## Abstract

We present a novel transceiver setup for Polarization Shift Keying (PolSK) modulation using a simple transmitter and a receiver based on differential demodulation. The transmitter is made up of a LiNbO _{3} phase modulator with the input fiber pigtailed at 45° with respect to the principal axes of the modulator. The receiver is composed of an asymmetric Mach-Zehnder Interferometer (AMZI) and a couple of balanced photodetectors (BPD), as usually employed for receiving DPSK. To our knowledge, it is the first time such receiver structure is applied to PolSK. In order to fully assess the system performance of the proposed setup, we have carried out numerical simulations using a semi-analytical technique for bit-error-rate evaluation and performed experimental measurements at 10 Gbit/s. After having optimized transceiver performances, we evaluated the resilience to receiver impairments to verify the viability of a realistic implementation. Surprisingly, PolSK shows a better sensitivity using a single-end receiver (with the AMZI tuned at the minimum transmittance point) than using a balanced one. Another improvement has been obtained optimizing the driving voltage at the transmitter: this leads to a “non-ideal” PolSK modulation with non-orthogonal symbols, which shows an enhanced performance thanks to a synchronous phase modulation.

© 2008 Optical Society of America

## 1. Introduction

The use of semiconductor optical amplifiers (SOAs) is a promising solution compared with other in-line optical amplifiers such as Erbium-doped fiber amplifiers (EDFAs) and Raman amplifiers (RAs). SOA technology offers several advantages: wide gain spectrum, low cost, small dimensions, integrability with other devices, and low power consumption. However this technology has not been widely deployed in commercial fiber systems yet because of the intrinsic nonlinear fast-gain dynamic [1]. In fact, when using conventional on-off keying (OOK) modulation in combination with wavelength division multiplexing (WDM), SOAs lead to strong waveform distortion and interchannel crosstalk. Cross gain modulation (XGM) is the principal limiting phenomenon: the use of Constant Envelope (CE) modulation formats, virtually XGM-free, mitigates the impact and seems to be an encouraging solution for future SOA-based low-cost optical systems. This is the approach followed by the TOSCA (Transmission of Optical Signals exploiting Competitive Amplification) project, funded by the Italian Ministry of University and Research, where the feasibility of a new generation of WDM metropolitan area networks based on the SOA technology and CE formats is analyzed. A good candidate in this class of modulation formats is PolSK, where information is encoded over the polarization state of the optical field: the two binary symbols are associated to orthogonal polarizations. In the past, several PolSK setups have been proposed and studied, but the complexity of the transmitter and, especially, of the receiver was one of the major drawbacks [2],[3],[4]. The system here proposed is composed by a very simple transmitter and a receiver based on an Asymmetric Mach-Zehnder Interferometer (AMZI), a component now technologically affordable and widely available at relatively low cost. A major advantage of this receiver structure is that it does not require any polarization control or polarization recovery circuit.

This paper presents simulative and experimental results about our new proposed PolSK setup. Preliminary sensitivity results have been presented in [5]. In this work we have assessed the performance of the PolSK transceiver conducting a comprehensive study of all major receiver impairments. We used an accurate semi-analytical technique based on Karhunen-Loève (KL) series expansion of signal and noise in the frequency domain [6] to evaluate the bit-error-rate (BER) as a function of OSNR. This technique applies to any modulation format but it becomes mandatory when using a differential receiver based on the AMZI. In fact, the widely used performance estimation technique based on the evaluation of the Q parameter, which gives quite accurate results for Intensity Modulation-Direct Detection (IMDD) systems, becomes unreliable for modulation formats such as DPSK [7] or differentially demodulated PolSK. We also carried out an experimental validation at 10 Gbit/s implementing the whole proposed transceiver structure.

The paper is organized as follows. In Section 2 we describe the novel PolSK transceiver setup analyzing its peculiarity with respect to previous layouts. In Section 3 we describe the semianalytical technique used for performance evaluation, then we present simulative sensitivity results together with performance optimization. In Section 4 we evaluate the penalty introduced by main receiver impairments. Then, in Section 5 we show measurement results obtained using the transceiver prototype we built in laboratory to check the simulation results.

## 2. The PolSK Transceiver Setup

#### 2.1. The transmitter

The transmitter is based on a *z*-cut LiNbO_{3} phase-modulator having the input pigtail rotated by 45° with respect to the standard orientation for phase modulation (see Fig. 1). This solution has been first proposed in [8] for polarization modulation. Such component is usually employed for high-speed polarization scrambling. It works thanks to the anisotropy of the electro-optic coefficients in lithium niobate (*r*
_{13}≠=*r*
_{33}), and to the fact that, due to the rotated input coupling, the light is launched on both waveguide axes. As a differential phase shift over the two signal components induces a polarization rotation, properly driving the modulator we can obtain the two orthogonal polarization states typical of PolSK. In detail, the output signal is:

where *x*̂ and *ŷ* are respectively vertical and horizontal axes on the transversal plane, *E*
* _{in}* is the continuous wave optical carrier to be modulated and

are phase shifts applied to the fields on *x*̂ and *ŷ* axes as a function of the common driving voltage *V*
_{pp·}
*V*
_{πx} and *V*
_{πy} are the voltage needed on the *x*̂ and *ŷ* axis to achieve a*π* phase rotation (i.e. they are related to *r*
_{13} and *r*
_{33}, respectively). *a _{n}* ∈{0,1} is the variable carrying the transmitted information and

*p*(

*t*) is the pulse shape, with max{

*p*(

*t*)}=1.

It can be easily shown that, in order to generate two orthogonally polarized states, a *π* radians differential phase shift is needed, so that *ϕ _{x}*-

*ϕ*=

_{y}*π*. Defining

*k*=

*V*/

_{πy}*V*

_{πx}=

*r*

_{33}/

*r*

_{13}, it turnes out that the driving voltage needed to obtain orthogonal states to generates a PolSK signal must be:

For lithium niobate, where *k* is roughly 3.3 [9] and *V*
_{πx} is about 4.0 V, we get *V _{PolSK}*=5.7

*V*:a driving voltage that can be easily obtained with state-of-the-art components.

This issue needs to be evaluated but is beyond the scope of this paper. The *z*-cut structure of the modulator further introduces a time delay of about 15 ps between the linear polarization components, due to large crystal birefringence: we have verified by simulation that such effect has a negligible impact on system performance. It could be important in case of upgrade to higher bit rates when it becomes comparable to the bit duration.

#### 2.2. The receiver

The receiver has been so far the major limiting factor for the development of PolSK systems: in the past all proposed solutions were based on the recovery of a polarization frame [10] [11], which requires several optical components and a complex electrical tracking circuit to follow the fiber birefringence time variations. The main novelty of our transceiver setup is in the simple receiver, which converts polarization modulation to amplitude modulation using a differential demodulator, usually employed for DPSK [6]. Such a receiver is based on an AMZI with delay equal to the bit time, followed by a Balanced Photodetector (BPD) on the upper and lower branch respectively (see Fig. 2). The AMZI compares adjacent bits, which can have parallel, i.e. the same, or orthogonal polarizations.

To our knowledge, it is the first time such receiver structure is applied to PolSK. The main advantage with respect to all previous proposals is that it does not require a polarization control at its input to track and follow polarization rotations due to fiber propagation. It must be noted that, as for DPSK, a differential electronic pre-coder [12] is needed at the transmitter side in order for the receiver to recover the original sequence.

The electric fields at the output of the two arms of the AMZI can be written as:

Ideally, *γ*=1 (infinite extinction ratio), *δϕ*=0 (AMZI perfect tuning) and *T _{AMZI}*=

*T*, where

*T*is the inverse of the bit rate

*R*.

_{B}At the output of the BPD we have:

where *R*
_{1} and *R*
_{2} are the responsivities of the upper and lower arm of the BPD, *I*
_{1}(*t*) and *I*
_{2}(*t*) are the two photocurrents and τ_{1} and τ_{2} are the propagation delays introduced by the two BPD arms. Ideally, for a perfectly balanced receiver, τ_{1}=τ_{2} and *R*
_{1}=*R*
_{2}.

Considering an ideal AMZI, and assuming to have at the input of the receiver a signal generated using a driving voltage perfectly matched to *V _{PolSK}* to obtain orthogonal symbols, at the optimum sampling instant we get the following expressions for the output fields of the lower and upper arm of the AMZI:

$$+\frac{{E}_{\mathrm{in}}}{\sqrt{2}}\left({e}^{j\frac{k}{k-1}\pi {a}_{n-1}}\hat{x}-{e}^{j\frac{1}{k-1}\pi {a}_{n-1}}\hat{y}\right)]$$

$${E}_{2}=\frac{1}{2}[\frac{{E}_{\mathrm{in}}}{\sqrt{2}}\left({e}^{j\frac{k}{k-1}\pi {a}_{n}}\hat{x}-{e}^{j\frac{k}{k-1}\pi {a}_{n}}\hat{y}\right)+$$

$$-\frac{{E}_{\mathrm{in}}}{\sqrt{2}}\left({e}^{j\frac{k}{k-1}\pi {a}_{n-1}}\hat{x}-{e}^{j\frac{k}{k-1}\pi {a}_{n-1}}\hat{y}\right)],$$

where *a _{n}* ∈{0,1}. Evaluating the output currents at each photodiode, we have:

$$\mathrm{if}\phantom{\rule{.2em}{0ex}}{a}_{n}\ne {a}_{n-1}\phantom{\rule{.2em}{0ex}}{I}_{1}=R\frac{{\mid {E}_{\mathrm{in}}\mid}^{2}}{2};\phantom{\rule{.2em}{0ex}}{I}_{2}=R\frac{{\mid {E}_{\mathrm{in}}\mid}^{2}}{2}$$

being *R*=*R*
_{1}=*R*
_{2} the responsivity of the two photodiodes. When using an ideal BPD the decision signal is given by *I*
_{1}-*I*
_{2} so that the two average eye levels for the two bits are respectively *R*|*E _{in}*|

^{2}and 0: differently from DPSK we do not get an antipodal eye diagram and we have only half of the average eye opening. When using a single-ended receiver we only get

*I*

_{1}or

*I*

_{2}obtaining half of the eye opening given by a balanced receiver.

## 3. Simulation results and performance optimization

The results presented in this section have been evaluated using a semi-analytical technique [13] based on Karhunen-Loève (KL) series expansion [14], [15] of signal and noise. In particular, we evaluated system performance using a KL expansion in the frequency domain, which was at first proposed in [14] and then applied to DPSK and DQPSK modulation formats in [6] and [16] respectively. Since the PolSK modulation proposed in this paper uses the same differential receiver as DPSK, the technique described in [6], extended to a dual polarization optical representation, can be directly applied to PolSK.

All simulations refer to the setup shown in Fig. 3 that allows for measurement of BER as a function of OSNR: it is based on a standard noise loading technique that we have also used in the experimental validation reported in Section 5. The PolSK modulated signal and the ASE noise generated by an EDFA are added using an optical coupler. Two optical attenuators, placed on each branch, allow to finely tune the OSNR and the average optical power at the receiver. We consider a realistic flat-top optical filter with a -3 dB bandwidth of 175 GHz, the same one we have used in the subsequent experimental validation: its transfer function has been measured and given as input to the simulator. Such wide filter fits the needs of TOSCA applications, where WDM is not very tight and low-cost solutions are preferred. After photodetection the electric filter is a 5 poles Bessel type with -3 dB bandwidth of 7 GHz.

We started evaluating the system performance considering ideal transmitter and receiver devices (not affected by any impairments). The BER vs. OSNR curve obtained by means of the KL semi-analytical technique implemented in the optical system simulator OptSim [17] is shown in Fig. 4. We define “sensitivity” as the OSNR needed to achieve a pre-FEC (Forward Error Correction) BER value equal to 10^{-6}. Note that our definition of OSNR assumes an ASE noise bandwidth equal to the bit rate *B _{R}* and takes into account ASE noise on both polarizations. Under these conditions, the back-to-back sensitivity corresponds to an OSNR value equal to 18.6 dB. In the following we describe the optimization of transmitter and receiver parameters in order to enhance the performance level of PolSK.

#### 3.1. Receiver optimization

First we analyze the use of an imbalanced receiver, to check if we can obtain a better performance in terms of sensitivity. We define a normalized imbalance parameter as:

where *R*
_{1} and *R*
_{2} are the values of the responsivities of the photodetectors placed on the upper and the lower arms respectively. In Fig. 5 the OSNR penalty is plotted with respect to *β*. An unexpected behavior is found: the optimum performance, minimizing the sensitivity, is obtained around *β*=-0.5. This means that a completely balanced receiver (*β*=0) is not the best for PolSK. If such imbalanced condition (*β*=-0.5) is difficult to achieve in practice, it is worth noting that a sensitivity gain of 0.6 dB with respect to the perfectly balanced case can be obtained at *β*=-1, reaching a sensitivity of 18.0 dB. This condition corresponds to *R*
_{1}=0, i.e. to the use of a single-ended receiver on the lower arm only. This RX configuration can also be obtained by using a single output AMZI, tuned with the channel frequency at the minimum transmittance, followed by a single photodetector. In this case a simpler receiver gives a better performance. We can also note that the opposite condition (*β*=1) gives a much worse performance.

In order to qualitatively explain why this happens, we show in Fig. 6 the eye diagrams for different BPD imbalance conditions, highlighting the normalized eye opening: ideal balanced receiver (*β*=0), optimum imbalance (*β*=-0.5), single-ended and AMZI tuned at maximum transmittance (*β*=+1), single-ended and AMZI tuned at minimum transmittance(*β*=-1). While the eye opening is maximized with a balanced receiver, the amount of noise is considerable on both symbols. On the contrary, the eye opening is minimized when the AMZI is tuned both at the minimum and at the maximum transmittance, but also the amount of noise resulting out of the reciver changes. When the AMZI is tuned at the minimum transmittance, a notch is centered at the channel frequency: it cuts out most of the ASE noise. Moreover the signal-noise beating has less impact because symbols present lower levels (check Eq. 8 and Fig. 6). The optimum condition is obtained choosing the best trade-off between eye opening and amount of noise. This is just a qualitative approach to help the reader comprehension: in all our simulations noise and signal are analytically taken into account without any simplified assumptions.

#### 3.2. Transmitter optimization

A further step in the optimization process can be carried out at the transmitter side analyzing if we can improve the sensitivity varying the driving voltage. Here we only consider the case of *β*=-1, close to the absolute optimum but more interesting from the implementation point of view because of its reduced complexity and lower cost.

Being VPolSK, as defined in Eq. (3), the nominal PolSK driving voltage, i.e. the amplitude required to obtain orthogonal symbols, we define a normalized driving signal as *V*
* _{pp}*/

*V*

*and in Fig. 7 we show the sensitivity as a function it. It can be seen that there is a minimum at*

_{PolSK}*V*

*/*

_{pp}*V*

*=0.75, where the best sensitivity achieved is 17.2 dB. This behaviour can be explained by the fact that, driving the phase-modulator with 45° pigtail, an hybrid polarizationphase modulation is generated. Even if symbols are not orthogonally polarized, the spurious phase modulation can concur to open the eye diagram (this can be easily verified evaluating analytically the eye opening), while the noise remains about the same.*

_{PolSK}Moreover, it is advantageous to have a smaller amplitude required at the output of the driver: only 4.3 V with respect to 5.7 V needed to obtain the ideal PolSK. In order to quantify the loss of orthogonality, consider that in the Stokes space two orthogonal polarization states are antipodal and the angle between them is 180°: when using*V _{pp}*/

*V*=0.75 the angle between the two symbols is 143°.

_{PolSK}At the end of this two-stage optimization process we have been able to improve the sensitivity by 1.4 dB, moreover we ended up with a simplified receiver based on a single photodetector, avoiding the need for a complex and expensive BPD. To have a fair comparison with DPSK, we need to consider also for it the performance when using a single-ended receiver. Using the semi-analytical technique described above we obtained a value of 15.0 dB vs. 17.2 dB for PolSK. Although PolSK does not achieve the same performance level of DPSK, it can still be an interesting solution because of its intrinsically polarization scrambled nature. Expecially in the context of the TOSCA project, where we envision the use of SOAs, it could give some advantages avoiding the need for in-line scramblers. In fact SOAs give raise to strongly polarization weighted nonlinear phenomena, such as FWM and XPM, that can be partially suppressed using scramblers.

## 4. Impact of receiver impairments

In this section we determine the impact of receiver non-idealities in terms of OSNR penalty, defined as the increase in OSNR with respect to the reference case needed to recover the target performance of BER=10^{-6}. The reference case is the one selected through the optimization process: imbalance *β*=-1 and normalized driving voltage *V _{pp}*/

*V*=0.75. We have considered the following impairments: AMZI frequency detuning, AMZI delay error and AMZI limited extinction ratio [7]. In the following subsections we present simulation results for all of them.

_{PolSK}#### 4.1. AMZI frequency detuning

It is defined as the detuning Δ*f* between the AMZI central frequency and the transmitter laser frequency, which is caused by the fact that the phase difference *δϕ* between the upper and the lower branch of the AMZI (see Eqs. (4) and (5)) is not perfectly equal to zero, as it should be for optimum demodulation of PolSK. It can be shown that Δ*f* and *δϕ* are linked by the following relationship:

where the detuning is normalized with respect to the bit rate.

In Fig. 8 the OSNR penalty is plotted with respect to the normalized detuning. As expected, we have a symmetric behavior, regardless of the direction of the laser detuning with respect to the AMZI: only the amount sets the penalty. Limiting the penalty to less than 1 dB requires an error in the tuning control below ±5% of *B _{R}*: at 10 Gbit/s it means ±500 MHz. Such tuning precision of the AMZI can be obtained with a temperature control, eventually driven by a feedback signal taken from the receiver.

#### 4.2. AMZI delay error

It is generated when the delay in the AMZI arm *T _{AMZI}* is not perfectly matched to the duration of one bit

*T*=1/

*B*. We define a normalized quantity with respect to the nominal bit slot:

_{R}The delay introduced by the AMZI can be greater (*δT _{AMZI}*/

*T*> 0) or smaller (

*δT*/

_{AMZI}*T*< 0) than a bit time

*T*. Note that

*δT*/

_{AMZI}*T*=-1 means that there is no delay between the two arms of the AMZI. In Fig. 9 the OSNR penalty is plotted with respect to the normalized AMZI delay error. PolSK shows good robustness to this impairments: the OSNR penalty is lower than 0.5 dB in the ±25% range (at 10 Gbit/s, where

*T*=100 ps, it means

*T*∈[75,125] ps). In this case, for a fiber based AMZI, the nominal

_{AMZI}*T*corresponds to about 20 mm: to limit the impact to 0.5 dB requires for a precision of 5 mm that is not difficult to achieve.

_{AMZI}#### 4.3. AMZI limited extinction ratio

The AMZI extinction ratio is related to the parameter *γ* through the following relationship:

where *γ* can assume values in the range [0,1], while *ε* ∈[1,+∞), where the extrema mean no extinction at all and ideal (infinite) extinction ratio, respectively. Note that, physically speaking, *ε* represents the highest possible power ratio that one could obtain between the two AMZI outputs. In Fig. 10 we show the OSNR penalty as a function of the extinction ratio parameter *ε* : it can be observed that the OSNR penalty is lower than 0.5 dB when *ε* > 18 dB. Commercial components are available with *ε* in the order of 20 dB, so we expect a negligible impact on performances.

From the analysis of receiver impairments we can conclude that PolSK sensitivity to component nonidealities is low: state-of-the-art components allow for negligible penalty. Only the AMZI detuning requires for an active control to keep the receiver aligned to the transmitted frequency.

To have a reference, we conducted a similar analysis on DPSK, evaluating receiver impairments of a single-ended structure having same parameters as used for PolSK. For all three studied impairments, we ended up with penalties comparable to PolSK. Both modulation formats show good resilience to receiver nonidealities: practical implementations are likely to reach the predicted performances.

## 5. Experimental validation

In order to validate the simulations results, we performed a set of measurements at 10 Gbit/s, following the setup shown in Fig. 3. By means of two optical attenuators, one at the end of the signal branch and the other one at the end of the ASE noise source branch, a finely tunable OSNR and received power are provided. The receiver is composed of a flat-top optical filter with a -3 dB bandwidth of 175 GHz, an AMZI and a PIN+TIA photoreceiver followed by the 5-poles Bessel electrical filter with 7 GHz bandwidth. We were able to tune the transfer function of the AMZI by varying the operating temperature, so measurements have been collected in both cases, i.e. AMZI tuned at minimum and at maximum transmittance. In order to measure the BER of the system, a 2^{31}-1 PRBS is supplied by a pattern generator and then processed by the final error detector.

In Fig. 11 we have superimposed measurements data to simulation results for nominal PolSK modulation (*V _{pp}*/

*V*=1.0) and a good agreement is found for both AMZI tuning positions. To further validate our simulation results, we also investigated the performance dependence on the modulator driving voltage, verifying the simulative optimization process carried out in Section 3.2. Using the gain control available on the driver, we swept the output voltage over a range of values around the ideal nominal

_{PolSK}*V*. In Fig. 12 we report the OSNR needed to achieve

_{PolSK}*BER*=10

^{-6}and we compare it with simulation results: once again a good agreement is found. To have a more comprehensive validation of our simulation technique applied to PolSK, we not only considered the best condition with single-ended receiver and AMZI tuned at minimum transmittance, but also the case of AMZI tuned at maximum transmittance. Looking at these results, we note the small dependence of OSNR sensitivity with respect to driving voltage: for a wide range of normalized values between 0.55 and 1.0 there is a penalty lower than 0.8 dB. This allow for a loose precision setting of the driver used in the PolSK transmitter. The best performance achieved experimentally by PolSK is an OSNR sensitivity of 16.5 dB, slightly better than expected: since we were not able to fully characterize all components in our experimental setup we may have improperly estimated some parameters that are not easily measurable.

A last validation of our simulation results has been achieved measuring the OSNR penalty as a function of frequency detuning. In Fig. 13 the OSNR penalty is shown with respect to the normalized detuning: note that 0% means AMZI tuned exactly at minimum transmittance (best case) and 50% at maximum transmittance. The perfect agreement is a further confirmation of the reliability of our simulation technique when applied to modulation formats that require an AMZI based receiver.

Finally, to give a qualitative confirmation of our findings, Fig. 14 shows the eye diagrams measured using a single-ended receiver with AMZI tuned at minimum (left) and maximum (rigth) transmittance at a OSNR level required to have BER=10^{-6}: 16.5 dB and 20.7 dB respectively. When the AMZI is tuned at minimum transmittance a smaller noise rail at the zero level can be noticed, that explains the better performance under this condition.

## 6. Conclusions

Constant envelope modulation formats are a promising solution to allow using advantageous SOAs in WDM metropolitan networks reducingXGM impact. In this class, polarization modulation has been extensively studied in the past but the complexity, mainly related to the receiver composed of a dynamic polarization tracking circuit, limited the attractivity of this format. In this paper we propose a simple architecture for transmitter and receiver. In particular, we show for the first time the use of a differential receiver based on an AMZI and a balanced photodetector. We fully assess the performance of this new scheme optimizing transmitter and receiver parameters to improve performances. Finally, we also evaluated the impact of receiver nonidealities. The surprising result obtained in this paper, showing that a single-ended receiver can enhance system performances with respect to the more complex balanced one, has been experimentally verified. In conclusion, even though PolSK does not reach the same performance level of another CE modulation format like DPSK, its intrinsically polarization scrambled nature can be useful in transmission systems avoiding the need for a supplemental polarization scrambler.

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