All-silicon interferometer with multimode waveguides for temperature-insensitive filters and compact biosensors

We report a novel design of an all-silicon temperature-independent filter employing a Mach-Zehnder interferometer (MZI) with multimode waveguides. The two arms of the MZI have equal lengths and equal widths but propagate different modes having different effective indices to guarantee an optical path difference (OPD) but similar temperature-dependence to diminish any thermal shifts of the interference pattern. A temperature-independent MZI filter with only one channel is also proposed and experimentally demonstrated. Measurements verify the principle of operation and a low temperature sensitivity of −20 to 10 pm/°C in the C-band for both MZI filters is achieved. The one-channel MZI structure is furthermore employed to achieve a compact sensor exhibiting a high sensitivity of 826 nm/RIU (refractive index unit). © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Silicon photonics is foreseen as a promising platform for emerging technologies within quantum communication [1,2] and artificial intelligence [3,4], and is taking a vital role on optical interconnects dealing with ultra-dense data [5][6][7][8] and biosensors for label-free detection [9][10][11][12]. The arguments for silicon photonic devices are mainly addressing their compactness and resemblance to silicon electronic integrated circuits (ICs) in terms of fabrication. However, there are yet some challenges hindering silicon photonic devices for broader practical implementations, among which a large thermal drift is detrimental to the performances of silicon photonic devices due to the inherently large thermo-optic coefficient (TOC) of silicon (1.86 x 10 −4 /°C [13]). For example, the two arms of a Mach-Zehnder interferometer (MZI)-based biosensor has to be approximately identical to cancel out the influence of thermal fluctuations but, therefore, the arms need to be very long (2 mm) to achieve enough phase shifts [14], challenging the practical integration of such with ICs.
To overcome the influence of thermal fluctuations on a silicon photonic chip, it is natural to use thermo-electric coolers (TEC) to externally stabilize the chip temperature or to use onchip heaters to locally compensate the temperature drift [15][16][17]. Nevertheless, both methods are dramatically increasing the complexity and the power consumption of the system. Alternatively, athermal schemes have been developed by covering the silicon photonic devices with negative TOC materials [18][19][20][21][22] or by using all-silicon asymmetric MZI to cancel out the thermal drift [23][24][25][26]. The first scheme will impose additional steps on the fabrication by cladding the silicon waveguides with e.g. polymers or titanium dioxide possessing a negative TOC, as well as inevitably employing narrow silicon waveguides with a larger loss [21] to increase the overlap of the mode with the negative TOC material. The allsilicon scheme typically involves the use of an asymmetric MZI structure, in which the two arms are designed to have either different widths [23][24][25], different modes [26,27] or even different waveguide configurations [28,29] to balance out temperature effects, which will restrict the design flexibility and limit the use of such especially for athermal filters with different free-spectral ranges (FSRs).
Here, we propose and experimentally demonstrate a novel temperature-insensitive allsilicon MZI having two waveguide arms of equal length and width. The design is based on the finding that a lower-order mode and a higher-order mode can experience an equal phase shift with respect to a change in temperature in a silicon multimode waveguide at specific critical width. If both arms of equal lengths of the MZI are designed with the critical width and separately propagate the lower-and higher-order modes, the MZI can achieve very low temperature sensitivity. The lengths of the arms will not be restricted but only depend on the desired FSRs. Recently, we presented such a design concept in our previous conference abstract [30]. In this paper, we will elucidate details of the design principle and -more importantly -we will experimentally verify the superiority of adjusting the arm lengths to achieve the desired FSRs while sustaining the athermal capability. Furthermore, as both arms are of equal lengths and widths, the present MZI can be designed to have only one channel. The one-channel MZI decreases the device area footprint and combining the two channels as a single one will mitigate sufferings from the more or less non-uniformity of the SOI wafer or the particles generating in the fabrication, in case they occur as an issue. Although onechannel interferometers employing multimode waveguides have already been theoretically [31] and experimentally [32,33] demonstrated for biomedical sensors, the coupling of light to the different modes are realized by offsetting the input waveguide, which may limit the design in only using few modes. Here, our one-channel MZI are realized by employing adiabatic tapers and directional couplers (DCs) exhibiting greater design flexibilities. Both of our two-channel and one-channel MZI temperature-insensitive filters can achieve a small temperature sensitivity of −20 to 10 pm/°C for the whole C-band, comparable with the previous results of <8 pm/K in a wavelength range of 30 nm [27]. Moreover, we demonstrate a biomedical sensor based on the one-channel MZI having sensitivity as large as 826 nm/RIU.

Structure and design
We used an eigenmode solver (Mode Solution from Lumerical Inc.) to calculate the effective indices (n eff , solid lines) and the temperature dependences (dn eff /dT, dashed lines) for transverse-electric (TE) modes of different orders with respect to the waveguide width w of a silicon waveguide of height h = 250 nm buried in silica (SiO 2 ), as shown in Fig. 1. In the calculations, TOCs and refractive indices at the wavelength of 1550 nm are chosen as 1.86 x 10 −4 /°C and 3.455 for silicon, and 0.08 x 10 −4 /°C and 1.445 for SiO 2 , respectively. For any width of a multimode waveguide, the higher-order mode will always have a smaller n eff than the lower-order mode, due to a weaker confinement in the higher-index core. However, the dn eff /dT curves may cross at some critical width. For smaller w, dn eff /dT increases rapidly with w since it is dominated by large changes in the mode confinement [34]. For larger w, dn eff /dT decreases slowly with a factor w −2 since the absolute value of n eff dominates and decreases with w −2 [23]. Due to a weaker confinement of the higher-order modes, the curves of dn eff /dT versus w are moved towards larger w compared to that of the lower-order modes. Thus, the lower-order mode and the higher-order mode will cross at a critical width, where they have different effective indices but the equal temperature dependences of the refractive indices. For example, the critical width w c for the TE 0 mode and the TE 1 mode is 623 nm, where dn eff /dT of both modes is 1.993 x 10 −4 /°C with effective indices Δn eff of 0.8246. In the following, we use the TE 0 mode and the TE 1 mode and choose w c = 623 nm as the widths for both arms of our temperature-insensitive MZI (TI-MZI).  Figure 2(a) schematically illustrates the configuration of the proposed TI-MZI with two channels. The fundamental TE 0 mode at 1550 nm inputted from the 450nm-wide single-mode waveguide is equally split into two parts by the first symmetric directional coupler (DC). The upper part is coupled to the TE 0 mode in the 623 nm-wide multimode waveguide of arm 2 by using an adiabatic taper with a length of 5 μm. The lower part is firstly coupled to the TE 0 mode in a narrow waveguide by an adiabatic taper with length 5 μm and subsequently coupled to the TE 1 mode in the 623nm-wide waveguide of arm 1 by an asymmetric DC (ADC). Finally, the TE 0 mode in arm 2 and the TE 1 mode in arm 1 are separately coupled back to the TE 0 mode in the 450nm-wide waveguide after propagating along the arms with a length of L, and interfere in the last symmetric DC. Since the two arms have the equal widths w c and the equal lengths L, the two-channel TI-MZI can be easily adjusted to have only one channel as shown in Fig. 2(b). The widths of the narrow waveguides are chosen to w narrow = 288 nm to achieve phase matching between the TE 0 mode and the TE 1 mode in the 623nmwide multimode waveguide. Figure 2(c) shows the calculated and normalized (to a straight waveguide) transmissions of the asymmetric DC which converts the TE 0 mode in the 288nmwide single-mode waveguide to the TE 1 mode in the 623nm-wide multimode waveguide as shown in the inset. The conversion efficiency is ~98% at 1550 nm resulting in an extinction ratio (ER) of ~21 dB between transmissions in the cross port and the thru port.
The TI-MZI contains different connecting waveguide sections with lengths L' (Fig. 2), which are not completely symmetric with this asymmetry being much pronounced for the one-channel design. This will possibly introduce differences in the accumulated dn eff /dT for the two arms. However, the influence of the different sections can be negligible if L>>L' according to the formula for the temperature sensitivity S of the TI-MZI, Here, λ is the interference wavelength and Δn g is the group index difference between the two modes in the multimode waveguide, i.e. 0.566 in the case for TE 0 and TE 1 . Δn g ' and Δ(dn eff '/dT) are the group index difference and the difference in temperature dependence of the effective indices of the upper and lower connecting waveguide sections averaged over L', respectively. The first part in the numerator will be always zero since the two modes have the same temperature dependence and for L>>L', S goes to zero.

Fabrication and characterization
The designed TI-MZIs are fabricated on a silicon-on-insulator (SOI) chip having a 250-nm top silicon layer on a 3-μm thick silica layer. A positive resist ZEP520A is spun on the chip and patterned using electron beam lithography to act as a soft mask in an inductively coupled plasma (ICP) etching machine using sulfur hexafluoride (SF 6 ) and octafluorocyclobutane (C 4 F 8 ) gases to etch the silicon. The etching is utilizing a Bosch process having alternations between an etch cycle (5 seconds) and a passivation cycle (3 seconds) with the platen temperature cooled down to 10 °C. The residual resist is stripped and the chip is covered with a 1-μm thick layer of silica. Optical microscope images of the fabricated two-channel and one-channel TI-MZIs are shown in Figs. 3(a) and 3(b), respectively. On-chip grating couplers (GCs) are used for coupling light to and from the chip [35]. Insets framed in green and red in Fig. 3(a) show scanning electron microscopy (SEM) images of the adiabatic taper (red) and the mode coupler (green). The SEM image in Fig. 3(b) shows the connecting part including the 50%:50% splitter, the adiabatic tapers and the mode coupler of the one-channel MZI. To verify the temperature-insensitivity of the fabricated MZIs, we have characterized the MZIs at different temperatures and normalized the recorded transmission spectra to the transmission of a straight waveguide at the corresponding temperatures to cancel out any temperature-dependence of the grating couplers. The normalized transmission spectra are shown in Fig. 4(a) for a two-channel TI-MZI with L = 1.097 mm, Fig. 4(b) for a two-channel TI-MZI with L = 0.276 mm, and Fig. 4(c) for a one-channel TI-MZI with L = 1.097 mm. The measured spectra have been fitted by trigonometric curves to get the exact destructive wavelengths but not shown in the figures. At 1550 nm, insertion losses of the 0.276mm-long and the 1.097mm-long two-channel filters are measured to ~0.1 dB and ~1.6 dB. The onechannel TI-MZI filter shows a low loss of ~0.7 dB with an ER ~11 dB around 1550 nm. Figure 4(d) shows the temperature sensitivity as a function of wavelength for all MZI configurations and we find temperature-dependent wavelength shifts lower than 1 pm/°C at 1547 nm for the two-channel and the one-channel MZI having the longer arm. In the whole C-band (1535 nm -1565 nm) the wavelength shift stays between −20 to 10 pm/°C. The wavelength for achieving zero thermal drift for the shorter two-channel filter moves to around 1535 nm since the two connecting parts introduce a relative higher temperature dependence of the filter. Nevertheless, the shorter filter can still achieve a temperature-dependent wavelength shift lower than 10 pm/°C in 20 nm wavelength region from 1525 nm to 1545 nm. Furthermore, we find the FSR of the shorter MZI (13.14 nm) to be ~3.6 times larger than that of the longer MZI's (3.67 nm), which illustrates the flexibility in the design of the TI-MZI filters with different bandwidths. The proposed one-channel MZI is applied as a compact biosensor utilizing the different responses to a change in the top cladding index of the modes in the multimode waveguide. We selectively open a window in the top cladding on the waveguide channel in the onechannel filter with L = 1.097 mm by etching the top silica cladding with a 5% hydrofluoric (HF) acid solution. Figure 5(a) shows a microscopy image of the fabricated sensor. The dependency of the effective indices of the modes at different waveguide widths on the refractive index of the analyte (dn eff /dn c ) flowing into the opened window are calculated and shown in Fig. 5(b) with the waveguide cross section illustrated in the inset. Here, the wavelength is 1550 nm and the waveguide height is 250 nm. The higher-order TE 1 mode has a larger dn eff /dn c due to a weaker mode confinement and, hence, a larger overlap with the analyte. For a width of 623 nm (indicated by the vertical brown dotted line in Fig. 5(b)) the Δ(dn eff /dn c ) between the TE 0 mode and the TE 1 mode is as large as 0.35, suggesting a large sensitivity of the sensor. We separately drop deionized (DI) water and a phosphide buffer solution (PBS) with different concentrations onto the sample and measure the transmission spectra of the sensor. Figure 5(c) shows the normalized measured spectra of the sensor when the sample is covered by DI water (black), 0.25x PBS (red), 0.5x PBS (green), 0.75x PBS (light blue), and 1x PBS (dark blue). Here, the standard 1x PBS was diluted with 3/1/0.33 times volume of DI water to achieve the 0.25x/0.5x/0.75x PBS, respectively. The ripples on the transmission spectra are caused by Fabry-Perot cavities formed between the waveguide couplers and the sensing window boards. Trigonometric curves are used to fit the measured spectra to extract the exact destructive interference wavelengths (not shown in the figure). The transmission spectra are found to red shift as the PBS concentration increases while the insertion loss of the sensor stays around 1.8 dB. Figure 5(d) plots the wavelength shift of the sensor compared to the case of applying DI water with respect to the refractive index change of the PBS at different concentrations. Here, as the concentration increases, the refractive index of the PBS linearly increases with a rate of ~0.005 per 3x [36]. The linear fitting yields a sensitivity, Δλ/Δn c , of 826 nm/RIU (refractive index unit). It is noted that the sensitivity of the present refractive index sensor is one order larger than that of a traditional silicon singlemode waveguide sensor (70 nm/RIU [9]) since by leveraging the higher-order mode light can be more effectively overlapped with the cladding analytes. The sensitivity S can also be calculated by S = λ(Δdn eff /dn c )/Δn g and a value of 728 nm/RIU is derived. Here, Δdn eff /dn c and Δn g are differences of dn eff /dn c and group indices between the two modes (TE 0 and TE 1 ), respectively, and λ = 1550 nm. A larger measured sensitivity can be attributed to an undercut of the silica beneath the waveguide in the HF etch. It is worth to note that the proposed biosensor design can be shortened while keeping a high sensitivity as the sensitivity S is independent on the arm length.

Conclusion
We have proposed and experimentally demonstrated a novel design of an all-silicon Mach-Zehnder interferometer with low sensitivity to temperature changes having two multimode waveguide channels of equal widths and lengths and, thus, being able to be adjusted to a more compact one-channel interferometer. The principle of operation is based on transmitting two different modes in a silicon multimode waveguide, which can have equal temperature dependence of the phase shift at a critical waveguide width. By choosing the waveguide width to 623 nm applicable for the TE 0 and the TE 1 mode, we have fabricated and measured the MZI filters and found that both the two-channel filter and the one-channel filter can achieve a low thermal drift in the range from −20 to 10 pm/°C in the C-band while exhibiting a low insertion loss of 1.6 dB for the two-channel interferometer and 0.7 dB for the onechannel interferometer. Measurements on the interferometers with different arm lengths show the design flexibility to achieve different free-spectral-ranges while keeping the athermal performance. The design of the one-channel interferometers is further applied as a compact biosensor having a measured sensitivity as large as 826 nm/RIU and a low insertion loss of 1.8 dB. It should be noted that in this work we did not try to extract a thermo-optic coefficient of the PBS solutions as they quickly condense in the present device and, thus, we didn't put focus on characterizing the MZI structure as an athermal biosensor, i.e. measuring the thermal dependency of the proposed biosensor. However, the proposed concept can easily be applied for such purpose if the liquid analyte is sealed in a microfluidic channel to avoid the evaporation, hence, realizing a highly sensitive and athermal biosensor. Resembling to all other all-silicon interferometer designs, the performances of the present design will also be degraded by the fabrication errors in the waveguide width and the fabrication tolerance of the present design is calculated to be −5 to 7 nm assuming a ± 10 pm/°C offset. The present design, both for the temperature-independent filter and the compact biosensor, can be easily expanded to use even higher-order modes to keep in step with the development of the emerging mode multiplexing technologies. We believe our design strategy opens for great design flexibility, low insertion losses, and low temperature sensitivities for integrated silicon temperature insensitive filters and compact biosensors.