Optical Comparison Operation for 8-Bit QPSK-Modulated Signal by Using Serially-Cascaded Delay Line Interferometer

: An all-optical comparator is desirable to realize large-capacity, fully-transparent, and energy-efﬁcient communication systems, as it is considered to be a fundamental component to perform most of the operations, including packet switching, label recognition, error detection and correction, and so on. However, most of the previous studies have been conﬁned to the on–off keying (OOK) modulation format, not phase-shift keying (PSK) modulation. In this paper, the author provides a novel optical comparator designed for quadrature PSK (QPSK)-modulated signal, which comprises a code word with 8-bit length, using a serially-cascaded delay line interferometer. The proposed comparator yields constellations having the information of a Hamming distance based on the designed code, when several patterns of QPSK signal are injected into the comparator. The paper experimentally demonstrates the feasibility of the optical comparison operation for 8-bit QPSK-modulated return-to-zero (RZ) signal at 10 Gbaud.

Among these components, the optical comparator is considered to be fundamental because it can perform most of the operations, including packet switching, label recognition, error detection and correction, etc. In this context, various optical comparators have been proposed by using the several platforms such as a semiconductor optical amplifier [17,18], a nonlinear fiber ring resonator [19], a Fabry-Perot laser diode [20], a micro ring resonator [21], and an electro-optical ring resonator [22].
On the other hand, the previous studies have been confined to on-off keying (OOK) modulation format, not phase-shift keying (PSK) modulation. The optical comparator for PSK modulation is desirable due to the requirement of coherent optical transmission for high-speed and long-haul communication. However, to our best knowledge there have been no reports of this kind of optical comparator. Previously, the author proposed a novel type of optical comparator for PSK modulation, and demonstrated the comparison operation for 4-and 6-bit length quadrature PSK (QPSK)-modulated signals [23]. In this paper, the author improves the valid number of code word to 8-bit length, and reports a newly evaluated comparison operation for 8-bit QPSK signal by using a serially-cascaded delay line interferometer (DLI) at 10 Gbaud. Figure 1 illustrates the operating principles of the optical comparator for QPSK modulation. The proposed comparator is defined for a particular 8-bit code which consists of four successive QPSK symbols; the designed code is named as "comparator code" in this paper. The main purpose of the comparator is to calculate comparison results based on the comparator code. When an arbitrary 8-bit code is injected into the comparator, our scheme yields an optical symbol whose constellation reflects the Hamming distance between the arbitrary 8-bit code and the comparator code. In this context, the Hamming distance is derived as:

Operating Principles
where x = x 0 , x 1 , · · · , x n−1 and y = y 0 , y 1 , · · · , y n−1 are n-bit code words, and the Hamming distance provides the number of coefficients in which they differ.  Figure 1. Operating principles of the optical comparator for an 8-bit quadrature phase-shift keying (QPSK) signal. In this figure, the comparator is designed for a "00 11 00 11" code to set their phase shifts at (0, π, 0, π), and the working example is illustrated when a "11 00 11 00" signal is input. It is shown that the Hamming distance of d H (00 11 00 11, 11 00 11 00) corresponds to the distance of both constellations.
The proposed comparator is designed for four successive QPSK symbols, and their constellation is given in the form of a Gray code. In this code, two adjacent constellations differ in only one bit, and the most-significant-bit and least-significant-bit contribute to the quadrature and in-phase component in the complex plane. The proposed comparator requires three operational steps, as follows: 1. S/P conversion: to convert serially-successive symbols into four parallel symbols. 2. Phase shift: to rotate the phases in each parallel symbol; the amounts of the phase rotation are determined according to the comparator code to convert their original constellations into a first quadrant in each QPSK symbol, which corresponds to a "00" constellation in Gray code. 3. Optical coupling: to yield a complex symbol from four parallel symbols optically.
As an example, an optical comparator designed for a "00 11 00 11" code (e.g., a "00 11 00 11" comparator) is considered. According to the design concept, in the comparator, four phase-rotations for each QPSK symbol are set at 0, π, 0, and π, respectively. By the phase rotations, every constellation in "00 11 00 11" code will be converted into a "00" constellation. When a "00 11 00 11" signal is injected into the comparator, the comparator generates the coupled symbol whose constellation is located at the vector sum of four "00" constellations in the complex plane; the constellation is named as "base constellation" in this paper. On the other hand, when a "11 00 11 00" signal is assumed, the set of the (0, π, 0, π) phase-shift contributes to rotate their constellations from (11, 00, 11, 00) to (11,11,11,11). As a result, the coupled symbol has a constellation corresponding to the vector sum of four "11" constellations. In this constellation, the distance from the base constellation coincides with the Hamming distance of d H (11001100, 00110011) = 8, because the difference vectors in each symbol, which are based on each symbol of the comparator code, can be surely aligned in a direction inclined by a π/4 angle with respect to the horizontal axis in the complex plane. Therefore, the comparator provides the constellation having the comparison result against an arbitrary 8-bit code. Figure 2 shows the experimental setup of an 8-bit optical comparator. The experimental setup mainly consisted of two components: (A) a QPSK signal generator with optical gate and (B) an optical comparator. The QPSK generator utilizes a tunable laser diode (TLD) (Santec, Tokyo, Japan), pulse pattern generator (PPG) (Anritsu, Kanagawa, Japan), lithium-niobate Mach-Zehnder modulator (LN-MZM) (Sumicem, Tokyo, Japan), and dual-parallel LN-MZM (Sumicem, Tokyo, Japan), respectively. In the generator, a probe light at 1550 nm was generated from the TLD, and the probe was QPSK modulated by using the dual-parallel LN-MZM and the PPG with a 2 9 − 1 pseudo random binary sequence (PRBS) at 10.72 Gbaud. The QPSK signal was then return-to-zero (RZ) modulated by the second LN-MZM driven by the PPG with a 10.72 GHz clock. The optical gate consisted of an LN-MZM and a PPG. The generated QPSK RZ-signal was injected into the third LN-MZM, and four successive QPSK symbols were selected from 2 9 − 1 PRBS by using the second PPG with a 400 ps gate pulse. Then, the selected symbols were injected into the following optical comparator. The optical comparator comprised two serially cascaded DLIs. The first and second DLIs had 5 and 10 GHz of free spectrum ranges (FSRs), respectively. In the four QPSK symbols at 10 Gbaud, the first and third symbols were optically overlapped in the 5 GHz DLI as well as the second and fourth symbols. The overlapped first + third and second + fourth symbols were then overlapped in the following 10 GHz DLI. As a result, the successive QPSK symbols were converted in parallel and optically coupled, and then the coupled symbol was detected at a following balanced photo detector (BPD).

Fundamental Property
The author experimentally evaluated the fundamental properties of the optical comparator. First, the impulse response was evaluated by using an optical short-pulse. The pulse was generated by a mode-locked laser diode emitting at 1550 nm wavelength, which had a 9.2 ps full width at half maximum (FWHM). Figure 3 shows an impulse response of the comparator: (a) input pulse and (b) output pulse train. In this figure, the short pulse is separated into four parts through the two DLIs, and the four pulses appear at equal intervals of time. A 93 ps time duration between first and second pulses offered 10.72 GHz of FSR, and 199 ps (93 ps + 106 ps) time duration between first and third pulses offered 5.03 GHz of FSR.  Then, the transmission spectra were evaluated with an amplified spontaneous emission (ASE) light. Figure 4 shows the transmission spectrum of the "00 00 00 00", "11 00 11 00", "11 10 10 00", and "00 10 01 00" comparators. In Figure 4a, as the "00 00 00 00" spectrum laterally shifted by 0.04 nm to a long-wavelength side, it exactly overlapped the "11 00 11 00" spectrum. The wavelength difference of 0.04 nm corresponds a half of a wavelength interval at 10 GHz (=0.08 nm/2), which is related to a π phase difference at 10 GHz DLI between "00 00 00 00" and "11 00 11 00" comparators. Similarly, in Figure 4b, the "11 10 10 00" spectrum exactly overlapped the "00 10 01 00" spectrum with a 0.04 nm shift, which corresponds to a π phase amount between "11 10 10 00" and "00 10 01 00" comparators.  Figure 4. Transmission spectra of the 8-bit optical comparator: (a) "00 00 00 00" and "11 00 11 00" comparator. (b) "11 10 10 00" and "00 10 01 00" comparator. In these figures, the "00 00 00 00" and "11 10 10 00" spectra exactly overlap the "11 00 11 00" and "00 10 01 00" spectra with 0.04 nm wavelength shift, which correspond to a π phase different at 10 GHz DLI.

Discussion
The important findings in this study are: (1) the optical comparator designed for a "00 00 00 00" code, which consists of a successive four QPSK symbols, yielded an optical symbol whose constellation was located in conformity with a Hamming distance based on the "00 00 00 00" code. (2) Three additional comparators were designed, whose code words were "11 00 11 00", "11 10 10 00", and "00 10 01 00", and same results were obtained. Therefore, it is concluded that the proposed comparator can be designed for an arbitrary 8-bit code, and it offers the comparison result based on the designed code.
Additionally, the author will discuss the feasibility from a point of a practical view: (i) high-order modulation, (ii) code length, and (iii) nonlinear effects. According to the operating principles, the comparator can be utilized for rotationally-symmetric modulations, such as 8-PSK and 16-PSK, since all constellations in the modulations are allowed to exchange each position by phase shift. Similarly, if it is assumed that the additional DLIs are further cascaded, the length of code word can be expanded to an arbitrary bit length. Furthermore, by using an optical compensator for nonlinear effects, it is considered that the comparator can minimize the effect of nonlinear phase noise. Considering the points mentioned above, it is concluded that the proposed comparator can provide highly extensible operation for actual communication systems. Acknowledgments: The author would like to thank Hiroyuki Uenohara of Tokyo Institute of Technology for assistance with the experimental installation and helpful discussions.

Conflicts of Interest:
The author declares no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: