Abstract:
A method includes determining spectral interference in real time on an optical signal by an optical path, the spectral interference being indicative of polarization mode dispersion by the optical path, and imposing optical pulses with a phase opposite to the spectral interference on the optical signal. Preferably, the imposing step comprises altering the amplitude or phase of a signal indicative of the spectral interference with an active element. The active element is preferably an acousto-optic modulator.

Description:
[0001]     This application claims the benefit of U.S. Provisional Application No. 60/804,668, entitled “All Order PMD Compensation Using Spectral Interference and Pulse Shaping”, filed on Jun. 14, 2006, the contents of which is incorporated by reference herein. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     The present invention relates generally to optical communications, and, more particularly, to all order polarization mode dispersion compensation using spectral interference and pulse shaping.  
         [0003]     Polarization mode dispersion (PMD) is an optical phenomenon that affects signal quality during optical transmission. During transmission in standard optical fibers, the optical signal undergoes changes in polarization due to uncontrollable physical changes in the optical fiber. Because light travels at slightly different velocities for different polarizations, the pulse shape is broadened over time and distorted. This pulse broadening phenomena is referred to as the PMD. Quantitatively, PMD is defined as the wavelength-averaged value of the differential group delay (DGD) between the propagation times at two orthogonal axes (planes) for the polarization.  
         [0004]     PMD is usually caused by environmental conditions such as physical stress, temperature variation and fiber imperfections. It is dynamic and varies over time. The individual factors that cause PMD cannot be measured or even observed in isolation, the phenomenon must be viewed as a constantly changing, unstable stochastic process. There are no known practical ways of eliminating its effects entirely.  
         [0005]     At lower bit rate transmissions, PMD is not an important factor and is often neglected. However as the transport speed increases above 10 Gb/s, particularly at 40 Gb/s and 160 Gb/s, the impairment from PMD becomes a serious issue due to the short bit period and it limits the transmission distance. At these high bit rates, higher order PMDs (such as the second-order PMD, which is the variation of first order PMD with wavelength/frequency) also become important factors in system degradation. As the demand of network traffic bandwidth grows and DWDM network transmission bit rate increases, compensation for first order and higher order PMD has attracted strong research interests.  
         [0006]     In recent years a variety of schemes have been proposed to counter the effect of PMD. Electronic dispersion compensation (EDC) can be used successfully to compensate for pulse distortion caused by many factors, including PMD, but EDC cannot handle high transmission rates when the bandwidth becomes large. In order to deal with PMD at high rates, some type of hardware compensation techniques have to be employed and are currently under investigation. Many compensating schemes are based on feedback loops and complex algorithms to optimize the control parameters. These schemes have the advantage that they do not require the knowledge of the PMD parameters. They are based on monitoring the degree of polarization and, using a feedback loop, changing the state of polarization in order to minimize an error signal. However, they are cumbersome and less practical for fast live compensation, because their algorithms rely on random guesses and iterative loops. More promising schemes are based on feed forward compensators, because they are faster and easier to implement. However, they require the knowledge of the fiber&#39;s PMD parameters at any given time. Measuring the state of polarization (SOP) and then using dispersive elements to compensate for PMD has been considered, but measuring SOP can prove to be difficult and time consuming, making a challenge for using these devices for live compensation.  
         [0007]     Accordingly, there is a need for practical technique for fast and live compensation for polarization mode dispersion in high bit rate transmissions.  
       SUMMARY OF THE INVENTION  
       [0008]     In accordance with the invention, a method includes determining spectral interference in real time on an optical signal by an optical path, the spectral interference being indicative of polarization mode dispersion by the optical path, and imposing optical pulses with a phase opposite to the spectral interference on the optical signal. Preferably, the imposing step includes altering the amplitude or phase of a signal indicative of the spectral interference with an active element such as acousto-optic modulator.  
         [0009]     In another aspect of the invention, a method includes compensating for distortion by an optical path on an optical signal by imposing a real time phase spectrum opposing the spectral interference indicative of the distortion by the optical path. In a preferred embodiment, the real time phase spectrum opposing the spectral interference is provided by a pulse shaper employing active amplitude or active phase changing at each frequency component of the spectral interference.  
         [0010]     In yet another aspect of the invention, an apparatus includes a pulse shaper in an optical path for imposing an opposing optical signal for compensating for distortion by the optical path, and a feed forward loop for determining phase spectrum of the distortion in real time for influencing the pulse shaper. Preferably, the pulse shaper includes an acousto-optic modulator for varying a phase or amplitude of a signal in accordance with the phase spectrum of the distortion. 
     
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0011]     These and other advantages of the invention will be apparent to those of ordinary skill in the art by reference to the following detailed description and the accompanying drawings.  
         [0012]      FIG. 1  illustrates the random birefringent fiber as a stack of randomly oriented waveplates;  
         [0013]      FIG. 2  is a schematic showing a Mach-Zender Interferometer to illustrate the phases along x and y that lead to spectral modulation due to interference;  
         [0014]      FIG. 3  is a graph showing the spectral interference obtained from a Mach-Zender interferometer;  
         [0015]      FIG. 4  is a schematic of a pulse shaper with AOM in a 4-f geometry;  
         [0016]      FIG. 5  is a schematic of an all-order compensator using feed-forward pulse shaper, in accordance with the invention;  
         [0017]      FIG. 6  is a schematic of an alternate embodiment of an all order PMD compensation scheme, in accordance with the invention;  
         [0018]      FIG. 7  depicts spectral interference patterns with 0, 10, 20, 30 and 40 picoseconds PMD delays;  
         [0019]      FIG. 8  depicts linear phase as a function of first order PMD;  
         [0020]      FIG. 9  depicts the spectrum of a wave unaffected by pulse shaping; and  
         [0021]      FIG. 10  shows various examples of spectrum manipulation via pulse shaping on the wave shown in  FIG. 9 . 
     
    
     DETAILED DESCRIPTION  
       [0022]     The inventive method of compensating for polarization mode dispersion PMD is based on a live measurement of the polarization dispersion using spectral interference, and compensation for the dispersion using pulse shaping.  
         [0023]     Referring to  FIG. 1 , there is shown a theoretical model  100  for polarization mode dispersion. When considering the propagation through single-mode fibers, although they are supposed to be single mode, in practice the optical fibers are anisotropic and support two modes of propagation distinguished by polarization. Because of the optical birefringence, the two modes travel with different group velocities. The random change of the birefringence leads to a random coupling between the modes. This is the basis of PMD, which results in pulse distortion and limits the transmission capacity of the optical fiber. It is useful for understanding the invention to consider the optical fiber as a series of successive optical waveplates  101   1 ,  101   2 ,  101   3  through 101 n  with their principal axis rotated one from another. At any given moment the waveplates have random orientation. Furthermore, they change their orientation on sub-millisecond time scale, mostly due to environmental changes such as temperature, stress, vibrations, etc.  
         [0024]     From the birefringence point of view, the fiber can be considered as a stack of the N waveplates 101 1−n  as shown in  FIG. 1 . Each waveplate is characterized by a differential time delay between its fast and slow axis.  
         [0025]     Choosing the x and y axis as defined by the linearly polarized (along x, for example) input beam. After propagating through the waveplate system  100 , the output electric field will be given by 
 
 E (ω)=| E   0 (ω)|[ {right arrow over (x)}a (ω)+ {right arrow over (y)}b (ω)],   1 
 
         [0026]     where a(ω) and b(ω) are complex coefficients which tell how much phase has been acquired along the respective axis. The “a” and “b” coefficients are wavelength dependent, and they also vary in time in a random fashion. Because of the birefringence, the phase changes are asymmetric, and this leads to the pulse distortion. This is the main cause of signal loss due to polarization mode dispersion PMD.  
         [0027]     Given the waveplate model of  FIG. 1 , if the “x” and “y” axis are considered independently, the phase accumulated in each of them is independent of the other, and spectral and/or power measurements along any or both of these axis will not tell us about the pulse distortion. However, if the electric field along the “x” axis is allowed to interfere with the electric field along the “y” axis, the phase difference between the two electric fields will be seen in the interference pattern. This spectral interference, i.e., the spectrum of the interference term, gives us the spectrum of the phase difference between the two channels, “x” and “y”. An amplitude measurement of the interference term will give us the phase difference, hence the birefringence, between “x” and “y” for every wavelength within the pulse&#39;s bandwidth.  
         [0028]     To understand how the spectral interference gives us the phase spectrum, consider two orthogonal axis x and y, and two arms of a Mach-Zender interferometer (A and B) as depicted in the schematic  200  in  FIG. 2  This interferometer&#39;s configuration consists of two beam splitters  203 ,  213  and two completely reflective mirrors  207 ,  209 . The source beam  201  depicted as a electric field wave “E”  202  with “x” and “y” axis components is split into paths as waves E (B)    204  and E (A)    210 .  
         [0029]     In one arm the phase along the x-axis is modulated by  211 , and in the other one the phase along the y-axis is modulated by  205 . The power spectrum is denoted with S(ω). Looking at the combination of the electric fields  214 ,  215  coming from the two paths A and B of the interferometer, it can be seen that the dispersive difference in phase will lead to a modulation in spectra as follows: 
 
 S=S   (A)   +S   (B) +2 √{square root over (S x   (A) S x   (B) )}  cos(φ x )−2 √{square root over (S y   (A) S y   (B) )}  cos(φ y )   (2) 
 
         [0030]     By appropriately choosing the orthogonal axis, one can enhance the interference term in Eq. (2). This can be done, for example, by placing a rotating polarizer before the optical spectrum analyzer. Referring to the graph  300  of  FIG. 3 , there is shown an example of a spectral interference obtained with a setup similar to that of  FIG. 2 .  
         [0031]     The measured power spectrum shown by line  301  is given by S=S (A)+S   (B)  which is the case when no phase has been introduced in either arm of the interferometer. As soon as the phase modulators  205 ,  211  introduce some phase difference between the arms of the interferometer, the spectrum analyzer  216  sees a spectrum that is modulated in frequency, shown by the line  305 .  
         [0032]     A spectrum of polarization changes can be obtained from the spectral interference a spectrum of polarization changes. An example of inferring polarization mode dispersion PMD from spectral interference has been shown, where the PMD was related to the transmission spectrum measured through an analyzer. There is a simple relationship between the spectral interference and the polarization change, given by:  
             P   =         2   ⁢                  S   x     (   A   )       ⁢     S   x     (   B   )           ⁢     cos   ⁡     (       ϕ   x     ⁡     (   ω   )       )         -           S   y     (   A   )       ⁢     S   y     (   B   )           ⁢     cos   ⁡     (       ϕ   y     ⁡     (   ω   )       )                  S     .             (   3   )             
 
         [0033]     Hence, using Eq. (3), one can infer the polarization change as a function of frequency simply by measuring the spectral interference between the two channels, x and y. In other words, by defining two orthogonal axis for the input, and recording the spectrum of the output through a properly placed polarizer, the spectrum of the phase difference between the two axis, i.e., the birefringence spectrum, can be measured. This way, the spectral interference gives us a measure of the polarization change as a function of wavelength, which is really all the information we need to be able to compensate for the PMD. Knowing how much phase has been accumulated at any frequency, allows knowing exactly what the polarization mode dispersion PMD is. Therefore by imposing on the optical pulses a phase opposite to the one measured by spectral interference, we can compensate for the phase accumulated in the fiber and recover the temporal shape which they had before entering the fiber. This can be observed as recovering the spectrum. When the accumulated phase variation is cancelled, the PMD in the transmission fiber is also compensated.  
         [0034]     Compensating for the PMD involves solving two steps: one, to measure the phase spectrum as described above; and two, to impose on the optical pulses a phase opposite to the measured one, in order to compensate for the phase accumulated in the fiber.  
         [0035]     The inventive technique is to recover the initial pulse through recovering the spectrum. Specifically, the invention imposes on the pulse, before the detector, a phase change to compensate for the phase distortion measured using spectral interference.  
         [0036]     After measuring the phase spectrum, i.e., the phase imposed by the propagation through the fiber at every frequency, the next step is the actual compensation. A pulse shaper is used to impose an opposite phase at each frequency. Once the phase introduced by the fiber is cancelled, the pulses will recover the temporal shape they had before entering the fiber.  
         [0037]     Pulse shaping is a technique used to change the phase and amplitude of a broadband pulse. The frequency components of the pulse are spatially separated using dispersive elements, and an active component changes the amplitude and/or phase of each frequency component. Liquid crystal arrays and acousto-optic crystals have been used successfully for this task. After this, the frequency components are combined again to form a new pulse, with a phase and amplitude spectrum modified by the active component.  
         [0038]     An example  400  of pulse shaping using an acousto-optic modulator (AOM)  409  as the active element to change the phase and amplitude is shown in  FIG. 4 . An input pulse  401  is directed off a mirror  403  onto a diffraction grating  405  that directs different frequency (wavelength) components of the pulse into different directions and each frequency component is focused at a particular spot in the focal plane of a lens  407 . The lens  407  directs the wavelength components to the acousto-optic modulator to diffract and shift the frequency of light according to amplitude/frequency modulated R.F. pulses  402 . The modified phase and amplitude spectrum, separated from the undiffracted beam  411 , is directed to another lens  417  which focuses the light onto a diffraction grating which directs the combined light off a mirror  419  to provide a shaped pulse  421 . Alternative pulse shaping can be liquid crystal, liquid crystal on silicon LCOS or a deformable mirror based, rather than acousto-optic based.  
         [0039]     An exemplary embodiment of the inventive method for compensating for PMD is schematically shown  500  in  FIG. 5 . The pulses acquire unknown phases at each frequency while propagating through a fiber  501 , which leads to pulse distortion. Part of the distorted signal is directed by the beam splitter  503  off a mirror  507  through a polarizer  509  to an optical spectrum analyzer (OSA)  511 . The optical spectrum analyzer monitors the spectrum through the polarizer  509  rotated to maximize the interference. The spectral interference pattern is transformed into a phase spectrum, which is then imposed with an opposite sign by a tool such as computer  513  onto the signals by the pulse shaper  505 . The pulses become short again because the initial undistorted phase spectrum is recovered. This measurement is preferably made on a probe pulse, with a bandwidth encompassing the spectral region required to be compensated for PMD. The pulse could be sent with a frequency permitted by the pulse shaper. For an acousto-optic modulator AOM system, compensation could be done on a microsecond scale, which is well within the requirements for real time PMD compensation. Unlike the inventive real time PMD compensation, prior pulse shaping to compensate for PMD involved compensating for a predetermined (not real time) PMD measured by a broadband polarimeter by using a liquid-crystal based pulse shaper.  
         [0040]     An exemplary alternative embodiment of the inventive all-order PMD compensation is schematically shown  600  in  FIG. 6 . The transmitted pulses  601  are linearly polarized by polarizer  603   1  and they acquire unknown phases at each frequency while propagating through the fiber  605 , which leads to pulse distortion. Part of the distorted wave is diverted at a tap through a polarizer  603   2 , rotated to maximize the interference, to an optical spectrum analyzer (OSA) that measures the spectral interference  605 . The spectral interference pattern is compared with the ideal spectrum at  607  with no PMD. The comparison result is transformed into a phase spectrum  609 , passed to a driver  611 , which is then imposed with an opposite sign onto the signals by the pulse shaper  505  just before the receiver end  613 . In a preferred embodiment, the spectrum comparison  607  and phase extraction  609  are implemented with computer hardware and software.  
         [0041]     A test system was built using a linearly polarized broadband ASE source at communication wavelength (1.55 μm) as the probing beam. The PMD introduced by a long single mode fiber was simulated by a PMD emulator which can introduce variable linear (first order) PMD. The output of the emulator was sent through an adjustable linear polarizer, and into an optical spectrum analyzer. The PMD delay was varied from 0 to tens of picoseconds and the spectral interference pattern on the spectrum analyzer was monitored. The spectral interference patterns measured for PMD delays from 0, 10, 20, 30 and 40 picoseconds are shown in respective graphs  701 ,  703 ,  705 ,  707  and  709  in the graphs  700  of  FIG. 7 . A linear relationship between the PMD delay and the fringe pattern was observed. This confirms the fact that the spectral interference is a good measure of the PMD.  
         [0042]     Since the emulator had only first order PMD, the spectral interference was pure sinusoidal and the frequency of the fringes was a direct measurement of the PMD delay. In a real optical transmission line, however, the PMD would be more complex, and the interference pattern would show that accordingly. Once the spectral interference measurement is obtained, extracting the phase spectrum is straightforward. A Fourier program could be used to perform the extraction. The graph of  FIG. 8  shows the extracted phase information as a function of the PMD value set by the PMD emulator and confirms a linear relationship between phase and first order PMD. In this case of test PMD emulator the extracted phase information is constant. For real fiber, a complicated phase spectrum would be obtained, and the capability of measuring the real phase spectrum would be limited only by the resolution of the optical spectrum analyzer.  
         [0043]     By way of example, an original waveform, see  FIG. 9 , was subjected to pulse shaping using an acousto-optic modulator (AOM). the graphs  1000  of  FIG. 10  depicts sample of waveforms  1001 ,  1003 ,  1005 ,  1007 ,  1009 ,  1011  as examples of spectrum manipulation via pulse shaping. The input spectrum,  FIG. 9 , can be arbitrarily modified by imposing patterns with different periods and depths. For PMD compensation application, the output spectral pattern of the pulse shaper is set to be the opposite of PMD-induced spectral change (similar to  FIG. 7 ). Therefore, combining the PMD extraction element and the pulse shaper, PMD in the optical link can be compensated.  
         [0044]     In summary, the invention teaches compensating for PMD to all orders. The invention takes the guess out of the PMD compensation by directly measuring the phase spectrum via spectral interference. The initial measurements demonstrate that spectral interference can be measured and used to determine PMD in a simple system. An acousto-optic based pulse shaper taking into account the spectral interference measured can be used to impose the opposite phase spectrum onto the signal beam, recovering the initial undistorted pulses. The inventive PMD compensation compensate a wide spectrum and therefore is suitable for PMD compensation in a WDM system.  
         [0045]     The present invention has been shown and described in what are considered to be the most practical and preferred embodiments. That departures may be made there from and that obvious modifications will be implemented by those skilled in the art. It will be appreciated that those skilled in the art will be able to devise numerous arrangements and variations which, although not explicitly shown or described herein, embody the principles of the invention and are within their spirit and scope.