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We propose an ultra-compact optical 90° hybrid with the smallest length of 107μm, consisting of a wedge-shaped 2 × 4 MMI coupler connected with a 2 × 2 MMI coupler using silicon nanowaveguide technology. Neither cascaded phase shifters nor waveguide crossings are attached to the proposed 90° hybrid in coherent receiving system. The proposed device is demonstrated on silicon-on-insulator (SOI) with 220nm thick top-silicon layer and 2μm thick buried oxide layer. A high performance of the proposed 90° hybrid is exhibited experimentally with a high extinction ratio larger than 20dB, an excess loss mostly less than 0.5dB, a common mode rejection ratio better than −20dB and phase deviation within the range of 5° over C-band spectral range.
©2013 Optical Society of America
1. Introduction
A lot of work on coherent transmission systems has been done since the early 1980’s [1,2], which has had a great revival thanks to the progress in digital signal processing and increasing demand on fiber capacity. Quadrature phase shift keyed (QPSK) modulation is considered as one of the efficient methods to maximize spectral efficiency and receiver sensitivity in multilevel coherent transmission system [3]. An optical 90° hybrid is demanded as one of the prerequisite components in coherent receiving system working as a demodulator of the QPSK modulated signals [4,5]. Optical waveguide-based 90° hybrids continue to attract attention for their characteristics of compactness and monolithic integration with photodetectors (PDs). Many different kinds of waveguide-based hybrids have been reported, such as hybrids with star couplers [6], arrayed waveguide gratings (AWG) [7], multimode interference (MMI) couplers [8–15]. Devices based on MMI coupler structure are mostly preferred to be suitable for realizing integrated optical 90° hybrids on chips due to the compact size and large fabrication tolerances. For example: the single 4 × 4 MMI coupler [10–12] and 2 × 4 MMI couplers connected with 2 × 2 MMI couplers [13–15]. Various materials have been adopted for optical 90° hybrids, such as InP [13,15], LiNbO3 [16], silicon-on-insulator (SOI) [10–12] and so on. To date, nanowaveguide technology based on SOI provides an attractive platform for waveguide-based devices, because it allows the realization of very compact designs due to its high-index contrast and is compatible with complementary metal oxide semiconductor (CMOS) process. An optical 90° hybrid with 4 × 4 MMI coupler based on SOI has recently been realized with a short length of 185μm and an excess loss less than 0.5 dB [11]. However, two SOI waveguide crossings are needed when the 4 × 4 MMI hybrid connects with balanced PDs, which inevitably brings undesirable extra excess loss and crosstalk. Besides, strong phase errors for the higher-order modes in MMI caused by high-index contrast in SOI hinder the accurate quadrature response of the optical 90° hybrid [12].
Here we pay attention to an optical 90° hybrid with a wedge-shaped 2 × 4 MMI coupler directly connected with a 2 × 2 MMI coupler [15], in which, both cascaded phase shifters and waveguide crossings are not included. What is more, this structure in SOI are more suitable for an optical 90° hybrid, because it decreases the number of the excited modes by sharply narrowing the width at input side and effectively eliminate the strong phase errors for higher-order modes. Thus the hybrid will have both more compact size and more accurate phase relationship. In this paper we focus on the ultra-compact 90° hybrid employing a wedge-shaped 2 × 4 MMI coupler with a 2 × 2 MMI coupler which is realized on SOI platform with 220nm thick top-silicon layer and 2μm thick buried oxide layer. The fabrication of the device only needs single-step E-beam lithography and fully-etching. Both analytical and experimental results show that a high performance of the proposed device is exhibited with a high extinction ratio lager than 20dB, an excess loss mostly less than 0.5dB, a common mode rejection ratio better than −20dB and phase deviation within the range of 5° over C-band spectral range. The proposed 90° hybrid is only 107μm long, the smallest size among the optical waveguide-based 90° hybrids based on MMI couplers that have already been reported [10–15].
2. The proposed optical 90° hybrid in SOI
The proposed optical 90° hybrid consists of a wedge-shaped 2 × 4 MMI coupler serially connected with a 2 × 2 MMI coupler. Figure 1 shows the schematic diagram of the proposed optical 90° hybrid considering balanced detection in coherent receiving system. The wedge-shaped 2 × 4 MMI coupler works as a 180° hybrid. Then phase relationship of its output signals coupled to the 2 × 2 MMI coupler are converted by 90° through the general interference in the 2 × 2 MMI coupler, which generates a quadrature phase relationship of the four output signals of the device.
Fig. 1 Schematic diagram of a coherent detection scheme connecting the proposed 90° hybrid and balanced PDs.
Restricted interference is considered for the wedge-shaped 2 × 4 MMI coupler with widths of Wa and Wb, which works relying on the self-imaging effect [17]. Define that Г is the ratio between Wa and Wb, i.e. Г = Wa /Wb. For the propagation constants of arbitrary modes βv (v = 0, 1, 2…), the net value of the 2 × 4 MMI coupler has been derived in [18] as following:
It can be concluded from Eq. (1) that the relative phase between output 3 and output 4 of the wedge-shaped 2 × 4 MMI coupler can be adjusted by the proportion parameter Г. In order to remove the phase shifters in [13], Г is should be optimized to bring additional –π/4 to the phase difference of output 3 and output 4 of the wedge-shaped MMI coupler [15]. Moreover, as the value of Г changes, the length of the wedge-shaped 2 × 4 MMI coupler L2-4 will also change, which can be expressed as following:
where Lπ is defined as the half beat length of the two lowest-order modes for a rectangular MMI coupler [19] and Wbeff is the effective width of Wb, approximately for all guided modes. Equation (2) implies that the length of a wedge-shaped MMI coupler will be shorter than that of a rectangular one with the same width as Wb. In previous work [14], we demonstrated a rectangular 2 × 4 MMI coupler compact length of ~97μm. Hence our design with a wedge-shaped 2 × 4 MMI instead of a rectangular-shaped MMI coupler can be more compact in size, and meanwhile decrease the number of excited modes in the wedge-shaped 2 × 4 MMI coupler, which effectively relieve the mode dispersion of higher-order modes resulting in better phase errors at output channels.Based on SOI platform, three-dimensional beam propagation method (3-D BPM) is used to simulate and calculate the length-decreasing ratio and the relative phase between output 3 and output 4 of the wedge-shaped 2 × 4 MMI coupler. We use light of TE mode to investigate the performance of the proposed device considering the high polarization dependence of the nanowaveguides on SOI with 220nm top-silicon layer. In the case of wedge-shaped 2 × 4 MMI, Wb is chosen as wide as 12μm in [14]. Then we simulate and plot the curve between 1/Г and the phase difference (Δθ34 = θ3–θ4) of output 3 and output 4 of the wedge-shaped 2 × 4 MMI, as shown in Fig. 2. It is manifested that the -π/2 (−90°) phase difference is achieved when the value of 1/Г is ~1.975 (Г≈0.5063). Based on the chosen ratio 1/Г, the reduction ratio of the length is calculated as ~53.8% deduced from the curve of 1/Г to length-decreasing ratio.
Fig. 2 Simulated curves between 1/Г (Г = Wa / Wb) and the phase difference Δθ34 as well as the length-decreasing ratio of the proposed wedge-shaped 2 × 4 MMI with Wb = 12μm in SOI.
Using the decided ratio Г, it is simulated and calculated that Wa of the wedge-shaped 2 × 4 MMI is (12 × Г)μm and the length L2-4 of the wedge-shaped 2 × 4 MMI coupler is 45.5μm. The size of 2 × 2 MMI coupler is simulated as 4.01 × 61.5μm2. The total length of the proposed 90° hybrid is only 107μm. Figure 3 shows the simulated light intensity patterns of the proposed device. With one light from either input waveguide, the hybrid separates it into four beams equally acting as a 6dB power splitter.
Fig. 3 Simulated transmission characteristics of the proposed 90° hybrid in SOI with an input channel of (a) I1 and (b) I2, at λ0 = 1550nm.
Imbalance is an important characteristic of MMI couplers which impacts the achievable extinction ratio of an interferometric device. The excess loss of the device is also considered as another important characteristic. Thus, the imbalance and the excess loss of the proposed 90° hybrid are simulated and calculated by 3-D BPM. In Fig. 4, the simulated imbalance among the quadrature output signals are better than 0.5dB across C-band spectral range, when either I1 or I2 is treated as the input channel. The simulation results of excess loss are shown in Fig. 5. The excess loss of the proposed 90° hybrid is less than 0.5dB from 1540nm to 1570nm and less than 1dB from 1530nm to 1540nm as a result of modes conversion.
To ensure that the wedge-shaped MMI coupler can effectively eliminate the strong phase errors for higher-order modes by reducing the width at input side, the quadrature phase relationship of output channels of the proposed 90° hybrid need to be simulated and calculated accurately. The expected phase deviation remains in a 5° range between the output channels of the proposed 90° hybrid. As to our design, the simulated phase deviation over C-band is shown in Fig. 6 within the range of 1.8°, which verifies that a compact wedge-shaped MMI coupler on SOI with a high-index contrast can exhibit a desired quadrature phase relationship of output signals.
3. Fabrication
The proposed 90° hybrid was fabricated on SOI with 220nm top-silicon layer. E-beam lithography technology was used to make the mask pattern. Then the process of fully-etching in SOI was easily performed for one time by inductively coupled plasma (ICP) technology. Finally an upper SiO2 cladding layer of 1μm thick was deposited onto the wafer using plasma enhanced chemical vapor deposition (PECVD) technology. Figure 7 shows the scheme, layout of the fabricated device and the SEM figure. To probe the phase behavior of the proposed device, a Mach-Zehnder (MZ) delay interferometer of ~140GHz was added before the 90° hybrid with length difference of ~480μm, as shown in Fig. 7(a). The two input light beams of the MZ delay interferometer come from a 1 × 2 MMI coupler acting as a 3dB beam splitter. The two output signals of the MZ delay interferometer are considered as the modulated optical signal and the local oscillation signal. In order to calculate the excess loss of the device, straight reference waveguides and the 1 × 2 MMI couplers were fabricated on the same wafer. The width of single mode waveguides is designed to be 500nm. Linear tapers with width changing from 0.5μm to 3.5μm were used at access channels of the device to improve the coupling efficiency. Several testing MMI structures were defined with varying lengths in 0.5μm steps. The bent waveguides were connected with the short output waveguides of the device to avoid the crosstalk and the radii of the curvature are 100μm and 250μm respectively.
Fig. 7 (a) Scheme, (b) partial layout and (c) scanning electron microscope (SEM) picture of access waveguide’s crossing section of the device in SOI nanowaveguide technology.
4. Measurement results and discussion
The experiment setup for testing the performances of the fabricated devices is shown in Fig. 8. Lensed single mode fibers were used for optical chip coupling. The light beam was launched from a tunable laser. The polarization of the beam was controlled to be TE mode via a deterministic polarization controller (DPC). The output signals were separated into two beams by using a 3dB beam splitter (BS). One beam went into the power meter to monitor the coupling efficiency and the other one was sent into the spectrometer to measure the transmission spectra of the fabricated devices.
The transmission spectra of the fabricated device are measured as shown in Fig. 9. As a result of MZ delay interferometer, the phase difference between signal beam and local oscillator change periodically as transmitting into the fabricated 90° hybrid so that the output signals will be periodic change in power, which generates the free spectral range (FSR). FSR is defined as the minimum wavelength difference by a shift of 2π of the phase difference between signal beam and local oscillator. Each FSR in the output signals spectra is related to the wavelength, which is determined by the group index (Ng ≈4.35) and the relation: λ2/(Ng · ΔL), where the length difference ΔL of the two arms of the MZ delay interferometer is 480μm corresponding to a FSR of about 1.15nm at wavelength of 1550nm. The FSRs of each output signals of the fabricated device can be calculated by the transmission curve minima in the measured spectra. The signal of each channel is normalized with regard to the intrinsic 3dB loss and the excess loss of the 1 × 2 MMI coupler. The fabricated device exhibits an excess loss less than 0.5dB from 1540nm to 1570nm and less than 1dB from 1530nm to 1540nm, which well matches the simulation results. Over C-band spectral range we obtain minimum extinction ratio larger than 20dB. A slight oscillation of the signal is probably due to reflections in the experiment setup.
Fig. 9 Measured transmission spectra of CH1 to CH4 of the fabricated 90° hybrid with Mach-Zehnder delay interferometer (a) over C-band spectral range and (b) around 1550nm. The signals are normalized with respect to the straight reference waveguide and the loss of 1 × 2 MMI.
The common mode rejection ratio (CMRR) is a measurement of the electrical power balance to each output channel of a 90° hybrid, which corresponds to the ratio of the weak signal measured under equal illumination of both PDs and the strong signal measured when a single detector is illuminated [20]. The performance of the fabricated 90° hybrid is also quantified in terms of the CMRR. We use the power data in transmission spectra of each output channel to estimate the photocurrent under the assumption that the responsibilities of each PD are identical. The measured FSRs of CH1 (CH3) is considered as reference to estimate photocurrents under dual-PD illumination of Quadrature channels (In-phase channel). And the maxima of the transmission spectra data of Quadrature and In-phase channels are used to estimate photocurrents under single-PD illumination. It is observed in Fig. 10 that the CMRRs of both Quadrature and In-phase channels of the fabricated device are better than −20dB over C-band spectral range.
As typical parameters in calculating the phase deviation, the FSRs of CH1 is measured as reference. The theoretical phase offsets of CH1 to CH2, CH3 and CH4 (defined as ΔφN1, N = 2, 3, 4) are equal to π, π/2 and 3π/2 respectively. Therefore the phase deviation Δφ can be calculated in the following relation:
where Δλ denotes the distance of the transmission curve minima at different output channels within the range of FSR1, which is one of the measured FSRs of CH1. Based on Eq. (3), the phase deviation of the fabricated device can be calculated. As shown in Fig. 11, the phase deviation of the fabricated 90° hybrid is within a range of 5°, well matching the simulation results and meeting the requirement of the coherent receiving system.We also obtain the constellation diagrams for the fabricated optical 90° hybrid as shown in Fig. 12 using experimental spectra data in Fig. 10 and the calculated data in Fig. 11. In the constellation diagrams, the vertical amplitudes of In-phase channels (Quadrature channels) show the wavelength sensitivity of transmittances for CH1 and CH2 (CH3 and CH4). The horizontal dispersion of the dots for In-phase channels and Quadrature channels corresponds to the calculated phase deviation. The degree of circularity of the depicted constellation diagram indicates the inter-channel imbalance for each output channel of the fabricated 90° hybrid. It can be estimated that the fabricated device has the wavelength sensitive loss less than 0.7dB, the phase deviation within the range of 5° and the inter-channel imbalance less than 0.5dB over C-band spectral range.
5. Conclusion
In this paper, we theoretically calculated and experimentally demonstrated an ultra-compact optical 90° hybrid with total length of 107μm in SOI using silicon nanowaveguide technology. The proposed 90° hybrid consists of a wedge-shaped 2 × 4 MMI coupler and a 2 × 2 MMI coupler without any phase shifter and waveguide crossing in coherent receiving system. What is more, the proposed 90° hybrid has the smallest size among optical 90° hybrids based on MMI couplers that have already been reported. The experimental results show that the demonstrated 90° hybrid exhibits an extinction ratio larger than 20dB, an excess loss mostly less than 0.5dB, a common mode rejection ratio better than −20dB as well as the phase deviation within the range of 5° over C-band spectral range.
Acknowledgments
This work was supported by the National Key Basic Research Program of China (Grant no. 2011CB309606) and National High Technology Research and Development Program of China (863 Program) (Grant No. 2011AA010302) and Program for New Century Excellent Talents in University.
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