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We propose a novel optical 45° hybrid employing a 2 × 8 paired interference based multimode interference (MMI) coupler, three phase shifters and three 2 × 2 optical couplers. Since the proposed 45° hybrid can demodulate an 8-ary differential phase shift keyed (8-DPSK) signal with only one delayed Mach-Zehnder interferometer (DMZI), the demodulator has simpler configuration and much smaller device dimensions than conventional 8-DPSK demodulators consisting of four pairs of DMZIs and 2 × 2 optical couplers. We calculate and experimentally demonstrate octagonal phase response of the proposed 45° hybrid with a relative phase deviation of < ± 5° over 32-nm-wide spectral range.
©2010 Optical Society of America
1. Introduction
Optical transmission systems using multilevel phase modulated signals have several advantages over spectral efficiency [1]. To date, from the viewpoint of simplicity of detection scheme and superiority of cost performance, direct detection techniques based on differential phase shift keyed (DPSK) modulation format have been reported [2]. In an effort to enhance spectral efficiency to be more than 1 bit/s/Hz, there have been many reports on differential quadrature phase shift keying (DQPSK) signal format [3,4]. Recently, toward even higher spectral efficiency, multilevel phase modulation formats such as 8-ary DPSK [5], and 16-ary DPSK [6,7] have been investigated.
Here, we report a novel optical 45° hybrid and its potential for use in 8-ary DPSK (8-DPSK) demodulator consisting of one pair of a delayed Mach-Zehnder interferometer (DMZI) and the optical 45° hybrid we propose. Since the proposed 45° hybrid utilizes only one DMZI, the 8-DPSK demodulator scheme has a potential to make the optical receiver more compact and much easier to precisely control the phase. As a preliminary study, we analytically and numerically calculate the proposed 45° hybrid. Based on the theoretical consideration, we fabricate the device, and experimentally demonstrate octagonal phase response with a relative phase deviation of < ± 5° for all output channels over 32-nm-wide spectral range.
In this paper, the device structure of the proposed 45° hybrid and its operation principle are explained analytically and numerically in Section 2. Section 3 describes the fabrication process, and experimental demonstration of fully passive optical octagonal phase behavior of the fabricated 45° hybrid.
2. Theoretical consideration
2.1. Configuration of device
Figure 1 shows a schematic drawing of the proposed 45° hybrid. The device is composed of three components; a paired interference (PI) based 2 × 8 multimode interference (MMI) coupler [8], three pairs of phase shifters and three 2 × 2 MMI couplers. As shown in Fig. 1, power splitting ratios of the three 2 × 2 MMI couplers are designed to be 50:50 (cross:bar) for a coupler A, and 85:15 for couplers B and C, respectively. Additionally, it should be noted that the amount of phase variation at the phase shifters needs to be optimized to satisfy phase matching condition between the 2 × 8 MMI coupler and each corresponding 2 × 2 MMI coupler.
Fig. 1 Schematic diagram of the proposed optical 45° hybrid consisting of a PI-based 2 × 8 MMI coupler, three pairs of phase shifters and 2 × 2 MMI couplers.
Figure 2 shows schematic diagrams of 8-DPSK demodulators employing four pairs of DMZIs and 180° hybrids based on a 2 × 2 optical coupler (a) and one pair of a DMZI and the proposed 45° hybrid (b). Usually, M-ary (M: multiplicity of phase modulation) DPSK signal can be demodulated by using as many (M/2) DMZIs in parallel where each DMZI normally works at the required optical phase threshold [4]. Consequently, since the number of required DMZIs typically increases in proportion to M/2, the optical receiver becomes much larger in size and much complicated in stabilizing the phase at each DMZI [see Fig. 2(a)]. Meanwhile, Fig. 2(b) indicates an alternative way to construct an 8-DPSK demodulator by employing only one DMZI and the proposed 45° hybrid.
Fig. 2 Schematic diagrams of 8-DPSK demodulators employing a conventional scheme (a) the proposed scheme (b).
Meanwhile, as can be seen in Fig. 1, the positions of the output channels with In-phase relation are mutually adjacent with each other, thus enabling to directly connect the 45° hybrid output channels to balanced photodiodes (PDs) without accompanying any waveguide intersections.
2.2. Analytical calculation
The operation principle of the proposed device can be explained as follows. When the 8-DPSK signal is incident on the proposed 45° hybrid (see Fig. 1), each of mutually adjacent four output pairs of the 2 × 8 MMI coupler exhibits In-phase relation, because the 2 × 8 MMI coupler normally works as a 180° hybrid due to its structural centro-symmetry. Then only the phase relations at the output components coupled to the 2 × 2 MMI couplers A, B and C are rotated by 90°, 45° and 135° by controlling the phase at each phase shifter (θ1~θ6) and the power splitting ratio at each 2 × 2 MMI coupler, which allows us to discriminate the phase state for the 8-DPSK modulated signal.
The octagonal phase behavior of the device can be analytically understood. First, in the case of the PI-based 2 × 8 MMI coupler, for imaging an input x to an output y, the output phases φx,y subtracted by common phase terms are given by the following equation [9],
where ρ = 0 for an odd integer y and ρ = 1 for an even integer y. If we suppose the same polarization between two input signals S1 and S2 (see Fig. 1), the electric fields for the two input signals ES1 and ES2 can be represented as Eqs. (3) and (4) by using complex notations, where PS1, ωS1 and ϕS1 stand for the power, the angular frequency and the phase of an input signals S1. Also, PS2, ωS2 and ϕS2 represent the power, the angular frequency and the phase of an input signals S2. If we set the ES1 and ES2 to the input component at input Ch-1 and Ch-2 at the 2 × 8 MMI coupler, each output field of the proposed device is represented by multiplying each transfer matrix for three components, In Eq. (5), [T1], [TPS] and [T2] indicate the transfer matrix for the 2 × 8 MMI coupler, the phase shifters where θ1~θ6 represent the amount of phase variation, and the 2 × 2 MMI coupler, respectively. Also, in Eqs. (6)-(8), κ28, κA, κB, and κC indicate power coupling coefficients of the 2 × 8 coupler and the 2 × 2 couplers A~C, respectively. As shown in Eq. (6), the phase relation of the 2 × 8 MMI coupler was obtained by using Eqs. (1) and (2). In order to achieve octagonal phase behavior with a low excess loss and low phase deviation from perfect octagonal phase relation, it is inevitable to make the phase matching between the 2 × 8 MMI coupler and three 2 × 2 MMI couplers. As a result of analytical calculation, we clarified that the excess loss and the phase deviation of the 8-DPSK signal can be minimized when the following relations are satisfied by the phase shifters (θ1~θ6), As a matter of course, there are a lot of ways to satisfy the phase matching conditions shown in (9)~(11) by properly allocating θ1~θ6 into each phase shifter. Figure 3 shows the analytically calculated transmittance of the proposed schemes with the phase shifters satisfying (9)~(11) (a) and without the phase shifters (b) as a function of the phase difference between the two input signals (ΔΦ = ϕS1– ϕS2). In this calculation, we assumed a lossless medium, same frequencies between the two signals (ω1 = ω2) and a perfect power splitting ratio of κ28 = 0.125, κA = 0.5 and κB = κC = 0.85, respectively.Fig. 3 Analytically calculated transmission spectra of the proposed schemes with the optimized phase shifters (a) and without the phase shifters (b) as a function of the phase difference between the two input signals (ΔΦ = ϕS1– ϕS2)
As shown in Fig. 3(a), each output transmittance varies sinusoidally against ΔΦ, and its relative phase is deviated by 45° with each other, thus enabling to discriminate 8 kinds of phase states of the signal. Meanwhile, as can be clearly seen in Fig. 3(b), unless the phase matching is made between the 2 × 8 MMI and 2 × 2 MMI couplers, the demodulated signal experiences excess loss, crosstalk and significant phase deviation (Δϕ). Therefore, it becomes almost impossible to discriminate all phase states of the signal.
2.3. Numerical calculation
In order to verify the octagonal phase behavior expected by the analytical calculation, we discuss the proposed 45° hybrid by using numerical simulation based on 2 dimensional finite difference beam propagation method (2D FD-BPM).
Figure 4 shows the numerically simulated transmittance of the proposed 45° hybrid as a function of ΔΦ (a) and the simulated Δϕ within the C-band spectral range (b). In the 2D FD-BPM, we assumed a lossless medium, a light wavelength of 1.55 μm, and an equivalent index of 3.2404. The waveguide width (W) and the narrowest gap between the access waveguides (Gap) were set to be 2.0 μm and 1.0 μm, respectively. Also, the coupling coefficient of the 2 × 2 MMI couplers were κA = 0.5 and κB = κC = 0.85. Details of coupler design for the PI-based 2 × 8 MMI and the 2 × 2 MMI couplers with symmetric and asymmetric splitting ratios can be found in Ref [9]. We assumed that the phase shifter has a butterfly-shaped tapered waveguide structure and a single phase shifter is located at either of two access waveguides between the 2 × 8 MMI and 2 × 2 MMI couplers. The parameters for each phase shifter were optimized to satisfy (9)~(11), as shown in Table 1 .
Fig. 4 Numerically simulated transmission spectra as a function of ΔΦ (a) and Δϕ of the proposed 45° hybrid within the C-band spectral range
Table 1. Parameters of each phase shifter in the proposed 45° hybrid
As seen in Fig. 4(a), each output transmittance of the proposed 45° hybrid shows octagonal phase response against ΔΦ, which agrees well with the analytically calculated result shown in Fig. 3(a). In this case, π-phase differences are clearly shown in the output pairs of Ch-1 and 2, Ch-3 and 4, Ch-5 and 6, and Ch-7 and 8. Thus, we can directly connect the output waveguides to the balanced PDs without accompanying any waveguide intersections, as schematically shown in Fig. 2(b). Moreover, there is neither a considerable excess loss nor crosstalk at the output channels coupled to the 2 × 2 MMI couplers A, B and C, which is based on the phase matching by the phase shifters, thus enabling to preserve the detection efficiency for all output signal components. Furthermore, the octagonal phase relation of the proposed device can be obtained over the broad spectral range. As shown in Fig. 4(b), the available bandwidth of |Δϕ|<5° was estimated to be ~32 nm.
3. Experimental results
Based on the theoretical considerations, the proposed 8-DPSK demodulator scheme was fabricated on an InP wafer with a 0.3-μm-thick GaInAsP core layer (λg = 1.3 μm). Using reactive ion etching technology, we formed deep-ridge waveguide with ~3.1 μm height. Subsequently, the InP substrate for the fabricated device was polished and cleaved. Finally, anti-reflection layers were coated at the input/output facets of the fabricated device. The waveguide parameters of the proposed 45° hybrid were set to be the same as those used in the numerical calculation shown in Fig. 4 and Table 1.
Figure 5 shows the top-views of the fabricated 8-DPSK demodulator scheme (a), the proposed 45° hybrid (b), and the magnified view around the phase shifters (c). As can be seen in Fig. 5(a), the DMZI is directly coupled to the 2 × 8 MMI coupler. A free-spectral range (FSR) of the DMZI was designed to be 520 GHz (~4.2 nm) for convenience. The total chip size including fan-out regions for a fiber butt-coupling measurement was 2.2 × 0.32 mm2. As seen in Fig. 5(b), the proposed 45° hybrid is composed of the PI-based 2 × 8 MMI coupler, three phase shifters and three 2 × 2 MMI couplers whose power coupling coefficient is κA = 0.5 for coupler A and κB = κC = 0.85 for couplers B and C. In this case, the device length (LDevice) which is defined as the sum of the lengths of the 2 × 8 MMI coupler ( = 446.7 μm), the phase shifter ( = 50.0 μm) and 2 × 2 MMI coupler ( = 102.9 μm) is 599.6 μm. As seen in Fig. 5(c), three phase shifters were formed as the butterfly-shaped waveguide and their phase variations (θ2, θ3 and θ5) were designed to satisfy the phase matching requirement shown in Table 1.
Fig. 5 Top-views of the fabricated 8-DPSK demodulator scheme (a), the proposed 45° hybrid (b) and the magnified view around the phase shifters (c)
To measure transmission spectra, we used an amplified spontaneous emission light of a semiconductor optical amplifier as a light source. The input polarization state was adjusted to be a linearly polarized TE-mode through a polarization controller. Figure 6 shows the measured transmission spectra of the fabricated 8-DPSK demodulator scheme. Each output transmittance periodically varied in accordance with the FSR of the DMZI. In Fig. 6, the envelopes for each measured transmission spectrum correspond to the amplitude spectral characteristics. A wavelength sensitive loss for all channels was evaluated to be <1.9dB within the C-band spectral range. Also, we were unable to observe a significant spectral asymmetry for all output channels, which originates from extremely low excess loss of the phase shifter (<0.1dB) and the 2 × 2 MMI coupler (<0.1dB). The extinction ratio of the output transmittance was measured to be 16~22 dB for all output channels within the C-band spectral range.
Fig. 6 Measured transmission spectra of the fabricated 8-DPSK demodulator scheme within the C-band spectral range
Figure 7 shows the magnified view of the measured spectra shown in Fig. 6 (a) and the experimentally estimated Δϕ within the C-band spectral range (b). In Fig. 7(a), each output transmittance sinusoidally changed in accordance with the phase differences at the DMZI. That is, a wavelength change in Fig. 7(a) corresponds to ΔΦ in Fig. 3(a). Consequently, the behavior of the measured transmittance for each output channel agrees well with that of the simulation result shown in Fig. 4(a). As clearly seen in Fig. 7(b), we experimentally verified that octagonal phase relation can be kept nearly constant within |Δϕ|<5° over 32-nm-wide wavelength span, which qualitatively agrees well with the simulation result shown in Fig. 4(b).
Fig. 7 Magnified view of the measured spectra shown in Fig. 6 (a) and the experimentally estimated relative phase deviation from the octagonal phase relation (Δϕ) within the C-band spectral range (b).
4. Summary
We proposed, theoretically analyzed and experimentally demonstrated the optical 45° hybrid consisting of a PI-based 2 × 8 MMI coupler, three phase shifters and three 2 × 2 MMI couplers. The proposed 45° hybrid has a potential to make the optical 8-DPSK demodulator scheme simpler and much easier to precisely control the phase in the device than conventional demodulator schemes. Octagonal phase behavior was analytically calculated by the transfer matrix method and numerically simulated by the 2D FD-BPM. Through the calculation, we made clear that the phase matching between the 2 × 8 MMI coupler and the 2 × 2 MMI couplers is crucial to minimize excess loss, crosstalk and excessive phase deviation for the 8-DPSK signal. Based on the 2D FD-BPM, we fabricated and characterized the proposed 45° hybrid with an InP-based deep-ridge waveguide structure. The device length was 599.6 μm. The fabricated device exhibited clear octagonal phase response (|Δϕ|<5°) over 32-nm-wide spectral range.
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