1. Introduction

To meet the ever-growing demand from the cloud computing, high-definition videos and computer vision, numerous researches emerged in exploring efficient techniques for high-speed coherent optical fiber systems. To further increase the spectral efficiency (SE) and total capacity, different multiplexing and modulation techniques have been wildly investigated like time-division multiplexing, polarization-division multiplexing (PDM), wavelength-division multiplexing, quadrature-amplitude modulation (QAM) and space-division multiplexing (SDM) [1–6]. With the 100 Gigabit Ethernet (GbE) coherent optical systems successfully deployed, the 400 GbE optical modules also started to flourish [7–9]. The industry will then be likely moving towards even 1 Tb/s. As a mature technology for industry commercialization, high-order QAM combined with PDM has attracted lots of interests, which is proved as a very effective way to increase the capacity and SE [10–12]. Coherent in-phase (I) and quadrature (Q) transmitter is one of the key parts to achieve dual-polarization (DP) QAM. An ultra-high-order PDM 4096-QAM based on IQ transmitter has recently been demonstrated with the SE up to 19.77 bit/s/Hz [13]. Furthermore, with Nyquist pulse shaping, a single carrier PDM-16-QAM up to 127.9 GBd was transmitted over 3000 km, achieving a ∼1 Tb/s line rate [14]. Consequently, DP-QAM based on IQ transmitter shows significant potentials for implementing 400-Gb/s or upcoming 1-Tb/s commercial optical fiber communications systems.

In the real implementation, the transmission performance of DP-QAM always suffers from various impairments. With the development of coherent transmitter toward advanced modulation formats and higher baud rates, the timing skew and power imbalance of each channel become more critical. The previous study shows that to limit the penalty of signal to noise ratio (SNR) at bit error rate (BER) of 10⁻² within 1 dB, the skew needs to be smaller than 26% of the symbol period for QPSK, and 11% of the symbol period for 16-QAM [15]. Meanwhile, the power imbalance could significantly affect the Euclidean distance between constellation points as the QAM order increases. Therefore, an accurate compensation and calibration method of timing skew and power imbalance is necessary. The power imbalances generally refers to the signal distortion caused by the unbalanced power between IQ or x- and y- polarized (XY) channels [15,16]. The IQ power imbalance is usually induced by imperfections of coherent IQ transmitters, while the XY power imbalance is also known as polarization dependent power (PDP) [17–19]. Some schemes have been proposed to monitor the power imbalances in the transmission link [20,21]. With the QAM order and baud rate increases, the sensitivity to uncompensated IQ and XY power imbalance is exacerbated, seriously degrading the system performance [22]. Several works have been carried out to solve the problem. The well-known Gram-Schmidt orthogonalization procedure (GSOP) can be used in power imbalance compensation at receiver side [23–25]. Besides, some methods is demonstrated by adjusting the finite impulse filter at the transmitter side [26,27]. In [26], an innovative cooperative coevolution genetic algorithm is proposed to compensate the time skew, bias voltage and power imbalances among channels. Meanwhile, several adaptive equalization and machine learning methods have also been proposed at the receiver side to compensate and calibrate the IQ power imbalance [17,28–31]. However, most of them are based on digital signal processing (DSP) module or need external equipment, meaning a larger power consumption to operate the system. Especially for integrated optical modules, a power-friendly way is much critical. Furthermore, adaptive equalization methods perhaps are not necessary choices since the IQ power imbalance rarely changes over time. Therefore, it is essential to find a power-efficient approach to compensate both IQ and XY power imbalances.

In this work, the impact of both XY and IQ power imbalances are investigated experimentally utilizing different QAM formats and high baud rate including 45, 64 and 86 GBd. Under different values of optical signal-noise-ratio (OSNR), we compared the impact of both XY and IQ power imbalances on different combinations of modulation formats and baud rates. The Q² penalty is measured as the performance of transmission. Then, the structure of interference-based scheme is proposed to compensate power imbalances, and the operating principle is described in detail. The scheme is further demonstrated experimentally. By feeding each channel with the periodic “01” coded binary phase-shift keying (BPSK) signal, the specific interference power can be obtained between two channels. When adjusting one of the electrical inputs until the optical interference power reaches the minimum, the corresponding IQ or XY power imbalance can be compensated. By utilizing a simple power meter or internal low-speed photodiode, it can be conducted as a pre-calibration procedure before using the DP-QAM transmitter. Compared with implementing DSP module at the transmitter or receiver side, it is more power-efficient and compatible for various modulation formats, data sequences, and waveforms.

2. System impact of power imbalances

Figure 1 depicts the impact of power imbalance of DP-QAM transmitter carrying a DP-QPSK signal. Under the ideal condition, the optical signal powers from each polarization and IQ channel should be equal after the IQ modulator. It can be clearly shown on the constellation diagram that the four constellation points of the quadrature phase shift keying (QPSK) are equally spaced in the four quadrants, as shown by the green points in the Fig. 1(a). However, they are usually not identical for the four channels (XI, XQ, YI and YQ) in practical scenarios, which introduce the IQ and XY power imbalances. Such as the x-polarization shown in Fig. 1(a), the output optical power of XI is slightly smaller than the one of XQ. Therefore, the distance between the constellation diagrams in the I-axis direction becomes closer as shown by the yellow points, so that it could degrade the system performance. Similarly, the same IQ power imbalance may also appear for the y-polarization, which would result in distortion of the IQ constellation. As for the XY power imbalance, the insertion loss of the device varying with the polarization state will cause a serious impact on the transmission quality as shown in Fig. 1(b). XY power imbalance will lead to different OSNRs between the two channels, and the system performance will be limited by the channel with lower OSNR. The XY power imbalance could bring large power fluctuations in the system, which can increase the BER of the system and even cause network failures. Combined with polarization mode dispersion (PMD), it can become a major source of pulse distortion. Thus, it is necessary to first investigate the effects of IQ and XY power imbalance under different modulation formats and baud rates for high-speed and long-distance coherent transmission systems.

 

Fig. 1. Concept of (a) IQ and (b) XY power imbalances of DP-QPSK (IQM: IQ modulator).

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The experimental setup of dual-polarization coherent optical system based on QAM formats is shown in Fig. 2. Electrical signals of four channels are generated by a 120 GSa/s 8-bit arbitrary waveform generator (AWG), whose typical analog 3-dB bandwidth is 45 GHz. After performing the digital pre-distortion at the transmitter side, the analog bandwidth can be extended to 50 GHz. Four output electrical signals are then connected to the corresponding input ports of an IQ modulator with 45 GHz 6-dB bandwidth. A built-in C-band continuous-wave laser is used as the input carrier for the coherent signal generation. Then, a dual-polarization signal optical output is generated and connected to the optical input port of a 70 GHz coherent receiver. The local oscillator is fed by the internal laser source of the receiver. The sampling rate and resolution of the real-time oscilloscope are 256 GSa/s and 10 bits, respectively. The low-pass filter bandwidth of the receiver is chosen as 0.8×baud rate. In the part of DSP, the sampled signals are first processed by performing square timing clock phase recovery. Next, an adaptive multiple-input multiple-output (MIMO) time-domain equalizer (TDE) with 13 taps is used for demultiplexing the X and Y channels and performing rotation to compensate for the state of polarization misalignment between the signal and receiver. Here, constant modulus algorithm (CMA) is selected in the adaptive TDE. After performing the compensation of frequency offset between the local oscillator and carrier, blind phase search algorithm is further utilized for compensation of the phase noise. In order to further confirm and adjust the power of each channel to obtain the accurate value of power imbalance, the radio frequency (RF) signal is fed for each channel respectively, while the other three are set to null and with no output power. Then, an external power meter is used to confirm the optical power of each channel precisely. Meanwhile, the power imbalances between each two channels are also measured at the receiver side by using optical modulation analyzer for further verification.

 

Fig. 2. Experimental setup of dual-polarization coherent optical system based on QAM formats (LO: local oscillator, OMFT: optical multi-format transmitter).

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Then the impact of power imbalances on transmission performance with different formats and baud rates is experimentally investigated. The impact of power imbalances on signal quality is measured as Q² penalty. As another reference, the error vector magnitude (EVM) at 0 dB power imbalance is also given in Table 1 for the used modulation formats under various conditions to represent the original signal quality. The back-to-back performance of different modulation formats with different IQ power imbalance are compared experimentally in Figs. 3(a) and (b). Here, the Q² degradation of 45 GBd DP-QPSK and DP-16-QAM are shown under various OSNRs. The results under a higher (35 dB) and a lower (22 dB) OSNR are shown for a better comparison. It can be clearly seen that the complex modulation format has larger penalty from the IQ power imbalance. Moreover, high OSNR region shows larger power imbalance penalty. It indicates that while higher OSNR means better signal quality, it is more sensitive to IQ power imbalances. At low OSNR regime, the influence from the other impairments are more dominant and becomes the key factor affecting the signal quality. As the OSNR increases, the influence of IQ power imbalance gradually becomes prominent. The impact of XY power imbalance on DP-16-QAM at various baud rates are shown in Figs. 3(c) and (d). Three high baud rates (45, 64 and 86 GBd) were selected for comparison to meet the needs of 400G or 600G coherent IQ transmitter. The results reveal that higher the baud rate is, the larger the penalty from the XY power imbalance is. When the baud rate increases, the limitation of the bandwidth will become more obvious, affecting the rise and fall time of the waveforms. At the same time, when there is XY power imbalance, the transmission performance will be restricted by the channel with lower optical power. Both of these make signals with higher baud rate more sensitive to the XY power imbalance. Furthermore, by comparing Figs. 3(c) and (d), it can be seen that high OSNR region shows larger XY power imbalance penalty, which has a similar trend with IQ power imbalance. Finally, the impact of IQ and XY power imbalances under the same condition were also compared experimentally in Figs. 3(e) and (f). Under the high OSNR regime, the penalty from the IQ power imbalance is larger. As the OSNR gradually decreases, the impact between the XY and IQ power imbalance become closer. When the OSNR equals 14 dB, the penalty from the XY power imbalance is even slightly larger. Therefore, when the system operates at larger OSNR, higher baud rate and more complex modulation format, its performance degradation caused by power imbalances will be more obvious. It indicates that the pre-calibration of both IQ and XY power imbalances is necessary for DP-QAM transmitter in high-speed applications.

 

Fig. 3. Q² penalty of (a) and (b): IQ power imbalance for different formats; (c) and (d): XY power imbalance for different baud rates; (e) and (f): 45 GBd QPSK influenced by IQ and XY power imbalance respectively.

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Table 1. Measured error vector magnitude (EVM) at 0 dB power imbalance for each format

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3. Principle

In general, the interference of two optical waves needs a stable phase difference and polarization components in the same direction [32]. When the phase difference is an even multiple of π, the optical power after interference reaches its maximum, and the power is the sum of the two input tributary waves, which is called constructive interference. On the contrary, destructive interference occurs when the phase difference becomes to an odd multiple of π; the output optical power reaches its minimum, which is the absolute value of the power difference between the input tributary waves. Except for these two extreme cases, the interference power generated by the other phase differences will be located between the maximal and minimal optical power. Theoretically, the change of the power difference between the two optical waves will also lead to changes in the power of interference, which is the basis for compensation and calibration of power imbalances.

Typically, the optical carriers of the four channels in a DP-QAM transmitter originate from the same continuous-wave (CW) laser after some optical couplers. Therefore, all the branches are inherently coherent and satisfy the conditions of interference ideally. The fundamental principle of reconfigurable interference is shown in Fig. 4. A₁, A₂, B₁, and B₂ are the input and output ports of the former 3-dB optical coupler, while C₁, C₂, D₁, and D₂ are the input and output ports of the latter 3-dB optical coupler in the QAM modulator. E₀₁(t) and E₀₂(t) represent the output optical fields after the former optical coupler and modulators. E₁(t) and E₂(t) are the input optical fields to the latter 3-dB optical coupler to identify the IQ imbalance, while E₃(t) and E₄(t) are the input optical fields to the 45° polarizer to evaluate the XY imbalance. Besides, the blue arrows in the figure represent the polarization states of the output optical signal after interference. First, two modulated channels are generated from one input CW laser as shown in Fig. 4(a). Here, a symmetric 3-dB optical coupler is used, so the transfer matrix of optical field between the input and output could be expressed as:

 

Fig. 4. Typical structure of (a) the generation of modulated optical channels, (b) interference of IQ channels using optical coupler, and (c) interference of XY channels using polarizer. (Mod: modulator; Pol: polarization).

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Figure 4(b) depicts the power imbalance detection of IQ channels based on reconfigurable interference. The polarizations of both I and Q branches are the same. It is worth mentioning that there is usually IQ skew between two branches in practice. The IQ skew mainly comes from three sources: the timing skew of the electrical signals, the difference of the optical path between the I and Q branches, and the difference of optical phase induced by the phase shifter (PS) [33]. They altogether contribute to the IQ time skew, as illustrated in Eq. (2):

It is worth noting that, after the electrical signals passing through the IQ modulator, the DAC power difference could be eventually represented as power differences of the optical output according to the transfer function of the modulator. Therefore, it is reasonable to directly introducing the unbalanced parameters (k₁ and k₂) in the optical domain to represent the overall effect of power imbalance for theoretical description. Here, as 3-dB couplers are used in the link, so the output optical power of each two channels passing through the couplers should be the same. Thus, for the case of constant input optical power, k₁ and k₂ satisfy the following expression:

Through the optical coupler shown in Fig. 4(b), the interference of IQ channels could be well realized. Therefore, the output optical field of the interference by the two arms of the coupler can be depicted in Eq. (6):

If there is no IQ skew (Δφ_IQ = 0), D₁ is the port with destructive interference and has minimal output power, while D₂ is the port with constructive interference and has maximal output power. Equation (7) can be simplified to Eq. (8):

When there is no power imbalance between the two channels (k₁= k₂= k), D₁ is the port with no output power, while D₂ reaches the maximum (${k^2}{P_0}{|{Mod(t )} |^2}$). On the contrary, if it is with the largest imbalance (k₁= 0 or k₂= 0), the output powers of D₁ and D₂ are the same ($\frac{1}{4}{k_1}^2{P_0}{|{Mod(t )} |^2}$ or $\frac{1}{4}{k_2}^2{P_0}{|{Mod(t )} |^2}$). Therefore, in the ideal case, when the power of one channel is adjusted until the output power of the interference is 0, the power imbalance of the IQ channels can be compensated.

Next, when it comes to XY channel, the operation will be different compared with IQ channel due to the orthogonal polarization states, which is depicted in Fig. 4(c). The interference of two orthogonal modulated waveforms (E₃(t) and E₄(t)) from the D₁ ports generated by two separate modulators can be achieved by using an optical polarizer, aligned 45° to the x- and y- polarized channels to satisfy the conditions of the interference. Similar to the IQ channels, there is also time skew between the XY channels. Similarly, the XY skew mainly comes from three sources: the timing skew of the electrical signals, the difference of the optical path between the X and Y branches, and the difference of optical phase induced by the beam splitter and polarization rotator [34], as shown in Eq. (9):

For each polarization, only one branch (i.e., YI) of the coupler in Fig. 4(b) is turned on, while the other one (i.e., YQ) is set to be off without output. Thus, the output power of port C₂ should be set to zero and the output of port D₁ and D₂ can be further derived as:

Finally, after passing through the 45° polarizer, E₃(t) and E₄(t) are changed into a same polarization state $\vec{{\boldsymbol e}}$. Then the interference occurs and the optical power after the polarizer can be easily calculated through Eq. (14):

When there is no XY power imbalance between the channels (k₃= k₄= k), P_XY(t) reaches the maximum ($\frac{1}{4}{k^2}{P_0}{|{Mod(t )} |^2}$). On the contrary, if it is with the largest imbalance (k₃= 0 or k₄= 0), P_XY(t) will change to $\frac{1}{4}{k_4}^2{P_0}{|{Mod(t )} |^2}$ or $\frac{1}{4}{k_3}^2{P_0}{|{Mod(t )} |^2}$ accordingly. In an ideal case, there is no XY power imbalance and power reduction between the channels (k₃ = k₄ = k = 1), P_XY(t) reaches the maximum ($\frac{1}{2}{P_0}{|{Mod(t )} |^2}$). But in practice, both channels could suffer from the power reduction, that is, k₃ < 1 and k₄ < 1. In this case, if it is with the largest imbalance (k₃ = 0 or k₄ = 0), P_XY(t) will change to $\frac{1}{2}{k_4}^2{P_0}{|{Mod(t )} |^2}$ or $\frac{1}{2}{k_3}^2{P_0}{|{Mod(t )} |^2}$ accordingly. On the contrary, if k₃ or k₄ is adjusted so that it is equal to the other, there is no XY power imbalance between two channels (k₃ = k₄ = k < 1). That means the P_XY(t) will reach the relative maximum in this case ($\frac{1}{2}{k^2}{P_0}{|{Mod(t )} |^2}$). Similarly, in the ideal case, when the power of one channel is adjusted until the output power of the interference reaches its maximum, the power imbalance of the XY channels can be compensated.

Therefore, if one wants to compensate the IQ and XY power imbalances through the interference scheme, the first step is to eliminate both the IQ and XY skews. This scheme can also provide effective skew compensation, which is similar with the [35]. However, there is no power imbalance assumption of each channel in [35]. In this Section, the influence of power imbalance on interference is discussed in depth, and the parameters k_i (i = 1,2,3,4) representing the effect of IQ and XY power imbalances are introduced in the equations. After considering the IQ and XY skews, the influence of power imbalance on the output interference power is further explored and discussed theoretically. Other methods can also be selected in practice to compensate the IQ and XY skews. For example, one can use digital communications analyzer (DCA) to compensate skews by aligning the waveforms of two channels. Consequently, we mainly focus on the power imbalance calibration here and the skew compensation is another byproduct.

4. Experimental setup and results

4.1 Conceptual diagram of skew and power imbalance detection

For a more precise compensation of power imbalances, one should first carefully adjust the timing skew of each channel. In [35], detection and alignment of IQ and XY skew has been successfully achieved based on similar scheme. Figure 5 shows the concept of adjusting skew and power imbalance using reconfigurable interference. In order to explain and compare with the implementation process of power imbalance more intuitively, the operation of the timing skew compensation is first explained. The detection and alignment of IQ skew is first depicted in Fig. 5(a). For two beams with the same polarization (i.e., XI and XQ), identical “01” pattern can be encoded periodically with BPSK for both IQ channels, while the other two branches are set to zero with no modulation and any output power in an ideal case. For a better performance of detection for small IQ skew, the destructive interference is set at “well-aligned” condition, meaning there is no IQ skew. Correspondingly, the constructive interference is set at “interleaved” condition with 1-unit-interval (UI) skew. Thus, a relative phase difference Δφ with π between two IQ branches is introduced by using a PS. By manipulating the skew Δt from -1 UI to 1 UI, the transfer function of the interference power can be obtained for each polarization. In [35], there was no IQ power imbalance between the two channels, so the transfer function is shown as the solid line in Fig. 4(a). While considering the IQ power imbalance, since the optical power of the two channels are not equal, there will be a certain residual optical power when destructive interference occurs, and the optical power after the interference is not 0. Similarly, when constructive interference occurs, since the optical power of one channel becomes smaller, the optical power after the interference will also be smaller than when the two channels have the same optical power, as displayed by the dash lines in Fig. 5(a). The above method using sub-UI can accurately measure IQ skew in a large dynamic range.

 

Fig. 5. Concept of detecting (a) IQ skew, (b) XY skew, (c) IQ power imbalance and (d) XY power imbalance using reconfigurable interference (UI: unit interval).

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The measurement of XY skew is shown in Fig. 5(b). Ideally, one of the branches of each polarization (i.e., XQ and YQ) is set to zero with no modulation and any output power, and the identical “01” pattern is encoded periodically with BPSK for the other two channels with orthogonal polarizations. To better distinguish the transfer functions between IQ and XY skews, there is no additional phase difference (Δφ = 0) between XY channels. Therefore, the constructive interference corresponds to “well-aligned” condition with no skew, while “interleaved” case with 1-UI skew means the destructive interference. By manipulating the skew Δt from -1 UI to 1 UI, the transfer function of the interference power after the 45° polarizer can be further obtained. In [35], there was also no XY power imbalance between the two channels, and the transfer function of interference is shown as the solid line in Fig. 5(b). After considering the XY power imbalance, as illustrated by the dash lines in Fig. 5(b), there will be a certain residual optical power when constructive interference occurs, while the optical power after the interference will be smaller when destructive interference occurs. Moreover, for larger IQ and XY skew measurement (Δt > 1 UI), using a longer periodic pattern would be sufficient, such as selecting consecutive m × “0” and m × “1” to measure skew up to ± m UI.

After completing the IQ and XY skew detection, it can be adjusted to any desired value by controlling the relative delays among the electrical signals and then perform a better detection of power imbalance. The method of manipulating power imbalance between IQ channels using reconfigurable interference is illustrated in Fig. 5(c). Due to an introduced π phase difference between IQ channels, the destructive interference occurs under “power-balanced” condition with no IQ power imbalance. Consequently, the IQ power imbalance could be eliminated through adjusting the output optical power of one branch to make the interference reach the minimum. As for the detection of XY power imbalance depicted in Fig. 5(d), the scheme is a bit similar. A 45° polarizer is utilized for aligning the two orthogonal polarizations and a phase difference with π is also utilized between XY channels for a more sensitive detection. Through scanning the output power of one polarization, the XY power imbalance can be eliminated when the interference power is minimal. An additional point to note for the XY power imbalance is that when the extreme imbalance case occurs (i.e., P_Y= P₄ = 0, P_X= P₃), there will be a “cos(45°)” term after passing through the polarizer, so the interference power should be 0.5P₃.

In addition, the BPSK signal with rectangular waveform is used for each channel to make a more intuitive explanation. Theoretically, the method is also suitable for other pulse shapes (e.g., non-return-to-zero (NRZ), and return-to-zero (RZ) etc.), data sequences (periodic, pseudorandom binary sequence (PRBS), etc.), and waveforms (sine wave, etc.). It is worth mentioning that, internal photodiodes are usually utilized to each polarization for real-time monitoring in commercial DP-IQ modulator. By adjusting the XY channels to be with the same output powers at the photodiodes, the power imbalance of the XY channels could also be roughly compensated. But when it comes to the IQ channels, one could not measure and adjust the IQ power imbalance according to the photodiode of each polarization. More importantly, the accuracy of the photodiodes in the DP-IQ modulator are not as good as the one of the external power meters, and thus using the internal photodiodes for power imbalance calibration is not very reliable. Furthermore, the proposed scheme uses the destructive interference effect of two optical fields, and leverages one photodiode for calibration. Only when the powers of two optical fields are exactly the same, the minimum value of the interference optical power can be achieved. Therefore, the proposed interference-based approach is much more accurate, without requiring high-precision internal photodiodes.

4.2 Experimental setup

The experimental setup used to adjust both IQ and XY power imbalance for DP-IQ transmitter is shown in Fig. 6. The input electrical signal with 30 GBd is generated by the transmitter, corresponding to a ∼33-ps time slot per UI. For the structure, both x- and y- polarizations are used in the DP-QAM transmitter for in-phase and quadrature modulation, respectively. Each polarization is composed by a set of IQ branches, forming a total of four channels (XI, XQ, YI and YQ). A PS is added to one of IQ branches for each polarization to change the relative phase difference. Then a phase rotator (PR) is implemented to achieve orthogonal polarization multiplexing.

 

Fig. 6. Experimental setup of IQ and XY power imbalance detection and adjustment for DP-QAM transmitter (BS: beam splitter; PS: phase shifter; PR: phase rotator; PBC: polarization beam combiner; CW: continuous-wave; Mod: modulator; PM: power meter; PC: phase controller; EDFA: erbium doped fiber amplifier; VOA: variable optical attenuator; Pol.: polarizer; PD: photodetector; DCA: digital communication analyzer).

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For the detection of IQ power imbalance, a pair of IQ branches of either polarization can be turned on (i.e., XI and XQ) and fed with periodic “01” patterns, while the other two are set to null. An inline power meter is inserted to measure the interference power, followed by a DCA to capture interference patterns. To detect the XY power imbalance, one can just feed one branch with periodic “01” patterns in each polarization. For instance, the BPSK signal encoded by periodic patterns is used for YI and XQ channels, while the other two are set to null and with no output power. A polarization rotator (PR) is used to restore the x- and y- polarization states, and a following 45° polarizer is set to align the output of two orthogonal polarizations. The interference power of the two channels is measured by a power meter at the end. In the experiment, a DCA is also used as an additional monitor to clearly identify the patterns. In practice, one can use a low-speed photodiode in the DP-IQ transmitter for power detection and calibration, which greatly reduces the complexity of hardware.

It is also worth noting that the 45° polarizer is not a necessary component in practical implementation for XY power imbalance calibration. Only using inline power meter or internal low-speed photodiode is also suitable for the case. After the IQ imbalance calibration, one can first turn on the IQ channels in x-polarization, while the other two channels in y-polarization are turned off. The output optical power of x-polarization could be obtained through the inline power meter. Similarly, the IQ channels in y-polarization are then turned on with the other two channels in x-polarization set to null. According to the power monitored by the inline power meter, the output power of y-polarization could be adjusted to be the same as that of x-polarization measured before, achieving XY power imbalance calibration.

4.3 Detection and adjustment of IQ time skew

For a better performance of power imbalance compensation, the adjustment of skew should be implemented first. Here, a 7.5 GHz sine wave is utilized for the measurement of the interference power caused by time skew with ∼133 ps time period of ±1 UI. Because of the introduced π phase difference between two IQ channels, the point where destructive interference occurs corresponds to the condition with no skew. Thus, the skew can be compensated by adjusting the relative time delay between electrical input signals to minimize the interference power. The measured transfer function is depicted in Fig. 7. It can be clearly seen that the power variation around the minimum value of the interference power is sharp, providing a sensitive and fine detection, and large dynamic ranges are realized of ∼22.9 dB and ∼23.3 dB for x- and y- polarizations, respectively. Furthermore, the power transfer function will be stretched or compressed along with the time period of the sine wave varying.

 

Fig. 7. Measured interference power for (a) x-polarization and (b) y-polarization skew using periodic “01” patterns.

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4.4 Detection and calibration of IQ and XY power imbalances

If the orthogonality between the IQ or XY channels is not perfect, the performance of the scheme is also affected. The different cases caused by orthogonality imperfection of IQ and XY imbalance are listed in Fig. 8. The length of the arrow in the figure represents the amplitude of the optical field, $\varDelta \varphi $ refers to the phase difference between IQ channels in the same polarization, and $\varDelta \theta $ means the polarization angle difference between x- and y- polarized optical fields. ${\vec{{\boldsymbol E}}_{{XI}}}$, ${\vec{{\boldsymbol E}}_{{XQ}}}$ and ${\vec{{\boldsymbol E}}_{{YI}}}$ represent the vector optical fields in the directions of XI, XQ and YI, respectively. In addition, the dot operator means the inner product of vectors in this section. In the case of IQ channel, due to an introduced π phase difference between IQ channels during the calibration process, $\varDelta \varphi \; $ should be π ideally. Here, x-polarization is taken as an example, the interference power should be ${|{{{\vec{{\boldsymbol E}}}_{{XI}}} \cdot \vec{{\boldsymbol e}} + {{\vec{{\boldsymbol E}}}_{{XQ}}} \cdot \vec{{\boldsymbol e}}} |^2} = {|{{E_{\textrm{XI}}} + {E_{\textrm{XQ}}}cos({\varDelta \varphi } )} |^2}$. ${E_{\textrm{XI}}}$ and ${E_{\textrm{XQ}}}$ represent the scalar optical fields of XI and XQ channel in the direction of $\vec{{\boldsymbol e}}$, respectively. When $\varDelta \varphi = \pi $, the interference power could be simply expressed as ${|{{E_{\textrm{XI}}} - {E_{\textrm{XQ}}}} |^2}$. However, in practice, considering the imperfection of the IQ orthogonality, $\varDelta \varphi $ is not strictly equal to π, as shown in Fig. 8(a) and Fig. 8(b). Both cases will cause the optical field of the Q channel to become ${E_{\textrm{XQ}}}cos({\varDelta \varphi } )={-} {E_{\textrm{XQ}}}cos({\pi - \varDelta \varphi } )\; (\frac{1}{2}\pi < \varDelta \varphi < \frac{3}{2}\pi ,\; \varDelta \varphi \ne \pi )$ on the I component. Therefore, the output power will be ${|{{E_{\textrm{XI}}} - {E_{\textrm{XQ}}}cos({\pi - \varDelta \varphi } )} |^2}$ at the destructive interference. At this time, when adjusting the input of Q channel to the minimum interference output power (${E_{\textrm{XI}}} - {E_{\textrm{XQ}}}cos({\pi - \varDelta \varphi } )= 0$), the actual optical power of the Q channel is larger than that of the I channel, and it is not strictly compensated. The larger the value of $|{\varDelta \varphi - \pi } |$, the worse the destructive interference effect.

 

Fig. 8. Different cases caused by orthogonality imperfection of IQ and XY imbalance (Pol.: Polarizer, $\vec{{\boldsymbol e}}$: the unit vector in the direction of ${\vec{{\boldsymbol E}}_{{XI}}}$, $\vec{{\boldsymbol w}}$: the unit vector along the direction of 45° polarization).

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As for the XY channels, because the two polarizations are orthogonal to each other, $\varDelta \theta $ should be $\frac{1}{2}\pi $ ideally. In order to achieve destructive interference, after passing through the 45° polarizer, a phase difference of π is introduced. Similarly, the interference power should be ${|{{{\vec{{\boldsymbol E}}}_{{XI}}} \cdot \vec{{\boldsymbol w}} + {{\vec{{\boldsymbol E}}}_{{YI}}} \cdot ({ - \vec{{\boldsymbol w}}} )} |^2}$ in 45° polarization state. Therefore, the field of XI channel in the 45° polarization can be expressed as the $\frac{{\sqrt 2 }}{2}{E_{\textrm{XI}}}$, while the field of YI channel in the 45° polarization is $- {E_{\textrm{YI}}}\cos \left( {\varDelta \theta - \frac{1}{4}\pi } \right).$ ${E_{\textrm{XI}}}$ and ${E_{\textrm{YI}}}$ represent the scalar optical fields of XI and YI channel in 45° polarization, respectively. When $\varDelta \theta < \frac{1}{2}\pi $, as depicted in Fig. 8(c), the output power of destructive interference could be expressed as ${\left|{\frac{{\sqrt 2 }}{2}{E_{\textrm{XI}}} - {E_{\textrm{YI}}}cos\left( {\varDelta \theta - \frac{1}{4}\pi } \right)} \right|^2}\; (\varDelta \theta < \frac{1}{2}\pi )$. One could adjust the input of YI channel to obtain the minimum interference output power (${E_{\textrm{YI}}}\cos \left( {\varDelta \theta - \frac{1}{4}\pi } \right) = \frac{{\sqrt 2 }}{2}{E_{\textrm{XI}}},\varDelta \theta < \frac{1}{2}\pi $), and the actual optical power of the YI channel is smaller than that of the XI channel at this time. When it comes to $\varDelta \theta > \frac{1}{2}\pi $ as shown in Fig. 8(d), the output power of destructive interference is ${\left|{\frac{{\sqrt 2 }}{2}{E_{\textrm{XI}}} - {E_{\textrm{YI}}}cos\left( {\varDelta \theta - \frac{1}{4}\pi } \right)} \right|^2}\; (\varDelta \theta > \frac{1}{2}\pi )$. Here, the actual optical power of the YI channel is larger than that of the XI channel at the minimum interference output power (${E_{\textrm{YI}}}\cos \left( {\varDelta \theta - \frac{1}{4}\pi } \right) = \frac{{\sqrt 2 }}{2}{E_{\textrm{XI}}},\varDelta \theta > \frac{1}{2}\pi $). Therefore, better orthogonality is also an important condition to ensure accurate compensation of power imbalance. Here, the first step is to correct the quadrature bias to π, which can be achieved by tuning the transmitter to minimize the power under the destructive interference. Then the power imbalance can be compensated by further minimizing the interference power. Finally, the ideal case will be realized with no power imbalance and no interference output power, ensuring the largest range of measurement.

An 8-bit digital to analog converter (DAC) is used to control the modulators, with electrical input scale from -128 to 127. The corresponding relationship between the input scale and the actual output optical power of each channel is shown in the Fig. 9(a). The output power of each channel can be adjusted from -30 dBm to -6 dBm by tuning the scale of the DAC. A finer part is also inserted in the Fig. 9(a). For IQ channels of each polarization, the power difference with the same input scale between XI and XQ is up to 0.3 dB. By contrast, it is much smaller between YI and YQ, all less than 0.1 dB within the scale from 40 to 120. As for XY channels, the power difference will be slightly larger. The power difference between XI and YI or YQ varies from 0.3 to 0.6 dB, while it is generally 0.3 dB between XQ and YI or YQ. It indicates that there will be some offset to the result of XY power imbalance compensation. Figure 9(b) illustrates the optical interference power with different electrical input scale, while the input scale of the complimentary I or Q channel is set to 80. It can be clearly seen that the minimal interference power of each channel is located around the input scale of 80, where the destructive interference occurs between each channel and the power imbalance is further compensated. It is consistent with the principle and concept shown before. The separation among the curves is caused by the power difference between the channels mentioned above.

 

Fig. 9. (a) Optical output power of four channels in DP-QAM transmitter with different electrical input scale. (b) Optical interference power with different electrical input scale (the input scale of the complimentary I or Q channel is set to 80).

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Moreover, to verify the applicability of this method at different optical power range for both IQ and XY power imbalances, different input scales are further tested. To compensate IQ power imbalance, the interference power is measured through adjusting the input scale of YQ for different scale of YI, as shown in Fig. 10(a). As there is very small power difference between YI and YQ, the minimum of each curve is exactly located at the position where the input scales of the two channels are equal, achieving a perfect IQ power imbalance compensation. Meanwhile, to verify the compensation performance of XY power imbalance, the interference power is measured through adjusting the input scale of YI for different scale of XQ, as depicted in Fig. 10(b). The power transfer function of Fig. 10(b) has a similar trend to that of Fig. 10(a). Ideally, the minimal power should also occur when the input scales are equal, but there is a slightly separation because of a larger power difference between XQ and YI. However, it should be noted the power difference is caused by the imperfection of the devices, which does not affect the XY power calibration. When the input scale of YI is adjusted to minimize the interference output of YI and XQ, the destructive interference occurs and the XY power imbalance is further compensated.

 

Fig. 10. (a) Measured interference power through adjusting the input scale of YQ for different scale of YI to detect IQ power imbalance and (b) adjusting the input scale of YI for different scale of XQ to detect XY power imbalance.

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5. Conclusion

DP-QAM based on coherent IQ transmitter is a potential solution for the next generation optical communication systems. Various impairments such as IQ and XY power imbalances are still barriers to realize high-speed long-haul transmission. The impact of both XY and IQ power imbalances are first investigated experimentally running at QAM format and high baud rate including 45, 64 and 86 GBd. The penalty from the IQ power imbalance is larger in the region of high OSNR, while the penalty from the XY power imbalance is slightly larger with low OSNR. Meanwhile, higher baud rate usually has larger power-imbalance-induced penalty, indicating the importance of power imbalance compensation and calibration. Furthermore, an interference-based scheme is proposed and experimentally demonstrated for detection and calibration of IQ and XY power imbalances in DP-IQ transmitter. The principle and the concept of the method are also given in detail. By injecting the “01” coded BPSK electrical signal, we use the existing couplers and modulators in the DP-IQ transmitter to obtain the interference power between two channels. The same structure can also be used to compensate IQ and XY skews. After removing the time skew, the power imbalance between two channels can be calibrated by minimizing the interference power. The measured results are consistent with the given theoretical analysis. Compared with utilizing DSP, it is a more power-efficient way using for long-haul transmission. Meanwhile, the proposed technique is also suitable for various modulation formats, data sequences, and waveforms.