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In this work, a compact and ultrahigh-resolution Fourier-transform spectrometer design is presented which is in great demand in numerous areas. The spectrometer is formed by sequentially-activated 60 Mach-Zehnder interferometers that are connected to photodetectors through very-low-loss beam combiners based on two-mode interference. The long optical delays are provided by tapping the propagating light out at certain locations on the optical waveguides by using electro-optically-controlled directional couplers. A design example with a spectral resolution of 500 MHz (~1 pm) and bandwidth of 15 GHz is presented for a device size of only 2 cm × 0.5 cm (1 cm2).
© 2017 Optical Society of America
1. Introduction
Optical spectroscopy is an essential tool in numerous areas including biochemical sensing, material analysis, optical communication, and medical applications [1]. The development of a high-resolution on-chip spectrometer could enable compact, low-cost spectroscopy for portable sensing and increase lab-on-a-chip functionality. Motivated by this demand, several integrated microspectrometers have been realized in different configurations [2–5]. Most of these spectrometers rely on dispersive components which are inevitably bulky because their spectral resolution scales inversely with optical path length. Fourier transform spectroscopy (FTS) is a technique that uses interference of light rather than dispersion to measure the spectrum of a sample [6]. It is basically a Michelson interferometer with a movable mirror. The basis of this technique is the Fourier-pair relationship between the interferogram of a sample and its spectrum. The primary advantages of FTS compared to dispersive spectrometers are high optical throughput thereby greater signal-to-noise ratio, compact size, and relatively easily attainable high resolution which is constant over the entire spectral region as determined by the mirror displacement from the origin.
Although FTS can be more compact in size, its scanning interferometric configuration makes it slow for some applications where speed is a critical constraint [7]. Spatial heterodyne spectroscopy (SHS) is an interferometric Fourier-transform (FT) technique based on a modified Michelson interferometer with no moving parts and relying on analysis of stationary interference patterns [8]. The SHS concept was successfully implemented in bulk optics so far, and recently it has been proposed for planar waveguide implementation by Cheben et al. as a Fourier-transform arrayed waveguide grating (FT-AWG) microspectrometer [4]. Florjańczyk et al., have generalized the waveguide SHS FT concept into a waveguide Mach-Zehnder interferometer (MZI) array which was based on an array of independent MZIs with different phase delays [9]. Even though it is a promising technique, it is still challenging to place long delay lines on a single wafer to achieve ultrahigh resolution. As a follow-up, they have presented a spiral-based SHS FT design with a spectral resolution of 40 pm, and footprint of 12 mm2 [10]. However, besides being quite lossy, the spectrometer size will still be significant if ultrahigh resolution is aimed at.
In this work, a novel FT spectrometer layout is introduced which offers ultrahigh-resolution of 500 MHZ (~1pm) in a very small footprint of 1 cm2. The design is comprised of N = 60 MZIs that are sequentially activated by voltage-controlled directional couplers. Compared to spiral-based FT spectrometer described in [10], the proposed layout will provide much smaller size for the same resolution in addition its N times larger throughput. The long optical delay between MZI arms is introduced by sequentially tapping the propagating light out at several locations on the light path which makes the overall device size very compact. The tapping operation is provided by electro-optically-controlled directional couplers that are placed on both interferometer arms with a certain length difference between consecutive tapping locations. A design example with spectral resolution of 500 MHz and bandwidth of 15 GHz is presented. Lithium niobate (LN)-on-silicon material technology was chosen for this specific design, however it can be applied to other electro-optic materials. The proposed design is the smallest FT spectrometer reported so far and can be easily adjusted to realize spectrometers with different bandwidth and resolution combinations. It is expected that the layout described in here will evoke some experimental interest and will be followed up by several research groups and companies.
2. Spectrometer design
2.1 Chip layout and working principle
Figure 1 is the schematic of the ultrahigh-resolution FT spectrometer layout. For ease of understanding the first two levels of the light tapping mechanism are demonstrated. Here a central wavelength of 800 nm is aimed at. There are several MZIs that are electro-optically-controlled in a sequential order. Input light will be divided into two arms with an integrated 3-dB directional coupler. Half of the light will travel through a multi-S-shaped path that is comprised of several curved waveguides and straight waveguide sections. This arm will be used for providing additional length difference between MZI arms. The other half of the light will be sent towards a straight waveguide section that can be considered as the reference arm of the interferometer. The end of the both arms can be a waveguide termination such as a matched load that decreases reflection.
Fig. 1 Schematic of the ultrahigh-resolution FT spectrometer design. The input light is divided equally by an on-chip 3-dB coupler and sent towards two different paths; one has several S-shaped waveguides and the other has a straight waveguide. There are several electro-optically-controlled directional couplers on both arms that act as optical switches. They cross-couple the light when there is no voltage, and keep it on the same arm when there is a π phase difference due to electro-optic effect. The cross-coupled light from both arms will be combined at the beam combiner and sent to a photodetector (PD). Here Ls is the length of the straight sections; R is the radius of the curved waveguides on the S-shaped path.
Each MZI consists of two electro-optically-controlled directional couplers one in each arm. The first MZI will have zero path length difference between its arms, therefore the length of segments |AB| and |DE| are equal. The length of the next segment on the multi-S-shaped path is |BC| = (2 × π × R) + (2 × Ls) where Ls is the length of the straight parts, and R is the radius of the curved waveguide sections. The length difference between the arms of the next MZI (i.e. |BC| – |EF|) is chosen in accordance with the resolution requirements. The resolution of the spectrometer is defined by the maximum delay ∆Lmax, which also determines the spectrometer size. The calculation of ∆Lmax refers to the Littrow condition and can be expressed as [10]:
where δλ is the resolution of the spectrometer, ng is the group refractive index of the waveguide stack, and λ0 is the center wavelength. For a spectral resolution of 500 MHz a maximum delay of ∆Lmax ≅ 30 cm is needed which makes it very challenging to accommodate such a spectrometer on a standard 10-inch wafer using existing waveguide SHS designs. The proposed design solves the size problem by using light tapping approach. As the light travels through a waveguide, the optical length gets increased, and by tapping the propagating light out at certain locations on the waveguide, the required optical delay can be obtained for each MZI. The multi-S-shaped sections of this waveguide will keep the length of the device short while straight sections in between (with length Ls) will mainly provide the optical delay. As a constraint on proper operation of the spectrometer, each MZI path length must be an integer multiple of some fixed path length, i.e. ∆Lmax/N. The light coming from both MZI arms will get interfered on an on-chip beam combiner and sent to a matched photodetector. The output power distribution digitally processed by using a Fourier transform to retrieve the input spectrum. Photodetectors can be fabricated on the same chip or a commercial photodetector array can be externally butt-coupled to the chip.2.2 Material system
The proposed spectrometer idea is simulated for the LN-on-silicon waveguide platform as it is being one of the most versatile and well-developed active optical materials [11]. The material system is 250-nm-thick ion-sliced lithium niobate film on oxidized silicon wafer. The oxide thickness is 3 μm. The refractive index of the LN layer is 2.25 at 800 nm, and its electro-optic (EO) coefficient is (r33 ~30 pm/V) [11]. Single mode rib waveguides with 0.2 µm of slab height and 0.9 µm of waveguide width were designed. Figure 2(b) demonstrates the cross-sectional beam profile of the mode obtained by using beam propagation method (BPM). The minimum bending radius of the curved waveguides was calculated to be R = 150 µm with a bending loss of −0.005 dB/cm. For defining the waveguides ion-implantation-assisted wet etching can be used as it provides lower propagation losses compared to other methods [12]. Metallic electrodes can be defined using gold or chromium. A 500-nm-thick silicon dioxide (SiO2) top cladding will be used to prevent propagation losses induced by the electrodes. The fiber-to-chip coupling losses (~6 dB) can be reduced to < 0.5 dB by using a high numerical aperture fiber [13]. The simulated beam profile and the relevant waveguide parameters are given in Fig. 2(b).
Fig. 2 a) The schematic of the electro-optically-controlled integrated- optics-based directional coupler. Here I1 is the input light, I2 is the transmitted light, I3 is the cross-coupled light, Lc is the electrode length, and d is the separation between coupler arms. b) Beam propagation method simulation of the optical mode. The blue outline shows the cross-sectional profile of the waveguide geometry. Relevant waveguide parameters are given. c) The amount of cross-coupling of the input light at different voltage values for different electrode lengths. The most optimum combination was obtained for an electrode length of 300 μm and an applied voltage value of V = 18 Volts. d, right) Voltage is OFF, the light will be cross-coupled to the other channel. d, left) Voltage is ON, V = 18 Volts, a π phase difference will be generated between coupler arms and the input light will stay in the same arm.
2.3 Electro-optic switch design
Directional couplers used in this system were designed to act as voltage-controlled electro-optic switches with nanosecond switch time. A metallic electrode was placed on top of one of the straight waveguides of the directional coupler as shown in Fig. 2(a). With applied voltage, the effective refractive index of the straight waveguide section is locally increased due to the electro-optic effect which induces a phase difference between coupler arms. When there is no voltage on the electrodes, the lights on both arms will be in phase and the incoming light will be cross-coupled to the other arm. (Fig. 2(d) left side). At a certain voltage value (i.e. V = 18 Volts for this design), a π phase difference is generated between coupler arms which avoids cross-coupling of the light and forwards it to the next stage where a different spectral information is obtained (Fig. 2(d) right side). This operation will be performed in a sequential order by switching the directional couplers on and off until all range is scanned (i.e. N times, see Fig. 1). It is assumed that the coupling ratios at each directional coupler does not vary substantially across the entire bandwidth which is relatively small for the example considered here (i.e. 15 GHz). However, the non-uniformity of light coupling among individual directional couplers can be calibrated out as described in [9]. Here, since all input light power is used at each sequence, the throughput of the proposed design will be significantly high which makes it very attractive for some applications which has very weak light intensity [7].
The effective refractive index of the waveguide stack was calculated to be 2.0 for TE polarization. The expected change in the mode effective refractive index due to applied voltage (Δn (V)) was calculated to be 12 × 10−5 × V using below equation [14]:
for an overlap factor of Г = 0.25, electro-optically active layer thickness of t = 0.25 μm, effective refractive index of ne = 2.0, and electro-optic coefficient of r33 = 30 pm/V. Due to small gap between coupler arms, a vertical electrode configuration was proposed for this specific design, however coplanar electrodes can also be used as well for larger waveguide spacing.BPM simulations were performed for designing and optimizing the optical components. The directional coupler was designed in two steps. Firstly, in-phase case was designed and the separation between waveguides was calculated to be d = 0.9 μm for full cross-coupling (Fig. 2(d) left). There is a trade-off between the length of the electro-optically defined part of the coupler (i.e. electrode length, Lc) and the applied voltage. For a π phase difference this length is defined as:
In the second stage, the electrode length was scanned from 250 μm to 350 μm with a 50 μm step size while applied voltage value was scanned from 0 to 25 Volts in 1 Volt steps as given in see Fig. 2(c). The most optimum case was obtained for an electrode length of 300 μm and an applied voltage value of 18 Volts to generate a π phase difference. At this voltage level, light will stay in the same arm and be directed to the next MZI section (Fig. 2(d) right). Based on the Nyquist sampling theorem, in order to scan 15 GHz of bandwidth with 500 MHz resolution, N = 60 directional couplers are needed which results in an overall device size of around 2 cm × 0.5 cm (1 cm2). The time needed for scanning 15 GHz bandwidth in 60 steps will be less than a millisecond.
2.4 Tolerance analysis of the electro-optic switch
The change in coupling ratio of the electro-optic switch due to the process non-uniformity and limitations in reproducibility has been investigated. The refractive index of the cladding layer can have non-uniformities of up to ± 3 × 10−4, and the core layer can show thickness variations up to ± 1% over the wafer. The waveguide width can vary by ± 0.1 μm.
The simulation results of the effects of these process-dependent deviations are summarized in Table 1. Variations in the refractive index of the cladding layer has the minimum effect on coupling ratio whereas the maximum variation in coupling ratio was calculated to be −2% for 0.1 µm increase in waveguide width which are both insignificant.
Table 1. The Effect of the Technological Tolerances on Electro-optic Switch Performance
The variations due to ambient temperature chance was also investigated. The thermo-optic coefficient of LN is around ~40 × 10−6 /°C [15]. The effective refractive index of the LN waveguide increases by ~39 × 10−6 for 1°C temperature increase which does not change the coupling ratios. The temperature control of the integrated chip can be easily done with very high precision (~0.01°C) by using off the shelf components at a relatively low power dissipation.
2.5 Beam combiner design
The beam combiner proposed in this design (Fig. 3(a)) is based on two-mode interference (TMI). Compared to an optical Y junction, it is more fabrication tolerant, and reproducible. Figure 3(b), 3(c), 3(d) demonstrate the BPM simulation results of the TMI-based beam combiner. The separation between input waveguides, the width and the length of the slab region are D = 0.9 μm, W = 3 μm, and L = 15 μm, respectively. The radiation loss of these kind of beam combiners is dependent on both the phase difference between the two arms and the relative power in each arm. When both arms are in phase with equal power (i.e. Δф = 0, Il/I2 = 1), all the input power is coupled into the first-order even mode and therefore transmitted through the slab region into the output waveguide. For the TMI-based beam combiner considered here, 96% of the incoming light was coupled into the output waveguide (Fig. 3(b)) for in phase input lights, whereas for a phase difference of π/6, output coupling became 91% (Fig. 3(d). Since the MZIs are designed at the Littrow condition, the phase delays in different MZIs are integer multiples of 2π, therefore it is expected to have zero or very small phase-induced loss for each MZI. The power inequality between interferometer arms was simulated for a power ratio of Il/I2 = 0.5, and only 2% of reduction was observed compared to equal power case (see Fig. 3(c)). The loss at the waveguide crossings in between beam combiners and the photodetectors can be reduced to 0.02dB using the same approach described in [16].
Fig. 3 a) Schematic of the TMI-based beam combiner. Here I1, and I2, are the power on the input waveguides and ф1, and ф2 are the corresponding phases of the input beams, I3 is the power of the out-coupled beam and ф3 is the corresponding phase, L is the slab length, W is the slab width, and D is the separation between input waveguides. b) When I2 / I1 = 1, and the phase difference between two arms is Δф = 0, 96% of the incoming light will be coupled to the output waveguide, whereas c) when one arm has lower light intensity (i.e I2 / I1 = 0.5), it will be reduced by 2%. d) When both arms have the same power, a phase difference of π/6 will reduce the output power by 5%.
3. Discussions
Even though the working principle of the proposed spectrometer is similar to the spiral-based FT spectrometer design described in [10], there are some main differences that make the proposed design superior. Firstly, the device size is relatively small when the same resolution value is aimed at. For example, for a spectral resolution of 1pm (i.e. 500 MHz), the footprint of the spectrometer given in [10] will be around 3.2 cm2 whereas for the design given in this work it will be only 1 cm2. In this sense, the proposed design can easily beat the resolution-footprint figure of merit of the spiral-based spectrometer design. Secondly, the throughput of the proposed spectrometer is N times larger than the spiral-based one, where N is the number of MZIs. This is due to fact that all input light is used for each point scan in contrary to dividing it into N separate channels demonstrated in [10]. The multi-aperture approach was proposed in [9] in order to improve the throughput, however it can only be useful in specific applications where input light is not fiber coupled but emitted from a large area. Thirdly, the loss of the spiral-based spectrometer is significantly larger than the design given in here. Propagation losses of −4 dB∕cm, and bending losses of −1.7 dB∕cm in the spiral sections were reported in [10] whereas the expected propagation and bending losses of the proposed design will be around −0.23 dB∕cm, and −0.005 dB∕cm, respectively. The additional losses due to electro-optical couplers, beam combiners, and waveguide crossings will relatively be small; i.e. −0.009 dB/electro-optical coupler, −0.018 dB/beam combiner, 0.02 dB/crossing, respectively.
Controlling electro-optical switches will be done by a custom-designed microprocessor chip, which could be comprised of a single or several multiplexers depending upon the cost. In total 60 channels, will be needed due to the fact that the same pin can be used to activate two couplers on each MZI at the same time. The repetition rate and overall scan time of the spectrometer will determine the microprocessor specifications which are not within the scope of this paper.
4. Conclusions
In summary, design and simulations of a compact, and ultrahigh-resolution FT spectrometer based on electro-optically-controlled MZIs are presented with a spectral resolution of 500 MHz and bandwidth of 15 GHz. The device size is estimated to be 2 cm × 0.5 cm (1 cm2) which is significantly smaller than the smallest FT spectrometer reported so far [10] when the same resolution value is considered. Due to the lack of cleanroom facilities at the current institute, the experimental performance of the proposed spectrometer could not be demonstrated in this work. However, it is expected that the layout described in here will evoke some experimental interest and will be followed up by several research groups and companies. The dynamic optical delay line design presented in this work can be applied to any situation in which a long delay line in a compact form is desired. It is anticipated that this design will greatly expand the availability of waveguide FT spectrometer concept in a wide range of applications.
Funding
Technology Foundation STW, Innovational Research Incentives Scheme Veni (SH302031).
Acknowledgments
The author thanks Dr. Bob van Someren, Prof. Wilfred G. van der Wiel, and Prof. Ton van Leeuwen for the fruitful discussions.
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