Method and apparatus for automatic compensation of first-order polarization mode dispersion (PMD)

<u>FIELD OF THE INVENTION:</u>

The invention relates to optical transmission systems and more particularly relates to dealing with so-called polarization mode dispersion in such systems.

<u>BACKGROUND OF THE INVENTION:</u>

Polarization Mode Dispersion (PMD) occurs in an optical fiber as a result of a small residual birefringence that is introduced in the fiber core by asymmetric internal stress or strain as well as random polarization coupling due to external forces acting upon the fiber. Consequently, PMD may severely impair the transmission of a signal in an optical fiber network.

It is well-known that PMD affects differently certain polarization components of an optical signal propagating through a optical fiber transmission line, such that differential time delays occur among the components as they travel through the fiber. These differential time delays may range from about 0.1ps/(km)^1/2 for low-PMD optical fibers of modern manufacture to several ps/(km)^1/2 for single-mode optical fibers of older manufacture. Disadvantageously, the differential time delay that may result over a "long-distance" fiber-optic link, for example, a 100 km terrestrial transmission system employing single-mode fiber, due to such differential delays may be more than 20 ps, or more than 10 ps for an transoceanic link employing modern low-PMD optical fiber.

The large time delays that occur between different polarization components of an optical signal may cause significant broadening of the optical pulses propagating through an optical link. This is especially true in modern digital lightwave systems which operate at bit rates of at least 10 Gbps per transmitted-wavelength-channel. In fact, the broadening of a pulse by a differential time delay of, e.g., about 20 ps, in a high-bit rate system may cause a partial closure of the "eye diagram" of the received electrical signal by about 0.5 dB, which will significantly distort a received signal.

It is well-known, however, that the differential time delay that might occur in a particular transmission fiber is not constant over time, but may vary over time as the physical environment, e.g., temperature, pressure, etc., of the fiber changes. Thus, the statistics of time-dependent differential time delay caused by PMD in optical fiber usually follows a Maxwellian distribution, and, therefore, at any point in time, may be substantially lower to several times higher than its average (or mean) value.

(Note that in some older high-PMD optical transmission fibers a differential time delay of up to, e.g., 100 ps, is theoretically possible. A time delay of that order may cause, for example, complete fading in the electrical signal, as reported in, for example, the article entitled "Polarization Effects on BER Degradation at 10 Gb/s in IM-DD 1520 km optical Amplifier System" by Y. Namihira et al, and published in Electronic Letters, Vol. 29, No. 18, p. 1654, 1993.)

Prior methods of dealing with signal impairments due to PMD in an optical fiber include, for example; (a) electrical equalization of the signal distortion caused by PMD, as discussed in the article entitled "Experimental Equalization of Polarization Dispersion", by M. A. Santoro and J. H. Winters, and published in IEEE Photonic Technology Letters, Vol. 2, No. 8, p. 591, 1990; and (b) electrical compensation of the differential time delay in the received electrical signals, as discussed in the article entitled "Polarization Mode Dispersion Compensation by Phase Diversity Detection", by B. W. Hakki and published in Photonic Technology Letters, Vol. 9, No. 1, p. 121, 1997. Such prior methods also include (a) optical compensation of the differential time delay before converting the optical signals into electrical signals, as discussed in the article entitled "Polarization-Mode-Dispersion Equalization Experiment Using a Variable Equalizing Optical Circuit Controlled by a Pulse-Waveform-Comparison Algorithm", by T. Ozeki et al, and published in the Technical Digest Conference on Optical Fiber Communication 1994 (OSA), p. 62; and (b) other forms of compensation as discussed in, for example, the article entitled "Automatic Compensation Technique for Timewise Fluctuating Polarization Mode Dispersion in In-Line Amplifier Systems", by T. Takahashi et al., and published in Electronic Letters Vol. 30, No. 4, p. 348, 1994.

Disadvantageously, such electrical equalization schemes can only compensate for a relatively small differential time delay. They also require expensive high-speed electronics. Moreover, prior art optical compensators in general cannot automatically adapt their respective compensation schemes to handle a varying differential time delay in an optical signal traveling in a fiber that is being affected by a fluctuating-random PMD. For example, the optical compensation described in the Takahashi et al. article generates a fixed optical time delay to compensate for the distortion caused by PMD in a transmission fiber. Therefore, such a scheme is limited to dealing with a relatively small range of differential time delays. As another example, although the compensation scheme described in the T. Ozeki et al. article is capable of generating a variable, adaptive differential time delay, it requires expensive high-speed electronics to analyze the shape of received waveforms and derive an error signal that may be used to drive the compensation process toward the desired differential time delay.

<u>SUMMARY OF THE INVENTION:</u>

We deal with the foregoing problems and advance the relevant by providing apparatus which automatically adapts to the level of first-order polarization mode dispersion that may be present in an optical signal received from an optical transmission line. Specifically, we use a variable optical birefringence element which, responsive to receipt of the optical signal, generates a differential optical time delay between at least two selectable mutually orthogonal polarization states. An optical signal analyzer coupled to the output of the variable birefringence element, in turn, generates a control signal proportional to the total differential optical time delay that is present in an optical signal appearing at the output of the variable birefringence element. The control signal is supplied to the birefringence element to control the amount of differential time delay that is generated to control which orthogonal polarization states are selected.

In this way, we automatically and adaptively generate a differential time delay that substantially equals the differential time delay that occurs in the transmission optical fiber, but of opposite sign, and, therefore, cancels out the undesired delay.

These and other aspects of our invention are set forth in the following detailed description, corresponding drawings and ensuing claims.

<u>BRIEF DESCRIPTION OF THE DRAWING:</u>

In the drawing: <ul id="ul0001" list-style="none"><li>FIG. 1 illustrates in block diagram form an illustrative system in which the principles of the invention may be practiced;</li><li>FIG. 2 is a block diagram of the distortion analyzer of FIG. 1;</li><li>FIG. 3 illustrates in graphical form a simulation of the feedback signal versus the total differential group delay for filtered, unfiltered and weighted 10 Gb/s pseudo-random sequences;</li><li>FIG. 4 illustrates in block diagram form another illustrative system in which the principles of the invention may be practiced;</li><li>FIG. 5 illustrates in graphical form a plot of the total differential group delay against the polarization transformation angle associated with a polarization transformer of FIG. 4;</li><li>FIG. 6 is a block diagram of an illustrative embodiment of an integrated circuit version of the differential delay line of FIG. 1; and</li><li>FIG. 7 is alternative embodiment of the system of FIG. 1 in which a signal scrambler is employed at the transmitter of an optical signal.</li><li>FIG. 8 illustrates a distortion analyzer that may be used to derive a feedback signal for the inventive PMD compensators in FIGs. 1 and 4.</li></ul>

<u>DETAILED DESCRIPTION:</u>

Polarization Mode Dispersion (PMD) occurs in single-mode fibers as a result of residual birefringence in the fiber core and coupling of random polarization at various points along the fiber. The polarization transformation that occurs in the fiber may be modeled using a simple unitary 2x2 Jones matrix, <u>U</u>, as shown by following expression;<maths id="math0001" num=""><img file="EP0909045A2_D0001.tif" /></maths> where u₁ and u₂ in general are complex functions which depend on the frequency, ω, of the optical signal and other physical parameters that influence the mode coupling in the fiber.

It is well-known that for any optical frequency, ω = ω₀, there exists two orthogonal states of polarization commonly referred to as the Principal States of Polarization (PSP). An optical signal propagating through a fiber does not experience any significant amount of differential time delay if it is polarized at one of the two PSP. Thus, at any optical frequency, ω = ω₀, the matrix <u>U</u> may be "diagonalized" in the following way<maths id="math0002" num="(2)"><math display="block"><mrow><munder accentunder="true"><mrow><mtext>U</mtext></mrow><mo>̲</mo></munder><mtext>(ω) = </mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(ω</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>) · </mtext><munder accentunder="true"><mrow><mtext>D</mtext></mrow><mo>̲</mo></munder><mtext>(ω) · </mtext><munder accentunder="true"><mrow><mtext>V</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(ω</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msup><mrow><mtext>)</mtext></mrow><mrow><mtext>-1</mtext></mrow></msup></mrow></math><img file="EP0909045A2_D0002.tif" /></maths> where:<maths id="math0003" num=""><img file="EP0909045A2_D0003.tif" /></maths> are unitary matrices and;<maths id="math0004" num=""><img file="EP0909045A2_D0004.tif" /></maths> The Jones vectors;<maths id="math0005" num=""><img file="EP0909045A2_D0005.tif" /></maths> and<maths id="math0006" num=""><img file="EP0909045A2_D0006.tif" /></maths> correspond to the input and output principal states of polarization, respectively. Also, the frequency dependency in matrix <u>D</u> can be approximated to a first order in (ω - ω₀), at least over a sufficiently small frequency interval Δω around ω₀, as follows:<maths id="math0007" num=""><img file="EP0909045A2_D0007.tif" /></maths> where<maths id="math0008" num=""><math display="block"><mrow><msub><mrow><mtext>τ</mtext></mrow><mrow><mtext>f</mtext></mrow></msub><mtext> = 2 </mtext><msqrt><msup><mrow><mfenced open="|" close="|"><mrow><mfrac><mrow><mtext mathvariant="italic">d</mtext></mrow><mrow><mtext mathvariant="italic">d</mtext><mtext>ω</mtext></mrow></mfrac><mtext mathvariant="italic">u</mtext><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>1</mtext></mrow></msub></mrow></mfenced></mrow><mrow><mtext>2</mtext></mrow></msup><mtext> + </mtext><msup><mrow><mfenced open="|" close="|"><mrow><mfrac><mrow><mtext mathvariant="italic">d</mtext></mrow><mrow><mtext mathvariant="italic">d</mtext><mtext>ω</mtext></mrow></mfrac><mtext mathvariant="italic">u</mtext><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>2</mtext></mrow></msub></mrow></mfenced></mrow><mrow><mtext>2</mtext></mrow></msup></msqrt></mrow></math><img file="EP0909045A2_D0008.tif" /></maths> is the Differential Group Delay (DGD) that causes the aforementioned differential time delay in optical signals that are not launched in one of the two Principal States of Polarization (PSP).

It can thus be appreciated from the above equations that a differential time delay, τ_f, occurs between the two PSP of the fiber. The differential time delay which an optical signal experiences as a result of propagating through an optical fiber may, therefore, be compensated for by introducing an opposite but equal amount of differential time delay, τ_c = -τ_f, at the output of the fiber, in accordance with an aspect of the invention. This may be readily done using an optical element having the following polarization dependent transfer function:<maths id="math0009" num=""><img file="EP0909045A2_D0009.tif" /></maths> where <u>D</u> and <u>W</u> are the matrices shown in equation (3). The matrix Ucomp describes first order PMD (i.e., uniform birefringence) at an arbitrary orientation.

As mentioned above, PMD in a fiber may change with changes in time and optical frequency. This change in PMD may be dealt with, in accordance with another aspect of the invention, by varying the amount and orientation of the birefringence in the inventive compensator to adaptively compensate for the DGD in the fiber. An adaptive, variable-birefringence compensator may be readily realized by disposing a polarization transformer 30, for example, the polarization transformer described in U. S. Patent No. 5,212,743 issued May 18, 1993 to F. Heismann, which is hereby incorporated by reference herein, in series with an element 50 that generates variable linear birefringence (such as, for example, the polarization mode dispersion emulator, model PE3 available from JDS Fitel Inc.), as shown in Fig. 1. Such birefringence may be so generated, in accordance with another aspect of the invention, by splitting the signal at the output of the polarization transformer into two orthogonal linear polarization states corresponding to the two PSP of the fiber, and delaying each of the two polarization states by a variable amount of time, τ_c, using a respective delay line 50 as shown in FIG. 1. In fact, if the polarization transformation that occurs in polarization transformer 30 and the time delay in the variable differential time delay line 50 are properly adjusted such that polarization transformer 30 generates the polarization transformation described by the matrix W^-1 expressed by equation (7) and such that variable differential time delay line 50 generates the differential time delay τ_c shown in (7), then a signal outputted by the compensator 25 will be free of the distortions caused by differential time delays occurring in transmission fiber 20.

Note that an optical element (such as, for example, a combination of properly aligned birefringent fibers connected in series) that generates variable frequency dependent birefringence may be used in a similar manner to compensate for signal distortions due to higher-order PMD. However, a polarization transformer in series with a variable birefringence compensator alone would not automatically adapt by itself to changes in the PMD of the fiber. Such automatic adaptation may be achieved, in accord with another aspect of the invention, by providing a feedback signal that controls the polarization transformation occurring in the polarization transformer 30 (i.e., the orientation of the variable birefringence) as well as the differential time delay in the variable differential time delay line 50 (i.e., the amount of linear birefringence). The desired feedback signal may be generated at the output of compensator 25 by monitoring the amount of distortion that is due to the differential time delay present in an optical signal after it has traveled through compensator 25.

We have recognized that, that in accordance with another aspect of the invention, only one feedback signal is needed to simultaneously adjust the polarization transformation and adjust the differential delay, τ_c, to achieve minimal distortion in the signal that compensator 25 outputs to optical receiver 90 via conventional signal tap 85, as is shown in FIG. 1 and as will be discussed below.

Specifically, a portion of the signal that compensator 25 outputs is supplied via optical tap 85 to path 87 extending to high-speed photodetector 55, which may be, for example the Hewlett Packard Co., model 11982 Wideband Lightwave Converter having an electrical bandwidth that is at least equal to the information bandwidth of the modulated optical signal transmitted by optical transmitter 10. The remainder of the signal is supplied to path 86 extending to receiver 90. Photodetector 55 converts the high-speed digital information signal modulated onto an optical carrier signal into an electrical signal. The electrical signal is then amplified by conventional amplifier 60 and coupled to electrical distortion analyzer 70 which measures the distortion in the amplified photocurrent and converts the amplified result into a voltage, V_f, that is proportional to the distortion. For example, voltage V_f reaches a maximum value when the optical signal is free of distortion due to first order PMD, i.e., when the combined differential time delay of optical fiber 20 and compensator 25 is substantially equal to zero. The combined DGD, τ_total, introduced in fiber 20 and compensator 25 may be expressed as follows:<maths id="math0010" num="(8)"><math display="block"><mrow><msub><mrow><mtext>τ</mtext></mrow><mrow><mtext>total</mtext></mrow></msub><mtext> = </mtext><msqrt><msubsup><mrow><mtext>τ</mtext></mrow><mrow><mtext mathvariant="italic">f</mtext></mrow><mrow><mtext>2</mtext></mrow></msubsup><msubsup><mrow><mtext> + τ</mtext></mrow><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext>2</mtext></mrow></msubsup><msub><mrow><mtext> + 2τ</mtext></mrow><mrow><mtext mathvariant="italic">f</mtext></mrow></msub><msub><mrow><mtext>τ</mtext></mrow><mrow><mtext mathvariant="italic">c</mtext></mrow></msub><mtext>cos(2θ)</mtext></msqrt></mrow></math><img file="EP0909045A2_D0010.tif" /></maths> where τ_f is the DGD in fiber 20, τ_c is the DGD in compensator 25 and 2θ is the angle between the so-called Stokes vectors corresponding to the PSP of fiber 20 and PSP of compensator 25, which is controlled directly by polarization transformer 30.

It is apparent from equation (8) that the total differential time delay, τ_total, is at a minimum value of |τ_f - τ_c| when 2θ is adjusted to a value of ±π, i.e., when the so-called slow and fast PSP of fiber 20 are respectively aligned parallel to the so-called fast and slow PSP of compensator 25. Thus, the adjustment of the angle θ may be achieved by adjusting polarization transformer 30 in response to the value of the feedback voltage, V_f, supplied via feedback path 71 such that V_f is driven to a relative maximum value.

Also, the differential time delay, τ_c, in compensator 25 may be adjusted in response to the value of feedback voltage, V_f, such that τ_c is substantially equal to the DGD, τ_f, in fiber 20, thereby resulting in a τ_total of zero. At that point, V_f would be at a maximum value. Thus, if the orientation and amount of differential time delay generated by polarization transformer 30 and variable differential time delay line 50 are adjusted in the foregoing manner, then the level of distortion in the optical signal that PMD compensator 25 outputs is minimal. Moreover, if either the orientation or the level of DGD in compensator 25 deviates appreciably from the desired values (i.e., 2θ = ±π and τ_c = τ_f), then the signal that compensator 25 outputs will be distorted due to the resulting non-zero differential time delay, τ_total.

It is well-known that the differential time delay, τ_total, between two orthogonal polarization components in an optical signal modulated with a high-speed information signal may cause, within an electrical frequency band centered around a frequency of f = 1/2τ_total, a partial or complete fading in the detected electrical signal at the receiver. It was specifically determined that after it has been detected by an optical photodetector, the frequency response of an amplitude-modulated optical signal that has experienced differential time delay τ_total in an optical transmission line may be described as follows:<maths id="math0011" num=""><math display="block"><mrow><mtext>S(f) = </mtext><msqrt><msup><mrow><mtext>1-4γ(1-γ)sin</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><msub><mrow><mtext>(πτ</mtext></mrow><mrow><mtext>total</mtext></mrow></msub><mtext>f)</mtext></msqrt></mrow></math><img file="EP0909045A2_D0011.tif" /></maths> where f is the detected electrical frequency, γ and (1-γ) are the fractions of the optical power transmitted in the fast and slow PSP of the fiber, and the function S describes a reduction in the photocurrent generated by photodetector 55, with 0 ≤ S ≤ 1. Note that S(f) is equal to 1 if the optical signal experiences no PMD in the transmission line (i.e., if τ_total = 0) and that S(f) reduces to zero at f = (2τ_total)^-1 if γ = 0.5, i.e., if τ_total ≠ 0 and the optical signal has the same power level in each PSP. S(f) is thus a unique measure of the distortion in the optical signal due to the total DGD in the transmission fiber and the compensator.

If the DGD is limited to values below a maximum value, τ_max, then the distortion in the optical signal may be quantified by simply measuring the amplitude of the received electrical signal of a particular frequency f ≤ 1/(2τ_max). The amplitude of this signal may then be used as a feedback signal to automatically adjust the orientation and level of DGD that is generated in PMD compensator 25, such that the feedback signal is maximized.

The above requirement set for the total DGD that may be inserted in a transmission system, τ_total ≤ τ_max, may limit the amount of DGD that may be compensated for in an optical transmission fiber, τ_f, as τ_total ≤ 2τ_f. For example, if in a 10 Gbps digital transmission system, the amplitude of the received electrical signal is measured at 5 GHz, then τ_f should always be smaller that 50 ps. Otherwise, the feedback signal that is generated as a function of the amplitude of the 5 GHz component may be ambiguous in the sense that it is difficult to determine by which amount and direction the polarization transformation, <u>W</u>^-1, and the differential time delay, τ_c, need to adjusted to obtain a τ_total = 0, which may occur, for example, when the amplitude of the feedback signal is the same for two different values of τ_total, which may result in generating faulty adjustments in the orientation and level of the differential time delay in PMD compensator 25.

We have recognized, however, that an "unambiguous" feedback signal (i.e., a signal that is a unique measure of τ_total) may be generated, without limiting the level of compensation that may be applied to DGD, by measuring the amplitude of a plurality of frequency components contained in the optical information signal propagating through an optical fiber. An illustrative embodiment of an inventive compensator which analyzes the amplitudes of substantially the entire received frequency spectrum using a broadband electrical power detector is shown in FIG. 2. The broadband electrical power detector 95, which may be, for example, model 8474 diode detector available from the Hewlett Packard Co., more particularly, converts such amplitudes into a single feedback voltage, V_f, that is proportional to the integral of the amplitudes (power levels) of substantially the entire high-frequency electrical spectrum. (It is noted that it is not necessary to include the DC component of the photocurrent in the generation of the feedback voltage, since this component is usually not affected by first order PMD.)

For the illustrative embodiment of FIG. 2, the feedback voltage, V_f, generated by the distortion analyzer 70 (FIGs. 1 and 2) may be expressed as follows:<maths id="math0012" num=""><img file="EP0909045A2_D0012.tif" /></maths> where i_d(f) is the amplified version of the photocurrent that photodetector 55 supplies to amplifier 60, f_min and f_max are respectively the lowest and highest frequencies of the above-mentioned spectrum, in which, preferably, f_min &lt; f_clock/100, where fclock is the clock frequency of the received digital information, and f_max &gt; f_clock. For example, to compensate for a DGD of up to 120 ps in a 10 Gbps transmission system, we found that a f_min of ≈ 100 MHz and a f_max of ≈ 15 GHz to be sufficient for deriving a feedback voltage, V_f, having a unique value. To obtain an "unambiguous" feedback signal, it may be necessary to either filter or apply a weighting scheme to the electrical spectrum possibly before or during the aforementioned integration process, based on the spectral components contained in the digital information signal modulated onto the optical signal. In that instance, the output of amplifier 60 is passed through electrical filter 65 before it is detected by power detector 95. This is graphically illustrated in FIG. 3 which shows a graph of the feedback voltage that is obtained by integrating the entire high-frequency spectrum of both unfiltered and filtered 10 Gbps digital information signals, carrying a random or pseudo-random bit sequence (PRBS), versus the total DGD, τ_total, experienced by a respective optical signal. Curve 310 shows that the feedback signal derived from an unfiltered optical signal carrying PRBS exhibits secondary maxima at values of τ_total above about 180 ps, besides the desired absolute maximum at τ_total = 0.

Curve 330 of FIG. 3 also shows that appropriate filtering, or weighting, represented by curve 320, of such frequency components removes the undesired secondary maxima and, thus, provides an "unambiguous" feedback signal that may be supplied to polarization transformer 30 and adjustable delay line 50 to provide the desired level of differential time delay in the desired polarization components of the received optical signal. The polarization angle, θ, in polarization transformer 30 and differential time delay, τ_c, in delay line 50 may be adjusted alternately until the level of the feedback signal, V_f, reaches a maximum using a simple maximum search algorithm, such as the algorithm disclosed in the aforementioned U. S. Patent No. 5,212,743. More specifically, the differential time delay in the delay line is continuously dithered around its current value to determine the absolute maximum value of the feedback voltage, V_f. Each time τ_c is set to a different value, the polarization angle, θ, is adjusted by the polarization transformer until the level of the feedback signal, V_f, supplied by distortion analyzer 70 reaches a maximum for that setting. This procedure is repeated for each value of differential time delay, τ_c, until V_f reaches an absolute maximum value, where the distortion due to first-order PMD in the received optical signal is minimized.

(Note that Fig. 8 illustrates a distortion analyzer that may be used to derive an "unambiguous" signal corresponding to curve 320.)

A second illustrative embodiment of our invention is shown in FIG. 4, and includes a source of optical signals 410, optical transmission fiber 420, and variable DGD compensator 425 formed from two sections each respectively comprising first and second automatic polarization transformer 430 and 440 and first and second high birefringence, single-mode (HBF) fiber 435 and 445 as shown. Fiber 435 (445) may be, for example, the SM.15-P-8/125 fiber having a DGD of about 1.4 ps/m and available from the Fujikura Company (Japan). The sections generate a differential time delay of τ₁ and τ₂, respectively, between the light signals polarized along the slow and fast optical axes of the respective section. The output HBF 445 is coupled to an optional tap 485 connected to optical receiver 490. A portion of the optical signal is fed via tap 485 to high speed photodetector 455. Similarly, the electrical output of photodetector 455 is supplied to amplifier 460 and the amplified result is then supplied to distortion analyzer 470 comprising electrical filter 465 and broadband electrical power detector 495, which generates a feedback signal that is supplied to polarization transformer 430 and polarization transformer 440.

Polarization transformer 440 in response to the feedback signal rotates the state of polarization of the optical signal between HBF 435 and HBF 445 such that transformer 440 effectively varies the angle, θ_c, between the fast axis of HBF 435 and the fast axis of HBF 445. The resulting differential time delay, τ_c, provided by the cascading of HBF 435 and 445 may be described by the following expression:<maths id="math0013" num="(10)"><math display="block"><mrow><msub><mrow><mtext>τ</mtext></mrow><mrow><mtext>c</mtext></mrow></msub><mtext> = </mtext><msqrt><msubsup><mrow><mtext>τ</mtext></mrow><mrow><mtext>1</mtext></mrow><mrow><mtext>2</mtext></mrow></msubsup><msubsup><mrow><mtext>+ τ</mtext></mrow><mrow><mtext>2</mtext></mrow><mrow><mtext>2</mtext></mrow></msubsup><msub><mrow><mtext> + 2τ</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext>τ</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><msub><mrow><mtext>cos(2θ</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><mtext>)</mtext></msqrt></mrow></math><img file="EP0909045A2_D0013.tif" /></maths> which shows that the differential time delay generated by compensator 425 is continuously variable between a minimal value of |τ₁ - τ₂| and a maximal value of (τ₁ + τ₂).

Note that by choosing τ₂ of HBF 445 to be substantially equal to τ₁ of HBF 435 , the differential time delay τ_c may be varied between 0 and 2τ₁ by varying the polarization transformation in polarization transformer 440. Also note that polarization transformer 430 operates similar to polarization transformer 30 of FIG. 1, since it is used to align the output PSP of the transmission fiber parallel to the input PSP of the variable birefringence compensator formed by HBF 435, polarization transformer 440 and HBF 445 by varying the value of θ in polarization transformer 430 such that the feedback signal reaches a maximum. Transformer 440 then adjusts the value of θ_c until τ_c = τ_f. An example of that type of an adjustment is shown in FIG. 5 in which the total DGD, τ_total, is plotted against θ and θ_c. The adjustment assumes that the fiber DGD is τ_f = 70 ps, and that the differential delay in the HBF 435 and HBF 445 are respectively τ₁ = 50 ps and τ₂ = 40 ps. It is seen from FIG. 5 that τ_total is approximately zero when the value of θ is π/2 radians (which means that the slow PSP of transmission fiber 420 is aligned parallel to the fast PSP of compensator 425) and when the value θ_c is approximately 0.68 radians (alternatively 2.46 radians).

The system of FIG. 4 also automatically adapts the level of compensation that it generates to a first-order PMD if polarization transformers 430 and 440 are controlled by a feedback signal that varies proportional to the level of distortion in the optical signal that compensator 425 outputs to tap 485.

As described above, the feedback paths respectively shown in FIGs. 1 and 4 include similar elements. However, the possible range of differential time delay that the system of FIG. 4 can compensate is limited by the total bandwidth of the optical signal, i.e., the high-speed information signal that is modulated onto the optical signal. Specifically, for the case where τ₂=τ₁, the frequency-dependent polarization transformation in compensator 425 may be described by the following unitary matrix:<maths id="math0014" num=""><img file="EP0909045A2_D0014.tif" /></maths><maths id="math0015" num=""><img file="EP0909045A2_D0015.tif" /></maths> where Δω = ω -ω_o, and <u>W</u>(θ) is the polarization transformation in polarization transformer 430. It is seen from equation (11) that for τ_c=2τ₁ · cosθ_c and to a first order in Δω, U_comp(ω) has the same desired form of Eq. (7). However, the off diagonal terms in the second matrix on the right side of Eq. (11) show that for large values of τ₁Δω, a significant amount of light is cross coupled between the PSP of the compensator. Specifically, at θ_c=π/4 radians and τ₁Δω=π radians, the light from either one of the input PSP is completely coupled to the orthogonal output PSP.

Thus, if the total bandwidth of the optical signal is large compared with either 1/τ₁ or 1/τ₂, then compensator 425 would not be capable of simultaneously generating the desired differential time delay for all frequency components of the optical signal to offset the effects of first-order PMD in the transmission fiber.

However, we have shown experimentally that for an amplitude-modulated optical signal carrying a pseudorandom 10 Gbps digital signal, a differential time delay of τ₁ ≅ τ₂ ≅ 50ps generated by compensator 425 still allowed for an adaptive PMD compensation with acceptable low levels of second-order PMD distortion

Note that compensator 425 may be readily arranged to generate a differential time delay greater than τ_c = τ₁ + τ₂ = 100 ps by merely adding additional sections, as needed, in which, as mentioned above, each such additional section comprises a polarization transformer and HBF with differential time delays of τ₃ = 50 ps, τ₄ = 50 ps, and so on. Such a compensator is also capable of compensating for the effects of second-order PMD in addition to first-order DGD.

A broad block diagram of another illustrative embodiment of an adjustable differential delay line operative for compensating for variable first-order PMD is shown in FIG. 5. Similarly, as shown in FIG. 1, the compensator system of FIG. 5 includes an element 540 at the input to split (separate) the polarization of an incoming optical signal and an element 541 at the output to recombine the transformed PSP of the transmission fiber. A variable time delay associated with one of the PSP is generated by a number of asymmetric, waveguide Mach-Zehnder interferometers 530 through 532 connected in series via adjustable directional couplers 560 through 563, respectively. The directional couplers may be controlled in a conventional manner to direct the optical signal either through the short or long leg of the Mach-Zehnder interferometers 530 through 532, thereby introducing a variable delay between 0 (zero) and τ_i = ΔL_i·n/c; where ΔL_i·n is the optical path difference in the i-th interferometer and c is the speed of light. It is thus possible to generate any desired differential time delay between 0 (zero) and τ_cmax = (2ⁿ - 1)·ΔL_in/c in discrete steps of Δτ_c = ΔL₁n/c.

To obtain an uninterrupted flow of the signal through the interferometers while the delay τ_c is being changed from one value to another, the relative optical phases in each of the interferometers need to be changed for constructive in-phase interference of the two optical signals which emerge from the two arms of each Mach-Zehnder interferometer and then enter the succeeding directional coupler. Therefore, it may be necessary to include a variable phase shifter, e.g., a respective one of the phase shifters 570 through 572, in each of the Mach-Zehnder interferometer.

A controllable waveguide delay line based on the foregoing principles may be readily constructed on a number of different electrooptic substrates, such as, for example, lithium niobate and semiconductor materials as well as other optical materials using, for example, thermo-optic or acousto-optic effects to control the directional couplers 560 through 563 and phase shifters 570 through 572.

It is noted that, for the PMD compensators shown in FIGs. 1 and 4, a very low level of distortion might occur in the signal that the transmission fiber outputs if most of the signal that is transmitted in one of the PSP of the fiber, i.e., if γ or (1- γ) is small. Also S(f) would be close to 1, even if a large value of τ_f is present in the transmission fiber. In that event, τ_c in the compensator would have some arbitrary value. Further, the level of distortion in the optical signal might become suddenly large if the state of polarization of the optical signal changes rapidly at some point along the fiber, thereby requiring rapid adjustment of the values of θ and τ_c in the PMD compensator.

The sudden adjustment of τ_c may be avoided by rapidly scanning the input state of polarization to the transmission fiber over a large number of different polarization states, such that, for example, averaged over time, all possible polarization states are excited with equal probability. Then, approximately one-half on the input signal, on average, would be in one of the PSP of the transmission fiber and the other one-half would in the other PSP, i.e., on average <maths id="math0016" num=""><math display="inline"><mrow><mover accent="true"><mrow><mtext>γ</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0909045A2_D0016.tif" /></maths> = 0.5 = 1-<maths id="math0017" num=""><math display="inline"><mrow><mover accent="true"><mrow><mtext>γ</mtext></mrow><mo>¯</mo></mover></mrow></math><img file="EP0909045A2_D0017.tif" /></maths>. Consequently, a sufficient level of distortion is consistently present in the optical signal supplied to the PMD compensator to ensure that τ_c is adjusted properly independent of changes in polarization in the corresponding fiber.

To ensure that the feedback circuit in the PMD compensator remains stable, the aforementioned scanning of the input polarization state to the transmission fiber has to be performed much faster than the response time of the polarization transformer that serves as the input to the PMD compensator. One example capable of performing such scanning is the electro-optic polarization scrambler disclosed in U. S. Patent No. 5,359,678 issued October 25, 1994 to F. Heismann et al, which is hereby incorporated by reference.

FIG. 7 shows an illustrative embodiment of the invention that uses a fast-electro-optic polarization scrambler 15 at the input of the transmission fiber. Scrambler 15 may be modulated with an arbitrary voltage, e.g., a sinusoidal or sawtooth voltage, as long as the average degree of polarization of the light signal that scrambler 15 outputs is substantially equal to zero.

The foregoing is merely illustrative of the principles of the invention. Those skilled in the art will be able to devise numerous arrangements, which, although not explicitly shown or described herein, nevertheless embody those principles that are within the scope of the invention. For example, based on the foregoing, it would be obvious to the skilled practitioner that the effects of still higher-orders of PMD may be dealt with by merely expanding the compensator, e.g., compensator 450, to include additional sections, as needed.