1. Introduction

Electro-magnetic (EM) wave interference is a phenomenon that is behind the operations of all EM devices such as waveguides, power and polarization splitters/dividers, couplers, 180- and 90-mixers (hybrids) etc. Among all, the EM mixers play major role in communications systems by allowing for transmission and reception of coherent signals. At the outputs of 180- and 90-mixers, the EM fields of two or more input signals [e. g. the signal and local oscillator (LO) in a coherent receiver] are superposed with a phase difference of multiple of 180° and 90°, respectively. In coherent systems, the EM mixers perform the critical operations of baseband to/from passband signal conversion and simultaneous resolving of in-phase (I) and quadrature (Q) components of multi-level quadrature amplitude modulated (QAM) signals. As the EM wave interference occurs between co-polarized waves only, the mixers are usually designed to operate for single polarization inputs i.e. for co-polarized signal and LO. Multi-mode interference (MMI) couplers [1], directional couplers (DC) [2], Y-junction [3] and adiabatic mode transformers [4] are normally used as mixers in integrated optical coherent transceiver. However, the optical coherent transceivers based on these devices often have bandwidths of < 50 nm because of the wavelength and fabrication sensitivity of MMIs, Y-junctions and DCs. The transceivers that use adiabatic couplers may require an optical phase locked loop to correct for fabrication induced phase errors at the outputs of long adiabatic couplers.

Here we report on novel architectures for 180- and 90-degree inter-polarization mixers in silicon photonics (SiPh) technology. First, a broadband and low-loss inter-polarization 180-degree mixer comprising only one input port mixing orthogonally polarized signal and local oscillator (LO) is reported. The device has a length of 80 μm and operates in S-, C- and L-bands. Second, using the above 180-degree optical mixer, we demonstrate a novel design for compact, broadband, low-loss and fabrication-tolerant 90-degree optical mixer. The device uses birefringence of silicon channel waveguide to achieve the required 90° phase difference for the signal/LO relative phases in the in-phase and quadrature components. The mixer comprises a single optical input, a polarization insensitive 3 dB splitter and an adiabatic inter-polarization mixer. Third, using the above two mixers, a single-polarization quadrature phase-shift keying (QPSK) receiver is designed and fabricated in a standard silicon photonic foundry. The receiver incorporates on-chip high-speed, AC-coupled germanium balanced-photodiodes. The operation of the receiver is demonstrated by the reception of single-polarization QPSK signals at symbol rates of 22 Gbaud and 44 Gbaud. These mixers pave the way for novel silicon photonic coherent transceiver designs with applications in long-haul and metro networks, passive optical networks (PON), and data-center interconnections (DCI).

2. Design and operation of the inter-polarization mixers

The 180-degree inter-polarization mixer (IPM) consists of a single optical input port, a polarization rotator section, a Y-junction splitter and a balanced photodiode, as shown in Fig. 1(a). The device is based on broadband and low-loss adiabatic mode conversion in channel-to-rib waveguide transitions. Both waveguide and slab widths are non-linearly tapered along the length of the device. The signal and LO are launched as quasi-TE₀ and quasi-TM₀ modes of the input waveguide, respectively. The device can be visualized as being divided into three sections. In the first section (I), polarization rotation of the input quasi-TM mode is carried out in the channel-to-rib waveguide transition. This is done by converting the second mode of the input channel waveguide — quasi-TM₀ — to the second mode of rib waveguide — quasi-TE₁ — with negligible inter-modal coupling. Then, the quasi-TE₁ mode of the rib waveguide is converted to the quasi-TE₁ mode of channel waveguide in the second — rib-to-channel — waveguide transition (II). In contrast to the quasi-TM₀, the input quasi-TE₀ mode propagates along the first and second sections unchanged. As a result, the quasi-TE₀ and quasi-TM₀ — the two lowest order modes — of the input channel waveguide are converted to the quasi-TE₀ and quasi-TE₁ — the two lowest order modes — of the output channel waveguide, respectively. This mode conversion mechanism is similar to the one reported in Ref. [5]. The width of the channel waveguide at the output of the second section is wider than the width of the input channel waveguide. Across the width of the output channel waveguide the quasi-TE₁ shows a phase jump of π between its two power maxima. Therefore, by following the second section with a Y-splitter based power divider (III), the fields of the input quasi-TE₀ and quasi-TM₀ modes can be added in- and out-of-phase at the two outputs of the Y-splitter, respectively. We have used a standard channel-waveguide based Y-junction [6].

 

Fig. 1 Design and working principle of 180- and 90-degree inter-polarization mixers. (a) Top view of the inter-polarization 180-degree mixer. (b) Design of inter-polarization 90-degree mixer using 180-degree IPMs and birefringence of a waveguide. (c) Design of polarization diversity coherent receiver incorporating two 90-degree IPMs, two polarization beam combiner (PBC), one polarization rotator splitter (PRS) and a 3 dB power divider.

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A 90-degree inter-polarization mixer can be designed using the above described 180-degree IPM. Figure 1(b) gives an exemple design of such a 90-degree mixer. The device comprises a single optical input port, a polarization insensitive 3 dB power divider and a pair of IPMs. For the detection of the I and the Q components of the signal, two identical copies of the signal and LO are obtained by means of a polarization insensitive 3 dB power divider. After the power divider, the two orthogonal polarizations of the channel waveguide are used to propagate the signal and LO, respectively. The signal and LO experience different retardation due to birefringence of the channel waveguide originating in the non-identical refractive index profiles along the vertical and horizontal axes. The I- and the Q-components can be detected by introducing an imbalance of $L_{\pi /2}=\lambda /4\times \mathrm{\Delta }{n}_{\text{eff},1550\text{nm}}^{-1}$ between the lengths of the two waveguides before the IPMs, where λ is the wavelength of light in vacuum, Δn_eff,1550nm is the difference of the effective refractive indices of quasi-TE₀ and quasi-TM₀ modes at the wavelength of 1550 nm. The outputs of both 180-degree IPMs are coupled to high-speed balanced photodiodes in order to generate electrical waveforms corresponding to the I and Q components of the optical signal.

Figure 1(c) gives the schematic diagram of a polarization diversity coherent receiver incorporating the reported IPMs. Here, the polarization multiplexed signal input to the chip is split in a polarization rotator splitter (PRS). Both X- and Y-polarizations are combined with their dedicated LO branches in the polarization combiners (PBC) just before the 90-degree IPMs. In the 90-degree IPMs described in Fig. 1(b), the polarization states of the signal and LO are required to be aligned parallel to the optical axes of the input channel waveguide before the polarization insensitive power divider. Such an alignment is not needed when designing a polarization diversity coherent receiver, such as given in Fig. 1(c).

3. Experimental results

Complementary metal-oxide-semiconductor (CMOS) compatible silicon photonics (SiPh) is the technology that allows for wafer-scale manufacturing of coherent transceivers including high-speed Ge photodiodes [7], in-phase and quadrature (IQ) modulators [7], power and polarization combiners/splitters and optical 90-degree mixers. We designed our optical mixers in 220 nm silicon photonics standard technology. The devices are fabricated on 8” silicon-on-insulator wafer with a buried oxide (BOX) thickness of 3 μm. Silicon channel waveguides are used for on-chip routing. The optical microscope image of the fabricated 180-degree IPM with a length of 84 μm is given in Fig. 2(a). The input channel waveguide with a width of 450 nm is non-linearly tapered to 550 nm wide rib waveguide and then back converted to channel waveguide with a width of 850 nm. As a result of the tapering, the input quasi-TE₀ and quasi-TM₀ modes are converted to quasi-TE₀ and quasi-TE₁ modes of the output channel waveguide, respectively. A 90 nm thick silicon slab layer is used to achieve vertical asymmetry in order to perform polarization rotation. Figure 2(b) gives the image of the fabricated 90-degree IPM. In our design, we use a Y-junction as a polarization insensitive 3 dB power divider. After the Y-junction, quasi-TE₀ and quasi-TM₀ modes of a silicon standard channel waveguide with a width of 500 nm are used to guide the signal and LO, respectively. The fabricated 90-degree IPM covers a chip-area of ∼145 μm× ∼60 μm, which, however, may be reduced down to ∼ 50 μm× ∼ 15 μm in the future if using shorter IPMs. Figure 3(a) gives the transmission spectra at the output ports of an IPM test-structure with an access waveguide with a length of 1 mm and for 45° linearly polarized light excitation. The access waveguide has a width of 500 nm. Light is coupled in the access waveguide by means of a lensed fiber (LF). A grating based vertical coupler (GC) is used at the outputs of the IPM in order to couple light out of the chip into a single mode fiber. The measured spectra show that the fields of the signal and LO are added in- and out-of-phase at the output ports of the IPM, as shown in Fig. 3(a). The optical power imbalance at the output ports of the IPMs amounts to 1–2 dB which most likely is caused by a slight misalignment of the output fiber relative to the grating couplers. The non-flat transmission spectra are consequence of the passband characteristics of the output grating couplers. Coupling losses at the LF-PIC and PIC-GC interfaces are expected to be about ∼6...7 dB and ∼5 dB, respectively. By analyzing the number of fringes for three test-structures with access waveguide lengths of 1 mm, 1.5 mm and 1.8 mm, as shown in Fig. 3(b), we extrapolate and find the deviation of the TE-TM relative phase from 90° in an access waveguide with a length of 571 nm which is needed for the 90° phase retardation. The fit and the extrapolation are needed to eliminate birefringence of the fiber-to-chip interface and inverse tapers. The results summarized in Fig. 3(c) indicate that the phase error in the mixer is within an acceptable range of ±5° across the measurement wavelength range of ∼90 nm.

 

Fig. 2 Optical microscope image of the photonic part of the (a) 180-degree and 90-degree inter-polarization mixers (IPM).

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Fig. 3 Characteristics of the photonic part of the inter-polarization mixers and birefringence of silicon channel waveguide. (a) Transmission spectra at the outputs of the 180-degree IPM with a 1 mm long access waveguide. The inset gives the experimental setup used to measure the performance of the device. The wavelength response of 1D grating coupler (GC) is given as light-gray solid line. Extra 6...7 dB coupling loss is estimated at the lensed fiber (LF)-PIC interface. (b) Phase retardation of the quasi-TE₀ relative to the quasi-TM₀ in access waveguides with widths of 500 nm and lengths of 1 mm, 1.5 mm and 1.8 mm. (c) Wavelength sensitivity of the TE₀-TM₀ relative phase in a mixer with L_π/2=571 nm.

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We have measured the optical losses in the adiabatic polarization rotator part (PR) [Section I and II in Fig. 1(a)] of the IPM for both quasi-TE₀ and quasi-TM₀ input excitations. On the same 8” wafer, we have fabricated test structures which allow for such conversion-loss evaluations, see Fig. 4. The test structure — the unit-cell — comprises a pair of PRs wherein the second PR is horizontally flipped and performs the reverse mode conversion of the quasi-TE₁ to the quasi-TM₀ mode. We have measured the transmission through various number of unit-cells cascaded in series. By linearly fitting the transmission values measured at the outputs of 1, 2, 3 unit-cells cascaded in series, we have estimated conversion losses of < 0.3 dB for both quasi-TE₁ and quasi-TM₀. The fringes in the loss spectra are consequence of the multi-path propagation caused by the reflections occurring at the multiple waveguide transitions along the test structures. The losses in the Y-junction — Section III — is simulated in time-domain using a three-dimensional, full-vectorial electromagnetic solver. We found that the Y-junction introduces broadband loss of about 1 dB and 1.5 dB for the quasi-TE₀ and quasi-TE₁, respectively. The IPMs are also tolerant to fabrication variations, as minor differences in the PR conversion losses have been measured for devices located in the center and on the edge of the 8” SOI wafer. We do not expect the section III to cause any significant performance variations as fabrication-tolerant Y-junctions have already been reported by other groups [8].

 

Fig. 4 Test structures used for characterization of the optical losses in the polarization rotator section — Section I and II — of the180-degree IPM with a length of 84 μm.

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4. Results of 22 Gbaud and 44 Gbaud QPSK experiments

We have fabricated monolithic single-polarization quadrature phase-shift keying (QPSK) receiver based on the reported mixer. The chip size is 1.5 ×1.5 mm and incorporates on-chip high-speed, AC-coupled and balanced Ge photodiodes which are optically coupled to the four output ports of two 180-degree hybrids, as shown in Fig. 2(b). On-chip 50 Ω terminations are used in parallel to the BPDs for interfacing to the 50 Ω coaxial cables without trans-impedance amplifiers. The photodiodes are wire bonded to the ceramic radio-frequency (RF) board. The entire assembly exhibits an opto-electrical bandwidth of ∼28 GHz, limited by the RF cables and connectors. An off-the-shelf lithium niobate based IQ modulator is used to generate QPSK signal. We did not use frequency pre-compensation and pulse shaping. The QPSK signal at the symbol rates of 22 Gbaud and 44 Gbaud is coupled in the input waveguide along with the LO. The optical power levels amount to +18 dBm and +1 dBm for the LO and the signal, respectively. A polarization-maintaining fiber is used to launch signal and LO in two orthogonal modes of the input waveguide. Analog-to-digital converters embedded in a real-time oscilloscope at a sampling rate of 80 GS/s are used to capture the electrical waveforms at the outputs of the on-chip BPDs. For receiver sensitivity measurements we have used standard noise loading setup comprising inline two erbium doped fiber amplifiers (EDFAs) and a Fabry-Perot filter with a passband spectral width of 2 nm in between. The signal-to-noise ratio (OSNR) is measured at input of device under test (DUT) with a reference resolution bandwidth of 0.1 nm. Receiver sensitivity measurement results for 22 Gbaud signal is given in Fig. 5. OSNR penalty compared to the theory is ∼4 dB which is caused by multiple factors such as birefringence of the inverse taper couplers and optical axes misalignment at the fiber/chip interface. The constellation diagrams for optical back-to-back experiments is given in Fig. 5. The measured bit error ratios (BERs) were less than 2.4 × 10⁻⁶ (no error measured in 425971 symbols) at 22 Gbaud and 3 × 10⁻⁴ at 44 Gbaud.

 

Fig. 5 Single-polarization QPSK signal reception experiments.

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5. Bandwidth discussion of the 90 ° IPM

Optical 90-mixers on silicon are usually realized by means of a single 4(2) × 4 [7,9–12] or four 2(1) × 2 multimode interference (MMI) couplers [13–20]. The 4 × 4 MMIs inherently provide the required 90° phase difference between the pairs of its outputs. Unfortunately, 4 × 4 MMIs have a typical length of 500 μm and are sensitive to the fabrication variations. Their operation bandwidth is limited in a wavelength range of only ∼50 nm [20]. The 90-degree mixer that consists of four 2 × 2 MMIs requires optical path length imbalance in the in-phase (I) and quadrature(Q) components to achieve the 90° phase difference between the signal/LO relative phases. The optical path difference is achieved by means of an active-tunable phase-shifter [13–17] or an asymmetry introduced either in the physical lengths [17] or waveguide cross-sections [18] of the two arms of LO (or signal) paths after the first 2 × 2 coupler. Although, an ultra-broadband 90-degree optical mixer can be realized by means of an active-tunable phase-shifter [14], the packaging complexity, power consumption and signal-processing requirements associated with the extra phase shifter makes this approach less favorable.

The 90-degree mixers which are based on an asymmetry introduced in the physical lengths or waveguide cross-sections are bandwidth-limited and fabrication sensitive, because the effective refractive index depends on the operating wavelength and the cross-section of the waveguide, as shown in Fig. 6(a) and 6(b). Figure 7(a) gives the example design of a traditional 90-degree optical mixer comprising four 2 × 2 identical couplers and asymmetric waveguide lengths for the signal and LO propagation in the I and Q paths. Introducing a length imbalance L_π/2 = λ/4 × Δn of 161 nm between the two branches of signal after the first 3 dB power divider, the difference of the signal/LO relative phases in I and Q components amounts to ${\varphi }_{\pi /2}(\lambda )=2\pi /\lambda \times n_{\text{eff}}^{\text{TE}}(\lambda )L_{\pi /2}$, where λ is the wavelength of light and $n_{\text{eff}}^{\text{TE}}(\lambda )$ is effective refractive index of the quasi-TE mode. As given in Fig. 7(b), this phase is a function of the wavelength and the condition for the 90° can be fulfilled for a specific wavelength only. Reduction of the wavelength sensitivity of the accumulated phase requires negative waveguide dispersion which is not straight forward to realize with low-loss silicon waveguides. Furthermore, the accumulated phase achieved with a physical length asymmetry has strong dependence on the waveguide dimensions. The blue solid lines in Fig. 7(b) give the deviation of the phase from 90° when the width w and the height h of the waveguide change with an amount of ± 25 nm and ± 10 nm, respectively. In this case, the operation bandwidth is limited within a wavelength range of ∼50 nm.

 

Fig. 6 Effective refractive indices n_eff of quasi-TE and quasi-TM modes of channel waveguide as a function of the waveguide width for Λ = 1550nm (a) and the operating wavelength for w = 500nm (b).

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Fig. 7 Designs of traditional and proposed 90-degree mixers. (a) Traditional design of a 90-degree optical mixer comprising four 2 × 2 identical couplers, and utilizing only quasi-TE₀. (b) Operating bandwidth of a traditional mixer using silicon channel waveguides with a width w of 500 nm and a physical length asymmetry of L_π/2 = 161 nm. The operating bandwidth is limited within a wavelength range of ∼50 nm. (c) The design of the proposed novel silicon photonic 90-degree mixer comprising a polarization insensitive coupler and two inter-polarization mixers. The birefringence of silicon channel waveguide with a width of 500 nm and the length of L_π/2 = 571 nm is used to introduce a 90° phase shift between the in-phase and quadrature components of the detection. (d) The wavelength response of the proposed mixer amounts to 150 nm even after taking into account the silicon-photonics foundry worst process-corners.

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In our 90-degree mixer, the birefringence of silicon channel waveguide provides broadband and fabrication-tolerant phase retardation between the signal and LO, as can be seen in Fig. 6. The reason is that the effective refractive indices of quasi-TE₀ and quasi-TM₀ modes follow a similar behavior with the variation of the wavelength and the waveguide cross-section. Consequently, the effective refractive index difference Δn is only a weak function of the wavelength and the waveguide cross-section, while, simultaneously, being large enough to allow for the necessary 90° phase delay. Figure 7(c) gives a possible layout design of 90-degree mixer on silicon. A physical length imbalance of L_π/2 = λ/4 × Δn_eff⁻¹ is introduced between the two waveguide branches after the first polarization insensitive 3dB splitter. Here, the phase is defined by birefringence parameter of $\mathrm{\Delta }{n}_{\text{eff}}(\lambda )=n_{\text{eff}}^{\text{TE}}(\lambda )-n_{\text{eff}}^{\text{TM}}(\lambda )$, where $n_{\text{eff}}^{\text{TE}}(\lambda )$ and $n_{\text{eff}}^{\text{TM}}(\lambda )$ are wavelength dependent effective refractive indices of quasi-TE₀ and quasi-TM₀ modes, respectively. Figure 7(d) gives the calculated accumulated relative phase as a function of the wavelength. The phase response is also given for the worst process-corners considering waveguide width / height variations of +25 nm / +10 nm and −25 nm / −10 nm, given as blue solid lines in Fig. 7(d). As can be seen, the birefringence of Si channel waveguide allows for fabrication-tolerant optical 90-degree hybrids with operating bandwidths of 150 nm. In addition to the variations in the width and the height, we have studied the deviation of the phase with the length L_π/2 in traditional and our hybrids, given as blue dash lines in Fig. 7(b) and 7(d). It has been found that the hybrid based on birefringence of silicon channel waveguide may sustain its operation bandwidth of ∼150 nm even when the variations in the length L_π/2 amount to ±5 nm, unlike the traditional hybrid which totally fails to tolerate such changes in L_π/2.

6. Conclusion

In conclusion, we report on novel silicon photonic adiabatic 180- and 90-degree mixers with small footprint, broadband response and low loss. The reported mixers have several unique features. First, the devices have only one physical input port which may allow for novel coherent system and digital-signal-processing implementations. Second, the waveguide birefringence allows for a broadband 90-degree optical mixer operation over the wavelength range of 150–200 nm. Third, by choosing the waveguide widths of ≥ 500 nm, the broadband operation can be preserved for waveguide width / height variations of ± 25 nm / ± 10 nm, respectively.