Abstract:
Methods and systems for higher-order PMD compensation are implemented by developing an effective mathematical model and applying economical design techniques to the model. By assuming a constant precession rate for a narrow band of frequencies in an optical signal, a simplified model of a higher-order PMD compensator can be derived. The model can be used produce an economical compensator by making multiple uses of selected optical components.

Description:
This nonprovisional application is a continuation and claims the benefit of U.S. application Ser. No. 11/701,730, filed on Feb. 2, 2007 now U.S. Pat. No. 7,333,728, which is a continuation and claims the benefit of U.S. application Ser. No. 11/240,066, filed on Sep. 30, 2005 now U.S. Pat. No. 7,203,423, which is a continuation and claims the benefit of U.S. application Ser. No. 10/657,873, filed on Sep. 9, 2003, now U.S. Pat. No. 6,980,744, which is a continuation of and claims priority to U.S. application Ser. No. 09/650,289, entitled “METHODS AND SYSTEMS FOR POLARIZATION MODE DISPERSION COMPENSATION,” filed on Aug. 29, 2000, now U.S. Pat. No. 6,674,972 which claims the benefit of the U.S. Provisional Application No. 60/151,959, entitled “A SIMPLE COMPENSATOR FOR HIGH-ORDER POLARIZATION MODE DISPERSION EFFECTS,” filed on Sep. 1, 1999. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     The invention relates to methods and systems that compensate for polarization mode dispersion. 
     2. Description of Related Art 
     As data rates transmitted over optical conduits such as long single-mode optical fibers increase, the effects of polarization mode dispersion (PMD) become increasingly important. PMD is a form of signal distortion and can be caused by subtle physical defects in an optical fiber giving rise to birefringence of the optical fibers. The effects of this phenomenon are often characterized into first-order PMD effects and higher-order PMD effects. 
     First-order PMD refers to the time dispersal of various components of an optical signal that is essentially constant for all frequencies in a narrow band of optical frequencies. First-order PMD is equivalent to splitting a transmitted optical signal into two orthogonal polarization components along a birefringence axis of an optical fiber, and delaying one of the polarization components relative to the other, to produce multiple images of the optical signal. 
     Second-order, or higher-order PMD, refers to temporal dispersal that, unlike first-order PMD, varies a function of frequency and can result when the axis of birefringence varies along the length of an optical fiber. While the use of a PMD compensator can mitigate the deleterious effects of PMD, the vast majority of PMD compensators are designed for first-order PMD only. Accordingly, there is a need for new technology to provide better PMD compensation. 
     SUMMARY OF THE INVENTION 
     The invention provides methods and systems for PMD compensation using an economical number of components. The technique includes passing an optical signal through a frequency-dependent polarization rotator, then through a first-order PMD compensation device, then again through a frequency-dependent polarization rotator, which has a fixed relation to the first frequency-dependent polarization mentioned above. This combination of elements allows compensation for certain high-order features of PMD. Further economy can be gained by applying economical optical design concepts such as selectively reusing common optical components in the compensation model. 
     Other features and advantages of the present invention will be described below or will become apparent from the accompanying drawings and from the detailed description which follows. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention is described in detail with regard to the following figures, wherein like numbers reference like elements, and wherein: 
         FIG. 1  is a block diagram of an exemplary optical transmission system; 
         FIG. 2  is an exemplary representation of changing polarization state of a polarized optical signal transmitted through an optical conduit; 
         FIG. 3  is an exemplary diagram of an imperfect optical conduit that can give rise to PMD; 
         FIG. 4  is a block diagram of an exemplary PMD compensator; 
         FIG. 5  is a flowchart outlining an exemplary operation of a method for compensating for PMD; and 
         FIG. 6  is a flowchart outlining an exemplary operation for adjusting the PMD compensator of  FIG. 4 . 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     As data rates over optical conduits such as single-mode optical fibers increase, the effects of polarization mode dispersion (PMD) become increasingly important. While the use of PMD compensators can mitigate the effects of PMD, the vast majority of PMD compensators only address first-order PMD. 
     The effect of first-order PMD is equivalent to splitting a transmitted optical signal into two orthogonal polarization components, along a birefringence axis of an optical fiber, and delaying one of the polarization components relative to the other, to produce multiple images of the transmitted optical signal. For polarized optical sources, as is usually the case, the two polarization components may differ in their magnitude, but generally have identical shape. An optical fiber whose axis of birefringence does not change throughout its length displays only first-order PMD effects. 
     However, when the axis of birefringence varies along the length of the optical fiber, higher-order PMD effects can appear. A fiber which supports higher orders of PMD can be pictured as a birefrigent element where the birefringence axes are dependent upon optical frequency. 
     Unfortunately, higher-order PMD compensators typically require a large number of controls to address the various frequency-dependent considerations of PMD. However, by approximating the effect of high-order PMD as a pure constant rate precession, in Stokes space, of the principal axes, a PMD compensator can be designed that compensates for both first- and higher-order dispersion based on the simplified model. Thus, economical compensators can be designed. 
       FIG. 1  shows an exemplary block diagram of an optical transmission system  100 . The system  100  includes an optical source  110 , an optical compensator  120  and an optical receiver  130 . The optical compensator  120  can receive an optical signal from the optical source  110  via conduit  112 , process the optical signal to compensate for polarization mode dispersion (PMD), then provide the compensated optical signal to the optical receiver  130  via conduit  122 . 
     The optical source  110  and the optical receiver  130  can be any one of a number of different types of optical sources and receiving devices, such as a computer or a storage device with optical transceivers and the like. It should be appreciated that the optical source  110  and receiver  130  can be any of a number of different types of sources and receivers, or any combination of software and hardware of capable of generating/receiving, relaying or recalling from storage any information capable of being transmitted/received in an optical signal without departing from the spirit and scope of the present invention. 
     The optical conduits  112  and  122  can be any known or later developed device or system for connecting the optical source  110  to the optical compensator  120  or the optical receiver  130  to the optical compensator  120 . Such devices include any number of optical conduits capable of propagating an optical signal, such as fiber optic cables including a single-mode fiber optic cables and the like. However, it should be appreciated that the optical conduits  112  and  122  can be any optical conduit capability of propagating an optical signal without departing from the spirit and scope of the present invention. 
       FIG. 2  is an exemplary representation of an elliptical, or time-varying, polarized optical signal  200  propagating through an optical conduit along a distance axis  230 . The exemplary conduit has a fixed linear birefringence due to which the vertical axis  210  and the horizontal axis  220  of the signal  200  acquire a phase difference as the optical signal  200  propagates along the distance axis  230 . Due to this acquired phase difference, the polarization state of the optical signal  200  changes as it propagates along the distance axis  230 , as shown in  FIG. 2 . 
     The exemplary optical signal  200  has a first vertical polarization state  240 . As the optical signal  200  propagates along the distance axis  230 , the polarization of the optical signal  200  changes to an elliptical polarization state  242  with its major axis aligned along the vertical axis  210 . As the optical signal  200  further propagates along axis  230 , the signal&#39;s polarization state changes to a circular polarization state  244 . Next, the polarization of the optical signal  200  changes to another elliptical phase  246 , but with its major axis aligned along the horizontal axis  220 . Then, as the optical signal  200  continues to propagate along the distance axis  230 , the polarization changes to a purely horizontal phase  248 . 
     As the optical signal  200  continues to propagate along the distance axis  230 , the polarization changes again to an elliptical phase  250  with its major axis aligned along the horizontal axis  220 , then to a circular polarization state  252 , then again to an elliptical polarization state  254  with its major axis aligned along the vertical axis  210 , then to a purely vertical polarization state  256 . The polarization state continues to oscillate between polarization states in this fashion as it continues to propagate along the distance axis  230 . 
     The rate at which the polarization state oscillates varies as a function of a variety of factors, including the frequency of an optical signal. Generally, the shorter the wavelength of light, the greater the oscillation rate. For an optical signal having a variety of frequency components propagating along an optical conduit, the oscillation rate for each frequency can vary and, thus, the instantaneous polarization state of the different frequencies can differ at any point along the conduit. 
       FIG. 3  shows a cross section of a non-circular optical conduit  300  capable of propagating an optical signal. The exemplary optical conduit  300  has a fast-axis  310  and a slow-axis  320  that are orthogonal to the direction of propagation of the optical signal. The two axes  310  and  320  define a principle plane having the property that light of a given wavelength will propagate faster as its polarization mode aligns with the fast-axis  310 , and will propagate slower as the polarization mode aligns with the slow-axis  320 . For an optical signal propagating with any other state of polarization than purely along the fast- or slow-axis  310  or  320 , the optical signal is resolved into its principal components along the fast and slow axis, and the two components are temporally dispersed into separate images of the original optical signal. 
     As a practical matter, it is difficult to make an optical conduit that does not have birefringence because optical conduits are rarely perfectly manufactured. If a defect of an optical conduit is constant throughout the length of the conduit, then the resulting PMD is limited to first-order PMD. However, if the dimensions vary along the length of an optical conduit, the birefringence of the optical conduit at any point can vary accordingly. As mentioned above, the oscillation rate of the polarization for different frequencies of light in an optical signal can vary with the frequency of light and, thus, each optical frequency can have a different polarization state at any point. Therefore, as a multi-frequency optical signal propagates through an optical conduit having varying birefrigent properties, each optical frequency can be resolved into different proportions of fast and slow components at any particular point along the length of the optical conduit, resulting in high-order PMD. 
       FIG. 4  is a diagram of an exemplary optical compensator  120  that can compensate for first- and higher-order PMD, with higher-order compensation including at least accounting for the fixed rate precession (with optical frequency) in Stokes space of the axis of input to output polarization rotation, which results from the accumulated effects of the birefringence of an optical conduit such as a fiber-optic cable. The optical compensator  120  has a first polarization rotator  410 , a circulator  420 , a frequency-dependent polarization state rotator  430 , a Faraday rotator  470 , a polarization-sensitive optical splitter/combiner  480 , a fixed mirror  490  and an adjustable mirror  492 . The frequency-dependent polarization state rotator  430  further has second and third polarization rotators  440  and  460  and an interferometer  450  with a first interferometer splitter/combiner  442 , a second interferometer splitter/combiner  462 , a fixed path  452  and a variable path  454  with an adjustable mirror  456 . The first polarization rotator  410  is connected to the circulator  420  via optical conduit  412 , the circulator  420  is connected to the frequency-dependent polarization state rotator  430  via optical conduit  422 , the frequency-dependent rotator  430  is coupled to the Faraday rotator  470  via optical conduit  432 , and the Faraday rotator  470  is coupled to the polarization-sensitive optical splitter/combiner  480  via optical conduit  472 . The polarization-sensitive optical splitter/combiner  480  is coupled to the fixed mirror  490  via conduit  484  and to the adjustable mirror  492  via conduit  482 . 
     The exemplary optical compensator  120  takes advantage of the fact that, within a limited bandwidth of optical frequencies, the rotation axis defined by the transmission matrix of an optical conduit tends to perform precession at a nearly constant rate. By discounting the differing precession rates of the various frequency components of an optical signal, a higher-order PMD compensator such as the optical compensator  120  of  FIG. 4  can be described by a Jones matrix given by equation (1) below: 
                     M   ⁡     (   ω   )       =       R   ⁡     (   θ   )       ⁢       R   ⁡     (     ω   ⁢           ⁢   K     )       ⁡     [           exp   ⁡     (     ⅈ   ⁢           ⁢   ω   ⁢           ⁢     τ   /   2       )           0           0         exp   ⁡     (       -   ⅈω     ⁢           ⁢     τ   /   2       )             ]       ⁢       R     -   1       ⁡     (     ω   ⁢           ⁢   K     )                 (   1   )               
where ω denotes the frequency deviation from the central angular frequency of the optical signal, R denotes an operator which is a unitary Jones matrix whose effect is equivalent to rotation in Stokes space and R(ωK) denotes a polarization rotation that varies as a function of frequency ω. The argument of the operator R is a three-dimensional Stokes vector whose orientation is the axis of rotation and whose magnitude is the rotation angle. Variable τ is the differential group delay for the first-order PMD compensator and can be controlled by the first optical delay associated with the variable mirror  492 . The magnitude of the three-dimensional vector K, or K, is the precession rate of the rotation axis defined by M, and can be controlled by a second optical delay associated with the variable mirror  456 . R(θ) denotes a frequency-independent polarization rotation of the optical signal that is incident to the design of the optical compensator  120 .
 
     In operation, the first polarization rotator  410  performs the function R(θ) in equation (1), which is the equivalent of performing a frequency-independent rotation in Stokes space, the group delay of the 2-by-2 Jones matrix in equation (1) is implemented using the Faraday rotator  470 , beam splitter/combiner  480  and mirrors  490  and  492  and the functions R(ωK) and R −1 (ωK), which are the equivalent of performing frequency-dependent rotations in Stokes space, are implemented using the interferometer  450  and the second and third polarization rotators  440  and  460 . While the exemplary compensator  120  performs both rotations R(ωK) and R −1 (ωK) using a single set of devices  440 ,  450  and  460 , it should be appreciated that rotations R(ωK) and R −1 (ωK) can be implemented using separate sets of interferometers and polarization rotators. 
     In operation, the optical signal is received by the first polarization rotator  410  via the optical conduit  112 . The first polarization rotator  410  then rotates the polarization angle of the optical signal in a frequency-independent fashion R(θ) and provides the rotated optical signal to the circulator  420  via the conduit  412 . The circulator  420  receives the optical signal from the first polarization rotator  410  and routes the signal to the second polarization rotator  440  of the frequency-dependent polarization state rotator  430  via the conduit  422 . 
     The circulator  420  of the exemplary optical compensator  120  can be any of a number of known or later developed species of optical circulators capable of routing signals entering from the conduit  412  to the conduit  422  and routing signals entering from the conduit  412  to the conduit  422  without departing from the spirit and scope of the present invention. 
     The frequency-dependent polarization state rotator  430  then performs a frequency-dependent rotation R(ωK) as the optical signal propagates from the second polarization rotator  440  through the interferometer  450  and to the third polarization rotator  460 . The optical signal is then provided to the Faraday rotator  470  via the conduit  432 . 
     The second and third polarization rotators  440  and  460  of the exemplary optical compensator  120  can perform complementary frequency-independent rotations. For example, if the second polarization rotator  440  is set to rotate the polarization vector in Stokes space by angle θ K  around some axis, the third polarization rotator  460  can be set to rotate the polarization vector of the optical signal by angle −θ K  around the same axis. 
     The first, second and third polarization rotators  410 ,  440  and  460  of the exemplary optical compensator  120  are adjustable polarization controllers capable of rotating the polarization state of an optical signal. Examples of polarization rotators include fiber squeezers, a combination of λ/2 and λ/4 optical delay components, optical fiber loop based Lefevre polarization controllers, Faraday rotators, Babinet-Soleil compensators. However, it should be appreciated that the polarization rotators  410 ,  440  and  460  can be any device capable of rotating the polarization state of an optical signal without departing from the spirit and scope of the present invention. 
     The interferometer  450  of the exemplary optical compensator  120  may be a Mach-Zehnder interferometer with an adjustable mirror capable of causing delay K. However, the interferometer  450  can also be any device capable that can receive an optical signal, split the optical signal into multiple images and cause the optical signal images to adjustably interfere with each other without departing from the spirit and scope of the present invention. 
     The Faraday rotator  470  receives the optical signal, performs a π/2 frequency-independent polarization state rotation around the circular axis in Stokes space on the optical signal, then provides the rotated optical signal to the polarization-sensitive optical splitter/combiner  480  via conduit  472 . The Faraday rotator  470  of the exemplary optical compensator  120  is any device performing a π/2 rotation around the circular axis in Stokes space and for which the direction of rotation is identical for two counter-propagating beams. The Faraday rotator  470  can also be any device capable of rotating the polarization mode of an optical signal, including an adjustable polarization rotator such as the polarization controllers of devices  410 ,  440  and  460 . Alternatively, the Faraday rotator  470  can any other known or later developed device capable of rotating the polarization angle of an optical signal without departing from the spirit and scope of the present invention. 
     The polarization-sensitive optical splitter/combiner  480  splits the optical signal into orthogonal components, directs the slow components of the optical signal to the fixed mirror  490  via conduit  484  and directs the fast components of the optical signal to the adjustable mirror  492  via conduit  482 . In operation, the first polarization controller  410  can be adjusted such that the splitter/combiner  480  provides slower optical components to the fixed mirror  490  and faster optical components to the adjustable mirror  492 . The polarization-sensitive optical splitter/combiner  480 , as well as the interferometer splitter/combiners  442  and  462 , of the exemplary optical compensator  120  can be any known or later developed device capable of splitting an optical signal as a function of the polarization angles of the different components of the optical signal without departing from the spirit and scope of the present invention. 
     The slow and fast optical components are reflected from mirrors  490  and  492  respectively, recombined in the optical splitter/combiner  480  and redirected back to the Faraday rotator  470 . The fixed mirror  490  reflects an optical signal received from the splitter/combiner  480  back to the splitter/combiner  480  along a constant path. The adjustable mirror  492  also reflects an optical signal received from the splitter/combiner  480  back to the splitter/combiner  480 ; however, the adjustable mirror  492  can be adjusted such that the path between the splitter/combiner  480  and the adjustable mirror  492  is a different length than the path between the splitter/combiner  480  and the fixed mirror  490 . The resulting effect is to perform a group delay τ on the signals traversing the longer path with respect to the signals traversing the shorter path. 
     In various exemplary embodiments, as discussed above, the faster optical components can be directed to the adjustable mirror  492 . By adjusting the delay τ/2 of the adjustable mirror  492 , the total additional group delay τ caused by the longer path length can reduce the time dispersion between the slow and fast optical components. In other exemplary embodiments, it should be appreciated that the splitter/combiner  480  and mirrors  490  and  492  can also be operated in an opposite way, where the fast component is directed to the fixed mirror  490 , the slow component is directed to adjustable mirror  492  and the value of τ is made negative. 
     It should further be appreciated that the mirrors  490  and  492  of the exemplary optical compensator  120  can be any known or later developed device that can reflect a polarized optical signal without departing from the spirit and scope of the present invention. 
     As the optical signal propagates back through the Faraday rotator  470 , the optical signal undergoes a second π/2 polarization rotation around the circular axis and the shifted optical signal is provided back to the third polarization rotator  460  via conduit  432 . As the optical signal propagates from the third polarization rotator  460  to the interferometer  450  and back to the second polarization rotator  440 , the frequency-dependent polarization state rotator  430  performs a second frequency-dependent rotation R −1 (ωK) on the optical signal. The second polarization rotator  440  then provides the signal to the circulator  420 , which routes the optical signal to the conduit  122 . 
       FIG. 5  depicts a flowchart outlining an exemplary method for compensating optical signals having first- and higher-order PMD according to the present invention. The operation starts in step  500  and continues to step  510  where an optical signal is received. Next, in step  520 , a frequency-independent rotation R(θ) of the optical signal is performed. While the exemplary technique uses an adjustable polarization controller, it should be appreciated that the polarization angle of the optical signal can be rotated using any device capable of performing a frequency-independent polarization angle rotation of the optical signal without departing from the spirit and scope of the present invention. The process continues to step  530 . 
     In step  530 , a first frequency-dependent rotation of the polarization angle of the optical signal R(ωK) is performed. While the exemplary technique uses two adjustable polarization controllers in conjunction with an interferometer to perform the frequency-dependent rotation, it should be appreciated that any device capable of performing a frequency-dependent rotation of the polarization angle of an optical signal can be used without departing from the spirit and scope of the present invention. The process continues to step  540 . 
     In step  540 , a group delay function is performed, effectively removing the first-order PMD of the optical signal. While the exemplary first-order compensation technique uses a fixed angle polarization angle rotator such as a Faraday rotator, a phase-sensitive beam splitter and a plurality of mirrors, it should be appreciated that any device or combination of devices that can receive an optical signal having first-order PMD, perform a group delay function or otherwise compensate for the first-order PMD and then provide the compensated signal to another device can be used without departing from the spirit and scope of the present invention. The process continues to step  550 . 
     In step  550 , a second frequency-dependent rotation of the polarization angle of the optical signal R −1 (ωK) is performed. The exemplary second frequency-dependent rotation uses the same components used in step  530  but uses the components in an opposite order and direction of step  530 . However, it should be appreciated that the second frequency-dependent rotation R −1 (ωK) can be performed by other components or some subset of the components used in step  530  without departing from the spirit and scope of the present invention. Next, in step  560 , the compensated optical signal is exported and the process continues to step  570  where the operation stops. 
       FIG. 6  is a flow chart outlining a method for adjusting the optical compensator  120  of  FIG. 4 . The optical compensator  120  has a delay τ and a first polarization device that can compensate for first-order PMD of an optical signal and a delay K associated with an interferometer and a second and third polarization rotation device that can adjust the frequency-dependent rotations R(ωK) and R −1 (ωK). 
     The operation starts in step  600  and continues to step  610  where the interferometer delay K is set to zero and the second and third polarization rotation devices are set to complimentary angles θ and −θ. By setting delay K to zero and the polarization rotation devices accordingly, the frequency-dependent transform R(ωK) is reduced to R(ωK)=I, with I being the identity operator, thus causing the frequency-dependent transform to pass signals unaffected. Next, in step  620 , a group delay that can compensate for first-order PMD is adjusted by manipulating the first polarization rotator and delay τ. Adjustment continues until the first-order PMD of the optical signal is substantially removed. 
     It should be appreciated that it can be advantageous to de-couple the process of removing first-order PMD and high-order PMD, i.e., subsequent adjustments directed to compensating for high-order PMD will not require revisiting either of steps  610  and  620 . Accordingly, in various exemplary embodiments, the process of removing high-order PMD can become de-coupled from the process of removing first-order PMD by strategically adjusting the various delays and polarization rotation devices. For example, de-coupling first-order and high-order PMD can be accomplished by fine-tuning delay K while simultaneously monitoring the polarization at the input and output of the frequency-dependent transform R(ωK) stage. The operation continues to step  630 . 
     In step  630 , second-order, or higher-order, PMD compensation is adjusted by manipulating the second and third polarization rotators and delay K. In the exemplary method, the second and third polarization rotators can be set to rotate the polarization angle of an optical signal at opposite angles θ K  and −θ K . The effect of the combination of the second and third polarization controllers used in conjunction with the interferometer is to cause light passing in one direction from the second polarization controller to the interferometer then to the third polarization controller to have a transformation R(ωK) and also cause an optical signal propagating in the reverse direction from the third polarization rotator through the interferometer to the second polarization rotator to have a transformation R −1 (ωK). Adjustment continues until the second-order PMD is substantially removed from the optical signal and control continues to step  640  where the operation stops. 
     It should be understood that each of the components shown in  FIG. 4  can be implemented as portions of a larger suitably structured device. Alternatively, each of the components shown in  FIG. 4  can be implemented as physically distinct components or discrete elements. 
     Furthermore, various components of the optical compensator  120  can be rearranged and combined without departing from the spirit and scope of the present invention. For example, the circulator  420  can precede the first polarization rotator  410 . For this case, the optical compensator  420  causes an extra frequency-independent phase shift according to equation (2):
 
 M ′(ω)= M (ω) R (θ)  (2)
 
where R(θ) is the additional polarization angle shift incurred as the optical signal propagates through the first polarization controller  410  a second time and M(ω) is the transform of Equation (1). Additionally, the first and second polarization rotator  410  and  440  can be combined into a single element. While the combination of rotator  410  and  440  can cause a loss in a degree of freedom and make compensation more difficult, the same transform as expressed in equation (2) can still be performed. It should be understood that any combination of hardware and software capable of implementing the flowchart of  FIG. 5  or equations (1) or (2) can be used without departing from the spirit and scope of the present invention.
 
     While this invention has been described in conjunction with the specific embodiments thereof, it is evident that many alternatives, modifications, and variations will be apparent to those skilled in the art. Accordingly, preferred embodiments of the invention as set forth herein are intended to be illustrated and not limiting. Thus, there are changes that may be made without departing from the spirit and scope of the invention.