources w 1  to w n )]  441   a – 441   n  (of which only radiation sources  441   a  and  441   n  are shown) in accordance with the fifth embodiment of the present invention. The system  440  comprises the plurality of n laser sources  441   a – 441   n , and a blue shift feedback stabilizing arrangement  442  (shown within a dashed line enclosed area). The blue shift feedback stabilizing arrangement  442  comprises a forward multiplexer, f 1   j (w),  443 , a first feedback multiplexer arrangement, f 2 (w),  444  (shown within a dashed line rectangle), a second feedback multiplexer arrangement, f 3 (w) (shown within a dashed line rectangle),  445 , a third feedback multiplexer arrangement, f 4 (w),  446  (shown within a dashed line rectangle), a first broadband power splitter  447 , a second broadband power splitter  448 , a first broadband reflector  449 , and a second broadband reflector  450 . The first feedback multiplexer arrangement, f 2   j (w),  444  comprises cascaded feedback multiplexer  444   g  and feedback multiplexer  444   h , and the second feedback multiplexer arrangement, f 3   j (w),  445  comprises cascaded feedback multiplexer  445   g  and feedback multiplexer  445   h , and the third feedback multiplexer arrangement, f 4   j (w),  446  comprises cascaded feedback multiplexer  446   g  and feedback multiplexer  446   h.    
   Each of the plurality of n laser sources  441   a – 441   n  is coupled from its front facet  441   p  to a corresponding one of a plurality of n first input/output ports  443   a  of the forward multiplexer  443  via an optical path A. A second input/output port  443   b  of the forward multiplexer  443  is coupled to a first input/output port  447   a  of the first broadband power splitter  447  via an optical path B. In the first power splitter  447 , a second input/output port  447   b  thereof is coupled to a first input/output port  448   a  of the second broadband power splitter  448  via an optical path C, a third input/output port  447   c  is coupled to a first input/output port  444   a  of the first feedback multiplexer, f 2 (w),  444  via an optical path F, and a fourth input/output port  447   d  is coupled to a first input/output port  446   a  of the third feedback multiplexer, f 3 (w),  446  via an optical path G. In the second broadband power splitter  448 , a second output port  448   b  thereof provides an output signal from the system  440  to any predetermined downstream device (not shown) via an optical path D, a third input/output port  448   c  thereof is coupled to a second input/output port  444   b  of the first feedback multiplexer, f 2 (w),  444  via an optical path E, and a fourth input/output port  448 d thereof is coupled to a first input/output port  445   a  of the second feedback multiplexer, f 4 (w),  445  via an optical path J. A second input/output port  446   b  of the third feedback multiplexer  446  is coupled to an input/output port  450   a  of the second reflector  450  via an optical path H. A second input/output port  445   b  of the second feedback multiplexer  445  is coupled to an input/output port  449   a  of the first reflector  449  via an optical path K. 
   The operation of the system  440  is essentially the same as that described for the system  420  of  FIG. 42  for the single laser source  421 . The main difference between the systems  440  and  420  is that, in the system  440 , the output signals from the plurality of n laser sources  441   a – 441   n  are multiplexed into a single multiplexed output signal by the forward multiplexer  443 , and each of the first, second, and third feedback multiplexer arrangements  444 ,  445 , and  446  first demultiplex a single input multiplexed signal received at a first side and then multiplex the demultiplexed signals to provide a single multiplexed output signal at the other side. The feedback stabilizing arrangement  442  also contains the first and second cavities as were described for the feedback stabilizing arrangement  422  of  FIG. 42 . The first cavity is the first and second reflectors  449  and  450  an involves the optical paths of K→J→E→F→G→H, and the other cavity comprises the optical paths H→C→E→F→G→H which add components to the output and feedback signals as was described for the cavities of  FIG. 42 . 
   The spectral responses obtained by the blue shift feedback stabilizing arrangement  442  is essentially the same as that shown in  FIG. 6 , where curves  46   a – 46   n  represent the forward filter spectral response F o (w), for each of the wavelengths generated by the corresponding one of the plurality of n laser sources  441   a – 441   n , and curves  47   a – 47   n  represent the feedback filter spectral response F f (w) for each of the wavelengths fed back to the corresponding one of the plurality of n laser sources  441   a – 441   n . The forward multiplexer  443  [with the spectral response f 1   j (w)] and the first, second, and third feedback transmission filters  444 ,  445 , and  446 , respectively, [with the respective spectral response f 2   j (w), f 3   j (w), and f 4   j (w)] must be designed such that the desired forward and feedback spectral responses F o (w) and F f (w) are achieved by a proper choice of the individual spectral responses f 1   j (w), f 2   j (w), f 3   j (w), and f 4   j (w) coupling ratios, and cavity length. As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  448   b  of the second power splitter  448 , maintains the polarization state. Still further, one or more optional delay lines can be added between any two components in the path of the feedback signal. Additionally, the power splitter function for the first and second power splitters  447  and  448  can be achieved in different technology platforms such as planar waveguide technology using directional couplers (DC), multimode interference (MMI) couplers, asymmetric Y junctions, Mach-Zehnder interferometers, etc., and free space optics using thin film, etc. A same spectral response effect can be achieved in the blue shift feedback stabilizing arrangement  422  when one or both of the second and third feedback transmission filters  445  and  446  are replaced with Delay Lines as is shown and described hereinafter in  FIG. 44 . 
   Referring now to  FIG. 44 , there is shown a system  460  similar to the system  440  of  FIG. 43  for blue shift feedback stabilizing a plurality of n radiation sources [Laser Sources (w 1  to w n )]  461   a – 461   n  (of which only radiation sources  461   a  and  461   n  are shown) in accordance with the fifth embodiment of the present invention. The system  460  comprises the plurality of n laser sources  461   a – 461   n , and a blue shift feedback stabilizing arrangement  462  (shown within a dashed line enclosed area). The blue shift feedback stabilizing arrangement  462  comprises a forward multiplexer, f 1   j (w),  463 , a first feedback multiplexer arrangement, f 2 (w),  464  (shown within a dashed line rectangle), a first optional delay line  465 , a second optional delay line  466 , a first broadband power splitter  467 , a second broadband power splitter  468  , a first broadband reflector  469 , and a second broadband reflector  470 . The first feedback multiplexer arrangement, f 2   j (w),  464  comprises cascaded feedback multiplexer  464   g  and feedback multiplexer  464   h . The interconnection of the devices of the system  460  is the same as that of the system  440  of  FIG. 43  except that the first and second delay lines  465  and  466  replace the second and third feedback multiplexers  425  and  426  of the system  440   FIG. 43 . The operation and spectral responses of the system  460  correspond to the operation and spectral responses obtained by the system  440  of  FIG. 43 . 
   Referring now to  FIG. 45 , there is shown a schematic of a system  480  providing a same functioning as found in the system  330  of  FIG. 33  for blue shift feedback stabilizing a plurality of n radiation pump sources (Laser)  481   a – 481   n  (of which only lasers  481   a  and  481   n  are shown) in accordance with the fifth embodiment of the present invention. The system  480  comprises the plurality of n laser radiation sources (lasers)  481   a – 481   n , a plurality of n optional polarization rotators (PR)  483   a – 483   n  (of which only PR  483   a  and  483   n  are shown), and a blue shift feedback stabilizing arrangement  482  (shown within a dashed line enclosed area). The blue shift feedback stabilizing arrangement  482  comprises an Arrayed Waveguide Grating (AWG) multiplexer  484 , a broadband power splitter  485 , an optional delay line  486 , a first reflector  487 , and a plurality of n second reflectors  488   a – 488   n  (of which only reflectors  488   a  and  488   n  are shown). The AWG multiplexer  484  comprises a first Free Propagating Region (FPR)  484   e , a second FPR  484   f , and a plurality of optical paths  484   g  interconnecting the first and second FPRs  484   e  and  484   f  as is well known in the art. Each of the plurality of laser sources  481   a – 481   n  is coupled at a front facet  481   p  thereof to an input/output port  483   p  of a corresponding one of the plurality of n optional polarization rotators (PR)  483   a – 483   n  via an optical path A. An input/output port  483   q  each of the optional PRs  483   a – 483   n  is coupled to a corresponding one of a plurality of n input/output ports  484   a  of the AWG multiplexer  484  via an optical path B. A second input/output port  484   b  of the AWG multiplexer  484  is coupled to a first input/output port  485   a  of the broadband power splitter  485  via an optical path C. In the power splitter  485 , a second output port  485   b  thereof provides an output signal from the system  480  to any predetermined downstream device (not shown) via an optical path D, a third input/output port  485   c  thereof is coupled to a third input/output port  484   c  of the AWG multiplexer  484  via an optical path E, and a fourth input/output port  485   d  thereof is coupled to a first input/output port  486   a  of the optional delay line  486  via an optical path G. A second input/output port  486   b  of the delay line  486  is coupled to an input/output port  487   a  of the first reflector  487  via an optical path H. Each of a plurality of n fourth input/output ports  484   d  of the AWG multiplexer  484  is coupled to an input/output port  488   p  of a corresponding one of the plurality of n second reflectors  488   a – 488   n . The AWG multiplexer  484  can be replaced by an Eschelle grating that provides essentially the same function as the AWG multiplexer  484 . 
   In operation, the optical signal from each of the lasers  481 – 481   n  is transmitted via optical path A to the corresponding one of the plurality of n optional polarization rotators (PRs)  483   a – 483   n . The optional PRs  483   a – 483   n  are included to rotate a laser output state of polarization (TE or TM or vice versa). Depending on the application of the system  480  and the number of PRs  483   a – 483   n  used, the input signals to the AWG multiplexer  484  may have the same polarization state (all TE or all TM) or different states of polarizations. For some applications such as Raman amplification, the polarization states of the adjacent ports (in the wavelength domain) must be orthogonal (TE and TM polarizations) to reduce a degree of polarization (DoP) and, therefore, reduce or eliminate the Raman amplification polarization dependent gain (PDG). Where there are even numbers of lasers  481   a – 481   n  in such application, they are grouped in pairs. The system  480  can be designed such that the resulting stabilized wavelengths of each pair of lasers of the lasers  481   a – 481   n  with orthogonal polarizations are exactly the same, or there is a slight shift between the two wavelengths. 
   In the AWG multiplexer  484  each of the received signals at the first input/output ports  484   a  via optical path B is filtered and multiplexed with other input signals from the other lasers  481   a – 481   n , and is routed to the second input/output port  484   b  thereof and sent to the first input/output port  485   a  of the broadband power splitter  485  via optical path C. The filter spectral response between ports  484   a  and  484   b  in the AWG multiplexer  484  is f 1   j (w) for a jth port which effectively represents any one of the plurality of n input/output ports  484   a . In the power splitter  485 , the multiplexed signal received at input/output port  485   a  is tapped and a major portion of the tapped signal is routed to the second output port  485   b  as the main output signal from the system  480  and the other portion is transmitted via the third input/output port  468   c  and optical path E to the third input/output port  484   c  of the AWG multiplexer  484  to be filtered and demultiplexed into their plurality of n wavelength signals and routed to the corresponding one the plurality of n input/output ports  484   d . In the AWG multiplexer  484  the spectral response between the third input/output port  485   c  and the fourth input/output ports  484   d , in either direction, is f 2   j (w). Each of the demultiplexed signals is sent to the corresponding one of the plurality of n second reflectors  488   a – 488   n  and returned via the corresponding fourth and third input/output ports  484   d  and  484   c  in the AWG multiplexer  484  where the signals are filtered and multiplexed and then transmitted to the input/output ports  485   c  of the power splitter  485 . In the power splitter  485  the reflected signal is tapped and a first portion is routed to the first input/output port  485   a . A second portion of the reflected signal is routed to the fourth input/output port  485   d  and through the optional delay line  486  to the first reflector  487  via optical paths G and H. The reflected signal from the first reflector  487  is returned to the fourth input/output port  485   d  of the power splitter  485  and tapped where first and second portions thereof are routed to the second and third ports  485   b  and  485   c . The first portion of the tapped signal from the third input/output port  485   c  is transmitted back through the AWG multiplexer  484  and the lasers  481   a – 481   n  via optical paths C→B→A and second portion is routed to the first reflector  487  via optical paths G→H. 
   The main output signal from the second output port  485   b  of the power splitter  485  has one main component obtained from the propagation of output signals from the lasers  481   a – 481   n  via optical paths A→B→C→D includes the spectral response of f 1   j (w) caused by the AWG multiplexer  484 . The output signal has other components due to the presence of a cavity between the first reflector  487  and the plurality of second reflectors  488   a – 488   n  including the optical paths F→E→G→H. Each signal round trip in the cavity adds one component to the output signal at output port  485   b  of the power splitter  485 . The feedback signal has one main component involving the optical paths of A→B→C→E→F→E→C→B→A. Each round trip in the cavity adds one component to the feedback signal. 
   The spectral responses obtained by the blue shift feedback stabilizing arrangement  482  is essentially the same as that shown in  FIG. 6 , where curves  46   a – 46   n  represent the forward filter spectral response F o (w), for each of the wavelengths generated by the corresponding one of the plurality of n laser sources  441   a – 441   n , and curves  47   a – 47   n  represent the feedback filter spectral response F f (w) for each of the wavelengths fed back to the corresponding one of the plurality of n laser sources  481   a – 481   n . The AWG multiplexer  484 , f 1   j (w) and f 2   j (w), is designed such that the center wavelength of a Feedback filter spectral response for a jth port, F f   j (w), (not shown in  FIG. 6 ) is shifted by δw toward the shorter wavelength with regard to the center wavelength of the Forward filter spectral response for the jth port, F o   j (w). The wavelength shift [(δw) or blue shift] and their respective bandwidth can be controlled through the design of the AWG multiplexer  484 . As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  485   b  of the broadband power splitter  485 , maintains the polarization state. Still further, one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 46 , there is shown a schematic of a system  490  as an alternative arrangement to the system  480  of  FIG. 45  for blue shift feedback stabilizing a plurality of n radiation sources (laser)  491   a – 491   n  in accordance with a fifth embodiment of the present invention. The system  490  comprises the plurality of n lasers  491   a – 491   n  of which only  491   a  and  491   n  are shown, a plurality of n optional polarization rotators (PR)  493   a – 493   n , and a blue shift feedback stabilizing arrangement  492 . The blue shift feedback stabilizing arrangement  492  comprises a first Arrayed Waveguide Grating (AWG) multiplexer  494 , a broadband power splitter  495 , a second AWG multiplexer  496 , a first broadband reflector  497 , an optional delay line  498 , and a second reflector  499 . The first AWG multiplexer  494  comprises a first Free Propagating Region (FPR)  494   e , a second FPR  494   f , and a plurality of optical paths  494   g  interconnecting the first and second FPRs  494   e  and  494   f  as is well known in the art. Similarly, the second AWG multiplexer  496  comprises a first Free Propagating Region (FPR)  496   e , a second FPR  496   f , and a plurality of optical paths  496   g  interconnecting the first and second FPRs  496   e  and  496   f . Each of the plurality of laser sources  491   a – 491   n  is coupled at a front facet  491   p  thereof to an input/output port  493   p  of a corresponding one of the plurality of n optional polarization rotators (PR)  493   a – 493   n  via an optical path A. An input/output port  493   q  each of the optional PRs  493   a – 493   n  is coupled to a corresponding one of a plurality of n input/output ports  494   a  of the AWG multiplexer  494  via an optical path B. A second input/output port  494   b  of the AWG multiplexer  494  is coupled to a first input/output port  495   a  of the broadband power splitter  495  via an optical path C. 
   In the power splitter  495 , a second output port  495   b  thereof provides an output signal from the system  490  to any predetermined downstream device (not shown) via an optical path D, a third input/output port  495   c  thereof is coupled to a third input/output port  494   c  of the AWG multiplexer  494  via an optical path E, and a fourth input/output port  495   d  thereof is coupled to a first input/output port  498   a  of the optional delay line  498  via an optical path H. A second input/output port  498   b  of the delay line  498  is coupled to an input/output port  499   a  of the second reflector  499  via an optical path J. Each of a plurality of n fourth input/output ports  494   d  of the AWG multiplexer  494  is coupled to a corresponding one of a plurality of n input/output port  496   a  of the second AWG multiplexer  496 . A second input/output port  496   b  of the second AWG multiplexer  496  is coupled to an input/output port  497   a  of the first broadband reflector  497 . The AWG multiplexer  484  can be replaced by an Eschelle grating that provides essentially the same function as the AWG multiplexer  484 . The only difference between the feedback stabilizing arrangement  480  of  FIG. 45  and the feedback stabilizing arrangement  490  of  FIG. 46  is that the plurality of n reflectors  488   a – 488   n  of  FIG. 45  have been replaced by the second AWG multiplexer  496  and a single broadband reflector  497  of  FIG. 46 . The operation and spectral responses obtained with the feedback stabilizing arrangement  490  is essentially the same as that provided by the feedback stabilizing arrangement  480  of  FIG. 45  and will not be repeated here. As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  495   b  of the broadband power splitter  495 , maintains the polarization state. Still further, one or more optional delay lines can be added between any two components in the path of the feedback signal. 
   Referring not to  FIG. 47 , there is shown a schematic of a system  500  for feedback stabilizing a plurality of n radiation sources (laser)  501   a – 501   n  (of which only lasers  501   a  and  501   n  are shown) in accordance with the fifth embodiment of the present invention. The system  500  comprises the plurality of n lasers  501   a – 501   n , a plurality of n polarization rotators (PR)  503   a – 503   n  (of which only PRs  503   a  and  503   n  are shown), and a blue shift feedback stabilizing arrangement  502  (shown within a dashed line enclosed area. The blue shift feedback stabilizing arrangement  502  comprises a plurality of n first power splitters  504   a – 504   n  (of which only power splitters  504   a  and  504   n  are shown), a first Arrayed Waveguide Grating (AWG) multiplexer  505 , a second AWG multiplexer  506 , a second broadband power splitter  507 , and an optional delay line  508 . The first AWG multiplexer  505  comprises a first Free Propagating Region (FPR)  505   e , a second FPR  505   f , and a plurality of optical paths  505   g  interconnecting the first and second FPRs  505   e  and  505   f  as is well known in the art. Similarly, the second AWG multiplexer  506  comprises a first Free Propagating Region (FPR)  506   e , a second FPR  506   f , and a plurality of optical paths  506   g  interconnecting the first and second FPRs  506   e  and  506   f . Each of the plurality of laser sources  501   a – 501   n  is coupled at a front facet  501   p  thereof to a first input/output port  503   p  of a corresponding one of the plurality of n optional polarization rotators (PR)  503   a – 503   n  via an optical path A. A second input/output port  503   q  of each of the optional PRs  503   a – 503   n  is coupled to a first input/output port  504   p  of a corresponding one of the plurality of n first power splitters  504   a – 504   n  via an optical path B. In each of the plurality of n first power splitters  504   a – 504   n , a second input/output port  504   q  is coupled to a corresponding one of a plurality of n first input/output ports  505   a  of the first AWG multiplexer  505  via an optical path C, a third input/output port  504   r  is coupled to a corresponding one of a plurality of n fourth input/output ports  505   d  AWG multiplexer  505  via an optical path G, and a fourth input/output port  504   s  is coupled to a corresponding one of a plurality of n first input/output ports  506   a  of the second AWG multiplexer  506  via an optical path H. A second input/output port  505   b  of the first AWG multiplexer  505  is coupled to a first input/output port  507   a  of the second power splitter  507  via an optical path D. In the second power splitter  507 , a second output port  507   b  provides an output signal from the system  500  to any predetermined downstream device (not shown) via an optical path E, a third input/output port  507   c  thereof is coupled to a third input/output port  505   c  of the first AWG multiplexer  505  via an optical path F, and a fourth input/output port  507   d  thereof is coupled to a second input/output port  508   b  of the optional delay line  508  via an optical path K. A first input/output port  508   a  of the delay line  508  is coupled to a second input/output port  506   b  of the second AWG multiplexer  506  via an optical path J. The first and second AWG multiplexers  505  and  506  can be replaced by an Eschelle grating that provides essentially the same function as the AWG multiplexers  505  and  506 . 
   In operation, the output signals from the lasers  501   a – 501   n  are optionally polarization rotated by the PRs  503   a – 503   n  and transmitted to the plurality of n first power splitters  504   a – 504   n . In the first power splitters  504   a – 504   n , the received signal from the corresponding one of the PRs  503   a – 503   n  is tapped and a first major portion is transmitted via second input/output port  504   q  to the corresponding one of the first input/output ports  505   a  of the first AWG multiplexer  505  for transmission to the first input/output port  507   a  of the second power splitter  507  via optical paths C and D. The spectral response in the AWG multiplexer  505  between the input/output ports  505   a  and  505   b  is f 1   j (w). A second portion of the tapped signal is transmitted via a third input/output port  504   r  to the corresponding one of the fourth input/output ports  505   d  for transmission to the third input/output port  507   c  of the second power splitter  507  via optical paths G and F. In the second power splitter  507 , the first portion received at input/output port  507   a  is tapped and a first major portion thereof is routed to the second output port  507   b  as the main output signal from the system  500  via optical path E, and the other portion thereof is transmitted via the third input/output port  507   c  to the third input/output port  505   c  of the first AWG multiplexer  505  to be filtered and demultiplexed into the individual plurality of n wavelength signals and routed to the corresponding one the plurality of n first power splitters  504   a – 504   n  via optical paths F and G. The spectral response in the first AWG multiplexer  505  between the input/output ports  505   c  and  505   d  is f 2   j (w). 
   In the second power splitter  507 , the second portion received at the third input/output port  507   c  is tapped and a first portion thereof is routed through the first AWG multiplexer  505  via optical path D, where it is filtered and demultiplexed, and each demultiplexed signal is routed to the corresponding one of the first power splitters  504   a – 504   n  via optical path C. The other portion is routed through the optional delay line  508  and to the second port  506   b  of the second AWG multiplexer  506  via optical paths K and J where the signal is demultiplexed and each of the demultiplexed signals is routed via optical path H to the corresponding one of the first power splitters  504   a – 504   n  where they are tapped and both portions are sent back through the first AWG multiplexer  504 . The spectral response in the second AWG multiplexer  506  between the input/output ports  506   b  and  506   a  is f 3   j (w). 
   The feedback stabilizing arrangement  502  includes a twisted loop reflector arrangement comprising the optical paths C→F→K→J→H→C. The feedback signal at the front facet  501   p  of each of the lasers  501   a – 501   n  comprises two main in-phase components with equal amplitudes. One component is obtained via the optical paths A→B→C→D→F→D→F→G→B→A, and the other component is obtained via the optical paths A→B→G→F→D→C→B→A. Each of the tapped signals in the plurality of n first power splitters  504   a – 504   n  is multiplexed and demultiplexed by the first and second AWG multiplexers  505  and  506 . Each signal round trip in the twisted loop reflector arrangement contributes an additional component to the feedback signal to the lasers  501   a – 501   n  as well as the output signal on optical path E. The purpose of selectively adding multiple components into a feedback signal is to provide the conditions that cause each of the plurality of lasers  501   a – 501   n  to enter into coherence collapse mode of operation and the laser output signal to become very stable. The spectral responses obtained by the blue shift feedback stabilizing arrangement  502  is essentially the same as that shown in  FIG. 6 , where curves  46   a – 46   n  represent the forward filter spectral response F o (w), for each of the wavelengths generated by the corresponding one of the plurality of n laser sources  501   a – 501   n , and curves  47   a – 47   n  represent the feedback filter spectral response F f (w) for each of the wavelengths fed back to the corresponding one of the plurality of n laser sources  501   a – 501   n . As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  507   b  of the broadband power splitter  507 , maintains the polarization state. Still further, one or more optional delay lines (not shown) can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 48 , there is shown a schematic of a system  510  for feedback stabilizing a plurality of n radiation sources (laser)  511   a – 511   n  (of which only lasers  511   a  and  511   n  are shown) in accordance with the fifth embodiment of the present invention. The system  510  comprises the plurality of n lasers  511   a – 511   n , a plurality of n polarization rotators (PR)  513   a – 513   n  (of which only PRs  513   a  and  513   n  are shown), and a blue shift feedback stabilizing arrangement  512  (shown within a dashed line enclosed area). The blue shift feedback stabilizing arrangement  512  comprises a first Arrayed Waveguide Grating (AWG) multiplexer  514 , a second AWG multiplexer  515 , a first broadband power splitter  516 , a second broadband power splitter  517 , and an optional delay line  518 . The first AWG multiplexer  514  comprises a first Free Propagating Region (FPR)  514   e , a second FPR  514   f , and a plurality of optical paths  514   g  interconnecting the first and second FPRs  514   e  and  514   f  as is well known in the art. Similarly, the second AWG multiplexer  515  comprises a first Free Propagating Region (FPR)  515   e , a second FPR  515   f , and a plurality of optical paths  515   g  interconnecting the first and second FPRs  515   e  and  515   f . Each of the plurality of laser sources  511   a – 511   n  is coupled at a front facet  511   p  thereof to an input/output port  513   p  of a corresponding one of the plurality of n optional polarization rotators (PR)  513   a – 513   n  via an optical path A. An input/output port  513   q  each of the optional PRs  513   a – 513   n  is coupled to a corresponding one of a plurality of n input/output ports  515   a  of the first AWG multiplexer  515  via an optical path B. A second input/output port  514   b  of the first AWG multiplexer  515  is coupled to a first input/output port  516   a  of the first power splitter  516  via an optical path C. 
   In the first power splitter  516 , a second input/output port  516   b  is coupled to a first input/output port  517   a  of the second power splitter  517 , a third input/output port  516   c  is coupled to a third input/output port  514   c  of the first AWG multiplexer  514  via an optical path F, and a fourth input/output port  516   d  thereof is coupled to a first input/output port  518   a  of the optional delay line  518 . In the second power splitter  517 , a second output port  517   b  provides an output signal from the system  510  to any predetermined downstream device (not shown) via an optical path E, a third input/output port  517   c  thereof is coupled to a second input/output port  515   b  of the second AWG multiplexer  515  via an optical path H, and a fourth input/output port  517   d  thereof is coupled to a second input/output port  518   b  of the optional delay line  518  via an optical path J. Each of a plurality of n first input/output ports  515   a  of the second AWG multiplexer  515  is coupled to a corresponding one of a plurality of n input/output ports  514   d  of the first AWG multiplexer  514 . Each of the AWG multiplexers  514  and  515  can be replaced by an Eschelle grating that provides essentially the same function as the AWG multiplexer  514  and  515 . 
   In operation, optical signals from the lasers  511   a – 511   n  go through the optional polarization rotators (PR)  513   a – 513   n  to rotate the signal state of polarization as required. Each of the signals from the PRs  513   a – 513   n  is filtered and multiplexed with the signals from the other laser  511   a – 511   n  in the first AWG multiplexer  514 . The multiplexed signal from the second input/output port  514   b  of the first AWG multiplexer  514  propagates through the first and second power splitters  516  and  517  to tap a portion of the multiplexed signal for feedback purposes, and a major portion of the signal is routed as the main output signal from the system  510  on optical path D. A twisted loop arrangement is implemented in the feedback stabilizing arrangement  512  after the output signals from the lasers  511   a – 511   n  have been multiplexed in the first multiplexer  514  using the optical paths F→G→H→J→K→F. A feedback signal at the front facet  511   p  of each one of the laser  511   a – 511   n  comprises two main in-phase components with equal amplitudes. One component is obtained via the optical paths A→B→C→F→G→H→D→C→B→A, and the other component is obtained via the optical paths A→B→C→D→H→G→F→C→B→A. Each signal round trip in the twisted loop arrangement contributes an additional component to the feedback signal as well as the main output signal on optical path D. 
   The filter spectral response between the input/output ports  514   a  and  514   b  of the first AWG multiplexer  514  is f 1   j (w) for a jth port, while the filter spectral response between the input/output ports  514   c  of the first AWG multiplexer  514  and the second input/output port  515   b  of the second AWG multiplexer is f 2 (w). The spectral responses obtained by the blue shift feedback stabilizing arrangement  512  is essentially the same as that shown in  FIG. 6 , where curves  46   a – 46   n  represent the forward filter spectral response F o (w), for each of the wavelengths generated by the corresponding one of the plurality of n laser sources  511   a – 511   n , and curves  47   a – 47   n  represent the feedback filter spectral response F f (w) for each of the wavelengths fed back to the corresponding one of the plurality of n laser sources  511   a – 511   n . The first and second AWG multiplexers  514  and  515  are each designed such that the center wavelength of the feedback spectral response for the jth port F f   j (w) is slightly shifted by an amount δw j  toward a shorted wavelength with respect to a center wavelength of the Forward filter spectral response F o   j (w) for the jth port. As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  517   b  of the broadband power splitter  517 , maintains the polarization state. Still further, one or more optional delay lines (not shown) can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 49 , there is shown a schematic of a system  520  for blue shift feedback stabilizing a plurality of n radiation sources (LASER)  521   a – 521   n  (of which only lasers  521   a  and  521   n  are shown) in accordance with the fifth embodiment of the present invention. The system  520  comprises the plurality of n lasers  521   a – 521   n , a plurality of n optional polarization rotators (PR)  523   a – 523   n , and a blue shift feedback stabilizing arrangement  522  (shown within a dashed line enclosed area). The blue shift feedback stabilizing arrangement  522  comprises a first Arrayed Waveguide Grating (AWG) multiplexer  524 , a second AWG multiplexer  525 , a first broadband power splitter  526 , a second broadband power splitter  527 , a first optional delay line  528 , a second optional delay line  529 , a first optional broadband reflector  530 , and a second optional broadband reflector  531 . The first AWG multiplexer, f 1   j (w),  524  comprises a first Free Propagating Region (FPR)  524   e , a second FPR  524   f , and a plurality of optical paths  524   g  interconnecting the first and second FPRs  524   e  and  524   f  as is well known in the art. Similarly, the second AWG multiplexer  525  comprises a first Free Propagating Region (FPR)  525   e , a second FPR  525   f , and a plurality of optical paths  525   g  interconnecting the first and second FPRs  525   e  and  525   f . The devices of the feedback stabilizing arrangements  512  of  FIG. 48  and the present  522  are essentially connected in a same manner except that the direct interconnection via the optional delay line  518  between the fourth output ports  516   d  and  517   d  of the first and second power splitters  516  and  517  of the feedback stabilizing arrangement  512  is replaced in the feedback stabilizing arrangement  522  by separate optical paths L and M including the delay line  528  and reflectors  530 , and J and K including the delay line  529  and reflectors  531 . 
   In operation, the output wavelength signal (w) from each of the lasers  521   a – 521   n  is transmitted through a corresponding one of the plurality of n optional PRs  523   a – 523   n  to rotate the signal state of polarization. This signal is then filtered and multiplexed with the other lasers  521   a – 521   n  in the AWG multiplexer  524  and transmitted through a first and second broadband power splitter  526  and  527  to tap a first portion of the multiplexed signal for feedback purposes, and route a major portion of the multiplexed signal to the output port  527   b  of the second power splitter  527  as the main output signal from the system  520 . The feedback stabilizing arrangement  522  contains a cavity between the first and second reflectors  530  and  531  via optical paths M→L→F→G→H→J→K. The feedback signal received at the front facet  521   p  of each of the lasers  521   a – 521   n  comprises two main in-phase components with equal amplitudes. One component is obtained via optical paths A→B→C→F→G→H→D→C→B→A while the other component is obtained via the optical paths A→B→C→D→H→G→F→C→B→A. The tapped signals in the cavity is multiplexed and demultiplexed by the AWG multiplexers  524  and  525 . Each signal round trip in the cavity contributes two additional components to feedback signal as well as the main output signal on optical path E. 
   The spectral response for a jth wavelength between the input/output ports  524   c  of the first AWG multiplexer  524  and the input/output port  527   b  of the second AWG multiplexer  525  is f 2   j (w). The spectral responses obtained by the blue shift feedback stabilizing arrangement  522  is essentially the same as that shown in  FIG. 6 , where curves  46   a – 46   n  represent the forward filter spectral response F o (w), for each of the wavelengths generated by the corresponding one of the plurality of n laser sources  521   a – 521   n , and curves  47   a – 47   n  represent the feedback filter spectral response F f (w) for each of the wavelengths fed back to the corresponding one of the plurality of n laser sources  521   a – 521   n . The AWG multiplexers  524  and  525  are designed such that a center wavelength of the Feedback filter spectral response for the jth port, F f   j (w), is slightly shifted by an amount δw j  toward a shorter wavelength with respect to the center wavelength of the Forward filter spectral response of port j of F o   j (w). 
   As indicated for prior systems (e.g.,  90 , and  110 ), all components and interconnects, except the output port  527   b  of the broadband power splitter  527 , maintains the polarization state. Still further, one or more optional delay lines (not shown) can be added between any two components in the path of the feedback signal. 
   Referring now to  FIG. 50 , there is shown a schematic of a system  540  that is similar to the system  70  of  FIG. 8  for blue shift stabilizing a plurality of n radiation sources [Laser Sources (w 1  to w n )]  541   a – 541   n  (of which only laser sources  541   a  and  541   n  are shown) in accordance with the fifth embodiment of the present invention. The system  540  comprises the plurality of n laser sources  541   a – 541   n  and a blue shift feedback stabilizing arrangement  542  (shown within a dashed line enclosed area). The blue shift feedback stabilizing arrangement  542  comprises a forward multiplexer  543 , a feedback multiplexer, f 3   j (w),  544 , a first broadband power splitter  545 , a first optional delay line  548 , a plurality n optional reflectors  549   a – 549   n  (of which only reflectors  549   a  and  549   n  are shown), and a loop arrangement  550   a  (shown within a dashed line area) comprising a broadband power splitter  546  and a second optional delay line  547 . Each of the plurality of laser sources  541   a – 541   n  is coupled at a front facet  541   p  thereof to a corresponding one of a plurality of n first input/output port  543   a  of the forward multiplexer  543  via an optical path A. A second input/output port  543   b  of the forward multiplexer  543  is coupled to a first input/output port  545   a  of the first broadband power splitter  545  via an optical path B. In the first power splitter  545 , a second output port  545   b  thereof provides an output signal from the system  540  to any predetermined downstream device (not shown) via an optical path C, a third input/output port  545   c  thereof is coupled to a second input/output port  546   b  of the second broadband power splitter  546  of the loop arrangement  550   a  via an optical path D, and a fourth input/output port  545   d  thereof is coupled to a first input/output port  548   a  of the second optional delay line  548  via an optical path F. In the loop arrangement  550   a , a first input/output port  546   a  of the second broadband power splitter  546  is coupled to a third input/output port  543   c  of the forward multiplexer  543  via an optical path E, and third and fourth input/output ports  546   c  and  546   d  are coupled to a second and first input/output port  547   b  and  547   a , respectively, of the delay line  547  via a respective optical path K and J. A second input/output port  548   b  of the second delay line  548  is coupled to a first input/output port  544   a  of the second feedback multiplexer  544  via an optical path G; and each of a plurality of n input/output ports  544   b  of the second feedback multiplexer, f 3   j (w),  544  are connected to an input/output port  549   p  of a corresponding one of the plurality of n reflectors  549   a – 549   n.    
   In operation, the output wavelength signals from the lasers sources  541   a – 541   n  are multiplexed in the forward multiplexer  543 , and the multiplexed signal is transmitted via optical path B to the first broadband power splitter  545  where it is tapped and a main portion thereof is transmitted as the output signal from the system  540  via optical path C. The other portion is used as a feedback signal to the laser sources  541   a – 541   n  and initially routed to the loop arrangement  550   a  comprising the second broadband power splitter  546  and first delay line  547 . Therefore, the optical path for the main output signal is A→B→C. The feedback signal has three main components. A first main component of the feedback signal involves the optical paths A→B→D→E→A. A second main component of the feedback signal comprises the optical paths of A→E→D→B→A, and a third main component involves the optical paths of A→E→D→F→G→H→G→F→D→E→A which includes the feedback multiplexer, f 3   j (w),  544 . When the signal passes through optical path of the feedback&#39;s third main component A→E→D→F→G→H→G→F→D→E→A, it also adds a component to the main output signal at the first power splitter  545 . Each signal round trip in the loop arrangement  550   a , or cavity arrangement  550   b , contributes additional components to the feedback signal to lasers  541   a  to  541   n . The forward multiplexer  543  is designed such that it provides two multiplexed output signals at the second and third output ports  543   b  and  543   c , where the second input/output port  543   b  is the main multiplexed output port, f 1   j (w), and the third output port  543   c  is a secondary multiplexer output port, f 2   j (w). In the forward multiplexer  543 , f 1   j (w) is the spectral response between the jth input/output port  543   a  (not shown) and the second input/output port  543   b , and f 2   j (w) is the spectral response between the jth input port  543   a  and the third input/output port  543   c . The center wavelength of f 2   j (w) is slightly shifted toward shorter wavelength relative to the center wavelength of f 1   j (w). 
   An alternative arrangement for the loop arrangement  550   a  is shown as the cavity arrangement  550   b  (shown within a dashed line area). The cavity arrangement  550   b  comprises the broadband power splitter  546  found in the loop arrangement  550   a , a first optional delay line  551  and a first broadband reflector  552  coupled in series to the fourth input/output port  546   d  of a broadband power splitter  546  via optical paths J and L, and a second optional delay line  552  and a second broadband reflector  553  coupled in series to the third input/output port  546   c  of the broadband power splitter  546  via optical paths K and M. 
   The operation for multiplexed signals received at the second input/output port  546   b  of the power splitter  546  is to provide multiple feedback signal components back to the laser sources  541   a – 541   n . The same operation occurs for any multiplexed signal received at the first input/output port  546   a  of the second power splitter  546  from the third input/output port  543   c  of the forward multiplexer  543  via optical path E. The main difference between, for example, of the systems  110 ,  130 ,  140 ,  280 , and  380  of  FIGS. 11 ,  13 ,  14 ,  28 , and  38 , respectively, is the presence of an additional loop arrangement  550   a  or  550   b  in the feedback signal path. The main concept is to tap a portion of the signal traveling through the feedback signal paths of D and E to generate additional components for the feedback signal. The purpose of selectively adding multiple components into a feedback signal using the loop arrangement  550   a  or  550   b  is to provide the conditions that cause each of the plurality of lasers  541   a – 541   n  to enter into a coherence collapse mode of operation and the laser output signal to become very stable. 
   Referring now to  FIG. 51 , there is shown a schematic of a system  580  for feedback stabilizing a plurality of n radiation sources (Laser)  581   a – 581   n  (of which only lasers  581   a  and  581   n  are shown) in accordance with the fifth embodiment of the present invention. The system  590  comprises the plurality of n lasers  581   a – 581   n , a plurality of n optional Polarization Rotators (PR)  583   a – 583   n  (of which only PR  583   a  and  583   n  are shown), and a blue shift feedback stabilizing arrangement  582  (shown within a dashed line enclosed area). The blue shift feedback stabilizing arrangement  582  comprises a plurality of n first power splitters  583   a – 583   n  (of which only power splitters  584   a  and  584   n  are shown), an Arrayed Waveguide Grating (AWG) multiplexer  585 , a first broadband power splitter  586 , and a loop arrangement  587   a  comprising a broadband power splitter  588  and a second optional delay line  589 . The AWG multiplexer  585  comprises a first Free Propagating Region (FPR)  585   e , a second FPR  585   f , and a plurality of optical paths  585   g  interconnecting the first and second FPRs  585   e  and  585   f  as is well known in the art. Each of the plurality of laser sources  581   a – 581   n  is coupled at a front facet  581   p  thereof to an input/output port  583   p  of a corresponding one of the plurality of n optional polarization rotators (PR)  583   a – 583   n  via an optical path A. A second input/output port  583   q  of each the optional PRs  583   a – 583   n  is coupled to a first input/output ports  584   p  of a corresponding one of the plurality of n first power splitters  584   a – 584   n  via an optical path B. In each of the plurality of n first power splitters  584   a – 584   n , a second input/output port  584   q  thereof is coupled to a corresponding one of a plurality of n first input/output ports  585   a  of the AWG multiplexer  585  via an optical path C, and a third input/output port  584   r  is coupled to a corresponding one of a plurality of n input/output ports  585   d  of the AWG multiplexer  585  via an optical path H. A second input/output port  585   b  of the AWG multiplexer  585  is coupled to a first input/output port  586   a  of the broadband power splitter  586  via an optical path D. In the broadband power splitter  586 , a second output port  586   b  thereof provides an output signal from the system  580  to any predetermined downstream device (not shown) via an optical path E, and a third input/output port  587   c  thereof is coupled to a first input/output port  588   a  of the broadband power splitter  588  in the loop arrangement  587   a  via an optical path F. A second input/output port  588   b  of the broadband power splitter  588  in the loop arrangement  587   a  is coupled to a third input/output port  585   c  of the AWG multiplexer  585  via an optical path G. The AWG multiplexer  585  can be replaced by an Eschelle grating that provides essentially the same function as the AWG multiplexer  585 . 
   In operation, the output signals from the lasers  581   a – 581   n  are optionally polarization rotated by the PRs  583   a – 583   n  and transmitted to the plurality of n first power splitters  584   a – 584   n . In the first power splitters  584   a – 584   n , the received signal from the corresponding one of the PRs  583   a – 583   n  is tapped and a first major portion is transmitted via input/output port  584   q  to the corresponding one of the first input/output ports  585   a  of the AWG multiplexer  585  for transmission to the first input/output port  586   a  of the broadband power splitter  586  via optical paths C and D. The spectral response in the AWG multiplexer  505  between the input/output ports  585   a  and  585   b  is f 1   j (w). A second portion of the tapped signal is transmitted via input/output port  584   r  to the corresponding one of the fourth input/output ports  585   d  of the AWG multiplexer  585  for transmission to the second input/output port  588   b  of the broadband power splitter  588  in the loop arrangement  587   a  via optical paths H and G. In the broadband power splitter  586 , the received multiplexed signal received via optical path D at the first input/output port  586   a  is tapped and a first major portion thereof is routed to the second output port  586   b  as the main output signal from the system  580  via optical path E, and the other portion thereof is transmitted via the third input/output port  586   c  to the first input/output port  588   a  of the broadband power splitter  588  of the broadband power splitter  588  of the loop arrangement  587   a . In the loop arrangement  587   a , a multiplexed signal received at either one of the first and second input/output ports  588   a  and  588   b  are split and a first portion is sent to the second and first input ports  588   b  and  588   a , respectively, and a second portion is transmitted through the optional delay line  589 . The first portion transmitted via the second input/output port  588   b  of the broadband power splitter  588  is a feedback signal being sent via the AWG multiplexer  585  and the optical paths G→H→B→A to the plurality of lasers  581   a – 581   n . The spectral response in the first AWG multiplexer  585  between the input/output ports  585   c  and  585   d  is f 2   j (w). 
   An alternative arrangement for the loop arrangement  587  is shown as the loop arrangement  587   b  (shown within a dashed line area). The loop arrangement  587   b  comprises the broadband power splitter  588 , a first optional delay line  590  and a first broadband reflector  591  coupled in series to the third input/output port  588   c  of a broadband power splitter  588  via optical paths L and M, and a second optional delay line  592  and a second broadband. reflector  593  coupled in series to the fourth input/output port  588   d  of the broadband power splitter  588  via optical paths O and P. The operation and purpose of each of the loop arrangements  587   a  and  587   b  is the same as that described for the loop arrangements  550   a  and  550   b , respectively, shown in  FIG. 50 . 
   It is to be appreciated and understood that the specific embodiments of the present invention that have been described are merely illustrative of the general principles of the present invention. Various modifications may be made by those skilled in the art that are consistent with the principles of the present invention. For example, one or more optional delay lines can be placed in the feedback path of the feedback arrangements of each of the systems of each of the embodiments to produce a desired incoherent feedback signal at the output port of each laser source in order to place the laser source in a “coherence collapse” mode, as is well known in the art, and thereby stabilize the laser source. In this regard see, for example, the paper entitled “Wavelength and intensity stabilization of 980 nm diode lasers coupled to fibre Bragg gratings” by B. F. Ventrudo et al., in Electronics Letters, 8th Dec. 1984, Vol. 30, No. 25, at pages 2147–2149, and the book entitled “Diode Lasers and Photonic Integrated Circuits” by L. A. Coldren and S. W. Corzine, Published by Wiley &amp; Sons, 1995, at pages 252–257. When in the specification the terms coupled or coupling or couples are used, it is meant to describe that two elements (components, devices) are connected together, either directly, or through some third element. For example, an output port of a laser can be coupled via air, or an optical waveguide, to an input of a power splitter, or a filter, or a multiplexer/filter. Still further, an output port of a first filter, whose input is coupled to an output of a laser, can be coupled through a second filter to an output of a laser. Furthermore, the part of a laser at which light is emitted during operation thereof may also be denoted as an output or as an input/output of the laser. In the case where a laser inherently generates an output signal having blue shift in wavelength in response to a feedback signal, the arrangements  34  and  44  of  FIGS. 3 and 5 , respectively, are more accurately described as “a red shift feedback stabilizing arrangement  34 ”.