Patent Publication Number: US-7218436-B2

Title: Optical instrument and measurements using multiple tunable optical polarization rotators

Description:
This application claims the benefit of U.S. Provisional Patent Application No. 60/578,700 entitled “Generation and Analysis of State of Polarization Using Tunable Optical Polarization Rotators” and filed Jun. 10, 2004. 
   In addition, this application is a continuation in part application of and claims the benefits of U.S. patent application Ser. No. 10/914,592 entitled “GENERATION AND ANALYSIS OF STATE OF POLARIZATION USING TUNABLE OPTICAL POLARIZATION ROTATORS” and filed Aug. 9, 2004 now U.S. Pat. No. 7,027,198 which claims the benefits of U.S. Provisional Patent Application No. 60/493,880 entitled “SOP Generator and Analyzer Based on Tunable Optical Polarization Rotators” and filed Aug. 8, 2003 and the above-referenced U.S. Provisional Patent Application No. 60/578,700. The above-referenced U.S. patent application Ser. No. 10/914,592 is also a continuation-in-part application of and claims the benefit of U.S. patent application Ser. No. 10/800,406 entitled “Monitoring Mechanisms for Optical Systems” and field Mar. 12, 2004. 
   The entire disclosures of the above referenced applications are incorporated herein by reference as part of the specification of this application. 

   BACKGROUND 
   This application relates to optical polarization devices and their applications including polarization-based optical monitoring devices and systems. 
   Optical properties or parameters of light in an optical device or system may be measured for various purposes. As an example, such an optical measurement may be used to determine the performance or an operating condition of the device or system. An optical property or parameter of light under measurement may include the optical polarization, the signal to noise ratio, the differential group delay between two orthogonal polarization states, and others. 
   The optical polarization is an important parameter of an optical signal in various optical systems. For example, in fiber optic communication systems, polarization-dependent effects in fibers and other devices, such as polarization-dependent loss (PDL) and polarization-mode dispersion (PMD), can have significant impacts on performance and proper operations of optical devices or systems. Hence, it may be desirable to measure and monitor the state of polarization (SOP) and the degree of polarization (DOP) of an optical signal in these and other systems. 
   Similarly, the signal-to-noise ratio (SNR) and the differential group delay (DGD) of an optical signal are also important parameters for various optical devices and systems and hence monitoring of these parameters may be desirable under certain circumstances. 
   SUMMARY 
   This application includes various implementations and examples of devices and techniques for monitoring the SNR, DOP, and DGD of one or more optical signals and for generation of various states of polarization. In one implementation, an optical scrambler and a polarizer may be used in the optical path for the measurements. In another implementation, a rotatable quarter waveplate and a rotatable half waveplate are used in the optical path for the measurements. In yet another implementation, a state-of-polarization generator and a linear polarizer may be used for the measurements. The optical monitoring devices described here may be used to measure WDM channels. 
   Example of various implementations include the following. 
   In one example, a device includes a fiber loop, an optical coupler in said fiber loop to couple input light into said fiber loop as two counter-propagating waves in said loop and to couple light in said loop out as an output beam, a polarization device in said fiber loop to change polarization of light in said loop to achieve a maximum power level and a minimum power level in said output beam, an optical detector to receive said output beam to produce a detector signal; and a circuit to process said detector signal to produce an output indicative of a signal-to-noise ratio or a degree of polarization in said input light from said maximum and minimum power levels. 
   In another example, a device includes a polarization scrambler to scramble polarization of received light to produce output light in a controlled manner in response to a control signal, a polarizer to receive said output light from said polarization scrambler to produce a transmitted beam, an optical detector to receive said transmitted beam to produce a detector signal, and a control unit to produce said control signal to said polarization scrambler and to process said detector signal to produce an output indicative of a signal-to-noise ratio or a degree of polarization in said input light. 
   In another example, a device is described to include a polarization device to adjust polarization of received light to produce output light to find a maximum power level and a minimum power level of each WDM channel of different WDM channels in said received light, a WDM demultiplexer to receive said output light and to separate different WDM channels in said output light, a plurality of polarizers in optical paths of said different WDM channels, respectively; a plurality of optical detectors to respectively receive said different WDM channels after transmission through said polarizers; and a circuit to process output signals from said optical detectors to produce an output for each WDM channel indicative of a signal-to-noise ratio or a degree of polarization in said each WDM channel from said maximum power level and said minimum power level. The polarization device may be a polarization scrambler which randomly changes said polarization in searching for said maximum power level and said minimum power level. The polarization device may be a polarization controller. 
   In another example, a device is described to include a polarization device to scramble adjust polarization of received light to produce output light to find a maximum power level and a minimum power level of each WDM channel of different WDM channels in said received light, a WDM demultiplexer to receive said output light to separate different WDM channels in said output light, a polarizer in an optical path of said output light between said polarization device and said WDM demultiplexer to transmit said output light to said WDM demultiplexer, a plurality of optical detectors to respectively receive said different WDM channels after transmission through said polarizers, and a circuit to process output signals from said optical detectors to produce an output for each WDM channel indicative of a signal-to-noise ratio or a degree of polarization in said each WDM channel from said maximum power level and said minimum power level. The polarization device may be a polarization scrambler which randomly changes said polarization in searching for said maximum power level and said minimum power level, and may be a polarization controller. 
   In another example, a device includes a polarization device to change polarization of received light to produce output light to find a maximum power level and a minimum power level of each WDM channel of different WDM channels in said received light; an optical polarizer to receive said output light to produce a beam; an optical diffraction grating to diffract said beam into spatially separated different WDM channels; a lens to transmit said different WDM channels; a plurality of optical detectors to respectively receive said different WDM channels from said lens; and a circuit to process output signals from said optical detectors to produce an output for each WDM channel indicative of a signal-to-noise ratio or a degree of polarization in said each WDM channel. The polarization device may be a polarization scrambler which randomly changes said polarization in searching for said maximum power level and said minimum power level and may be a polarization controller. 
   In another example, a device includes a polarization device to change polarization of received light to produce output light to find a maximum power level and a minimum power level of each WDM channel of different WDM channels in said received light; a WDM demultiplexer to receive said output light to separate different WDM channels in said output light; a plurality of polarization beam splitters in optical paths of said different WDM channels, respectively, wherein each polarization beam splitter splits a corresponding WDM channel into two monitor beams that are orthogonally polarized; a plurality of filters disposed in one of said two monitor beams for said different WDM channels, respectively, each operable to produce a difference in power between noise power levels in said two monitor beams for each WDM channel without affecting signal power levels in said each WDM channel in said two monitor beams; a plurality of pairs of optical detectors provided for different WDM channels, wherein two optical detectors in each pair are positioned to respectively receive said two monitor beams for a corresponding WDM channel to produce two detector outputs for said WDM channel; and a control unit to produce said control signal and to process detector signals to produce an output for each WDM channel indicative of a signal-to-noise ratio or a degree of polarization in said each WDM channel. The polarization device may be a polarization scrambler which randomly changes said polarization in searching for said maximum power level and said minimum power level and may be a polarization controller. 
   In another example, a device includes a polarization device to change polarization of received light to produce output light to find a maximum power level and a minimum power level of each WDM channel of different WDM channels in said received light; a polarization beam splitter to split said output light into first and second beams of orthogonal polarizations; a first WDM demultiplexer to receive said first beam to separate different WDM channels in said first beam; a second WDM demultiplexer to receive said second beam to separate different WDM channels in said second beam, wherein said first WDM demultiplexer is different from said second WDM demultiplexer in way that a noise power level in an output WDM channel from said first WDM demultiplexer is different from a noise power level in the same WDM channel from said second WDM demultiplexer; a first set of optical detectors located to receive different WDM channels from said first WDM demultiplexer; a second set of optical detectors located to receive different WDM channels from said second WDM demultiplexer; and a control unit to produce said control signal and to process detector signals from said first set and said second set of optical detectors to produce an output for each WDM channel indicative of a signal-to-noise ratio or a degree of polarization in said each WDM channel. The polarization device may be a polarization scrambler which randomly changes said polarization in searching for said maximum power level and said minimum power level and may be a polarization controller. 
   In another example, a device includes a polarization element operable to adjust optical polarization of input light; a polarizer to receive light from said polarization element to produce a transmitted beam; an optical detector to receive said transmitted beam from said polarizer; and a signal processing circuit to process output of said optical detector to extract information on a state of polarization of said input light. The polarization element may be implemented by a polarization controller, a rotatable quarter-wave plate, or a state-of-polarization generator. 
   A method is also described to include obtaining a monitor beam from a fiber line carrying WDM channels; spatially separating WDM channels from said monitor beam; separating each WDM channel into a first beam and a second beam with orthogonal polarizations in a way that noise power level in said first beam is different from a noise power level in said second beam; adjusting polarization of each WDM channel prior to separation into said first and said second beams to find a maximum power level and a minimum power level in each of said first and said second beams; and determining both a signal-to-noise ratio and a degree of polarization of each WDM channel in said monitor beam. 
   Additional examples and implementations are also described. 
   One example of devices described here includes first and second polarization rotators sequentially positioned in an optical path, a quarter waveplate in the optical path to receive output light from the first and second polarization rotators, and third and fourth polarization rotators sequentially positioned in the optical path to receive output light from the quarter waveplate. Each polarization rotator is adjustable in response to a control signal and may be operate at two binary rotation angles. 
   In another example, a device includes at least four polarization rotators positioned in an optical path and each polarization rotator is adjustable in response to a control signal to rotate the polarization by either +22.5° or −22.5°. The device also includes a quarter wave plate in the optical path. 
   Methods for generates states of polarization and analyzing polarization are also described here. In one example, a device is described to include at least four polarization rotators positioned to form an optical path, each polarization rotator being adjustable to change a rotation of polarization of light transmitting therethrough along the optical path, and an optical polarization device placed in the optical path at one side of the polarization rotators to transmit light of a selected linear polarization. As another example, at least four adjustable polarization rotators in an optical path are used to transmit light and to control a state of polarization of the transmitted light. Each polarization rotator is controlled to rotate polarization by two different predetermined angles; and the at least four polarization rotators are controlled to operate in different rotator settings and to generate at least four different states of polarization. 
   Yet another described example uses at least four polarization rotators and a quarter wave plate in an optical path to transmit light. Each polarization rotator is controlled to rotate polarization by two different predetermined angles. The at least four polarization rotators are controlled to operate in different rotator settings and to generate at least four different states of polarization. 
   These and other implementations and applications are described in greater detail in the attached drawings, the detailed description, and the claims. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIGS. 1 and 2  show two exemplary optical monitoring devices with a polarization scrambler or controller. 
       FIG. 3  shows an implementation of the monitoring device in  FIG. 2  in a transmission system. 
       FIG. 4  shows a monitoring setup for a wavelength-division-multiplexed (WDM) transmission line where the input includes signals at different WDM wavelengths. 
       FIG. 5  shows one implementation of an all-fiber dynamic PMD controller  500  based on the above monitoring techniques. 
       FIG. 6  shows one implementation of a microprocessor-based monitoring device. 
       FIG. 7  shows a monitoring device that uses a WDM demultiplexer in the output of the polarization scrambler or controller to separate different WDM channels. 
       FIG. 8  shows another implementation where a diffraction grating is used to separate different WDM channels. 
       FIG. 9  shows one implementation of a PMD-insensitive monitoring device for WDM applications where only a single polarization scrambler is used for all wavelength channels. 
       FIG. 10  shows another implementation of a WDM monitoring device where a single polarization beam splitter is combined with two WDM demultiplexers. 
       FIG. 11  shows a system having a real-time DGD monitoring device and a dynamic PMD compensator. 
       FIG. 12  illustrates the processing operation by a DGD processing circuit in  FIG. 11  with reference to the Poincaré sphere for the polarization. 
       FIGS. 13 ,  14 , and  15  show three examples of optical monitoring devices that use a rotatable quarter waveplate and a rotatable polarizer as a polarization scrambler. 
       FIG. 16  shows a fiber system that uses a Fabry-Perot filter and sequential or parallel multi-channel polarimeters to monitor the SOP of each channel. 
       FIG. 17  illustrates operations of the Fabry-Perot filter in  FIG. 16 . 
       FIGS. 18A and 18B  show two examples of WDM optical monitoring devices that use a rotatable quarter waveplate and a rotatable half waveplate as part of the device. 
       FIGS. 19A ,  19 B,  19 C,  19 D, and  19 E illustrate examples of optical monitoring devices that use a SOP generator and a fixed optical polarizer. 
       FIGS. 20 and 21  show exemplary implementations of a SOP generator. 
       FIG. 22  shows a device that uses a SOP generator as a SOP analyzer to measure the degree of polarization of light. 
       FIG. 23  shows an example of a 4-rotator polarimeter with a control and processing unit. 
       FIGS. 24 and 25  show examples of 4-rotator and 6-rotator polarimeters using optical fibers. 
       FIG. 26  shows another example of a 6-rotator polarimeter. 
       FIG. 27  shows an example of a 8-rotator polarimeter. 
       FIG. 28  shows a testing system for testing multi-rotator devices described above. 
       FIGS. 29 ,  30 ,  31 ,  32 A, and  32 B show measurements of actual multi-rotator devices based on the 4-rotator and 6-rotator designs. 
       FIG. 33  shows an example of a system for measuring polarization property of a sample or device using a multi-rotator SOG generator and a separate multi-rotator polarimeter. 
       FIGS. 34A ,  34 B,  35 , and  36  show examples of systems for measuring polarization property of a sample or device based on a folded design that uses a single set of multiple rotators for both generating SOPs and analyzing the output from the sample or device due to optical reflection. 
       FIGS. 37A and 37B  show two examples of multichannel SOP analyzers. 
       FIG. 38  illustrates operation of the multichannel SOP analyzers in  FIGS. 37A and 37B . 
   

   DETAILED DESCRIPTION 
     FIG. 1  illustrates one exemplary implementation of a monitoring device  100  for monitoring both SNR and DOP in the received light. The monitoring device  100  may use a fiber to receive an optical signal  101  under monitoring, and an optical loop  120  such as a fiber loop to perform the monitoring. An optical coupler  110 , such as a 50% fiber coupler, may be coupled to the two ends of the fiber loop  120  to split the input signal  101  into two counter-propagating beams in the loop  120  and to combine the two counter-propagating beams to produce an output beam  140 . Hence, the coupler  110  and the loop  120  provide a mirroring mechanism. A polarization scrambler or controller  130  is placed in the fiber loop  120  to either randomly scramble the polarization of light in the loop  120  or to systematically control the polarization to vary through all possible states of polarization so that a maximum power level and a minimum power level in the output beam  140  can be obtained and measured. The polarization scrambler or controller  130  may be optionally controlled in response to a control signal  163  to adjust the state of polarization of light passing therethrough. 
   In one implementation of the device  130  as illustrated in  FIG. 1 , the polarization scrambler or controller  130  may include two or more fiber squeezers  131  and  132  under control of the controllers  133  and  134 , respectively. The squeezing directions of the fiber squeezers  131  and  132  are oriented to be 45 degrees with respect to each other to perform the scrambling operations. 
   An optical detector  150  may be coupled to receive the output light  140  from the loop  120 . An optional optical isolator  103  may be placed in the path of the input beam  101  to prevent any optical feedback to the input path. A processing circuit  160  is coupled to receive the detector output from the detector  150  to produce an output signal  162  which includes information about the SNR or DOP. 
   In operation, the detector  150  detects the maximum and the minimum optical power levels in the output signal  140 . The processing circuit  160  can be designed to compute the extinction ratio based on measured maximum and the minimum optical power levels. In various applications, the signal  101  is generally polarized and the noise is not polarized. Hence, the extinction ratio can directly relate to the SNR and DOP. As the extinction ratio increases, the DOP and the SNR increase accordingly, and vice versa. The processing circuit  160  may also includes a control unit that controls the operation of the polarization scrambler  130 . 
     FIG. 2  shows a monitoring device  200  based on another implementation. The polarization scrambler  130  is used to scramble the input light  101  and a polarizer  210  is used to transmit the output light of the scrambler  130 . The polarizer  210  is used here to replace the mirroring loop  120  in the monitoring device  100  in  FIG. 1 . The optical detector  150  is then used to receive the transmitted light from the polarizer  210 . The processing circuit  160  receives and processes the detector output to produce the output  162 . 
     FIG. 3  shows an implementation of the monitoring device  200  in a transmission system  300 . An optical coupler  310  is placed in the path of the input beam  301  to tap a fraction of the input  301  as a monitoring beam  320  and the remaining  302  of the input  301  continues along the input path as an output of the system  300 . The monitoring device  200  is coupled to receive the monitoring beam  320  to perform the measurement. Notably, a housing  303  may be used to enclose the coupler  310 , the path for the monitoring beam  320 , and the monitoring device  200 . All optical paths may be fibers, dielectric waveguides, or a combination of fiber paths and waveguide paths. The housing may be hermetically sealed to provide an integrated package for deployment in a fiber transmission line or system. A substrate may be used to fabricated waveguides and other optical components in a single-chip package enclosed within the housing  303 . It is understood that, the monitoring device  100  in  FIG. 1  may also be used to replace the device  200  in  FIG. 3  and other systems shown in this application. 
     FIG. 4  shows a monitoring setup for a wavelength-division-multiplexed (WDM) transmission line where the input  301  includes signals at different WDM wavelengths. The coupler  310  may split all WDM signals at the input to produce the monitoring beam  320 . A WDM coupler may be used as the coupler  310 . A tunable optical filter  410  is coupled between the coupler  310  and the monitoring device  200  or  100  to sequentially filter the WDM signals so that only one signal at a single WDM wavelength is transmitted to the device  200  or  100 . As the filter  410  is tuned sequentially through all signal wavelengths, one at a time, each and every WDM signal is measured by the device  200  or  100 . A control device  420  may be implemented and coupled to the filter  410  and the monitoring device  200  or  100  to control such sequential filtering and monitoring operations. The tunable filter  410  may be implemented in a number of configurations, such as a tunable Fabry-Perot filter, a tunable fiber grating filter (e.g., coupled with a fiber stretcher), multiple filters with different transmission wavelengths on a rotation wheel which may be controlled by a step motor, and others. 
     FIG. 5  shows one implementation of an all-fiber dynamic PMD controller  500  based on the above monitoring techniques. An adjustable polarization controller  510  is coupled in the input fiber to control the polarization of the input beam  501 . A polarization-maintaining fiber segment  520  is coupled to the output of the polarization controller  510  to produce the desired differential group delay in the output light from the controller  510 . Fiber fusion splicing may be used to connect the PM fiber segment  510 . A fiber coupler  310  is used to split the output of the controller  510  into an output beam  502  in the input fiber and a monitoring beam  320  to the monitoring device  200  in  FIG. 2  (or the device  100  in  FIG. 1 ) for monitoring the degree of polarization. The circuit  160  is coupled to supply the output  162  to control the polarization controller  510  so that the polarization controller  510  can be dynamically adjusted in response to the measurement by the circuit  160 . The polarization controller  510  may be implemented in various configurations. The PMD controller  500  may include multiple, e.g., three or more, fiber squeezers. U.S. Pat. No. 6,493,474 granted to Yao on Dec. 10, 2002 discloses some examples based on four sequential fiber squeezers and is incorporated herein in its entirety as part of the specification of this application. 
   The system in  FIG. 5  may be used to achieve a number of advantages, such as low optical loss at less than 0.5 dB and low cost due to the unique designs based on simple optical layout and simple components. A hermetically-sealed housing  530  may be implemented as illustrated. 
     FIG. 6  shows one implementation of a microprocessor-based monitoring device  600 . A polarization controller  630  is used to adjust the SOP of the input light  612  under monitoring and a polarizer  210  is used to transmit the output light of the controller  630  to an optical detector  150 . The output signal  152  from the detector  150  may be electrically amplified by an amplifier  660  and the amplified signal is sent to a microprocessor-based processing circuit  650 . The processing circuit  650  converts each received analog signal into digital bits and performs the signal processing operations by using a microprocessor in the digital domain. An output  651  is then produced to indicate the monitoring result on either the DOP or the SNR of the light  612 . As illustrated, a laser  610  or other light source may be used to produce the input light  612 . 
   Optionally, a beam splitter  620 , such as a fiber coupler, may be used to split a fraction of the input beam  612  as a reference beam  622  to a second optical detector  640 . This beam splitter  620  should be insensitive to the light polarization. The output  642  of the second detector  640  is then fed into the circuit  650  for processing. This reference beam  622  provides a measurement of the power variation in the input beam  612  so that a part of the variation in the received signal  152  caused by the power variation alone may be deducted from the variation caused by the polarization change caused by the scrambler  630 . 
   In operation, the circuit  650  may produce a control signal  652  to adjust the controller  630  in search for the maximum power (V max ) and the minimum power (V min ) at the detector  150 . The control signal  652  may be digitally generated by the microprocessor and then converts into an analog signal. Based on measurements on the Vman and Vmin, the processor in the circuit  650  computes the DOP or SNR of the light. The DOP may be computed as follows: 
   
     
       
         
           DOP 
           = 
           
             
               
                 
                   V 
                   max 
                 
                 - 
                 
                   V 
                   min 
                 
               
               
                 
                   V 
                   max 
                 
                 + 
                 
                   V 
                   min 
                 
               
             
             . 
           
         
       
     
   
   The polarization controller  630  may use a two-squeezer design as the element  130  in  FIG. 1  or a three-squeezer design as illustrated in  FIG. 6 , or five- or six-squeezers to provide increased control in adjusting the SOP of input light.  FIG. 6  shows a termination design where the input beam is entirely used for the monitoring operation. Alternatively, the monitoring device  600  may be implemented as an in-line package similar to the design in  FIG. 3  where an additional splitter  310  is used to split the main input beam  301  to produce the input to the monitoring device  600  and the remaining of the main input beam continues to propagate in the transmission system. 
   In the above and other monitoring devices in this application, a tunable optical filter may be inserted in the input path to allow for sequential monitoring of different WDM channels in the input.  FIG. 4  shows one example. This multi-channel technique based on a tunable filter can be implemented in various monitoring devices of this application. However, this technique is limited to sequential monitoring of one channel at a time. 
     FIGS. 7 and 8  illustrate two multi-channel monitoring techniques for simultaneous monitoring of different WDM channels. Such techniques allows for taking snap shots of different channels at the same time. 
     FIG. 7  shows a monitoring device  700  that uses a WDM demultiplexer  710  in the output of the polarization scrambler or controller  130  to separate different WDM channels. In the optical path of each separate WDM channel, a polarizer  210  and an optical detector  150  are used to receive and detect the power levels of each channel. Hence, power levels of different channels can be measured at the same time. The output signals from the detectors  150  are then fed into the circuit  160  for data processing to monitor the WDM channels. Multiple polarizers  210  are placed in the optical paths between the dmux  710  and the detectors  150 . Alternatively, a single polarizer may be placed between the polarization scrambler  130  and the WDM demultiplexer  710  to replace with multiple polarizers  210  in front of the detectors  150 . 
     FIG. 8  shows another implementation  800  where a diffraction grating  820  is used to separate different WDM channels. A collimator  810  is used to receive the output of the polarization scrambler  130  to produce a collimated output. A polarizer  210  is placed between the polarization scrambler  130  and the collimator  810 . The grating  820  diffracts the input light at different WDM wavelengths at different diffraction angles. This diffraction spatially separates different WDM channels. A second collimator  830 , such as a lens, is used to collect the diffracted beams of different channels and focus the diffracted beams onto different detector elements of an array of optical detectors  840 . A processing circuit  850  may be optionally used to condition the detector output signals prior to the circuit  160 . 
   The above monitoring devices based on a polarization scrambler may be sensitive to the PMD in the input signal that includes two or more WDM channels. This sensitivity on the PMD may cause an error in the measurement. In general, the greater the PMD in the input, the larger the error of the monitoring device. Hence, it may be desirable to mitigate this PMD effect in monitoring the DOP or SNR. 
     FIG. 9  shows one implementation of a PMD-insensitive monitoring device  900  for WDM applications where only a single polarization scrambler is used for all wavelength channels. The device  900  includes a universal polarization scrambler  910  to receive input WDM channels in an input fiber  901 . One or more optical amplifiers  902  may be used in the input optical path to amplify the input WDM channels. A WDM demultiplexer  920  is used to receive the output from the scrambler  910  and to split different WDM channels by their wavelengths as separate optical output signals  922 . In each optical output, a polarizing beam splitter (PBS)  930  or a suitable polarization device is used to split the received light based on their two orthogonal polarizations to produce two beams with orthogonal polarizations. A bandpass filter  940  is used to filter one of the two outputs of the PBS  930  so that the power levels of the noise power levels in two output beams are different while the power levels of the signals in the output beams are essentially unaffected by the filtering. As illustrated, the filter  940  may be positioned to filter light from the port that transmits light along the direction of the input beam. 
   The above optical filtering causes an imbalance between the noise power levels in the two output beams with orthogonal polarizations. This imbalance is used for simultaneous and independent monitoring of both SNR and DOP. Two orthogonally oriented polarizers  941  and  942  may be optionally placed at the two output ports of the PBS  941  to ensure the output beams are orthogonally polarized. Two optical detectors  951  and  952  are positioned to receive the two outputs of the PBS  930 , respectively. The output signals of the detectors  951  and  952  are fed into a processing circuit  970  for measurements and data processing. Two electrical signal amplifiers  961  and  962  may be optionally used to amplify the detector outputs, respectively, prior to the processing by the circuit  970 . 
   In one implementation, the bandpass filter  940  may have a bandwidth broader than the actual bandwidth of each signal channel to allow each signal channel to pass without filtering but narrower than the bandwidth of the WDM device for each channel to filter out some noise components to create the power imbalance in the noise between the two output beams. For example, for WDM channels with 100 GHz in the channel spacing and 10 GHz in the channel bandwidth, the WDM demultiplexer  920  may be designed to have a channel bandwidth of 50 GHz. The bandpass filter  940  may have a bandwidth of 25 GHz, between the 10-GHz channel bandwidth and 50-GHz device channel bandwidth, to allow a channel to pass through without being filtered. However, the noise components outside the 25 GHz window are filtered out in the transmitted beam of the PBS  930 . 
   The maximum and minimum detected power measurements of all SOPs detected at the two detectors  951  and  952  are: 
                 {             V   1   max     =       G   1     ⁡     [         P   s     ⁡     (     1   -   δ     )       +     0.5   ⁢     P   N         ]               (   1   )                 V   1   min     =       G   1     ⁡     [         P   s     ⁢   δ     +     0.5   ⁢     P   N         ]               (   2   )                 V   2   max     =       G   2     ⁡     [         P   s     ⁡     (     1   -   δ     )       +     0.5   ⁢   α   ⁢           ⁢     P   N         ]               (   3   )                 V   2   min     =       G   2     ⁡     [         P   s     ⁢   δ     +     0.5   ⁢   α   ⁢           ⁢     P   N         ]               (   4   )                   
where P S  is the signal power, P N  is the noise power, α is less than 1 and is the noise power filtering factor of the bandpass filter  940 , and δ the depolarization factor caused by, e.g., the PMD in the input signal, the nonlinear birefringence, and imperfection of the PBS  930 . Notably, in absence of the filter  940  which produces the an imbalance between the two output beams from PBS  930 , the Eqs. (1) and (2) would be identical to Eqs. (3) and (4). The filter  940  is specifically used to break the degeneracy and to provide separate measures of SNR and DOP.
 
   Equations (1) and (2) are added to obtain the following:
 
 V   1   max   +V   1   min   =G   1 ( P   S   +P   N )  (5)
 
Equations (1) and (2) are subtracted:
 
 V   1   max   −V   1   min   =G   1   P   S (1−2δ)  (6)
 
Similar manipulations of Equations (3) and (4) yield:
 
 V   2   max   +V   2   min   =G   2 ( P   S   +αP   N )  (7)
 
 V   2   max   −V   2   min   =G   2   P   S (1−2δ)  (8)
 
Additionally, the following signal processing can be carried out:
 
                       G   2     ·     Eq   .           ⁢     (   5   )         -       G   i     ·     Eq   .           ⁢     (   7   )           =       ⁢         G   2     ⁡     (       V   1   max     +     V   1   min       )       -       G   1     ⁡     (       V   2   max     +     V   2   min       )                     =       ⁢         G   1     ⁢     G   2     ⁢     P   S       +       G   1     ⁢     G   2     ⁢     P   N       -       G   1     ⁢     G   2     ⁢     P   S       -                     ⁢     α   ⁢           ⁢     G   1     ⁢     G   2     ⁢       P   N     .                   
Hence, the following can be obtained:
 
                         G   1     ⁢       G   2     ⁡     (     1   -   α     )       ⁢     P   N       =         G   2     ⁡     (       V   1   max     +     V   1   min       )       -       G   1     ⁡     (       V   2   max     +     V   2   min       )           ,   and     ⁢     
     ⁢       P   N     =       1     1   -   α       ⁡     [           V   1   max     +     V   a   min         G   1       -         V   2   max     +     V   2   min         G   2         ]                 (   9   )               
From Eq. (5), the following can be derived:
 
                     G   1     ⁢     P   S       =       ⁢       (       V   1   max     +     V   1   min       )     -       G   1     ⁢     P   N                     =       ⁢       (       V   1   max     +     V   1   min       )     -       1     1   -   α       ⁡     [       (       V   1   max     +     V   1   min       )     -         G   1       G   2       ⁢     (       V   2   max     +     V   2   min       )         ]                     =       ⁢         (     1   -     1     1   -   α         )     ⁢     (       V   1   max     +     V   1   min       )       +           G   1       G   2         1   -   α       ⁢     (       V   2   max     +     V   2   min       )                     =       ⁢         1     1   -   α       ⁡     [           G   1       G   2       ⁢     (       V   2   max     +     V   2   min       )       -     α   ⁡     (       V   1   max     +     V   1   min       )         ]       .                 
Therefore, the following expressions can be derived:
 
                   P   S     =       1     1   -   α       ⁡     [           V   2   max     +     V   2   min         G   2       -       α     G   1       ⁢     (       V   1   max     +     V   1   min       )         ]               (   10   )                 S   /   N     =         P   s       P   N       ⁢     
     ⁢           =               V   2   max     +     V   2   min         G   2       -       α     G   1       ⁢     (       V   1   max     +     V   1   min       )                 V   1   max     +     V   1   min         G   1       -         V   2   max     +     V   2   min         G   2           ⁢     
     ⁢           =             G   1     ⁡     (       V   2   max     +     V   2   min       )       -     α   ⁢           ⁢       G   2     ⁡     (       V   1   max     +     V   1   min       )                 G   2     ⁡     (       V   1   max     +     V   1   min       )       -       G   1     ⁡     (       V   2   max     +     V   2   min       )           .                                     Let   ⁢           ⁢       V   _     1       =       1   2     ⁢     (       V   1   max     +     V   1   min       )         ,       and   ⁢           ⁢       V   _     2       =       1   2     ⁢     (       V   2   max     +     V   2   min       )         ,                           
the SNR can be computed as follows:
 
                   S   N     =           G   1     ⁢       V   _     2       -     α   ⁢           ⁢     G   2     ⁢       V   _     1               G   2     ⁢       V   _     1       -       G   1     ⁢       V   _     2                   (   12   )               
If G 1 =G 2 , then SNR becomes
 
             S   N     =             V   _     2     -     α   ⁢           ⁢       V   _     1               V   _     1     -       V   _     2         .           
Hence, the signal to noise ratio only depends on the average V 1  and V 2 . This approach essentially excludes all the effects of PMD, the nonlinear birefringence, and the PBS imperfection.
 
   From Equations (6), (9), and (10), the depolarization factor δ can be calculated as: 
               G   1     ⁢       P   S     ⁡     (     1   -     2   ⁢           ⁢   δ       )         =       V   1   max     -     V   1   min                       1   -     2   ⁢           ⁢   δ       =       1       G   1     ⁢     P   S         ⁢     (       V   1   max     -     V   1   min       )         ,   and               δ   =         1   2     ⁡     [     1   -       1       G   1     ⁢     P   S         ⁢     (       V   1   max     -     V   1   min       )         ]       ⁢     
     ⁢           =       1   2     [     1   -         (     1   -   α     )     ⁢     (       V   1   max     -     V   1   min       )               G   1       G   2       ⁢     (       V   2   max     +     V   2   min       )       -     α   ⁡     (       V   1   max     +     V   1   min       )             ]             
For G 1 =G 2 , the depolarization factor can be simplified as:
 
   
     
       
         
           δ 
           = 
           
             
               
                 1 
                 2 
               
               ⁡ 
               
                 [ 
                 
                   1 
                   - 
                   
                     
                       
                         ( 
                         
                           1 
                           - 
                           α 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             V 
                             1 
                             max 
                           
                           - 
                           
                             V 
                             1 
                             min 
                           
                         
                         ) 
                       
                     
                     
                       2 
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               V 
                               _ 
                             
                             2 
                           
                           - 
                           
                             α 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 V 
                                 _ 
                               
                               1 
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 ] 
               
             
             . 
           
         
       
     
   
   The contribution to δ from the imperfection of the PBS  930  can be eliminated by placing polarizers  941  and  942  at the outputs of the PBS  930  in  FIG. 9 . Accordingly, the depolarization caused by PMD can be precisely measured. This mechanism may also be used to monitor the PMD effect. 
   The device in  FIG. 9  uses multiple PBSs for the separated WDM channels. Alternatively,  FIG. 10  shows another implementation  1000  where a single PBS  930  is combined with two WDM demultiplexers  1010  and  1020 . In this design, the two demultiplexers  1010  and  1020  may be purposely designed to be different to introduce the noise power imbalance with a factor of α(λi) (i=1, 2, . . . , N). For example, the device channel bandwidths of the two demultiplexers  1010  and  1020  may be different, e.g., one is 50 GHz and the other is 75 GHz for WDM signals with a channel bandwidth of 10 GHz and a channel spacing of 100 GHz, where each WDM channel transmits without being attenuated but the noise power levels of the same channel in the outputs of the demultiplexers  1010  and  1020  are different. Hence, the filter  940  in  FIG. 9  may be eliminated. If the two demultiplexers  1010  and  1020  are identical, then the filtering is needed to introduce the power imbalance. 
   Now turning to  FIG. 11 , a real-time DGD monitoring mechanism is shown in the fiber system  1100  and is used in connection with a dynamic PMD compensator. The fiber system includes three main modules: a transmitter terminal, the fiber transmission line  1103  which may include a fiber link with optical amplifiers, and a receiving terminal. The transmitter terminal may include multiple optical transmitters  1101  at different channel wavelengths and a WDM multiplexer  1102  to multiplex the different channels for transmission in the fiber link  1103 . The receiving terminal includes a DGD monitor, a demultiplexers  1120 , dynamic PMD compensators for different channels, and optical receivers  1180  for different channels. An optical coupler  1110 , such as a fiber coupler, may be placed in the input of the demultiplexer  1120  to split a fraction of the input signal as a monitor beam  1112  to the DGD monitor and the main input signal is received by the demultiplexer  1120 . 
   The DGD monitor in the system  1100  includes a tunable filter  1130 , a polarimeter  1140 , and a DGD processing circuit within a control unit  1190 . The filter  1130  is tuned to sequentially scan through different WDM or DWDM channels to allow for different channels to reach the polarimeter  1140 , one at a time. The bandwidth of the filter  1130  is sufficiently narrower than the bandwidth of each channel. The polarimeter  1140  is operable to measure the SOP at a high speed for the real-time monitoring. The DGD processing circuit within the control unit  1190  receives and processes the SOP signal generated by the polarimeter  1140  to determine the DGD in each channel. 
   In operation, the tunable filter  1130  is tuned to a channel at its center wavelength λi and is scanned around λi for a duration longer than the time for the polarimeter  1140  to measure the SOP of that channel. During this scanning around λi, the polarimeter processes the input optical signal at λi to produce the information on the SOP of this channel. 
     FIG. 12  illustrates the processing operation by the DGD processing circuit with reference to the Poincaré sphere for the polarization. Let the angular variation in the SOP angle around the principal axis Ω be Δθi for the channel λi, and the frequency tuning range around the center wavelength λi be Δfi, the DGD can be calculated as follows: 
             Δ   ⁢           ⁢     τ   i       =         Δθ   i       2   ⁢   πΔ   ⁢           ⁢     f   i         .           
This calculation is performed by the DGD processing circuit.  FIG. 12  shows that, both the DGD and direction of the principal axis Ω can be determined.
 
   Next, the control unit  1190  uses the DGD information to control the PMD compensator to produce a DGD that negates this measured DGD. This completes the monitoring and control operation on one channel. The control unit  1190  then commands the filter  1130  to tune to the next channel to repeat the monitoring and compensation operation. This process repeats for all channels sequentially. 
   The DGD monitoring mechanism in  FIG. 11  is shared by all channels. The PMD compensation, however, is implemented individually for each channel. Hence, multiple PMD compensators are used in the example in  FIG. 11  for different channels, respectively. Only one compensator for the channel λ 1  is depicted for simplicity. 
   In the optical path for each channel after the demultiplexer  1120 , the PMD compensator for that channel is placed before a respective channel receiver  1180 . The PMD compensator may include an optical polarization controller (PC)  1150 , a variable DGD (VDGD) element  1160  to produce a variable DGD, a DOP monitor  1170  for measuring the degree of polarization of the light, and a PMD control circuit within the control unit  1190 . The polarization controller  1150  may use various implementations, including the fiber-squeezer controllers disclosed in the incorporated U.S. Pat. No. 6,493,474. The DOP monitor  1170  may be configured to tap a portion of the signal for the monitoring operation and send the remaining signal to the channel receiver  1180 . As illustrated, the PMD control circuit controls both the polarization controller  1150  and the variable DGD element  1160  in response to the measured DOP from the monitor  1170 . Hence, the control is a feedback control and operates dynamically to produce real-time PMD compensation. In implementations, a microprocessor may be used in the control unit  1190  to perform the computations for the DGD measurement and the PMD compensation. 
   The polarimeter  1140  in  FIG. 11  may be implemented in various configurations.  FIG. 13  shows one exemplary implementation  1300  by using a rotatable quarter-wave plate  1310  and a rotatable polarizer  1320  to sequentially process input light. The plates  1310  and  1320  are controlled, e.g., by the circuit  1350 , to rotate at different rotational speeds or frequencies. In this and other implementations, the rotatable wave plate  1310  may be replaced by a polarization controller such as the fiber-squeezer controller disclosed in the U.S. Pat. No. 6,493,474. An optical detector  1330  converts the processed light into a detector signal and a signal processing circuit  1350  further processes the detector signal to measure the SOP of the light. A signal amplifier  1340  may be optionally coupled between the detector  1330  and the circuit  1350  to amplify the signal. Hence, in the configuration in  FIG. 11 , as the filter  1130  scans through different channels, the polarimeter  1300  measures the SOP one channel at a time. Alternatively, the configuration in  FIG. 11  may be modified to place the tunable filter  1130  between the detector  1330  and the polarizer  1320  of the polarimeter  1300 . 
   A polarimeter may also be configured to measure the SOPs of multiple channels in parallel at the same time.  FIGS. 14 and 15  show two examples. In  FIG. 14 , the polarimeter  1400  uses a demultiplexer  1120  to separate different channels output by the quarter-wave plate  1310  and the polarizer  1320 . For each channel, a designated optical detector  1330  and a designated signal processing circuit  1350  are used to process the channel signal to determine the SOP of that channel. Hence, all channels are monitored in parallel with one another at the same time. 
     FIG. 15  shows a different design  1500  where a diffraction grating  820  and a collimating lens  830  are used to spatially separate the different channels in a manner similar to the design in  FIG. 8  for a different application. A processing circuit  1520  is used to process the detector outputs to produce the SOP signals for different channels. 
   In absence of PMD in an input optical signal, the SNR of the signal can be directly determined from the DOP measurement. Assume P s  is the power of the signal which is polarized and P n  is the power of the noise which is unpolarized. The DOP can be computed by the following equation: 
           DOP   =         P   s         P   s     +     P   n         =           P   s     /     P   n         1   +       P   s     /     P   n           .             
Accordingly, the SNR can be computed from DOP:
 
           SNR   =         P   s       P   n       =       DOP     1   -   DOP       .             
Here, the DOP can be computed from the maximum and minimum power levels from the measurements. When DOP is 1, the SNR is infinite and when DOP is zero, the SNR is zero.
 
     FIG. 16  shows a fiber system  1600  that uses any one of the above sequential or parallel multi-channel polarimeters to monitor the SOP of each channel. A fiber coupler  1110  is used to split a fraction of the input light with multiple channels to produce a monitor beam  1112 . A tunable Fabry-Perot filter  1610  is used to filter the monitor beam  1112  to transmit all WDM channels at the same time to a multi-channel polarimeter  1620 . This may be accomplished by designing the Fabry-Perot filter  1610  to have a free spectral range (FSR) equal to the channel spacing of the WDM channels or a multiplicity of the channel spacing. In operation, the tunable Fabry-Perot filter  1610  is tuned to measure the DGD as illustrated in  FIG. 12 .  FIG. 17  further shows the spectrum of the filter  1610  where a tuning in the filter  1610  causes the same amount of frequency shift in the transmission of all channels. The polarimeter  1620  may be a sequential multi-channel polarimeter having a tunable filter or a parallel multi-channel polarimeter as shown in  FIGS. 14 and 15 . 
   In some WDM systems, the channel spacing may be 50 GHz, 100 GHz, or 200 GHz. Assuming the finesse of the filter  1610  is 100, the resolution bandwidth of the filter is 1 GHz and should be sufficient to resolve the spectrum of a 10 Gb/s signal. As described above, the DGD of each channel can be calculated based on the measured SOP in each channel as illustrated in  FIG. 12 . 
     FIGS. 18A and 18B  show two exemplary implementations  1801  and  1802  for providing independent monitoring of the signal to noise ratio (SNR) and DGD in WDM systems. In both systems, the input light is sequentially processed by a rotatable quarter-wave plate  1310  and a rotatable half-wave plate  1810 . The waveplates  1310  and  1810  rotate at different rotation speeds. Also in both systems, each channel is split into two beams with orthogonal polarizations to have different power levels. In the system  1801 , this is achieved by using two different demultiplexers  1010  and  1020  with different channel bandwidth. In the system  1802 , a filter  940  is inserted in one of the two output beams to produce the difference. The processing techniques in connection with  FIGS. 9 and 10  are applicable here. 
   In the above described examples shown in  FIGS. 13 ,  14 ,  15 ,  18 A and  18 B, the polarization scrambler formed by the rotatable waveplate  1310  and the rotatable polarizer  1320  may be replaced by a SOP generator and a downstream fixed optical polarizer. The SOP generator may be used to manipulate the polarization of received light to produce any desired SOP among a set of predetermined SOPs on the Poincare sphere. 
     FIGS. 19A ,  19 B,  19 C,  19 D, and  19 E illustrate examples  1901 ,  1902 ,  1903 ,  1904 , and  1905  of optical monitoring devices that use a SOP generator  1910  and a fixed optical polarizer  1920 . The SOP generator  1910  may be configured to be adjustable to produce various SOPs. An external control signal may be used to control the SOP generator  1910  in producing SOPs. In actual implementation, the control signal includes individual control signals for different rotators in the SOP generator  1910 . 
     FIG. 20  shows one example of a SOP generator. In this example, the SOP generator includes four controllable polarization rotators  1 ,  2 ,  3 , and  4  that are sequentially placed in the optical path. A quarter waveplate is placed between the rotators  2  and  3  to separate the  4  rotators into two pairs: rotators  1  and  2  as one pair and rotators  3  and  4  as another pair. In addition, an optional input polarizer may be placed in front of the first rotator  1  for aligning the input polarization with respect to the optical axis (c-axis) of the λ/4 plate. The input polarizer may be oriented in various directions, e.g., aligned with the c-axis, or 45° from the c-axis, or other predetermined angle. Each of the polarization rotators in  FIG. 20  may be individually controlled by a control signal as illustrated. Polarization rotations of the rotators are controlled to produce the desired SOPs at the output. 
   Notably, the SOP generator in  FIG. 20  is specifically designed to generate at least 4 and generally more than 4 distinctively different polarization states from an input light beam with a linear input polarization. This feature of the SOP generator in  FIG. 20  is significant because any state of polarization of light can be represented by a set of 4 Stockes parameters for polarization. Therefore, when at least 4 measurements can be obtained from an optical sample, an optical device, or an optical module with at least 4 different states of polarization in the probe light, a set of 4 linear equations can be solved to determine the values of the set of 4 Stockes parameters and thus to determine the polarization property of the sample, device or module under test. 
   In addition, the SOP generator in  FIG. 20  may also be used as a SOP analyzer or polarimemter to determine the SOP of the received light in any SOP by obtaining at least 4 different measurements of the input light and solve for the set of 4 Stockes parameters of the SOP of the input light. 
   It is well known that the Poincare sphere can be used to represent any and all states of polarization. Each point on this Poincare sphere has a unique set of coordinates defined by the sphere&#39;s three-dimensional axes S 1 , S 2  and S 3 . A Stokes vector is a 4×1 real matrix of 4 associated Stokes parameters (S 0 , S 1 , S 2 , S 3 ) that completely describes the SOP of the light. As an example, points on the equator of the Poincare sphere represent linear polarization states, the poles represent right-hand and left-hand circular polarization, and other points on the Poincare sphere represent elliptical polarization states. 
   Mathematically speaking, a minimum of 4 distinctively polarization measurements can be used to completely determine the Stockes parameters. In principle, these 4 distinctively polarization measurements may be obtained in any suitable manner in a particular application. As an example, the 4 Stockes parameters of a beam with an unknown SOP may be determined based upon measured power levels in the following measurements: 1) a polarizer at 0° (e.g., along the horizontal direction) is inserted in the input light and the optical power after the polarizer is measured; 2) Next, the polarizer is rotated by 45° and the corresponding optical power after the polarizer is measured; 3) the polarizer is then rotated by 90 degrees (or −45°) and the optical power after the polarizer is measured; and 4) finally, a right-hand-circular (RHC) or left-hand-circular (LHC) polarizer is inserted into the input light and the optical power after the RHC or LHC polarizer is measured. 
   The above power measurements can then be used to determine the Stockes parameters of the input SOP as follows: S 0  is the average power of the entire light beam (I); S 1 , is the difference in power between the horizontal (0 degree) and vertical (90 degrees) linear polarization components of the beam (I 0 −I 90 ); S 2  indicates the power difference between the +45-degree and −45-degree linear polarizations, (I 45 −I −45 ); and S 3  is the power difference between the right hand circular (RCP) and left-hand circular (LCP) polarizations: (I RCP −I LCP ). The Stokes vector has a magnitude equal to (s 1   2 +s 2   2 +s 3   2 ) 1/2  and originates from the center of the Poincare sphere. The three Stokes parameters can be normalized by the relative optical power values (s 1 =S 1 /S 0 , s 2 =S 2 /S 0 , s 3 =S 3 /S 0 ). 
   In one implementation of the SOP generator in  FIG. 20 , each polarization rotator may be a magneto-optic (MO) rotator to avoid any mechanical moving part in the SOP generator. This use of MO rotators or other polarization rotators without moving parts can improve the reliability and operating life of the device. 
   A polarization rotator, such as a MO rotator, suitable for the SOP generator in  FIG. 20  may be designed to have the following properties: (1) when a positive voltage above the saturation voltage Vsat of the MO rotator is applied to the MO rotator (i.e., V≧+Vsat), the MO rotator rotates the SOP of light by +22.5°; (2) when a negative voltage above the saturation voltage Vsat is applied (i.e., V≦−Vsat), the rotator rotates the SOP by −22.5°; (3) when rotators  1  and  2  (or  3  and  4 ) are rotated in the same direction, the net rotation of the pair of rotators  1  and  2  or rotators  3  and  4  is 45°; and (4) when rotators  1  and  2  (or  3  and  4 ) are rotated in the opposite directions, the net rotation of the pair is 0°. Alternatively, other types of polarization rotators such as liquid crystal polarization rotators and solid-state birefringent crystal polarization rotators may also be configured with the above operating states with appropriate control signals. 
   Accordingly, this particular SOP generator can be used to generate at least the following 5 distinctly different states of polarization when the input SOP is linear and is aligned with the c-axis of the λ/4 plate: 
   (1) A linear SOP at 0° is generated when rotators  1  and  2  are rotated at opposite directions and rotators  3  and  4  are rotated at opposite directions; 
   (2) A linear SOP at +45° is generated when rotators  1  and  2  are rotated at opposite directions, but rotators  3  and  4  are each rotated by +22.5°; 
   (3) A linear SOP at −45° is generated when rotators  1  and  2  are rotated at opposite directions, but rotators  3  and  4  are each rotated by −22.5°; 
   (4) A right-hand circular (RHC) polarization state is generated when rotators  1  and  2  are each rotated by +22.5°; and 
   (5) A left-hand circular (LHC) polarization state is generated when rotators  1  and  2  are each rotated by −22.5°. 
   TABLES 1 and 2 are logic tables with SOPs of different settings of the rotators  1 ,  2 ,  3 , and  4  for two configurations of the SOP generator in  FIG. 20 . The first row in each table shows both the direction and rotation in each of the four rotators and the remaining rows show only the directions of the rotations by the rotators and the amount of rotation is fixed at 22.5 degrees. The SOP generator in the 45-degree configuration in TABLE 2 has 6 distinctively different polarization states. The SOP in both configurations has degenerate states where two sets of different settings of the rotators generate the same state of polarization 
                   TABLE 1                  SOPs when Input SOP is aligned with quarter wave plate                                 Rotator 1   Rotator 2   Rotator 3   Rotator 4   SOP               +22.5°   −22.5°   +22.5°   −22.5°   0° linear       +   −   −   +   0° linear       −   +   +   −   0° linear       −   +   −   +   0° linear       +   −   +   +   45° linear        −   +   +   +   45° linear        +   −   −   −   −45° linear        −   +   −   −   −45° linear        +   +   +   +   RHC       +   +   −   +   RHC       +   +   +   −   RHC       +   +   −   −   RHC       −   −   +   +   LHC       −   −   −   +   LHC       −   −   +   −   LHC       −   −   −   −   LHC                    
at the output. For example, the top four different settings for the 4 rotators all generate the same 0-degree linear polarization at the output.
 
                   TABLE 2                  SOPS when Input SOP is aligned 45° from       c-axis of the quarter wave plate                                 Rotator 1   Rotator 2   Rotator 3   Rotator 4   SOP               +22.5°   −22.5°   +22.5°   −22.5°   RHC       +   −   −   +   RHC       −   +   +   −   RHC       −   +   −   +   RHC       +   −   +   +   RHC       −   +   +   +   RHC       +   −   −   −   RHC       −   +   −   −   RHC       +   +   +   +    90° linear       +   +   −   +    45° linear       +   +   +   −    45° linear       +   +   −   −    0° linear       −   −   +   +    0° linear       −   −   −   +   −45° linear       −   −   +   −   −45° linear       −   −   −   −   −90° linear                      FIG. 21  shows an example of a packaged SOP generator based on the design in  FIG. 20  where the generator is packaged or pigtailed with polarization-maintaining (PM) or single mode (SM) fibers. As illustrated, a housing may be used to hold the rotators and the waveplate along with the optional input polarizer. Two fiber collimators may be used at the input and output ports of the SOP generator and may be engaged to the input and output PM or SM fibers. The fibers may also be single mode PM fibers.
 
   In operating the SOP generator in  FIG. 20  or  FIG. 21  to generate different output SOPs, the SOP of an input light signal with a linear polarization is first determined and then the relative orientation between the input SOP and the quarter wave plate is set at a predetermined angle, e.g., at the zero degree as in the configuration in TABLE 1 or at 45 degrees as in TABLE 2. 
   When the SOP generator in  FIG. 20  or  FIG. 21  is used as an SOP analyzer to measure SOP and DOP of light, an input beam with an unknown SOP is sent into the SOP generator from the right port (the rotator  4 ) in  FIG. 20  and an optical detector at the left port (rotator  1 ) to receive the light transmitting through the SOP generator.  FIG. 22  shows one exemplary setup for using the SOP generator as a SOP analyzer or polarimeter. An output polarizer with a fixed linear polarization is placed between the output of the SOP generator and the optical detector to filter the output light from the SOP generator so the received light at the optical detector is polarized by the fixed polarizer. The power of the output from the output polarizer is measured and used to determine the SOP of the input light. 
   In this operation, the SOP generator may be used to generate the minimum 4 different polarization states for the polarizer to analyze by rotating the SOP of the input light. Hence, the 4 rotators in the SOP generator used for analyzing unknown SOP of the input light in  FIG. 22  are controlled to rotate the SOP to generate 4 different output states for the measurement. For the previous example for making 4 different polarization measurements by rotating a polarizer and using a RHC or LHC polarizer in order to determine the 4 Stockes parameters, the SOP generator in  FIG. 22  may be used to rotate the SOP of the input light instead to achieve the 4 equivalent power measurements: 1) the 4 rotators are controlled so the input SOP is not changed and is directly sent to the polarizer in front of the optical detector and the optical power after the polarizer is measured; 2) the 4 rotators are controlled to rotate the SOP by 45° and the optical power after the polarizer is measured again; 3) the 4 rotators are controlled to rotate the input SOP by 90 or −45° and the optical power after the polarizer is measured for the third time; and 4) the 4 rotators are controlled to convert the input SOP into RHC (or LHC) and measure the optical power after the polarizer. The above steps are used here to illustrate the mechanism that the SOP generator in  FIG. 22  is used to convert the input SOP into 4 different SOPs in order to get 4 different power measurements. In actual operation of the SOP generator in  FIG. 22 , 4 or more different settings for generating different output SOPs can be used to obtain different measurements. For example, if the direction of the polarizer in front of the optical detector in  FIG. 22  is aligned with the optic axis of the λ/4 plate in the SOP generator, the 4 rotators may be set to 4 different combinations in TABLE 1 that produce different output SOPs in TABLE 1 to obtain the 4 measurements. When the direction of the polarizer in front of the optical detector in  FIG. 22  is aligned at 45 degrees with respect to the optic axis of the λ/4 plate in the SOP generator, the 4 rotators may be set to 4 different combinations in TABLE 2 that produce different output SOPs in TABLE 2 to obtain the 4 measurements. 
     FIG. 23  further shows a polarimeter based on the design in  FIG. 22  where the polarizer in front of the optical detector is aligned to be parallel to the slow axis of the λ/4 plate. Assume the 4 polarization rotators  1 ,  2 ,  3 , and  4  operate with polarization rotation angles of α, β, γ, and δ, respectively, and there is no optical loss in the transmission through the polarimeter, the Mueller matrix of the polarimeter can be expressed by the following 4×4 matrix M(T): 
               M   ⁡     (   T   )       =     (         1         cos   ⁢           ⁢   2   ⁢     (     α   +   β     )     ⁢   cos   ⁢           ⁢   2   ⁢     (     γ   +   δ     )             sin   ⁢           ⁢   2   ⁢     (     α   +   β     )     ⁢   cos   ⁢           ⁢   2   ⁢     (     γ   +   δ     )             sin   ⁢           ⁢   2   ⁢     (     γ   +   δ     )               1         cos   ⁢           ⁢   2   ⁢     (     α   +   β     )     ⁢   cos   ⁢           ⁢   2   ⁢     (     γ   +   δ     )             sin   ⁢           ⁢   2   ⁢     (     α   +   β     )     ⁢   cos   ⁢           ⁢   2   ⁢     (     γ   +   δ     )             sin   ⁢           ⁢   2   ⁢     (     γ   +   δ     )               0       0       0       0           0       0       0       0         )       ,         
When the Stokes vector S=(S 0 , S 1 , S 2 , S 3 ) represents the input polarization state, then the output optical power (S 0 ′) is
 
   
     
       
         
           
             S 
             0 
             ′ 
           
           = 
           
             
               
                 1 
                 2 
               
               ⁡ 
               
                 [ 
                 
                   
                     S 
                     0 
                   
                   + 
                   
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       
                         α 
                         + 
                         β 
                       
                       ) 
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       
                         γ 
                         + 
                         δ 
                       
                       ) 
                     
                     ⁢ 
                     
                       S 
                       1 
                     
                   
                   + 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       
                         α 
                         + 
                         β 
                       
                       ) 
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       
                         γ 
                         + 
                         δ 
                       
                       ) 
                     
                     ⁢ 
                     
                       S 
                       2 
                     
                   
                   + 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       
                         γ 
                         + 
                         δ 
                       
                       ) 
                     
                     ⁢ 
                     
                       S 
                       3 
                     
                   
                 
                 ] 
               
             
             . 
           
         
       
     
   
   In the expression for the output optical power of the polarimeter, the 4 different rotation angles for the rotators appear in pairs where the rotation angles for the rotators  1  and  2  on one side of the λ/4 plate appear as a sum of (α+β) and the rotation angles for the for the rotators  3  and  5  on the other side of the λ/4 plate appear as a sum of (γ+δ). Hence, two double stage rotation angles θ and φ can be defined to represent the two sums, respectively:
 
θ=α+β, and
 
φ=γ+δ
 
In the exemplary design shown in  FIGS. 20–22 , the rotators, such as magnetooptic crystals, are assumed to have the following binary steady-state values
 
α=β=γ=δ=±22.5°
 
Under this condition, the possible combinations for the double stage rotation angles become
 
             (         θ           φ         )     =     {             45   ⁢   °               0   ⁢   °                 -   45     ⁢   °           .             
Therefore, the optical output S 0 ′, the double stage rotation angles θ and φ, and the binary values for the rotation angles of the 4 rotators can be used to show that there are total 5 different output power values for all possible combinations of θ and φ). Any 4 of such combinations yield enough information for the calculation of the input SOP.
 
   More specifically, the optical output S 0 ′ can be expressed as a function of the angles of θ and φ: 
                 S   0   ′     ⁡     (     θ   ,   φ     )       =       1   2     ⁡     [       S   0     +       S   1     ⁢   cos   ⁢           ⁢   2   ⁢   θcos   ⁢           ⁢   2   ⁢   φ     +       S   2     ⁢   sin   ⁢           ⁢   2   ⁢   θcos   ⁢           ⁢   2   ⁢   φ     +       S   3     ⁢   sin   ⁢           ⁢   2   ⁢   φ       ]         ,         
Accordingly, the following output states for the output S 0 ′ can be obtained by controlling the rotators:
 
                 S   0   ′     ⁡     (       0   ⁢   °     ,     0   ⁢   °       )       =       1   2     ⁢     (       S   0     +     S   1       )         ,     
     ⁢         S   0   ′     ⁡     (         ±   45     ⁢   °     ,     0   ⁢   °       )       =       1   2     ⁢     (       S   0     ±     S   2       )         ,   and   ,     
     ⁢         S   0   ′     ⁡     (     θ   ,       ±   45     ⁢   °       )       =       1   2     ⁢       (       S   0     ±     S   3       )     .               
Therefore, the Stockes parameters for the unknown SOP of the input light to the polarimeter can be determined as follows:
   S   0   =S   0 ′(θ,45°)+ S   0 ′(θ,−45°)= S   0 ′(45°,0°)+ S   0 ′(−45°,0°)   S   1 =2 S   0   ′−S   0 ′(45°,0°)− S   0 ′(−45°,0°)   S   2   =S   0 ′(45°,0°)− S   0 ′(−45°,0°)   S   3   =S   0 ′(θ,45°)− S   0 ′(θ,−45°) 
   In an actual implementation of the polarimeter, a control and processing unit may be used to generate control signals  1 ,  2 ,  3 , and  4  to control the rotators  1 ,  2 ,  3 , and  4 , respectively, and to process the detector outputs from the optical detector that correspond to different combinations of rotator settings for the rotators. A microprocessor or computer may be included in the control and processing unit and programmed to perform certain control and data processing operations. The Muller matrix equation is then solved based on the detector outputs to determine the SOP of the receive light. The DOP of the input light can then be determined from the SOP. The signal to noise ratio (SNR) of the input signal can also be determined based on the relation of SNR=(DOP)/(1−DOP). 
     FIG. 24  shows an exemplary fiber implementation of the polarimeter in  FIG. 23  where an input fiber is used to deliver the input light and an output fiber is used to receive the output light. Fiber optical collimators C 1  and C 2  are respectively coupled to the input to the polarimeter and the output, respectively. 
   In the above SOP generators and SOP-based polarimeters, 4 polarization rotators are used to form two pairs of rotators. To further increase the number of different SOPs of such SOP generators and polarimeters, additional pairs of rotators may be added. The quarter wave plate (QWP) may be placed between any two pairs of rotators. 
     FIG. 25  shows one example of a polarimeter with a total of 6 polarization rotators R 1 , R 2 , R 3 , R 4 , R 5 , and R 6  to form three pairs of rotators (R 1 , R 2 ), (R 3 , R 4 ), and (R 5 , R 6 ). The quarter wave plate is shown to be between the pairs (R 3 , R 4 ) and (R 5 , R 6 ). Alternatively, the quarter wave plate may be placed between the pairs (R 1 , R 2 ) and (R 3 , R 4 ). Again, assuming each rotator is configured to operate at two binary polarization rotation angles of ±22.5°, the SOP generator with the three pairs of rotators in this polarimeter can produce 6 distinctly different SOPs when the input is a linear polarization. 
   TABLE 3 is a logic table for the output SOPs of the SOP generator with the three pairs of rotators in the polarimeter in  FIG. 25  when the input light has a linear polarization that is aligned with the slow axis of the quarter wave plate. The 6 distinctly different SOPs are 4 different linear polarization states at 0, +45, −45, and +/−90 degrees, and 2 circularly polarized states in RHC and LHC. 
   
     
       
         
             
           
             
               TABLE 3 
             
           
          
             
                 
             
             
               Logic table for 6−state polarization generator 
             
             
               (0, +45, −45, +/−90, RHC, and LHC) 
             
          
         
         
             
             
             
             
             
             
             
          
             
               Rotator 
               Rotator 
               Rotator 
               Rotator 
               Rotator 
               Rotator 
               Output 
             
             
               1 
               2 
               3 
               4 
               5 
               6 
               SOP 
             
             
                 
             
          
         
         
             
             
             
             
             
             
             
          
             
               +22.5 
               −22.5 
               +22.5 
               −22.5 
               +22.5 
               −22.5 
               0 
             
             
               + 
               − 
               + 
               + 
               − 
               − 
               0 
             
             
               + 
               − 
               + 
               − 
               − 
               + 
               0 
             
             
               + 
               − 
               − 
               − 
               + 
               + 
               0 
             
             
               + 
               − 
               − 
               + 
               − 
               + 
               0 
             
             
               + 
               − 
               − 
               + 
               + 
               − 
               0 
             
             
               + 
               − 
               + 
               + 
               + 
               − 
               45 
             
             
               + 
               − 
               + 
               + 
               − 
               + 
               45 
             
             
               + 
               − 
               + 
               − 
               + 
               + 
               45 
             
             
               + 
               − 
               − 
               + 
               + 
               + 
               45 
             
             
               + 
               − 
               − 
               − 
               + 
               − 
               −45 
             
             
               + 
               − 
               − 
               − 
               − 
               + 
               −45 
             
             
               + 
               − 
               − 
               + 
               − 
               − 
               −45 
             
             
               + 
               − 
               + 
               − 
               − 
               − 
               −45 
             
             
               + 
               − 
               + 
               + 
               + 
               + 
               90 
             
             
               + 
               − 
               − 
               − 
               − 
               − 
               −90 
             
             
               − 
               + 
               + 
               − 
               + 
               − 
               0 
             
             
               − 
               + 
               + 
               + 
               − 
               − 
               0 
             
             
               − 
               + 
               + 
               − 
               − 
               + 
               0 
             
             
               − 
               + 
               − 
               − 
               + 
               + 
               0 
             
             
               − 
               + 
               − 
               + 
               − 
               + 
               0 
             
             
               − 
               + 
               − 
               + 
               + 
               − 
               0 
             
             
               − 
               + 
               + 
               + 
               + 
               − 
               45 
             
             
               − 
               + 
               + 
               + 
               − 
               + 
               45 
             
             
               − 
               + 
               + 
               − 
               + 
               + 
               45 
             
             
               − 
               + 
               − 
               + 
               + 
               + 
               45 
             
             
               − 
               + 
               − 
               − 
               + 
               − 
               −45 
             
             
               − 
               + 
               − 
               − 
               − 
               + 
               −45 
             
             
               − 
               + 
               − 
               + 
               − 
               − 
               −45 
             
             
               − 
               + 
               + 
               − 
               − 
               − 
               −45 
             
             
               − 
               + 
               + 
               + 
               + 
               + 
               90 
             
             
               − 
               + 
               − 
               − 
               − 
               − 
               −90 
             
             
               + 
               + 
               + 
               − 
               + 
               − 
               RHC 
             
             
               + 
               + 
               + 
               + 
               − 
               − 
               RHC 
             
             
               + 
               + 
               + 
               − 
               − 
               + 
               RHC 
             
             
               + 
               + 
               − 
               − 
               + 
               + 
               RHC 
             
             
               + 
               + 
               − 
               + 
               − 
               + 
               RHC 
             
             
               + 
               + 
               − 
               + 
               + 
               − 
               RHC 
             
             
               + 
               + 
               + 
               + 
               + 
               − 
               RHC 
             
             
               + 
               + 
               + 
               + 
               − 
               + 
               RHC 
             
             
               + 
               + 
               + 
               − 
               + 
               + 
               RHC 
             
             
               + 
               + 
               − 
               + 
               + 
               + 
               RHC 
             
             
               + 
               + 
               − 
               − 
               + 
               − 
               RHC 
             
             
               + 
               + 
               − 
               − 
               − 
               + 
               RHC 
             
             
               + 
               + 
               − 
               + 
               − 
               − 
               RHC 
             
             
               + 
               + 
               + 
               − 
               − 
               − 
               RHC 
             
             
               + 
               + 
               + 
               + 
               + 
               + 
               RHC 
             
             
               + 
               + 
               − 
               − 
               − 
               − 
               RHC 
             
             
               − 
               − 
               + 
               − 
               + 
               − 
               LHC 
             
             
               − 
               − 
               + 
               + 
               − 
               − 
               LHC 
             
             
               − 
               − 
               + 
               − 
               − 
               + 
               LHC 
             
             
               − 
               − 
               − 
               − 
               + 
               + 
               LHC 
             
             
               − 
               − 
               − 
               + 
               − 
               + 
               LHC 
             
             
               − 
               − 
               − 
               + 
               + 
               − 
               LHC 
             
             
               − 
               − 
               + 
               + 
               + 
               − 
               LHC 
             
             
               − 
               − 
               + 
               + 
               − 
               + 
               LHC 
             
             
               − 
               − 
               + 
               − 
               + 
               + 
               LHC 
             
             
               − 
               − 
               − 
               + 
               + 
               + 
               LHC 
             
             
               − 
               − 
               − 
               − 
               + 
               − 
               LHC 
             
             
               − 
               − 
               − 
               − 
               − 
               + 
               LHC 
             
             
               − 
               − 
               − 
               + 
               − 
               − 
               LHC 
             
             
               − 
               − 
               + 
               − 
               − 
               − 
               LHC 
             
             
               − 
               − 
               + 
               + 
               + 
               + 
               LHC 
             
             
               − 
               − 
               − 
               − 
               − 
               − 
               LHC 
             
             
                 
             
          
         
       
     
   
   Like the SOP generator with 4 rotators, the SOP generator in the polarimeter in  FIG. 25  has degenerate SOPs that are produced by different combinations of rotator settings. The rotator settings and the corresponding SOPs may be organized under the 6 different SOPs with respect to different combined rotations of the rotator pairs. Because the rotator pairs (R 1 , R 2 ) and (R 3 , R 4 ) are on the same side of the quarter wave plate, the net rotation for the first four rotators R 1 , R 2 , R 3 , and R 4  is used as an independent control parameter while the net rotation by the pair (R 5  and R 6 ) on the other side of the quarter wave plate is used as another independent control parameter. The combinations of these two net rotation parameters for the 6 distinctly different SOPs are listed in TABLE 4. 
   
     
       
         
             
           
             
               TABLE 4 
             
           
          
             
                 
             
             
               Six Different SOPs of SOP Generator in FIG. 25 
             
          
         
         
             
             
             
             
          
             
               Combined 
               Combined 
                 
                 
             
             
               rotation angle 
               rotation angle 
                 
               Orientation 
             
             
               of R5 and R6 
               of R1~R4 
               Output SOP 
               definition 
             
             
                 
             
             
               0° 
                0° 
               Linear along X 
               X axis is along 
             
             
               0° 
               45° 
               Linear along 45° 
               polarizer P, Y 
             
             
               0° 
               −45°  
               Linear along −45° 
               vertical to P, Z 
             
             
               0° 
               90° 
               Linear along Y 
               point from C2 to 
             
             
               45°  
               Arbitrary 
               LCP 
               C1 
             
             
               −45°  
               Arbitrary 
               RCP 
             
             
                 
             
          
         
       
     
   
   Similarly, the SOP generator with 4 rotators in the polarimeter in  FIG. 24  can be controlled by controlling the net rotations by the two pairs (R 1 , R 2 ) and (R 3 , R 4 ) in the listed 5 different combinations to produce the 5 SOPs. 
   
     
       
         
             
           
             
               TABLE 5 
             
           
          
             
                 
             
             
               Five Different SOPs of SOP Generator in FIG. 24 
             
          
         
         
             
             
             
             
          
             
               Combined 
               Combined 
                 
                 
             
             
               rotation angle 
               rotation angle 
                 
               Orientation 
             
             
               of R3 and R4 
               of R1 and R2 
               Output SOP 
               definition 
             
             
                 
             
             
               0° 
                0° 
               Linear along X 
               X axis is along 
             
             
               0° 
               45° 
               Linear along 45° 
               polarizer P, Y 
             
             
               0° 
               −45°  
               Linear along −45° 
               vertical to P, Z 
             
             
               45°  
               Arbitrary 
               LCP 
               point from C2 to 
             
             
               −45°  
               Arbitrary 
               RCP 
               C1 
             
             
                 
             
          
         
       
     
   
     FIG. 26  show another 6-rotator SOP generator where the quarter wave plate is placed between the first two pairs (R 1 , R 2 ) and R 3 , R 4 ).  FIG. 27  shows an example where 8 polarization rotators are used to form a SOP generator. 
   In the above examples, the position of the quarter-wave plate is shown to be between different pairs of rotators, e.g., between the third and fourth rotators. This position makes the analysis of the operation of the system intuitive. The quarter-wave plate, however, may be placed in any position in the train of 4 or more rotators, e.g., before the first rotator, after the last rotator, or any position in between. In addition, the number of rotators may be 4, 5, 6, 7, 8 and so on. Furthermore, the above binary rotation angles for each rotator may be set to values other than 22.5 degrees. For example, in order to increase the number of states, smaller angles may be used such as +/−11.125 degrees and other desired values. 
   The above exemplary 4-, 6-, and 8-rotator SOP generators are used to generate at least four distinctive SOPs for solving the Muller matrix equation for either determining the SOP of input light or measuring the polarization property of an optical device or module or an optical birefringent material. The 4-rotator SOP generator is in principle sufficient with its 4 different SOPs. However, more than 4 rotators may be used to generate additional distinctive SOPs to facilitate the measurements when there are additional uncertainties caused by non-ideal settings of various optical elements. For example, the linear polarizer used in the measurement may not be perfectly aligned with the slow or fast axis of the quarter wave plate but has an angular offset relative to the axis of the quarter wave plate. As another example, the rotators may have angular offsets from the desired angles. 
   The SOP generators with 4 or more rotators are designed in part to produce different SOPs that are distributed over the Poincare sphere to provide as much coverage of the entire sphere as possible for accurate measurements. Different SOPs are uniformly distributed over the Poinscare sphere in some implementations. The 4-rotator SOP generator provides 3 three SOPs on the equator of the Poincare sphere and 2 SOPs for the two poles where the 6-rotator SOP generator provides an additional SOP on the equator of the sphere. When more than 4 different SOPs are available, measurements may be performed for different combinations of 4 SOPs and the results from different combinations may be averaged to obtain the final result. 
   The fiber implementations of the 4-rotator design in  FIG. 24  and 6-rotator design in  FIG. 25  were tested. The input optical beam can be coupled to either of the C 1  and C 2  ports. However, each device performs different functionalities when input light beam is coupled to the device from different ports. When the input optical beam is coupled to the C 1  port, the polarizer before C 2  port allows only the polarization state projected to its passing axis to be transmitted to C 2  port. Therefore, the output optical power at the C 2  port at different rotation angles is a function of the input polarization state. This feature can be used to construct a polarization analyzer or polarimeter for measuring the SOP of the input light. On the other hand, when the input beam is coupled to the C 2  port and aligned to the transmission axis of the polarizer, the output optical beam at the C 1  port maintains a constant output power (depending on the device PDL) but the SOP is now a function of the rotation angle of the MO rotators. Due to the binary (saturation) nature of each MO rotator, the number of discrete SOPs can be generated depending on the number of rotators and the rotation angle of each rotator. In the test devices, the rotators are substantially identical with one another and are all set at ±22.5 degrees when magnetic field along ±z axis is applied. The polarizer at C 2  port can also be aligned to other angles that will generate a different set of SOP. TABLES 4 and 5 above show the output SOPs at the port C 1  when the port C 2  is used as the input port. When light enters the port C 2  in each device in  FIGS. 24 and 25  and propagates through a section of the single mode fiber after the port C 1 , the output SOP is transformed to SOPs that are different from the SOPs listed in TABLE 4 and TABLE 5 due to the birefringence of the SM fiber. However, the relative angle between different SOPs, that is, the angle between any two distinctive SOPs on the Poincare sphere, will remain the same. 
     FIG. 28  shows a testing setup for testing the 4-rotator and 6-rotator devices which are presented by a box labeled as “PSG-4S/6S.” The polarization controllers # 1  and # 2  are placed at the two sides of the device under test. A laser source, e.g., a tunable laser (Agilent 81680 TSL), may be used to generate the input light and the first polarization controller # 1  is used to control the polarization of the beam when entering the device under test. The first polarization controller # 1  is used to maximize the output optical power that occurs when the input polarization state is aligned to the internal polarizer. The second polarization controller # 2  is optional and may be used to move SOP on the Poincare sphere for easy display. A polarization analyzer, such as the Agilent 8509C lightwave polarization analyzer, is used to analyze the SOP of the light transmitted through the device under test. A 9-Volt DC power supply can be used to supply power to the MO rotators in the device under test. The control unit for the device under test may include a driver board designed for the MO rotator driving control. A personal computer (PC) may be used as the control and processing unit for the device under test. The 6-rotator device was assembled in an optical head package and mounted on the driver board for this test. The test procedures for 4-rotator and 6-rotator devices are slightly different because the test procedures for the 4-rotator device depend on how the optical head is connected to the driver board. 
   The 6-rotator device was tested as follows. Prior to the test, the tunable laser source (TLS) was turned on and warmed up (e.g., for 2 hours). Before connecting any cables, the DC power supply is set at 9V and the power supply was turned off. Next, the power cable was connected and wires corresponding to bit  1  through bit  6  for the 6 rotators were connected to a digital I/O card output block. The 6-bit TTL control signals may also be obtained from other means. After the 6-rotator device was connected, the 9V DC power supply was turned on. The default setting was that all LED indicators were on. For best SOP repeatability, it is recommended that 6-rotator device under test can be warmed up for 20 minutes. 
   A total 6 distinctive SOP states can be generated by a 6-bit digital highs and lows, as shown in the logic table below. The logic high and low of each bit can be directly verified by inspecting the corresponding LED indicator on the module board. A LED “on” represents “1” for the logic table; LED “off” represents “0” for the logic table. 
                                           Logic Table   SOP                          (000101)   State 1           (001101)   State 2           (011101)   State 3           (011100)   State 4           (111101)   State 5           (111011)   State 6                        
In the above logic table, the bit order is bit  1  to bit  6  from far left to far right. When this logic table is used, states [1, 3], [2, 5] and [4, 6] form orthogonal state pairs. The logic table presented here is not unique for controlling the 6-rotator device under test and is one of many combinations that can generate 6 distinctive states. There are 64 combinations for 6-bit binary TTL code but only 6 distinctive polarization states. Therefore, some output SOPs are degenerate or nearly degenerate among 64 combinations. A different logic table can be obtained by monitoring output polarization states with a polarization analyzer.
 
   Next, the control program and test TTL signals were launched according to the logic table. Check whether the 6 green LEDs located on the PSG-6S board are blinking when inputting TTL control signals to the module. The blinking LED indicates that logic highs (LED on) and lows (LED off) are successfully sent to the module from the controller. Otherwise check the connection to make sure that the computer and the module are correctly connected. The optical signal from the laser source is directed into the device from the proper input to the proper output because this device is unidirectional as a polarization state generator. The SOP values are then controlled according to the above logic table to measure the optical insertion loss, switching state dependent loss, and switching transient loss. 
   The insertion loss without any connector was measured during device fabrication. A polarization controller was used to align the output polarization state along the transmission axis of the polarizer P. The measured values for the insertion loss of the 4-rotator and 6-rotator devices tested at the light wavelength of 1550 nm are 0.83 dB in comparison to a theoretical value of 0.65 dB and 0.90 dB in comparison to a theoretical value of 0.75 dB, respectively. 
   The SOP dependent loss was measured by recording the optical power at different output SOP. Before the measurement, the switch time for each rotator was set at 1 second so that the a stable power reading can be obtained. The difference between the maximum and the minimum readings was used as the SOP dependent insertion loss and was 0.06 dB and 0.08 dB at the light wavelength of 1550 nm for the 4-rotator and 6-rotator devices under test, respectively. 
   In both the 4-rotator and 6-rotator devices under test, when reversing the magnetic field applied on a MO crystal in a rotator during the action of switching, there was a brief insertion loss increase when the magnet field passes the zero field point. This loss increase is often described as switching transient loss (or simply transient loss) and can be measured with a fast photodetector and an oscilloscope. The transient loss can be expressed as 
             IL   tr     =       -   10     ·     log   ⁡     (     1   -       Δ   ⁢           ⁢     V   s         V   DC         )               
where ΔV s  is the magnitude of the voltage dip during the switching, V DC  is the DC voltage output level without switching.
 
     FIG. 29  shows the measured transient loss in one MO rotator in the chart on the left and the DC voltage corresponding to the total optical signal level without switching in the chart on the right. Based on the measured single stage switching ΔVs (the peak-to-peak value of the Channel  1  in the chart on the left) and VDC (Cursor Delta in the chart on the right), the calculated transient loss is 0.37 dB for each stage. In a typical arbitrary 2-state switching, up to 5 stages can be switched, as evidenced by the switching from 000101 to 111011 in the above logic table. 
   The SOP switching times for the tested 4-rotator and 6-rotator devices were measured with a TEK210 digital oscilloscope. The switching time in each tested device included two main contributions: a switch delay of about 100 μs and a rise time of about 50 μs. 
   A SOP generator may be designed to generate distinctive polarization states uniformly distributed on the Poincare sphere and separated by 90 degrees for the angles between any two distinctive SOPs. Such polarization states allow for measurements with high accuracy. In actual devices, the SOP accuracy may be limited by a number of device limitations, e.g., the switching angle of the MO crystals. The MO crystal rotation angle is a function of the crystal thickness, the optical wavelength of light, the environment temperature, and the crystal orientation. When crystal thickness and orientation are well controlled and uniform (such as from the same fabrication lot), the absolute SOP accuracy depends mainly on the optical wavelength and environment temperature. 
     FIG. 30  shows the measured wavelength dependence of the rotation angle on the Poincare sphere for the tested 6-rotator device. The actual physical rotation angle may be one half of those measured on the Poincare sphere. Therefore, the actual slope of the MO crystal wavelength dependence is −0.0668 deg./nm, within 2% of the manufacturer supplied data (−0.068 deg./nm). 
   Another performance parameter for the SOP generators is the repeatability of the generated SOPs. The SOP generation repeatability for the tested 6-rotator device was measured by switching the device between two arbitrary SOPs repetitively. A typical switching trace between two SOPs for 100 times is shown in  FIG. 31 . The spots representing starting and ending states remain as two very clearly defined dots which indicate good SOP repeatability of the tested device.  FIG. 31  also shows that the switching from SA to SB and from SB to SA do not follow the same trace and have two different traces that are interwoven together. 
   Referring back to TABLE 5, an ideal 4-rotator device can generate 5 distinctive polarization states. In our test on the SOP coverage, all 64 binary states that were available from the driver card were used to drive both the rotators in both 4-rotator and 6-rotator devices.  FIGS. 32A and 32B  show snap shots of the Poincare sphere for the SOPs in the 4-rotator and 6-rotator devices, respectively. In  FIG. 32A , the 5 distinctive polarization states from a tested 4-rotator device are marked on the sphere. It is noticeable that near SOPs A and C, there are a few other states that are close to A and C. There is no clear explanation why these states do not overlap at the points A and C.  FIG. 32B  shows the 6 distinctive SOPs as states A–F on the Poincare sphere from a tested 6-rotator device. The states B, C, and F have small spreading, while the states A, D, and E have a few nearly degenerated states depending on the initial and final switching states. Comparing  FIGS. 32A and 32B , it is obvious that the 4-rotator device provides only partial coverage on the Poincare sphere (i.e., one half of the sphere), while the 6-rotator device provides a symmetrical coverage on the entire Poincare sphere and thus more accurate measurements. 
   The above multi-rotator SOP generators may be used for both generating distinctive SOPs and analyzing SOP of input light. In certain applications, the polarization properties of optical elements, devices, modules and birefringent materials may be measured in an optical system where a multi-rotator SOP generator (i.e., a polarization state generator or PSG) is used to generate probe light with distinctive SOPs to illuminate the device or sample under test and a SOP analyzer or polarimeter (i.e., a polarization state analyzer or PSA) using another multi-rotator SOP generator to measure the output light from the device or sample under test. Since the input SOP and the output SOP are known in this system, the polarization parameters for the device or sample under test can be obtained by solving the Muller matrix equation. In this system, and polarization state analyzer (PSA) can be used to analyze the birefringence properties of a sample. The PSG and PSA can be constructed with 4 or more pieces of Faraday rotators with +/−22.5 degree rotation angles. Other polarization-rotating mechanism may also be used. As an example, the rotators can also be constructed with liquid crystal cells. Basically, PSG can generate 4 distinctive states of polarization over the Poincare Sphere. As described above, PSA is simply a PSG which is optically reversed with the polarizer at the output end and a photodetector for receiving the light. In this design, the PSA can also generate four distinctive SOPs over the Poincare Sphere of a light beam, whose power is analyzed by a polarizer. Four power readings corresponding to the four SOPs can be used to uniquely determine the SOP of the incoming beam. 
     FIG. 33  illustrates one example of such a system for measuring a sample or an optical device. A holder is provided to hold the sample or device under test. A PSG is placed in the input optical path to control the input SOPs and an PSA is placed in the output optical path to analyze the SOP of the transmitted light. In the PSG, a linear input polarization can be used to control the input polarization. 
   Notably, when the PSG and PSA are based on the same multi-rotator design, the PSA is essentially the mirror image of the PSG. Therefore, a mirror or reflector may be used at the sample or device under test to direct the light that transmits through the sample back to the sample and the PSG in the reversed direction for the SOP detection without needing a separate PSA. Such a SOP system may be viewed as a “folded” system by folding the system in  FIG. 33 . 
   Such a folded system has a number of advantages. For example, only one PSA device, such as the 4-rotator or 6-rotator PSG, is used in the folded system and thus the system is simplified and the cost is reduced. As another example, the relative SOP errors can be significantly reduced or eliminated in a folded system in comparison with the unfolded system in  FIG. 33  because both the generator and the analyzer experience the exactly the same imperfections or offsets. Also, the folded system has easier sample placement than the unfolded system in  FIG. 33 , especially for mounting samples on a x-y translation stage. Furthermore, the probe light travels through the sample twice in the folded system and effectuates a two-fold increase in the sample interaction thickness to improve the measurement and the signal to noise ratio. The folded system also has a compact design than the unfolded system in  FIG. 33  and may be suitable for various portable applications. 
     FIGS. 34A ,  34 B,  35 , and  36  show examples of folded systems. In each example, a polarization beam splitter (PBS) is used as the input polarizer along one direction for the SOP generation and the output polarizer along an orthogonal direction for the SOP analyzing operation. In  FIG. 34A , a collimating lens is used to direct the input light into the device via the PBS and the photodetector is positioned to directly receive the reflected light from the device via the PBS. In  FIG. 34B , a second collimating lens is placed between the PBS and the photodetector to collimate the reflected light. In  FIGS. 35 and 36 , the sample under test is a coil of fiber and a third collimating lens is placed between the polarization rotators and the fiber coil for collimating both the light going into the coil and the reflected light from the coil. 
   The sample or the device under test may be measured at a single optical wavelength or at multiple optical wavelengths as illustrated in  FIG. 35 . A broadband light source is used in  FIG. 35  to produce input light at different wavelengths. Alternatively, different single-wavelength light sources may be used to produce light at different wavelengths and the beams at different wavelengths are combined and sent into the system. In detection, the output light may be spectrally separated by optical filtering, e.g., using a wavelength demultiplexer or a spectrum analyzer. Output beams at different wavelengths are then received and detected by different optical detectors. Therefore, the polarization properties of the sample or device under test at different wavelengths can be simultaneously measured. 
   The above and other folded systems described here may be used for various applications, including compact birefringence analyzers, portable sugar content analyzers for fruit, sugar cane, and kidney diseases (sugar is optically active and rotate SOP and the amount of SOP rotation relates to sugar content), and optical window birefringence analysis. 
     FIGS. 37A and 37B  show two examples of multi-wavelength polarization analyzers with 4 or more polarization rotators. Such systems may be used in WDM applications for simultaneous multichannel measurements. 
     FIG. 37A  shows a use of an optical diffraction grating and a lens to separate light at different wavelengths. The light passing through the polarizer is separated in wavelength by the diffraction grating and then is focused by a lens to different locations on a photodetector array. Analyzing the optical power in different channels can obtain the SOP, DOP, PMD information of each channel. In  FIG. 37B , the incoming light containing all different channels are separated by a WDM or dense WDM channel demultiplexer after passing through the polarizer. The optical power levels in each channel for different SOP states are then monitored and used to obtain complete information of SOP, DOP, and PMD of each channel. 
   To improve the spectrum resolution, a tunable Fabry-Perot filter may be used to filter the output of the output polarizer before the light is spectrally separated by the grating and the lens or the demultiplexer. The free spectrum range of the tunable filter may be the same as that of the channel spacing of the multiwavelength channels in the WDM or DWDM signals. For example, for a DWDM system of 100 GHz spacing, the free spectrum range (FSR) of the filter is also chosen to be 100 GHz. The resolution increases with the finesse (F) of the filter. For example, a finesse of 100 in a Fabry-Perot filter corresponds to a spectrum resolution is 1 GHz. For a finesse of 1000, the spectrum resolution is 0.1 GHz. For a 10 Gb/s signal, the bandwidth is about 10 GHz. Scanning the F-P filter across the signal spectrum and measuring the SOP of each frequency components yield the value of fiber&#39;s differential group delay (DGD) and the direction of fiber&#39;s principle state of polarization (PSP).  FIG. 38  illustrates the operations of such a multichannel analyzer. 
   In the absence of depolarization, the optical signal to noise ratio (OSNR) directly relates to DOP of each channel: OSNR=DOP/(1−DOP). Therefore, the device can be used as a performance monitor for the spectrum, OSNR, SOP, DOP, and PSP of each channel. Because of the extremely high spectral resolution, the OSNR can also be directly measured by scanning the F-P filter across the channel. The minimum detected power in each scan corresponds to the noise power p n (ν) in each channel. The signal power p s (ν) at each frequency ν is the measured power p(ν) minus the noise power p n (ν): 
   
     
       
         
           
             
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   In the absence of depolarization, the OSNR results from the DOP measurement and from the spectrum scan measurement should be identical. Therefore, a calibration factor between the two measurement can be obtained by using a short fiber with negligible DGD. 
   In the presence of PMD (depolarization), the DOP can be expressed as: 
           DOP   =         P   pol         P   pol     +     P   nonpol         =         (     1   -   δ     )     ⁢     P   s           P   s     +     P   n                 
where Ps and Pn are the signal and noise powers of a given bandwidth and δ is the depolarization factor which is 0 if the signal has no depolarization and is 1 if the signal is totally depolarized. The OSNR is related to DOP by:
 
           SNR   =         P   s     /     P   n       =     DOP     1   -   δ   -   DOP               
Therefore, with both the independent DOP and OSNR measurements, the depolarization factor can be calculated:
 δ=1 −DOP−DOP/SNR   
   The SOP generator described here can be used to replace the rotating quarter wave and polarizer assembly shown in  FIGS. 13 ,  14 , and  15  on multichannel polarimeter/polarization analyzers. Other applications of such SOP generator may also be possible. 
   The above examples of the PSG-based devices use four or more polarization rotators in combination with a quarter wave plate. The quarter wave plate, however, may be eliminated in some implementations. In other implementations, the quarter wave plate may be replaced by a wave plate with a relative phase delay between the two principal polarization different from the quarter wave delay. Just like the quarter wave plate, the substituting non-quarter wave plate may be placed in any position with respect to the polarization rotators. 
   Another implementation of the PSG-based devices uses only two polarization rotators to generate at least three polarization states, such as three linear polarizations at three different directions (e.g., at relative angles of 0°, +45°, and −45°). Therefore, two or more polarization rotators can be cascaded to generate some desired SOPs according to the techniques described in this application. 
   Only a few examples and implementations are described. However, other implementations, variations, modifications, and enhancements are possible.