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Abstract
A novel concept of on-chip Fourier transform spectrometer is proposed. It consists of semiconductor waveguide directional couplers and NEMS actuators. The optical path difference can be tuned by controlling the NEMS actuators to couple or decouple the directional couplers. With 9 stages of directional couplers, we demonstrate numerically that the spectral resolution can reach up to 4 nm in 1.5 μm to 1.8 μm wavelength range. Further enhancement can be achieved by increasing the number of integrated NEMS driven directional couplers. This design meets the requirement of small size, weight and power and may be useful in future on-chip spectroscopic sensors.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Infrared (IR) spectroscopy is widely recognized as a gold standard for chemical analysis [1] owning to its superior specificity. Molecules can be identified/detected by its unique optical absorption characteristics. IR spectroscopy has been used in a variety of applications including industrial process control, healthcare, environmental monitoring, remote sensing, and food quality assessment. Traditional IR spectrometers, such as Fourier Transform Infrared (FTIR) spectrometers, however are bench-top instruments typically used in controlled laboratory environments. Their cost is high and size is large, and more importantly, they contain fragile optomechanical moving parts that require accurate optical alignment. These prevent them from practical field use. While for an increasing number of applications, on-chip spectrometers with advantages of Size, Weight, and Power (SWaP) are highly expected. Various on-chip spectrometer designs have been reported [2–21] including Mach-Zehnder interferometer based spectrometers [8,9,12,13,16], Michelson interferometer based spectrometers [4], detectors array [19], et al.
Here we demonstrate a novel concept of on-chip FTIR spectrometer that can acquire high-resolution spectra via time-domain modulation. This FTIR is based on a planar photonic integration platform and has a number of outstanding advantages including size and weight reduction, low-cost, and without the necessity of optical alignment thereby leading to enhanced manufacturing throughput and system raggedness. In the proposed design, with 9 stages of directional couplers, we numerically demonstrate that the spectral resolution can reach up to 4 nm in the wavelength range from 1.5 μm to 1.8 μm. Further enhancement can be achieved by increasing the number of integrated NEMS driven directional couplers.
2. Design and simulation
The concept of this device is similar to Fourier transform infrared (FTIR) spectrometer which is based on the optical path difference (OPD) modulation. However, different from traditional FTIR spectrometers, the OPD modulation in this device is achieved with semiconductor waveguide directional couplers. The directional couplers used here consist of a pair of single transverse-electric (TE) mode rectangular silicon waveguides whose width and height are 360 nm and 240 nm, respectively. When the two waveguides are placed closed enough, two supermodes will be formed due to the mode coupling as shown in Fig. 1(a). The fundamental supermode SM0 is a laterally symmetric mode while the supermode SM1 is a laterally anti-symmetric mode. If light is launched from one waveguide, the light will be split up into two equal components to propagate via SM0 and SM1 modes. Since the effective indices of SM0 and SM1 are different, the optical path length of these two modes are different when they propagate through a certain coupler length. Therefore, interferograms can be observed at the output ports by varying the coupler length, or in other words, by modulating the OPD. In our proposed design, the gap between these two waveguides is set at 100 nm for strong coupling throughout this study.
Fig. 1 (a) If two single waveguides are placed closed enough, two supermodes are formed. (b) Schematic of a typical directional coupler.
As presented in Fig. 1(b), there are four ports in a directional coupler which are designated as input, isolated, through, and coupled ports, respectively. Waveguides coupling makes the optical power transfer back and forth between these two waveguides while propagating along the coupling region. Consequently, the power outputs from through port and coupled port vary as functions of the coupling length L.
The whole spectrometer schematic diagram is presented in Fig. 2(a). The spectrometer consists two waveguides which form M stages of cascaded directional couplers. Each stage contains a directional coupler combined with a nanoelectromechanical systems (NEMS) actuator. The NEMS actuator is used for controlling the coupling condition of the directional coupler to operate in an “on” and “off” mode. The coupling length of each directional coupler is doubled of its former stage. Then, if the coupling length of the first stage is L1, the total coupling length can be tuned from zero to (2M-1)L1 with a step of L1 by controlling the coupling condition of each stage in a similar way to a M-bit electrical digital to analog converter (DAC). In our design, L1 and M are 2 μm and 9, respectively. In other words, the shortest and longest coupling length of the 9 stages are 2 μm and 512 μm, respectively. As a result, the total coupling length can reach up to 1022 μm. As discussed before, the total coupling length is equivalent to the OPD in a typical optical interferometer, so that the OPD here can be tuned step-by-step and interferograms can be achieved by this NEMS controlled method. As shown in Fig. 2(a), the connections between every adjacent stage are straight waveguides with length of 20 μm. Two identical detectors are connected to the through and coupled ports of the last stage, respectively, for collecting the outputs. As a result, full complex Fourier transform can be performed and the signal-to-noise ratio can be improved by factor of [22].
Fig. 2 (a) System schematic of the spectrometer. (b) Out-of-plane bending actuation using electrostatic parallel plates. (c) In-plane actuation using electrostatic comb drives.
With the help of NEMS actuators, the coupling conditions of the directional couplers can be controlled digitally. Two methods are highlighted here, as presented in Fig. 2(b) and Fig. 2(c), which are out-of-plane bending actuation using electrostatic parallel plates [23] and in-plane actuation using electrostatic comb drives [24], respectively. Suppose that the two waveguides are strongly coupled in the initial condition, out-of-plane bending structure can bend one arm vertically to decouple these two waveguides, whereas electrostatic comb drive can laterally displace one arm far away from the other in order to decouple the waveguides.
For this 9-stage cascaded NEMS on-chip FTIR system, assuming that the actuation time of each directional coupler is about 10 μs [25], the total time required to acquire a complete interferogram is then estimated to be 29 × 10 μs, i.e. about 5 ms. Besides, the mechanical natural frequency of a typical NEMS actuator is in the range of a few hundreds of kHz owing to the extremely small mass of the actuator. This natural frequency is much higher than the usual mechanical noise frequency from the environment. Hence, the proposed on-chip FTIR is expected to be quite robust again the external mechanical disturbances.
It should also be noted that the 512 μm long suspended waveguide in the last stage in our conceptual design here is challenging to be implemented practically using the current NEMS technology. The waveguide could encounter stiction problems during the NEMS release process. However, there are potentially two approaches that may overcome this problem. The first is to use multiple low-loss suspensions to strengthen the structure [26]. And the second is to break down the 512 μm long waveguide into multiple sections with shorter lengths, each attached with its own NEMS actuator. These waveguide sections and actuators are synchronized and response to a common drive signal so that they act coherently as one controlled coupler.
The working principle of the interferometer is as follows. Consider a single directional coupler with coupling length L, light launches into the input port and propagates through the directional coupler. The power observed at output ports can be given as [27]:
where Pthrough and Pcoupled are the light power at the through and coupled ports, respectively. B0 is the intensity of the incident light. ∆n is the effective index difference between SM0 and SM1. λ0 is the wavelength in vacuum.For a Michelson interferometer, the interferogram can be described as:
where ID is the intensity of the interferometer output and x is the OPD.Comparing both Eq. (1) and (2) with (3), we find that the equivalent OPD in the proposed device can be described as x = L∆n. Therefore, Eq. (1) and (2) can be rewritten as
so that the light spectrum B0(λ0) can be recovered by performing a fast Fourier transform (FFT) of the interferogram.3. Results and discussions
The 360 nm × 240 nm sized rectangular silicon waveguide in air performs ideal single TE mode from 1.5 μm to 1.8 μm wavelength range. As shown in Fig. 3(a), the numerically calculated effective indices of SM0 and SM1 decrease with the increasing wavelength. However, the indices of SM0 and SM1 follow different varying slopes, which makes their index difference, ∆n, increases monotonically as a function of wavelength. Consequently, ∆n increases from 0.06 at 1.5 μm to 0.37 at 1.8 μm as shown in Fig. 3(a). And therefore, λ/∆n decreases monotonically with the increasing wavelength as Fig. 3(b) presented. This relationship between λ and λ/∆n will be used in our unit conversion after FFT.
Fig. 3 (a) Effective indices of SM0, SM1 and their difference ∆n. (b) Relationship between λ/∆n and wavelength λ.
To simulate the device performance, scattering parameter (S-parameter) models are involved. S-parameters describe the behavior of a linear electrical network when it undergoes various steady-state stimuli by electrical signals. The directional coupler is a linear electrical network with 4 ports. Therefore, the whole system performance can be determined by combining the S-parameter models of all 9 stages instead of simulating the whole structure which will consume a large amount of calculation resources and time.
A directional coupler can be modelled using a 4 × 4 S-parameter matrix. The outputs of the coupler can be obtained by the multiplication of the inputs with its S-parameter matrix. For an ideal coupler, the relationship between inputs and outputs can be described as:
where τ is the transmission coefficient, κ is the coupling coefficient, and the 4 × 4 matrix is the ideal S-parameter matrix. Ethrough, Ecoupled, Ein and Eisolated are the complex electrical fields at the four ports. Hence, the τ and κ are complex numbers, too. Moreover, the S-parameters and fields are dependent of wavelength, and this is indicated with the subscript λ in the Eq. (6). When the waveguides are decoupled,κ can be regarded as 0 and τ is a complex number with a norm of 1. The outputs Ethrough and Ecoupled are connected to the inputs Ein and Eisolated of the next stage using two identical decoupled waveguides (see the schematic in Fig. 2(a)), respectively. In our system model, a connection block model having two identical decoupled connection waveguides are taken into consideration, and their non-zero S-parameters are complex variables each with a norm of 1. So, the S-parameters of connection waveguides will introduce different phase delays for different wavelengths. Subsequently, the performance of the proposed on-chip spectrometer can be simulated by cascading all the S-parameter models of the 9 NEMS controlled directional couplers and 8 connection blocks. It is noted that, as expected, the phase delays induced by the connection waveguides do not make any difference in the intensity of the recorded interferogram, because the interferogram is an integration of the output power across all wavelengths.To obtain the S-parameters of all the 9 NEMS controlled coupler stages (each separately simulated in coupled and decoupled states) and the connection blocks, 3D Finite Differential Time Domain (FDTD) simulations are used. For example, in our simulation of a NEMS controlled directional coupler, the light source is placed at Ein port with amplitude of 1. So, the amplitude observed in Ethrough and Ecoupled ports are corresponding to τ and κ, respectively. The simulations are performed at different wavelengths to determine the wavelength dependent characteristics of the S-parameters. For a brief presentation, the S-parameters of the first NEMS controlled coupler stage whose coupling length is 2 μm are presented in Fig. 4, with (a) and (b) showing those when the two waveguides are coupled and (c) showing those when decoupled.
Fig. 4 The S-parameters (a) τ and (b) κ of the first stage, respectively, when waveguides are coupled. (c) The S-parameters τ of the first stage, when waveguides are decoupled.
The process of spectrum recovery is described as follows. As Fig. 5(a) presented, here we take a light source with two Gaussian peaks in its spectrum as the input. The peaks are located at wavelength 1.65 μm and 1.66 μm with full width at half maximum (FWHM) of 5 nm. The interferogram can be simulated using our system-level S-parameter model by digitally controlling the coupling in each NEMS coupler stage and varying the overall coupling length from 0 to 1022 μm with steps of 2 μm. Consequently, the interferograms can be collected in the through and coupled ports of the final stage, as presented in Fig. 5(b). Then based on these two interferograms, full complex FFT is performed and the quasi-recovered spectrum is obtained as Fig. 5(c) presented. It is worth noting that the two peaks in this quasi-recovered spectrum are located at 8.3 μm and 8.73 μm instead of 1.65 μm and 1.66 μm. The reason is that the horizontal axis of this quasi-recovered spectrum is λ/∆n according to Eq. (1) and (2). Finally, the horizontal axis is translated from λ/∆n into wavelength using the relation plotted in Fig. 3(b), so that the final recovered spectrum can be achieved as Fig. 5(d) presented.
Fig. 5 (a) One target spectrum. (b) The interferograms collected in the through and coupled ports of the final stage. (c) The quasi-recovered spectrum which the horizontal axis is λ/∆n. (d) The final recovered spectrum.
Then followed this process, the performance of this spectrometer is further demonstrated. A light source with a spectrum having three Gaussian peaks, which are located at 1.53 μm, 1.66 μm and 1.69 μm with intensities of 0.45, 0.9 and 1, respectively, is used as the input for the spectrometer. The bandwidths of the three peaks are 10 nm, and the targeted spectrum is presented as the black solid curve in Fig. 6. Through a set of simulations using the system-level S-parameter model, the interferograms are obtained and the recovered spectrum is presented as the red dashed line in Fig. 6. Clearly, the spectrometer recovers all the three peaks and their intensities correctly with a satisfactory performance.
Fig. 6 Recovered spectrum vs. the original. The light spectrum has three Gaussian peaks with different intensities.
At last, the spectral resolution is investigated. Single wavelength light is set as the source to obtain the FWHM of the peak in the recovered spectrum, which is defined as the FWHM resolution [7]. For a brief presentation, the recovered spectra of single wavelength light source at 1.5, 1.6 and 1.7 μm are presented in Fig. 7(a). And their FWHMs are 7.5 nm, 4.5 nm and 3.4 nm, respectively. Interestingly, the longer the wavelength, the better the spectral resolution. The reason is that the effective OPD is longer as a result of larger ∆n, according to Fig. 3(a), at longer wavelength region. Then, the source wavelength is swept so that the detailed FWHM resolution is obtained across the spectral range and the results are presented in Fig. 7(b). As predicted, the FWHM resolution enhances monotonously with the increasing wavelength. Finally, we note that the spectral resolution can be further improved by cascading more directional coupler stages, which will introduce a longer OPD scan in the interferogram.
Fig. 7 (a) Recovered spectra of single wavelength light source at 1.5, 1.6 and 1.7 μm. (b) Simulated FWHM resolution.
4. Conclusions
An on-chip integrated Fourier transform spectrometer is proposed. The spectrometer consists of several stages, each containing a semiconductor waveguide directional coupler and a digital NEMS actuator. The OPD scanning in the spectrometer is obtained by tuning the coupling condition (“on” or “off” digitally) through controlling the NEMS actuators. This spectrometer presents a good performance in the wavelength range from 1.5 μm to 1.8 μm, where the spectral resolution can reach up to 4 nm. Moreover, the spectral resolution can be further improved by cascading more stages. This design meets the requirements of small size, weight and power advantages, and is promising in the future spectroscopic sensing applications, particularly for on-chip based sensors.
Funding
MOE Tier 1 project R-265-000-557-112.
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