We present a direct strip-slot waveguide mode coupler without any auxiliary structures. Contrary to popular belief, an apparent mode mismatch between strip and slot waveguide does not deteriorate conversion efficiency. Separated electric and magnetic field distributions in a slot waveguide lead to highly efficient modal coupling in the direct strip-slot coupler and result in high conversion efficiency. Accurate experimental characterization shows that the direct strip-slot waveguide mode coupler is capable of up to 96% conversion efficiency with a broad bandwidth. Being simplest and of high efficiency, the direct strip-slot waveguide mode coupler can encourage potential applications of slot waveguides.
© 2016 Optical Society of America
Taking advantage of CMOS manufacturing technology, silicon (Si) photonics makes it practical to integrate a large number of photonic devices with sub-micrometer dimensions. Silicon photonic waveguides offer strong confinement of optical modes in the waveguides due to high index contrast between silicon and the cladding materials. However, high confinement inside the waveguide prevents the optical modes from interacting with surrounding materials. A slot waveguide, two adjacent rectangular waveguides with sub-wavelength spacing, overcomes this limitation by concentrating and enhancing electric field in the sub-wavelength space . This field distribution has advantages for various applications such as bio-sensing, chemical sensing, and nonlinear optical modulation [2–5]. However, slot waveguides suffer from relatively high propagation loss (~10 dB/cm) compared to that of strip waveguides (~2 dB/cm) [6–8]. In order to integrate slot waveguides with other silicon photonics devices based on strip waveguides, an efficient and compact strip-slot coupler is highly desirable.
It has been assumed that the optical mode mismatch between slot (non-Gaussian-like) and strip waveguides (Gaussian-like) deteriorates the conversion efficiency of direct coupling [8–10]. To avoid this mode mismatch, many efforts towards strip-slot coupling have been proposed and experimentally demonstrated [8–11]. However, these structures are based on either sharp tips, which break the continuity of the waveguide, or multi-mode interference. Sharp tips are difficult to fabricate due to high aspect ratios that increase sidewall roughness and can cause the structure to collapse. Multi-mode interference based structures require long taper lengths to suppress the higher order modes generated during multi-mode interference. These can be limitations to those applications sensitive to device size, for example a silicon micro-racetrack resonator  that we will present later in this paper.
In this work, we show that direct coupling between the strip and slot waveguide modes, aside from being the most compact option, can perform as well as, if not better than, previous couplers with axillary structures.
2. Mode overlap analysis
Figure 1(a) shows the coupler schematic. A strip waveguide with a width of Wstrip is directly connected to a slot waveguide with the same total width. A representative slot waveguide consists of two identical rectangular waveguides with a width of Wslot = 300 nm and a gap of Wgap = 50 nm between them. The direct strip-slot mode coupler is based on a silicon-on-insulator (SOI) platform with a 220 nm top silicon layer. The waveguides are surrounded by 2m of buried oxide (BOX) as under cladding and 1 m of SiO2 upper cladding. Figure 1(b) shows the simulated main electric and magnetic field distributions of both the fundamental TE strip and slot waveguide modes at two cross-sections A-A’ and B-B’ in Fig. 1(a).
As expected, for the slot waveguide mode, the electric field is highly confined within the gap area and the magnetic field is confined in the waveguide area, while both the electric field and the magnetic field of the strip waveguide mode show Gaussian-like distributions confined in the waveguide area. Popular belief is that the direct coupling efficiency between strip and slot modes is low due to different field distributions, and previous coupler designs all attempted to circumvent direct coupling [8–11]. This assumption is apparently supported by simplified mode overlap calculations, which consider only the electric field distributions, using the following formula:Fig. 2 show the simplified modal overlaps using Eq. (1) at the wavelength of 1550 nm, with generally having a value lower than 75%. Equation (1) assumes that intrinsic impedance (E/H) is constant in the area where the mode exists. For the non-Gaussian-like slot waveguide mode, however, Eq. (1) is not valid because the intrinsic impedance varies significantly between the gap and waveguide areas. Therefore, a more rigorous formula should be used [13–15]:Fig. 2 show the rigorous modal power coupling using Eq. (2) with Wgap = 50 nm (blue), 100 nm (green), and 150 nm (red), respectively. It is important to note that η2 is always larger than η1. In particular, the modal overlap η2 can be as high as 98% for strip widths of 650 nm when the gap size is 50 nm.
In Eq. (2), the numerators of the first and second terms indicate that the conversion efficiency is proportional to the integrals of cross products between electric and magnetic fields, rather than the cross product between electric fields only. Figure 1(b) shows the major components of the electric (Ex) and magnetic (Hy) fields of the strip and slot TE waveguide modes, and we can use those distributions to estimate roughly the various integrals. For either the cross products between the electric field of the strip mode (Ex1) and the magnetic field of the slot mode (Hy2), or between the magnetic field of the strip mode (Hy1) and the electric field of the slot mode (Ex2), the field distributions of the strip mode cover most of the field distributions of the slot mode, and lead to reasonable amounts of overlap. On the other hand, the cross product of the electric (Ex2) and the magnetic (Hy2) fields of the slot mode itself (denominator in the first term) is quite small due to the significant separation in field distributions of the electric and magnetic fields. Therefore, the small overlap integral in the denominators and the reasonable amount of overlaps in the numerators together yield a high conversion efficiency.
With the above intuitive understanding, we present two design guidelines to maximize the conversion efficiency. One is to choose a reasonably large slot width (Wslot), e.g. 300 nm. If the Wslot is not large enough to fully confine the magnetic field of the slot waveguide mode inside the waveguide area, the leaked magnetic field in the gap area increases the overlap with the electric field of the slot waveguide mode, leading to a degradation of the conversion efficiency. The other is to satisfy Wstrip = 2Wslot + Wgap while keeping the gap size small, e.g. Wgap ≤ 50 nm), since the size of the strip mode becomes comparable to that of the slot mode when Wstrip = 2Wslot + Wgap. If Wstrip < 2Wslot + Wgap or Wstrip > 2Wslot + Wgap, the mode mismatch increases and results in a decrease in the conversion efficiency.
To validate the theoretical analysis, we first use the finite-difference time-domain (FDTD) method to numerically calculate the coupling efficiency. Simulations were run with 10 nm uniform mesh sizes. The structural parameters are Wstrip = 660 nm, Wslot = 300 nm, and Wgap = 60 nm. Conversion efficiency refers, in this paper, to the power transmission from the fundamental TE strip mode to the fundamental TE slot mode. Figure 3(a) shows the simulated mode propagation of the direct slot coupler from the input strip TE mode on the left side to the output slot TE mode on the right side. The input strip TE mode couples directly to the output slot TE mode without any intermediate structure. Direct coupling has its biggest advantage in this ultra-short device length. Since most couplers are based on a mode evolution scheme, such couplers have long device lengths to satisfy the adiabatic transition. However, this direct coupling scheme is based on mode coupling so that we do not need to consider an adiabatic transition. Figure 3(b) shows the simulated conversion efficiencies of a direct strip-slot mode coupler with various cladding indices: 1.44 (for SiO2), 1.6 and 2. A refractive index of 1.6 is a typical value for polymer materials, and 2 is representative of silicon nitride. All of these materials are suitable cladding materials for Si slot waveguides. The couplers maintain their high efficiencies over a broad wavelength span. Note that the efficiency increases with increasing upper cladding refractive indices. With the refractive index of 2, the direct coupler achieves 97.5% conversion efficiency since the higher refractive index cladding materials lead to lower index mismatch and consequently less reflection. By using a mode expansion, we distinguish the influence of the higher order mode in the output slot mode. The simulation results suggest that 1% of the input power is converted to higher order modes.
3. Experimental results
3. 1. Race-track resonator approach
The direct measurement of low loss (e.g. <5% loss) couplers is complicated by inseparable fiber-to-chip coupling loss. Such losses are typically large compared to that of our direct strip-slot couplers, e.g. 1-3 dB or 20~50%, and unpredictable, i.e. having large device-to-device variations. Previous use of cutback methods  reduces, but does not eliminate, the influence of fiber-to-chip coupling loss.
Here we introduce and demonstrate a method to accurately characterize the direct strip-slot coupling loss by measuring the intrinsic quality factor (Qi) of high-Q resonators . Qi can be interpreted as the round trip loss of the resonator, and can be experimentally determined from the transmission spectra, independent of fiber-to-chip coupling losses. If one can incorporate the structure of interest into a resonator, then the direct coupling loss and propagation loss during the round trip can be calculated by measuring and fitting the Qi.
We are able to incorporate a pair of our strip-slot couplers into a Si micro-racetrack resonator, due to the compactness of the direct coupling scheme. Figure 4(a) shows a fabricated racetrack resonator (left) and the pair of strip-to-slot and slot-to-strip couplers incorporated in the straight section of the racetrack (right) with a total slot waveguide length of 4 m. As shown previously, the direct coupling occurs in a length of less than a half micron The compact length between couplers minimizes measured gap size dependent propagation losses of the slot waveguide while maintaining enough length to fully couple between two modes. The geometric parameters of the direct couplers are set to Wslot = 300 nm, Wgap = 60 nm and Wstrip = 660 nm, and Fig. 4(b) shows that the fabricated structure matches well with the designed parameters. The width of the remaining part of the racetrack is set to Wtrack = 450 nm to maintain single mode operation, and there are two adiabatic tapers to expand/shrink the widths between Wstrip and Wtrack. The circumference of the racetrack is 180 m, and the bus waveguide also has a width of 450 nm. The gap between the bus and racetrack is set to 200 nm.
These devices were fabricated on a silicon-on-insulator (SOI) wafer with a 220 nm thick Si top layer and a 2m thick buried oxide (BOX). The waveguides and resonators are patterned with a negative tone resist, hydrogen silsesquioxane (HSQ), exposed with a 100 kV electron beam lithography system (Raith EBPG 5200). Inductively coupled plasma etching was performed to define the waveguides. Silicon dioxide upper cladding was deposited with a thickness of 1μm using a low-pressure chemical vapor deposition (LPCVD) tool. To separate the coupler loss from the round-trip loss of the racetrack itself, we fabricated another racetrack resonator without direct couplers to serve as a reference resonator. The reference resonator shares the same structure except for the region where the direct couplers are incorporated. For measurement set-up, two lensed fibers are used to couple light in and out of the fabricated chip. Polarization of the input light is calibrated by maximizing optical power after passing a polarizer at a chosen TE polarization angle. Figure 4(c) shows the measured transmission spectra of the resonator with the coupler (red), and the reference resonator without the coupler (blue). Clear resonant dips on the spectrum of the resonator with the direct coupler indicate that the loss of the direct coupler is comparable to the round trip loss of the reference resonator. The reduced extinction ratios compared to those of the reference resonator are due to additional round-trip loss, which effectively takes coupling to the under-coupled regime.
Since a Qi of a resonator accounts for the round trip loss of the resonator, we can extract the loss of the direct coupler by comparing the Qi of the resonator with the direct couplers and the reference resonator [17,18]. Figures 5(a) and 5(b) show two resonant dips of the reference resonator and the resonator with the direct couplers, respectively. These are selected for comparison because they are very close in resonant wavelengths. The resonant dips are curve fitted to a Lorentzian shape to extract the quality factors and corresponding round trip losses. The loaded or total quality factors (Qt) are extracted from the Lorentzian curve fitting, and the Qi are retrieved by calculating18,19]. The characterized Qi of the reference resonator is 57854 which results in a round trip loss of 0.24 dB, while that of the resonator with the direct coupler is 25764 corresponding to a round trip loss of 0.55 dB. Since we introduced one pair of two identical couplers consecutively in the racetrack, the measured transmission of the direct coupler corresponds to roughly half of the difference in the round trip losses of the two racetracks, which is 96.5%.
One of the main sources of error is whether the Qi of the reference resonator is an accurate representation of propagation loss in the resonator containing couplers. In the most pessimistic scenario, all of the 0.55 dB loss is attributed to the pair of direct couplers, and this would result in a conversion efficiency of 93.9%. Another source of error is that some input power will be converted to high-order modes of the slot waveguide and then convert back into the fundamental mode. Simulation shows that this may lead to an over-estimation of ~1%. On the other hand, our estimation is also conservative as it includes losses from the two adiabatic tapers that convert the waveguide widths between Wslot and Wtrack, as well as the additional propagation loss caused by the slot waveguide section (about 4 μm in length). To have an understanding of wavelength dependence, we analyzed multiple resonant dips and plotted the conversion efficiencies in Fig. 5(c). The efficiency varies from 93% to 97% across a 30 nm bandwidth from 1547 nm to 1577 nm.
This rigorous characterization approach with racetrack resonators confirms that the direct strip-slot coupler can have high conversion efficiencies for certain geometries with small gap sizes. The coupler is compact enough to allow its integration with various types of micro-resonators, and promises potential applications in sensing and nonlinear photonics.
This new method, while separating the coupler and propagation loss from edge coupling loss, has the limitation that it can only be measured at discrete resonant frequencies. To measure the coupler loss across a continuous wavelength regime, we resort to the conventional method of measuring transmission of a device structure with lensed fibers.
3. 2. Direct characterization by cascading devices
To reduce the influence of variations in fiber-to-chip coupling losses on the direct coupler loss measurement, low loss (around 3 dB/facet) inverse taper fiber-to-chip couplers were used . The tips of fiber-to-chip edge couplers are defined with optical lithography rather than through cleaving the substrate to achieve uniform losses for different waveguides. In addition, 30 pairs of the direct strip-slot couplers, each consisting of one strip-to-slot coupler and one slot-to-strip coupler, are cascaded for a total of 60 direct strip-slot couplers as a device under test. This would make the loss due to direct strip-slot couplers to be around 11 dB, and reduce the relative error due to uncertainty of the fiber-to-chip coupling. The same geometric structures without the direct strip-slot couplers are also fabricated as a reference to characterize and subtract fiber-to-chip coupling loss. The transmission of devices with the direct couplers (Ttotal) and a reference device without the direct couplers (Tref) are measured, and Tref is subtracted from Ttotal to extract the loss due to the direct strip-slot couplers. Then the transmission of the direct strip-slot couplers is divided by the number of direct strip-slot couplers to characterize the strip-slot conversion efficiency ().
Figure 6 shows the measured transmission spectra (blue lines) and the characterized conversion efficiency (solid red line). The blue solid and dashed lines are the transmission spectra of the device with direct strip-slot couplers and the reference device, respectively. As shown with a red solid line (characterized), the direct strip-slot coupler can have conversion efficiencies over 95% throughout the optical communication C-band and 96% at 1550 nm. This result agrees well with the previous simulation and the optical characterization with a racetrack resonator.
To characterize the conversion efficiencies with different geometries, additional sets of devices are also fabricated and measured. The cross points in Fig. 2 are the characterized conversion efficiencies for various coupler geometries. Generally, a smaller gap size allows higher conversion efficiency, and there is an optimum strip width for each gap that maximizes the conversion efficiency. Figure 2 also shows that for larger slot sizes, a direct coupler would have low efficiency. However, we can start with a small gap size e.g. 20 nm, and introduce an adiabatic taper to increase the gap size. FDTD simulation shows that such an adiabatic taper does not introduce any loss related to mode coupling, though the taper would increase the coupler length and increase the fabrication difficulty.
Table 1 summarizes the conversion efficiencies and the device lengths of the previous works and this work. Since most of the previous work relies on the mode evolution or the multimode interference, the device lengths are in the range from several microns to several tens of microns. Compared to these works, the direct mode coupler has a much shorter length at sub-micron range, while having comparable conversion efficiency.
In conclusion, we have investigated the conversion efficiencies of a strip-slot direct coupler both numerically and experimentally. The conversion efficiency can be 96% or above, with certain geometry and cladding materials. Contrary to popular belief, at typical gap sizes where the slot wave guiding effect is significant, the apparent mode mismatch between strip and slot waveguides does not deteriorate conversion efficiency significantly due to the separation of electric and magnetic fields in a slot waveguide. The direct mode coupler is simple, offers an instantaneous transition, and is fully compatible with other photonic waveguides and applications. The racetrack-resonator approach characterizes the conversion efficiency rigorously, and demonstrates a possible integration path with other photonic devices.
This research is supported in part by National Science Foundation (NSF) (ECCS-1509578, CMMI-1120577); Defense Threat Reduction Agency (HDTRA110-1-0106); Air Force Office of Scientific Research (FA9550-12-1-0236); and DARPA PULSE program from AMRDEC (W31P40-13-1-0018)
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