## Abstract

Dual-polarization quadrature amplitude modulation (DP-QAM) is one of the feasible paths towards 100-Gb/s, 400-Gb/s and 1-Tb/s optical fiber communications systems. For DP-QAM transmitter, the time mismatch between the in-phase and quadrature (IQ) or *x*-polarized and *y*-polarized (XY) tributary channels is known as the IQ or XY skew. Large uncompensated IQ or XY skew can significantly degrade the optical fiber communications system performance. Sometimes, time-interleaved return-to-zero (RZ) DP signal is preferred with lower nonlinear polarization scattering induced penalty. In this work, detection and alignment of DP-QAM transmitter IQ and XY skews using reconfigurable interference is experimentally demonstrated. For IQ skew detection, a total dynamic range of 26.4 dB is achieved with ~1-dB power change for 0.5-ps skew from well alignment. For XY skew detection, it shows 23.2-dB dynamic range, and ~1.5-dB power change is achieved for 1-ps XY skew. Fast detection algorithm for arbitrary skew is also proposed and experimentally verified. The scheme is compatible with different modulation formats, flexible data sequences, and variable waveforms.

© 2016 Optical Society of America

## 1. Introduction

Optical fiber communications, as the backbone of today’s telecommunications infrastructure, supports information exchange through global networks. To meet the ever-growing requirement for data-carrying capacity, a few degrees of freedom of photon (amplitude, phase, time, wavelength, and polarization) have been used to multiplex low speed electrical data streams [1,2]. Recently, another promising dimension of photon that has gained much interest is to transmit independent data streams, each in a different core using multicore fibers (MCF) or each on a different spatial mode using few-mode fibers (FMF) [3–6].

For industry commercialization, mature technology is always preferred. Dual-polarization quadrature phase-shift keying (DP-QPSK) modulation format has been adopted by the optical fiber communications industry for its latest efforts on 100-Gb/s line-side coherent solutions. Multiplexing two orthogonal polarizations is proved to be a very effective method to increase the capacity and spectral efficiency of an optical communications system by a factor of 2 [7,8]. Furthermore, by using the complex in-phase (I) and quadrature (Q) domain, a record 2048 quadrature amplitude modulation (QAM) of optical signal has recently been demonstrated, which gives >10 × increase for the capacity and spectral efficiency simultaneously [9]. Consequently, DP-QAM is the promising path towards 400-Gb/s and 1-Tb/s commercial optical fiber communications systems [10–12].

For DP-QAM transmitter, the time mismatch between the IQ or *x*-polarized and *y*-polarized (XY) tributary channels is known as the IQ or XY skew. Large uncompensated IQ or XY skew, especially for the IQ skew, can significantly degrade the system performance in the coherent optical communications system. This issue is even more critical for higher-order QAM formats [13,14]. The transmitter-side XY skew can combine with the differential group delay (DGD) and polarization mode dispersion (PMD) in the optical transmission system. Sometimes, for long-haul transmission, time-interleaved return-to-zero DP signal is preferred with lower nonlinear polarization scattering induced penalty [15]. Consequently, it is crucial to detect and align IQ and XY skews in the coherent optical communications system.

Delay-interference method has been used to differential quaternary phase-shift keying (DQPSK) signals with additional detection and processing [16,17]. Moreover, several other methods have been proposed and demonstrated for skew estimation and compensation at the coherent receiver end [13,14]. To measure the DP-QAM transmitter skew at the transmitter end, one straightforward way is to use a high-speed oscilloscope. However, this requires external equipment, which is quite bulky and expensive. A laudable goal would be to detect and align the timing skews of all tributary channels for DP-QAM transmitter with a simple, sensitive, and fast method, which can be potentially built within the transmitter [18,19].

In this paper, we experimentally demonstrate IQ and XY skew detection and alignment of optical DP-QAM transmitter using reconfigurable interference. By interfering two tributary channels with identical binary phase-shift keying (BPSK) modulations, either both tributaries from same polarization, or one tributary from each polarization, periodic power transfer function with >23-dB dynamic range is obtained to detect and align IQ or XY skew of DP-QAM transmitter. For IQ skew detection, a total dynamic range of 26.4 dB is achieved with ~1-dB power change for 0.5-ps skew from well alignment. For XY skew detection, it shows 23.2-dB dynamic range, and ~1.5-dB power change is achieved for 1-ps XY skew. The scheme tolerance to different performance degradation effects is theoretically analyzed and experimentally investigated. Moreover, fast detection scheme for arbitrary skew measurement is also proposed and experimentally verified. The scheme is compatible with different modulation formats (such as on-off keying (OOK), PSK, non-return-to-zero (NRZ), return-to-zero (RZ), etc.), flexible data sequences (such as periodic, pseudorandom binary sequence (PRBS), inverted, etc.), and variable waveforms (such as rectangular, sine wave, etc.).

## 2. Principle of operation

In optics, interference is a phenomenon in which two optical waves superpose with each other, and form a resultant wave with larger or smaller amplitude. Interference usually refers to the interaction of optical waves that are coherent (i.e., with a constant phase difference and the same frequency), especially if they come from the same optical source. Constructive interference gives maximal optical power, and occurs when the phase difference between the optical waves is an even multiple of π; while destructive interference produces minimal optical power, and occurs when the phase difference between the optical waves is an odd multiple of π. If the phase difference is between these two extremes, then the magnitude of the resultant wave resides between the maximal and minimal optical power values [20].

Optical DP-QAM transmitter has four tributary channels, each one starts from the same continuous-wave (CW) laser. Every two channels have a constant phase difference and the same frequency, and thus all of them are inherently coherent. Consequently, it provides the ideal conditions to utilize optical interference.

Figure 1 illustrates the principle of operation by interfering DP-QAM transmitter tributary channels with identical modulated waveforms. First of all, we need to generate identical waveforms for tributary channels from one shared CW laser, which is shown in Fig. 1(a). Here, we use a 2 × 2 optical coupler (OC) model to represent the 1 × 2 beam splitter (BS). The 2 × 2 OC has two input ports and two output ports. The relationship between input and output ports can be represented as a transfer matrix [21]:

To detect the IQ skew from tributary channels with same polarization, one can interfere the identically modulated waveforms using an OC, which is shown in Fig. 1(b). The IQ skew of the DP-QAM transmitter comes from three sources. One is from the timing skew of the electrical signals into the optical modulators, the second one is from the optical path length difference between the I and Q tributary channels, and the last one is from the optical phase difference induced by the phase shifter (PS) and OC [21]. They altogether will contribute to the IQ skew ${{\displaystyle \Delta t}}_{IQ}$, which is expressed in Eqs. (2) and (3):

By implementing the effects of optical modulation and accumulated phase difference between the two arms of I and Q tributaries, one can obtain Eq. (4):

To achieve completely destructive interference, symmetric 2 × 2 OC is utilized, with a coupling ratio of $\epsilon =0.5$. By cascading all these effects mentioned above and interfering I and Q tributaries at ${c}_{1}$ and ${c}_{2}$, we finally reach the optical field transfer function from the CW laser input at ${a}_{1}$ to the two complementary output ports of the quadrature amplitude modulator ${d}_{1}$ and ${d}_{2}$, which is depicted in Eq. (8):

From the transfer function Eq. (8) one can see, the ${d}_{1}$ and ${d}_{2}$ ports have a total output power of ${\left|Mod(t)\right|}^{2}\cdot {E}_{0}^{2}$. Note that high-speed optical modulators are applied to modulate the optical field, while low-speed optical power meter is used to measure the output power. Consequently, ${\left|Mod(t)\right|}^{2}$ gives a constant average value over the optical power meter measurement time. Furthermore, the output power from ${d}_{1}$ or ${d}_{2}$ port changes periodically, as a function of the IQ skew (${\mathrm{sin}}^{2}(\frac{\Delta {t}_{IQ}\cdot \omega}{2})$ or ${\mathrm{cos}}^{2}(\frac{\Delta {t}_{IQ}\cdot \omega}{2})$). If there is no IQ skew (${{\displaystyle \Delta t}}_{IQ}=0$), ${d}_{1}$ is the port with destructive interference and has no output power, while ${d}_{2}$ is the port with constructive interference and has maximal output power ${\left|Mod(t)\right|}^{2}\cdot {E}_{0}^{2}$.

To detect the XY skew from tributary channels with orthogonal polarizations, one can interfere the identically modulated waveforms (${E}_{3}(t)$ and ${E}_{4}(t)$) from the ${d}_{1}$ ports of two separate quadrature amplitude modulators using an optical polarizer, aligned 45° to the *x*- and *y*- polarized tributary channels, which is shown in Fig. 1(c). The XY skew of the DP-QAM transmitter comes from three sources. One is from the timing skew of the electrical signals into the optical modulators, the second one is from the optical path length difference between the *x*- and *y*- polarized tributary channels, and the last one is from the optical phase difference induced by the BS, polarization rotator (PR) and polarization beam combiner (PBC) [22–25]. They altogether will contribute to the XY skew ${{\displaystyle \Delta t}}_{XY}$, which is expressed in Eqs. (9) and (10):

Note that for each polarization, only one tributary (i.e., XI) is turned on, while the other tributary (i.e., XQ) is set to be off with no output power. Correspondingly, we set ${c}_{2}=0$ in the transfer function Eq. (11). Similarly, by considering the effects of optical modulation and accumulated phase difference between the two arms of X and Y tributaries, one can obtain Eq. (14):

The optical fields of the two tributary channels (${d}_{1}$ and ${d}_{1}^{\text{'}}$) from the output port of the DP-QAM transmitter have identically modulated waveforms, and orthogonal polarizations along axes $\widehat{y}$ and $\widehat{x}$. After passing the optical polarizer, which is aligned 45° to the *x*- and *y*- polarized tributary channels, ${E}_{3}(t)\widehat{y}$ and ${E}_{4}(t)\widehat{x}$ are projected into a state of polarization parallel to the polarizer’s transmission axis $\widehat{w}$. As a result, one can calculate the final output optical field $e$ from the polarizer, which is depicted in Eq. (15):

From the result we can see, the polarizer output power is $\frac{1}{2}{\left|Mod(t)\right|}^{2}\cdot {E}_{0}^{2}{\mathrm{cos}}^{2}(\frac{\Delta {\phi}_{XY}}{2})$. It is a periodic function of the XY skew (${\mathrm{cos}}^{2}(\frac{\Delta {t}_{XY}\cdot \omega}{2})$). If there is no XY skew (${{\displaystyle \Delta t}}_{XY}=0$), one has constructive interference from the polarizer output, and it gives the maximal output power $\frac{1}{2}{\left|Mod(t)\right|}^{2}\cdot {E}_{0}^{2}$.

## 3. Conceptual diagram and experimental setup

In this section, we describe the concepts for IQ and XY skew detection and alignment using reconfigurable interference. The experiments are carried out with external optical and electrical equipments. In principle, to perform these procedures, one can build polarization elements and photodiodes within the DP-QAM transmitter using micro or integrated optics.

The conceptual diagram of sub-unit-interval (UI) and multi-UI IQ skew and XY skew detection and alignment using reconfigurable interference is shown in Fig. 2. As illustrated in Fig. 2(a), for sub-UI IQ skew measurement, identically periodic “01” patterns are encoded on BPSK signal for both of XI and XQ tributary channels, while modulator YI and YQ tributaries are set to null point with no electrical modulation. As a result, there is no output power from YI and YQ tributary channels in an ideal case. To achieve larger sensitivity for small IQ skew value, we set destructive interference at no-skew (well-aligned) condition, while constructive interference for interleaved (1-UI IQ skew) case. Consequently, the relative phase difference (*Δϕ*) between Ch. XI and Ch. XQ is adjusted to π using a PS. After passing through the OC, power transfer function with a period of two UIs is obtained to determine the sub-UI IQ skew value (*Δt*) for *x*-polarization. Similarly, one can determine the sub-UI IQ skew value for *y*-polarization by turning YI and YQ tributaries on, instead of the above mentioned XI and XQ tributaries. IQ channels with close performance can provide good destructive interference and thus large measurement dynamic range.

As shown in Fig. 2(c), for sub-UI XY skew measurement, identically periodic “01” patterns are encoded on BPSK signal for both XI and YI tributary channels, while modulator XQ and YQ tributaries are set to null point with no electrical modulation. As a result, there is no output power from XQ and YQ tributary channels in an ideal case. As there is no introduced phase difference (*Δϕ* = 0) between XI and YI paths, one can obtain constructive interference for well-aligned (0-UI XY skew) case, while destructive interference for interleaved (1-UI XY skew) case. After passing through a polarizer, which is aligned 45° to XI and YI tributary channels, power transfer function with a period of two UI is obtained to determine the sub-UI XY skew value (*Δt*). Close XI and YI tributary channels with well 45° polarization alignment to the polarizer can provide good destructive interference for interleaved case and thus large measurement dynamic range.

The sub-UI method can be used to measure IQ skew and XY skew with fine resolution. The ultimate skew detection resolution is mainly limited by the electrical input baud rate and the resolution of optical power meter. To achieve larger IQ or XY skew measurement range, electrical input with longer repetitive length should be used instead. As depicted in Figs. 2(b) and 2(d), a periodic pattern with consecutive *m* “0”s and *m* “1”s can be used to determine multi-UI IQ or XY skew value (*n* × *t _{UI}*) and measure the skew value up to 2

*m*UI.

After performing the sub-UI and multi-UI IQ skew or XY skew measurement, one can compensate or configure it to desired value by adjusting the relative delays among the electrical driving signal inputs. Here, we only illustrate the concept and perform the experimental demonstration for periodic NRZ-BPSK modulation with rectangular waveform. In principle, the scheme is compatible with different modulation formats (such as OOK, PSK, NRZ, RZ, etc.), flexible data sequences (such as periodic, PRBS, inverted, etc.), and variable waveforms (such as rectangular, sine wave, etc.) [26].

Figure 3 shows the experimental setup of IQ skew and XY skew detection and alignment for DP-QAM transmitter. The DP-QAM transmitter is composed of four tributary channels XI, XQ, YI, and YQ, which are used for in-phase and quadrature modulation of both *x*- and *y*- polarizations. PS is implemented to adjust the relative phase difference between I and Q tributary channels. The transmitter is set to a baud rate of 31.79 GHz, which corresponds to a UI of 31.46 ps. The electrical input skew is adjustable at a 0.5-ps resolution. This limits the skew detection resolution in the following experiment.

To detect the *x*-polarized IQ skew, we can turn on XI and XQ only, and feed them with identical patterns. As an example, identically periodic patterns are encoded on BPSK signal for both of XI and XQ tributary channels, while modulator YI and YQ tributaries are set to null point with no electrical modulation. As shown in Fig. 3(a), an inline power meter with 0.001-dB resolution is inserted to measure the output power of DP-QAM transmitter. A digital communications analyzer (DCA) is used to capture waveforms of the tributary channels and their interference pattern.

To detect the XY skew, we can turn on one tributary channel from *x*-polarized ones, one tributary channel from *y*-polarized ones, and feed them with identical patterns. As an example, identically periodic patterns are encoded on BPSK signal for both of XI and YI tributary channels, while modulator XQ and YQ tributaries are set to null point with no electrical modulation. As displayed in Fig. 3(b), a polarizer, which is aligned 45° to XI and YI tributary channels, is connected to the output of the DP-QAM transmitter. A power meter with 0.001-dB resolution, following the polarizer, is used to measure the interference power of the two tributary channels. Partial DP-QAM transmitter output is tapped to DCA, which is used to capture waveforms of the tributary channels and their interference pattern.

In the above concept introduction and the following experiment, we only turn on and interfere two tributary channels, while turning off the other two. In fact, one can still perform this IQ and XY skew detection and alignment process, even all the four tributary channels are on. For *x*- or *y*- polarized IQ skew detection, one can leverage the polarizer to eliminate the other undesired polarization. As an example, for *x*-polarized IQ skew detection, by adjusting the DP-QAM transmitter output with the polarization controller (PC), one can align $\widehat{x}$ to $\widehat{w}$. In such a case, only XI and XQ tributary channels can pass the polarizer to interfere with each other and determine the *x*-polarized IQ skew. For XY skew detection, one can set both XI&XQ and YI&YQ to constructive interference condition. By interfering these two resultant constructive interference waves using the polarizer, one can still determine the XY skew.

## 4. Experimental results

In this section, we demonstrate the experimental results of IQ and XY skew detection and alignment for optical DP-QAM transmitter. Measured optical power and captured waveforms are provided with different experimental scenarios.

Figures 4(a) and 4(c) show the measured inline optical power for sub-UI IQ skew and XY skew using identical periodic “01” patterns. The period of the power transfer function is ~63 ps, which is 2 × 31.46 ps. For sub-UI IQ skew detection, as there is an introduced π phase difference (*Δϕ* = π) between XI and XQ paths, 0-skew case gives destructive interference, which has the smallest output power. A total dynamic range of 26.4 dB is achieved, with ~1-dB power change for 0.5-ps IQ skew from well alignment. For sub-UI XY skew detection, as there is no introduced phase difference (*Δϕ* = 0) between XI and YI paths, 0-skew case gives constructive interference, which has the largest output power. A total dynamic range of 23.2 dB is achieved, with ~1.5-dB power change for 1-ps XY skew from interleaved case. By using a multi-UI periodic pattern with consecutive 16 “0”s and 16 “1”s, a maximum of 32-UI skew can be measured with 27.4-dB dynamic range for IQ skew and 27.6-dB dynamic range for XY skew, which is displayed in Figs. 4(b) and 4(d). From Figs. 4(a)–4(d) we can see, the destructive interference region has sharp change, and thus provides better measurement sensitivity and resolution.

Figure 5 illustrates the observed DCA waveforms of original periodic pattern (16 “0”s & 16 “1”s) from DP-QAM tributaries with BPSK modulation and their interference with different multi-UI skew. As the DCA can only capture the intensity information, the DP-QAM tributary channels with BPSK modulation are always with intensity “1” output. The dips in the pattern are due to the modulation phase change from “0” to “π”. The time interval between two intensity dips is 16 UI. From the interference patterns in Fig. 5, we can clearly see the periodicity of 32 UI and the related power variation. For 0-UI IQ skew, it is totally destructive interference, and thus the interference pattern is close to intensity “0” across the period. When the IQ skew is 16 UI, it is totally constructive interference, and thus the interference pattern is close to the original pattern of each tributary channel (Ch. XI or Ch. XQ). For 0 UI XY skew, it is totally constructive interference, and thus the interference pattern is close to the original pattern of each tributary channel (Ch. XI or Ch. YI). When the XY skew is 16 UI, it is totally destructive interference, and thus the interference pattern is close to intensity “0” across the period. For other amount of multi-UI IQ or XY skew, some part of the pattern is constructive interference and shows intensity “1”, while the other part of the pattern is destructive interference and shows intensity “0”.

The periodicity of the measured optical power as a function of multi-UI IQ and XY skew for patterns with different consecutive “0”s and “1”s is shown in Fig. 6. By doubling the period of the consecutive pattern, one can have twice the skew detection range. Pattern with longer consecutive bits can be used to detect larger skew, while pattern with shorter consecutive bits can provide better measurement sensitivity and resolution. As distinct relative-phase-difference settings are used for IQ and XY skew detection, one power transfer function starts with destructive interference, while the other one starts with constructive interference.

As measured in Fig. 7, the channel power of one tributary channel is dependent on the number of consecutive bits in periodic patterns for multi-UI IQ and XY skew detection. BPSK signal with smaller number of consecutive bits pattern has more power dips in the modulated optical waveform and thus lower channel power. The tributary channel power difference for pattern with 1 and 16 consecutive bits can be up to 4.8 dB. The difference in the absolute values of the channel power in Figs. 7(a) and 7(b) is due to the different setups used for IQ and XY skew detection.

## 5. Scheme tolerance and compatibility

In Section 2, “principle of operation”, we detail the fundamental physics theory and mathematical equations with an ideally operational scenario. In the actual implementation, the operating conditions are more sophisticated. Figure 8 depicts the potential performance degradation effects of IQ skew detection scheme for DP-QAM transmitter. In the figure, the blue, green, and red arrows represent the optical fields of Ch. I, Ch. Q, and the resultant after their interference, respectively. The length of the arrow stands for the amplitude of the electrical field, while the angle between blue and green arrows illustrates the relative phase difference between Ch. I and Ch. Q. The perfect operating condition for destructive interference is shown in Fig. 8(a). The optical fields of tributaries Ch. I and Ch. Q have same amplitude and exactly 180° phase difference. This gives theoretically no output power for destructive interference, and thus the largest measurement dynamic range and best IQ skew detecting resolution.

The actual operation conditions fall into the scenarios described in Figs. 8(b)–8(d). For power imbalance only case, the optical fields of tributaries Ch. I and Ch. Q have different amplitudes, but exactly 180° phase difference. For quadrature bias imperfection only case, the optical fields of tributaries Ch. I and Ch. Q have same amplitude, but potentially a 170° phase difference. The real operating case is usually combined with both power imbalance and quadrature bias imperfection, which is shown in Fig. 8(d). Even if it is destructive interference, these cases have certain left output power. Thus it will sacrifice the IQ skew detecting resolution, but not the detecting range. Furthermore, by finely tuning the transmitter, one can minimize these performance degradation effects for larger measurement dynamic range.

To investigate the compatibility and robustness of the scheme, we also experimentally studied the inline power as a function of sub-UI IQ skew for different phase difference between IQ channels using PRBS7 pattern. As illustrated in Fig. 9, PRBS7 pattern can still provide a power transfer function for sub-UI skew measurement. 10° variation of Δϕ from the optimized 180° induces a ~4.7-dB power measurement dynamic range reduction.

Similar to the IQ skew, there are some performance degradation effects of XY skew detection scheme. Power imbalance and polarization alignment imperfection of the actual operating scenarios can leave certain output power at destructive interference condition, and thus sacrifice only the XY skew detecting resolution.

During the skew detection and alignment process, only two tributary channels are turned on, while the other two are set to be off. However, as the inner modulator bias may not be ideally adjusted to the null point, there can still be certain output power from those unused tributary channels. Together with the above discussed degradation effects, it will limit the minimal destructive interference power, and thus the total power measurement dynamic range. As a result, the power transfer function can be flat for certain range of skew value, which is close to the destructive interference condition. In such a case, one can still determine the destructive interference condition, which is the central point of the flat region in the power transfer function. Moreover, by artificially introducing certain degradation effect (i.e., quadrature bias imperfection), one can still locate the destructive interference condition at the minimal power in the shallowed transfer function.

## 6. Fast detection algorithm for arbitrary skew

The demonstrated scheme above can determine the skew value in a sweeping manner. However, by using regular multi-UI scheme, not only the detection speed is low, but also the resolution that can be detected is limited, for a transmitter with large multi-UI and residue sub-UI skew. Therefore, it is highly desirable to have a fast detection algorithm for arbitrary skew with high resolution.

Here, we propose and experimentally demonstrate a potential scheme to achieve the above mentioned features altogether. As depicted in Fig. 10, we can use the fast skew detection method to double the skew detection range with single-short optical power measurement. First, we can use BPSK signals with identically periodic “01” patterns for both Ch. A and Ch. B tributary channels. By sweeping the time delay between two BPSK signals, we can deskew the sub-UI time misalignment between Ch. A and Ch. B. The multi-UI skew monitoring range can potentially be doubled by simply doubling the period of pattern. With a single-shot power measurement for low or high power value, one can determine quasi-even or quasi-odd multi-UI skew. This fast detection algorithm for arbitrary skew is compatible with both IQ and XY skew detection and alignment schemes, which are discussed in details above.

Table 1 summarizes the fast tracking demonstration of 15.x UI IQ skew. At the beginning, we artificially set the DP-QAM transmitter with 15.x UI IQ skew for one polarization. The outputs of the tributaries from the other polarization are turned off, and the DP-QAM transmitter output power is measured with an inline power meter, as shown in Fig. 3. To detect certain skew, we need to at least double the measurement range of the skew to cover the positive and negative skew value cases. Consequently, we use a periodic test pattern with up to 32 UIs in the following demonstration.

First, we use a test pattern “01” to determine sub-UI skew. By finely tuning the electrical inputs relative delay between I and Q tributaries within sub-UI range, we find a local maximal power, which is −2.3 dBm. This confirms it is under constructive interference condition, and the skew is an odd multiple of UI. Second, we shift the skew artificially with + 1 UI to even multiple of UI. It is then under destructive interference condition, and we measure a low power −28.4 dBm. Third, we use a test pattern “0011” to determine if it is with 4n or 4n + 2 UI skew. A −24.5-dBm lower power is measured and confirms it is with 4n UI skew. Fourth, we use a test pattern “0000,1111”, and find out that it is with 8n UI skew (−26.1 dBm). Fifth, a “0000,0000,1111,1111” test pattern is implemented, and it indicates a 16n UI skew with a low power −24dBm. Finally, by using “0000,0000,0000,0000,1111,1111,1111,1111” test pattern and measuring a 2.2-dB high power, we affirm that it is with positive 16-UI skew.

By interpreting the steps and measured power values above, we can determine this artificially setting, 15.x UI IQ skew, which is an example of arbitrary skew.

## 7. Discussion

The above experimental demonstrations for detection and alignment of DP-QAM transmitter IQ and XY skews use NRZ-BPSK modulation with external fiber optic components and optical power meter. Nonetheless, its fundamental principle of operation is compatible with different optical platforms and modulation schemes. This potentially paves the way for its implementation into highly-integrated commercial DP-QAM transmitter, and applications beyond.

First of all, the scheme has a simple structure, and thus it is easy to be implemented into the commercial product. It can be realized with different optical platforms, such as free-space optics, fiber optics, micro optics, or integrated optics system with OC, polarization controller, polarizer, and optical power meter. For integrated optics system, different material systems (Si, SiN, Silica, or III-V etc.) are also inherently compatible with the scheme. Instead of external optical power meter, integrated photodiodes can be implemented to perform the same skew detection function, by simply monitoring the DP-QAM transmitter output power.

Furthermore, as long as one uses identical electrical inputs to the optical modulators, the scheme is compatible with different modulation formats, flexible data sequences, and variable waveforms. As discussed in Section 5, the minimal power of the destructive inference is limited by a few degradation effects. The maximal power of the constructive interference is limited by the laser output power. Another key limiting factor to the maximal power is the modulation format ${\left|Mod(t)\right|}^{2}$ applied. As NRZ-BPSK has the lowest modulation loss, it provides the highest power measurement dynamic range, and thus the best skew detection resolution.

Last but not least, the demonstration is specifically for pre-calibrating the DP-QAM transmitter-side skews. In general, the working principle can be applied to align and correlate any coherent optical waveforms.

## 8. Conclusion

In conclusion, DP-QAM is very promising to be implemented in the next generation high-speed optical fiber communications systems. Controlling DP-QAM transmitter IQ and XY skews are critical to different application scenarios. This work experimentally demonstrates detection and alignment of DP-QAM transmitter IQ and XY skews using reconfigurable interference. For IQ skew detection, a total dynamic range of 26.4 dB is achieved with ~1-dB power change for 0.5-ps skew from well alignment. For XY skew detection, it shows 23.2-dB dynamic range, and ~1.5-dB power change is achieved for 1-ps XY skew. The scheme shows good tolerance to different performance degradation effects. Furthermore, fast detection algorithm for arbitrary skew measurement is proposed and experimentally demonstrated. The skew measurement range can be doubled with an extra single-shot optical power measurement. The scheme shows great potential for commercial DP-QAM transmitter implementation, and applications beyond.

## Acknowledgments

The authors would like to acknowledge Dr. Theodore J. Schmidt for fruitful discussions.

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