Multilevel phase modulation formats have been extensively utilized to enhance spectral efficiency [1-4] in optical communication systems. In addition to long-haul optical transmissions, these technologies have also been applied to several kinds of technical areas in passive optical networks [5], online surface profile measurements [6], and global networks satellite systems [7] and so on. As a cost-effective and simple detection approach where no additional local oscillator is needed, differential phase shift keying modulation formats [4] have been investigated. Multilevel differential phase modulation formats equivalently lower the baud-rate of optical signals, which then tolerates more dispersion, allows for more efficient optical filtering, and enables us to make the channel spacing much closer when the modulation is combined with wavelength division multiplexing technologies.

To date, various kinds of optical hybrid devices allow demodulation of multilevel differential phase modulated signals such as 90° hybrid [8-10], 45° hybrid [11], 120° hybrid [12], and 72° hybrid [13] etc. Although the discrete component type optical hybrids [10, 11] exhibited a lower insertion loss, a better detection efficiency and a wider operating wavelength range, the waveguide type optical hybrids based on semiconductor materials such as InP-based [8] or silicon (Si)-based [9, 13] have the advantages of compactness of device size and monolithic integration with other photonic functional components.

In this paper, we report a novel 45° optical hybrid for demodulating 8-level differential phase shift keying (8DPSK) signals. The operation of the proposed device is based on the two 90° optical hybrids cascade-connected by the phase control region including optical paths with one waveguide cross junction. In case of the 90° optical hybrid, it is normally required to retrieve in-phase (I) and quadrature-phase (Q) components of the transmitted optical signals. Many previously reported waveguide-type optical hybrid devices [8, 9, 12, 13] are based on multimode interference (MMI) phenomena [14] caused by the relative phase difference of the two input signals. Besides the tetragonal, trigonal and pentagonal phase discriminations, to realize other specific (i.e. octagonal) phase control resolution such as a 45° optical hybrid by using MMI phenomena, we need to newly design MMI couplers with increased output channel count of 8. As an alternative way, if we actively or passively control the relative phase state of the identical two 90° optical hybrids, we can discriminate the phase information spaced by 45° in the phase domain.

The above-mentioned phase control region is composed of two 2 × 2 optical couplers in parallel and four access waveguides that are optically coupled to the two 90° optical hybrids. This concept inherently requires the waveguide crossover to mix the signal from the two 2 × 2 optical couplers. If the two 90° optical hybrids are assumed to have an ideal quadrature phase response, the phase discrimination balance of the newly constructed 45° optical hybrid is strongly influenced by the presence of the waveguide crossover. Thus, care must be taken to accurately control their relative phases for each output channel to keep an optimal octagonal phase balance.

Since the phase control region includes four circularly bent waveguides as well as the waveguide crossover, the octagonal phase balance is susceptible to the control accuracy of optical path length for each waveguide array. Furthermore, the phase adjustability becomes more sensitive for high-index-contrast (HIC) waveguide-type (InP-based or Si-based) devices rather than for low-index-contrast (LIC) waveguide-type (silica-based) devices. These difficulties forced an active phase control region to be formed in the 90° optical hybrids [15, 16], which makes the devices unattractive from the viewpoint of simple phase control and low power consumption.

Here, we report all-passive phase control scheme in the optical hybrid circuit with the waveguide crossover. Then, we apply the proposed concept to the 45° optical hybrid. In section 2, we explain the operation principle of the proposed device. We also theoretically discuss why accurate phase control is required in the proposed 45° optical hybrid and how to overcome the drawbacks caused by the excess phase error at the waveguide crossover. Section 3 describes the device fabrication and experimental characterization. The fabricated 45° optical hybrid exhibited clear octagonal phase response with an excess loss of <0.8 dB and a phase deviation of <±5.0° over 31-nm-wide spectral range in the C-band regime.

2.1. The 45° Optical Hybrid Without Intentional Phase Control

Figure 1 shows the schematic diagram of the 45° optical hybrid without using an intentional phase control for the waveguide crossover. As schematically shown in Fig. 1, the two 90° optical hybrids are parallelly located with a discrete phase shifter (δφ_SH) of −π / 4 (rad.). We assume that the 90° optical hybrid consists of a 2 × 4 MMI coupler, a phase shifter, and a 3-dB 2 × 2 MMI coupler based on the splitting and remixing of the optical signal [8].

Figure 1. Schematic diagram of the 45° optical hybrid employing only the phase shifter δφ_SH in the phase control region.

When the signal is incident on the 90° optical hybrid, each of mutually adjacent two output pairs of the 2 × 4 MMI coupler exhibits in-phase relation. Then only the phase relation of the signal components coupled to the 2 × 2 MMI coupler is rotated by 90°, which allows us to discriminate four quadrature phase states of the signal. It is noted that other types of the 90° optical hybrids can be applied to the scheme shown in Fig. 1.

Since the relative input phase relation of the 90° optical hybrid located in the lower portion is rotated by −π / 4 (rad.) passing through the phase shifter (δφ_SH), the device scheme shown in Fig. 1 works as a 45° optical hybrid. As a matter of course, this assumption is available only when the four output waveguide arrays suffer from exactly the same phase variation in the phase control region (see Fig. 1). However, the waveguide crossover in the phase control region inherently causes the excess phase error depending on the waveguide geometry and the relative index contrast (∆n) of the waveguide.

Here, the excess phase change at the crossover (δφ_EX) directly has an effect on the initial phase relation of the two 90° optical hybrids. The influence of δφ_EX over the initial phase relation can be described in Eqs. (1)_–(4). In Fig. 1, each phase change Φ₁, Φ₂, Φ₃ and Φ₄ passing through the four optical paths in the phase control region are approximated by

(1)$${\text{Φ}}_1=\left(2\pi /\lambda \right)\cdot n_A\cdot L_D,$$

(2)$${\text{Φ}}_2={\text{Φ}}_3=\left(2\pi /\lambda \right)\cdot n_A\cdot L_D+\delta {\phi }_{\text{EX}},$$

(3)$${\text{Φ}}_4=\left(2\pi /\lambda \right)\cdot n_A\cdot L_D+\delta {\phi }_{\text{SH}},$$

(4)$$\delta {\phi }_{\text{EX}}=\left(2\pi /\lambda \right)\cdot \Delta n\cdot \Delta L,$$

where λ, n_A and L_D indicate a light wavelength, an equivalent index of the waveguide, and the optical path length at the phase control region, respectively. Also, ∆n and ∆L stand for the refractive index difference at the crossover and the optical path length for traversing the crossover, respectively. δφ_SH is set at the fixed phase change of −π / 4 (rad.). Then, the initial phase difference for each 90° optical hybrid ΔΦ₁₂ and ΔΦ₃₄ are represented by

(5)$${\text{ΔΦ}}_{12}={\text{Φ}}_1-{\text{Φ}}_2=-\left(2\pi /\lambda \right)\cdot \Delta n\cdot \Delta L=-\delta {\phi }_{\text{EX}},$$

(6)$${\text{ΔΦ}}_{34}={\text{Φ}}_3-{\text{Φ}}_4=\delta {\phi }_{\text{EX}}-\delta {\phi }_{\text{SH}}.$$

Then, the phase difference between ΔΦ₁₂ and ΔΦ₃₄ is given by

(7)$$\text{Δ}{\Psi }_{\text{A}}={\text{ΔΦ}}_{12}-{\text{ΔΦ}}_{34}=\delta {\phi }_{\text{SH}}-2\cdot \delta {\phi }_{\text{EX}}.$$

Consequently, as can be seen in Eq. (7), ΔΨ_A is normally deviated from the optimum value (δφ_SH) by −2 ∙ δφ_EX. Moreover, as seen in Eq. (4), the excess phase deviation caused by δφ_EX becomes remarkable in proportion to ∆n, which means the initial phase relation of the two 90° optical hybrids is degraded more for the HIC waveguide-based devices. Meanwhile, due to the dispersive nature of n_A, ΔΨ_A depends on a light wavelength.

Figure 2 shows the analytically estimated δφ_EX within a C-band spectral range. In the calculation, we assumed an InP-based deep-ridge waveguide with a GaInAsP core bandgap wavelength of λ_g = 1.3 μm and a waveguide width of 2.0 μm. n_A, L_D, and ΔL were set to 3.240431 (evaluated by numerical simulation based on finite element method), 330 μm, and 2.0 μm, respectively. As shown in Fig. 2, δφ_EX was estimated to 12.7°–13.1° within a C-band spectral range. That is, ΔΨ_A is deviated by more than −π / 8 (rad.) in the phase control region, which is large enough to be a serious obstacle to discriminate the phase states of the 8DPSK signal.

Figure 2. Calculated excess phase deviation at the waveguide crossover (δφ_EX) within a C-band spectral range.

2.2. The 45° Optical Hybrid Employing Phase Compensation

The deterioration of the initial phase relation for the two 90° optical hybrids can be overcome by compensating for the excess phase change at the crossover. Figure 3 shows a schematic diagram of the proposed 45° optical hybrid based on the compensation of the excess phase changes.

Figure 3. Schematic diagram of the proposed 45° optical hybrid employing the phase shifter δφ_SH and the two additional phase shifters δφ_MP in the phase control region.

As can be seen in Fig. 3, each optical path Φ₂ and Φ₃ includes additional phase shifters (δφ_MP) whose sign of the phase change are opposite to those of δφ_EX. In this case, Eq. (2) is rewritten by

(8)$${\text{Φ}}_2={\text{Φ}}_3=\left(2\pi /\lambda \right)\cdot n_A\cdot L_D+\delta {\phi }_{\text{EX}}-\delta {\phi }_{\text{MP}}.$$

As a result, the phase difference between ΔΦ₁₂ and ΔΦ₃₄ can be rewritten by

(9)$$\text{Δ}{\Psi }_B=\delta {\phi }_{\text{SH}}-2\cdot \delta {\phi }_{\text{EX}}+2\cdot \delta {\phi }_{\text{MP}}.$$

That is, the excess phase change at the crossover can be compensated for by carefully adjusting the physical quantity of δφ_MP. However, it is important to note that since the phase shifters used in the phase control region (δφ_MP and δφ_SH) normally have a wavelength sensitivity that is different from that of δφ_EX, there would be some difficulty in compensating for δφ_EX over a broadband spectral range.

2.3. The 45° Optical Hybrid Employing Phase Optimization

An alternative way to overcome the aforementioned drawback is to optimize the entire phase relation by using a single phase shifter in the phase control region. Figure 4 shows a schematic diagram of the proposed 45° optical hybrid employing the total phase optimization.

Figure 4. Schematic diagram of the proposed 45° optical hybrid employing the single phase shifter δφ_TS in the phase control region.

As seen in Fig. 4, the only one phase shifter (δφ_TS) is located in the phase control region. Thus, Eq. (4) is rewritten by

(10)$${\text{Φ}}_4=\left(2\pi /\lambda \right)\cdot n_A\cdot L_D+\delta {\phi }_{\text{TS}}.$$

As a result, the phase difference between ΔΦ₁₂ and ΔΦ₃₄ can be given by

(11)$$\text{Δ}{\Psi }_C=\delta {\phi }_{\text{TS}}-2\cdot \delta {\phi }_{\text{EX}}.$$

In Eq. (11), since the desired value of ΔΨ_C should be −π / 4 (rad.), we can optimize δφ_TS as to satisfy the following relation:

(12)$$\delta {\phi }_{\text{TS}}=-\pi /4+2\cdot \delta {\phi }_{\text{EX}}.$$

As shown in Fig. 2, since δφ_EX gives a positive phase variation of 12.7–13.1 [deg.] the absolute value of δφ_TS can be adjusted to be much smaller than −π / 4 (rad.), which makes the phase shifter δφ_TS less wavelength sensitive. Moreover, since the number of phase shifters is reduced to only one, we could achieve stable octagonal phase behavior over a broader spectral range, together with much simpler and easier phase controllability.

In this work, the butterfly-shaped waveguide configuration was used for the three kinds of the phase shifters (δφ_SH, δφ_MP, δφ_TS). Figure 5 shows (a) the schematic diagram of the butterfly-shaped phase shifter with the definition of several parameters, (b) the calculated phase variations of the phase shifters as a function of |∆W| defined in Fig. 5(a), and the magnified view of the shaded area in Fig. 5(b). L_PS was assumed to be 50 μm (L_TP = 0.5 ∙ L_PS). As shown in Fig. 5(b), the amount of the phase shift can be adjusted by controlling |∆W| (equivalently taper angle). It is noted that the wavelength sensitivity of the amount of δφ becomes remarkable as the required δφ increases. As seen in Fig. 5(c), when we set the δφ_SH (=−45°), we need to consider ±1.3° of the phase deviation within a C-band spectral regime. It should be noted that the wavelength sensitive phase deviation becomes negligible as the required δφ gets close to 0.

Figure 5. Theoretical analyses of the phase shifters used in the optical hybrid devices: (a) schematic diagram of the butterfly-shaped phase shifter with the definition of several parameters, (b) the calculated phase variations of the phase shifters as a function of |∆W|, and the magnified view of the shaded area in Fig. 5(b). L_PS was assumed to 50 μm (L_TP = 0.5 ∙ L_PS).

Figure 6 shows the calculated relative phase difference at the three types of the phase control regions (∆Ψ_A, ∆Ψ_B, ∆Ψ_C) as a function of the phase shift amount of the correspondingly required phase shifters (δφ_MP or δφ_TS) within a C-band spectral range. The analytic calculation was implemented based on the Eqs. (4), (7), (9), (11) taking into account the wavelength sensitivity of each phase shifter (δφ_SH, δφ_MP, δφ_TS). Considering δφ_SH (=−45°) of the required relative phase difference for operating as the 45° optical hybrid, there is no way of satisfying the condition of δφ_SH for ∆Ψ_A. Meanwhile, in the case of ∆Ψ_B and ∆Ψ_C, we can overcome the drawback from δφ_EX by properly setting each phase shifter δφ_MP and δφ_TS.

Figure 6. Calculated relative phase difference at the three types of the phase control regions (∆Ψ_A, ∆Ψ_B, ∆Ψ_C) as a function of the phase shift amount of the correspondingly required phase shifters (δφ_MP or δφ_TS) within a C-band spectral range.

Basically, the wavelength sensitivity becomes significant as the amount of the phase shift and the number of the phase shifters increase. Consequently, a smaller amount of phase shift and a smaller number of phase shifters are desirable to minimize the adverse influence caused by the wavelength dependent phase change. As can be clearly seen in Fig. 6, since the total phase optimization scheme requires a single phase shifter with a smaller phase shift of δφ_TS~−0.1 [π rad.], the degree of the phase deviation can be markedly suppressed compared with the case of the phase compensation scheme (φ_MP~−0.14 [π rad.] × 2, and φ_SH = −0.25 [π rad.]).

Based on the theoretical considerations, the proposed 45° optical hybrids were fabricated on InP wafers with a 0.3-μm-thick GaInAsP core layer (bandgap wavelength λ_g = 1.3 μm). By using inductively coupled plasma reactive ion etching, deeply etched ridge waveguide with 3.5-μm-height were formed. We designed and tested three types of devices described in Section II. The device parameters for the fabricated devices were the same as those used in Figs. 1–6. The waveguide width was set to 2.0 μm, which satisfies a single lateral mode condition. Also, we utilized a butterfly-shaped taper waveguide as the phase shifter. The locations of the phase shifters were the same as the cases shown in Fig. 1, Fig. 3 and Fig. 4. Each physical quantity of the phase variation was the same as those used in the calculations shown in Figs. 5 and 6.

Figure 7 shows the top-views of the fabricated 45° optical hybrid (a), and cross-sectional views for the 2 × 4 MMI coupler [W_{2 × 4 MMI} = 18 μm, L_{2 × 4 MMI} = 224 μm] (b), the 2 × 2 MMI coupler [W_{2 × 2 MMI} = 5 μm, L_{2 × 2 MMI} = 105 μm] (c), the single mode waveguide [W = 2 μm] (d) and the crossover region [W_Cross > 5 μm, L_Cross = 2 μm] (e). In this case, the waveguide width (W) of 2 μm is wide enough to be crossed without any further width optimization, unlike the case of relatively narrow Si nanowire waveguides [17]. As seen in the magnified views around the phase control region in Fig. 7(a), the waveguide arrays were designed to be perpendicularly crossed to minimize a loss and crosstalk at the crossover. To equalize four kinds of optical path lengths, the curvature radii of bending regions were set to 100 μm for the outer-side bent waveguides (Φ₁ and Φ₄) and 200 μm for the inner-side bent waveguides (Φ₂ and Φ₃), respectively. In this experiment, to measure the phase behavior of the fabricated devices, a delayed interferometer whose free-spectral range was designed to 530 GHz was directly coupled to the above-mentioned three devices. For all cases, total chip size including the delayed interferometer was 2.5 mm (length) × 0.4 mm (width).

Figure 7. Fabricated devices and their structures: (a) top-views of the fabricated 45° optical hybrid, (b) cross-sectional views for the 2 × 4 multimode interference (MMI) coupler, (c) the 2 × 2 MMI coupler, (d) the single mode waveguide, and (e) the crossover region.

Figure 8 shows the experimental setup for measuring the transmission spectra for the fabricated devices. We used a broadband spontaneous emission as a light source. The transmission spectra of the fabricated devices were characterized for a linearly polarized TE mode by using a polarization controller. Due to the equivalent index differences at the access waveguides and each MMI region, the device designed for the TE-mode does not work for the TM-mode input. The continuous wave light was butt coupled into the cleaved facet of the device by using a lensed single mode fiber (SMF). The coupling loss between the lensed SMF was estimated to be 2 dB/facet. For the measurement of the transmittance of the fabricated devices, we subtracted the coupling losses at the two facets to figure out the excessive losses within the device.

Figure 8. Experimental setup for measuring optical transmission spectra for the fabricated devices. ASE, amplified spontaneous emission; SMF, single mode fiber.

Figure 9 shows the measured spectra of the device with the phase shifter δφ_SH of −0.25π rad. only. The inset of Fig. 9 shows the magnified spectra at around λ = 1.55 μm. Each output transmittance sinusoidally changed in accordance with the phase differences at the delayed interferometer within the measured spectral range. In Fig. 9, the quadrature phase response was observed at the Ch-1/2 and the Ch-3/4 for the 90° optical hybrid located in the upper portion, and at the Ch-5/6 and the Ch-7/8 for the 90° optical hybrid located in the lower portion. This is due to inherent quadrature phase nature of each 90° optical hybrid [8]. However, the superimposed spectra show that the relative phase relation between the two 90° optical hybrids is not deviated by the designed value of δφ_SH, which is most likely due to the excess phase change (φ_EX) at the waveguide crossover as theoretically described in Fig. 2. From the measured spectra, the extra phase deviation represented by −2 ∙ δφ_EX was estimated to be ~–21° at around λ = 1.55 μm, which is comparable to the theoretical prediction (~–25°) shown in Fig. 2.

Figure 9. Measured transmission spectra of the fabricated device shown in Fig. 1.

Then, we characterized the proposed device based on the phase compensation. Figure 10 shows the measured transmission spectra of the device employing the phase shifter δφ_SH (−0.25π rad. at λ = 1.55 μm) and the two additional phase shifters δφ_MP (−0.14π rad. at λ = 1.55 μm). In this case, the envelope of the measured spectra corresponds to the wavelength sensitivity of the transmittances. From these, a wavelength sensitive loss and interchannel imbalance were measured to be less than 0.8 dB and 0.5 dB within a C-band spectral range. It is noted that the wavelength sensitive loss is mainly attributed to a spectral behavior of the 2 × 4 MMI coupler. That is, the top spectral envelope in Fig. 10 corresponds to the spectral behavior of the 2 × 4 MMI coupler. Since the wavelength sensitivity of the 2 × 2 MMI coupler in the two 90° optical hybrids can be neglected, each transmittance for all output channels of the 45° optical hybrid is almost the same. The inset of Fig. 10 shows the magnified spectra at around λ = 1.55 μm. As shown in the inset, we did not measure any obvious phase mismatch that was observed in Fig. 9. The measured spectra clearly exhibited an octagonal phase relation, resulting from the phase compensation shown in Fig. 6.

Figure 10. Measured transmission spectra of the fabricated device shown in Fig. 3.

Figure 11 shows the measured spectra of the fabricated devices employing the single phase shifter δφ_TS (−0.1π rad. at λ = 1.55 μm). A wavelength sensitive loss and interchannel imbalance were measured to be nearly identical to the case shown in Fig. 10. As can be seen in the inset, we also observed clear octagonal phase response based on the total phase optimization.

Figure 11. Measured transmission spectra of the fabricated device shown in Fig. 4.

Subsequently, we characterized the relative phase deviation (Δϕ) from the ideal octagonal phase relation for all output channels of the fabricated devices shown in Fig. 10 and Fig. 11. Figure 12 shows the experimentally estimated Δϕ for the two devices based on 12(a) the phase compensation and 12(b) the total phase optimization within a C-band spectral range. The relative phase difference was estimated by measuring each relative peak difference in a wavelength domain. The accuracy of the phase estimation is <±0.5°.

Figure 12. Experimentally estimated phase deviation (Δφ) of the fabricated devices with (a) the phase compensation scheme and (b) the total phase optimization scheme.

If we allow for a penalty of |Δϕ| < ±5°, the available spectral bandwidths were estimated to be ~17 nm for the phase compensation scheme and ~31 nm for the total phase optimization scheme. That is, although both device schemes exhibited good octagonal phase characteristics at around λ = 1.55 μm, the operating bandwidths were markedly broader for the total phase optimization scheme than for the phase compensation one. As discussed earlier, we ascribe this discrepancy to the number and wavelength sensitivity of the phase shifters at the phase control region. That is, the phase optimization scheme has only one phase shifter whose phase variation is much smaller than any of the additional phase shifters in the phase compensation scheme, which makes it easier to preserve the octagonal phase relation over a broader spectral range.

Overall, the availability of the proposed phase control scheme is not restricted for use in the 45° optical hybrid we proposed. As a matter of course, the proposed phase control scheme can also be utilized with other optical demodulator schemes such as a dual-polarization quadrature phase shift keying (DP-QPSK) receiver system [18, 19].

We theoretically analyzed and demonstrated the 45° optical hybrid employing two 90° optical hybrids with the novel phase control scheme including the crossed waveguide junction. We discussed why the excess phase error occurs at the waveguide crossover in the phase control region, and how to overcome this drawback without using an active phase control that is accompanied with complexity and power consumption. Two novel phase control schemes including the phase compensation and the total phase optimization were analytically calculated and the latter scheme was predicted to be broadband operational due mainly to fewer number and lower wavelength sensitivity of the phase shifter to be used.

Based on the theoretical analyses, the two types of proposed devices were fabricated with an InP-based ridge waveguide. The measured spectra revealed that irrespective of how to control the phase in the phase control region, the two types of devices successfully operated as the 45° optical hybrid. Additionally, it was experimentally verified that since the phase optimization scheme uses a single phase shifter whose phase change is less than any other phase shifters used in the phase compensation scheme, the requirement of the phase deviation of −π / 4 (rad.) at the phase control region was more precisely controlled, thereby enabling to achieving a 31-nm-wide operating range in the C-band regime (>1.83 times broader bandwidth than the case based on the phase compensation scheme).

This work was supported by the University of Suwon, 2019.