10 nm SiO2 TM Slot Mode in Laterally Mismatched Asymmetric Fin-Waveguides

In this paper we demonstrate that by breaking the left/right symmetry in a bi-planar double-silicon on insulator (SOI) photonic crystal (PhC) fin-waveguide, we can couple the conventionally used transverse-electric (TE) polarized mode to the transverse-magnetic (TM) polarization slot-mode. Finite difference time domain (FDTD) simulations indicate that the TE mode couples to the robust TM mode inside the Brillouin zone. Broadband transmission data shows propagation identified with horizontal-slot TM mode within the TE bandgap for fully mismatched fabricated devices. This simultaneously demonstrates TE to TM mode conversion, and the narrowest Si photonics SiO2 slot-mode propagation reported in the literature (10 nm wide slot), which both have many potential telecommunication applications.


INTRODUCTION
The investigation of photonic crystal (PhC) structures has been a fruitful area of research since it was pioneered in the late-1980s [1][2][3][4]. However, despite the fact that the first 1D periodic dielectric waveguide was first demonstrated as early as 1978 [5] in the form of a fiber Bragg grating, it was not until the development of the first hole-defined line-defect PhC waveguides (PCWs) in the early 2000s [6][7][8][9] that the practical applicability of silicon-on-insulator (SOI) PCWs to telecommunications and sensing applications became obvious. PhCs are an attractive technology to work with because of the many interesting phenomena that can be engineered in them. PhCs can be designed to exhibit a photonic bandgap (PBG) [10,11], low or zero group velocity slow-light [12][13][14][15], low effective volume (V eff ) confinement with high Q-factor [16][17][18], increased Purcell effect [19,20], orbital angular momentum [21], and transverse spin angular momentum [22]. There have been several demonstrations of PhC slot-waveguides [23,24] which have relied on slot widths >100 nm. There has been no demonstration of a PhC transverse-electric (TE) to transverse-magnetic (TM) polarization converter on an SOI platform.
A low refractive-index (n) slot waveguide structure, first described in 2004 [25] and demonstrated shortly thereafter [26][27][28][29], can be used to confine a large proportion of the fundamental propagating mode within the small low-n volume. This concentration increases the electric field density, optical power and optical intensity compared to what can be achieved in conventional waveguides. This increases the electric field interaction with electrically-active low-n slot-materials as well as the high-n sidewall material ∼2-3 nm into the sidewall. This can be taken advantage of in many applications including optical amplification, electro-optic modulation [27], sensing and all-optical switching.
Much of the development of SOI based PhCs has focussed on planar hole-defined PhCs because of their inherent compatibility with conventional wire waveguides [30] and relative ease of fabrication compared to pillar-defined PhCs. Also, most slotwaveguide development has focussed on vertical-slot waveguides, because of their compatibility with conventional photonic integrated circuit (PIC) designs and fabrication methods. However, there has been some development of horizontal slotwaveguide structure devices that are designed to operate in the fundamental TE-mode of the wire waveguide for modulator [31][32][33] and resonator [34] applications. These can be referred to as double-SOI structures. This design is particularly useful for accumulation modulators that rely on the electrical properties of the metal-oxide-semiconductor capacitor (MOSCap) structure, usually defined around an SiO 2 capacitor layer, and the optical properties of the wire-waveguide with the electric field intensity concentrated in the center of the waveguide to maximize electric field overlap with charge carrier accumulation regions.
Conventional hole-defined and pillar-defined PhC waveguides defined in bi-planar horizontal-slot Si/low-n/Si structures have been proposed [35,36], but not yet experimentally demonstrated. There is currently no way to define a PCW on a double-SOI platform to couple from the high-n TE mode propagation observed in the entry wire waveguide to the low-n TM slotmode propagation in the PhC waveguide. This can be done with adiabatic coupling [23,37] or self-imaging multi-mode interferometer (MMI) coupling [38] for vertical-slot-waveguides, but this is not possible for horizontal-slot waveguides. Also, due to the fabrication challenges associated with etching high height/width aspect ratio vertical-slots, vertical-oxideslots width must be >100 nm, or a complex sidewall oxide growth/amorphous Si deposition/recrystallization process must be carried out [39,40].
Recently, fabrication methods have been developed that demonstrate that it is possible to realize bi-planar asymmetric finwaveguides, with the top-fin on one side of the waveguide freestanding whilst the lower-fin on the other side of the waveguide is connected to the buried oxide layer [41]. These asymmetric fins form a 1D pseudo-Bragg grating, the parameters of which can be defined to realize a photonic bandgap for example. Previous work has shown that asymmetric wire-waveguides and "doublestair-waveguides" can be used as effective passive polarization mode converters [42][43][44][45]. By breaking the left-right symmetry, TE/TM polarization modes hybridize, and through a modebeating design the optical power can be transferred from one mode to another.
In this work we propose and demonstrate that when a lateral mismatch is introduced between the left and right fins in an asymmetric, double-SOI fin-waveguide, a bandgap appears for the quasi-TE-mode only and couples to the robust quasi-TM-mode within the Brillouin zone. quasi-TE to quasi-TM coupling and slot-mode propagation is demonstrated in two device types, (1) a straight, mismatched, fin-waveguide device, where Fabry-Pérot Resonance (FPR) can be identified with a propagating mode with effective refractive index, n eff = 1.37 (quasi-TM slot-mode), and (2) an MZI incorporating a mismatched fin-waveguide section on one arm, showing a clear free-spectral range (FSR) dependence on wavelength which is expected for low-wavelength quasi-TM mode, highwavelength quasi-TE mode as predicted from simulations. This is an initial proof-of-principle design that demonstrates how to couple to the ultra-narrow (10 nm wide) oxide region, which is useful for modulator devices and devices that rely on ultrahigh confinement for increased light-matter interaction in the slot region.
The paper is organized as follows. In section 2, we introduce the laterally mismatched fin-waveguide design and FDTD simulations. In section 3, we detail the fabrication process. In section 4, we present results of broadband transmission spectrum data demonstrating low-energy TE-mode bandgap shrinking as mismatch between left and right fins is increased, and slot-mode TM propagation in a straight waveguide as well as a passive MZI device. Section 5 provides a conclusion.

DESIGN AND SIMULATION
The horizontal-slot asymmetric fin-waveguide was designed on a double-SOI platform. A schematic of the aligned and misaligned fin-waveguide is shown in Figure 1. The top and the bottom Si layers are from (110) crystal orientation SOI wafers, and because the top SOI wafer was flipped and bonded during fabrication, both Si layers have mirrored crystal orientation. The design consists of a 450 nm wide rectangular waveguide with a Si (100 nm)/SiO 2 (10 nm)/Si (100nm) stack. The sidewalls of this central region are defined by the stable (111) crystal plane of both the top and bottom SOI layers. The top left fin is suspended whilst the bottom right fin is in contact with the buried oxide (BOX). The sidewalls are both defined by the (11-1) crystal planes of their respective SOI layers, and they are angled at 20 • from perpendicular to the central waveguide. The layer thicknesses are determined by substrate preparation. The degree of left-fin/right-fin misalignment is defined using the mismatch parameter m, where m = 0 indicates maximum fin-alignment ( Figure 1A), and m = 0.5 indicates maximum fin-misalignment ( Figure 1B). Figure 1A shows the left and right fins aligned along the z-axis and (Ai,Aii) show the cut through of lines i-i ′ /ii-ii ′ in (A), showing the periodically repeating strip (Ai) and fin (Aii) waveguide structure. Figure 1B shows the left and right fins are maximally misaligned along the z-axis and (Bi,Bii) show the cut through of lines i-i ′ /ii-ii ′ in (B), showing the periodically repeating left (Bi) and right (Bii) waveguide structure. The m = 0 design ( Figure 1A) has already been presented and experimentally demonstrated [41]. The focus on this work is the mismatched fin-waveguide (m = 0). Two-dimensional finite difference eigenmode simulations were performed to establish field profiles for both high n eff TE wire mode and low n eff TM slot-mode operation in aligned  fin-waveguides. Figure 2 shows linear-scale profiles of |E|, |H|, energy density, and dominant E component (amplitude) for both modes. E x is the dominant TE electric field component and E y is the dominant TM magnetic field component. This demonstrates the potential for slot-mode propagation in finwaveguide devices. Enlarged views of the dominant E-field components for the TE and TM modes at the horizontal slot itself are shown in Figures 2J,K, respectively. This clearly shows E-field enhancement in the slot in TM mode as opposed to TE mode.
The asymmetric nature of the waveguide leads to the formation of hybridized polarization modes which are neither purely TE nor purely TM. One also expects some degree of diagonal polarization. The degree of linear, diagonal and circular polarization can be determined by calculating the Stokes parameters S 1 , S 2 and S 3 , respectively, for each polarization field  profile [22,46]. The Stokes parameters at each x, y point can be calculated using the following equations:  quasi-TE will couple to quasi-TM at this energy. Mode-splitting by application of lateral-mismatch has been reported in literature for line-defect waveguide planar PhC designs [15,22,47,48], where degenerate, crossed TE 1 + and TE 1 − modes split, but this is the first demonstration of a single mode splitting. Figure 5 shows the log-scale |E|, |H|, |P|, |E y | substratenormal cut-through profiles at various positions of interest above the BOX for the fully-3D FDTD simulation carried out at m = 0.5, k z = 0.43 * 2π . The fin-waveguide design is = 400 nm, fill-factor = 0.5 and the profiles were extracted at f = 0.264 (λ = 1,517 nm), in the middle of the TE-only bandgap. Profiles are a substrate-normal cut-through of the 400 nm long, 2,600 nm wide simulation region (min-z and max-z Bloch boundary conditions to simulate the periodically repeating structure), at displacements from the BOX/SOI interface which are of particular interest. All four profiles show field distributions across the 3D area of the simulation in accordance with expected slot-mode confinement, for their respective components. The mode dominant component |E y |, which corresponds to the TMmode, is shown in Figure 5D to be strongly confined within the 10 nm SiO 2 slot, as well as showing minor peaks on the low-n side of both the BOX/SOI and SOI/cladding interfaces. This result is in agreement with the 2D TM mode-profile result presented in

FABRICATION
Fabrication of the double-SOI platform and subsequent finwaveguide structure has been detailed elsewhere [41] and is simply outlined here. Five nanometers thermal oxide was grown on the surface of two (110) crystal-orientation SOI wafers (SOI thickness = 100, 115 nm), which were bonded and thinned creating the double-SOI substrate. Fin-waveguides (aligned and misaligned) as well as input/output waveguides, bends and MMIs, were patterned using electron-beam and conventional inductively coupled plasma (ICP) etching. Local oxidation of silicon (LOCOS) and tetramethylammonium hydroxide (TMAH) anisotropic wet etching was used to under and overetch the top and bottom fins simultaneously. The left top-fin sidewalls are aligned to the (11-1) crystal plane and act as an etch-stop to TMAH. Due to the mirrored crystal alignment, the same is true of the right bottom-fin sidewalls. The unprotected fin-sidewalls (left-lower and right-upper) are etched. Partiallyetched grating couplers (GCs) were defined and ICP etched separately. The structure has an air cladding. The devices were subsequently measured. Figure 6 shows an SEM image of a fabricated fin-waveguide structure without mismatch (m = 0.0). The image was taken with 54 • tilt, which makes the suspension of the top SOI layer fins clearly visible. The periodic bumps protruding from the central section of the waveguide as well as the edge of the fins are caused by semi-stable crystal planes which were not completely removed by the TMAH etching. As these bumps are uniform and periodic across the structure they are not necessarily expected to increase scattering loss. They change the periodic Bragg structure and therefore alter the dispersion relation of the structure, but as they are small compared to the structure overall, they are not expected to significantly affect the nature of the structure or the nature of the quasi-TE to quasi-TM mode conversion. The sharp white lines underneath the suspended left-side fins are the edges of pyramidal semi-stable planes which have not been fully etched. As these are in a region of low EM field intensity according to simulations, they are not expected to significantly effect the performance of the device.

CHARACTERIZATION
The fabrication process is complex and requires significant optimization before it can produce reliably uniform features across a sample area. To account of likely simulation expectation vs. experimental observation "drift" a large search area of device designs was included. In this section we present three sets of devices which demonstrate three phenomena predicted by simulation results presented in Figures 4, 5.
Waveguide device broadband spectra were measured using a TE polarized continuous-wave (CW) tunable (1,525-1,625 nm) laser light source. A fiber polarization controller was used to ensure maximum transmission through TE optimized GC waveguide devices. Light coupled from a single mode fiber into and out of the device using GCs, and transmission power was measured using a photodetector. Section 4.1 shows the transmission spectra for straight waveguides with = 450 nm, fill-factor = 0.5, m = 0-0.5. Section 4.2 shows the transmission spectra for straight waveguides with = 350 nm, fill-factor = 0.5, m = 0, 0.5. Section 4.3 shows the transmission spectra for an MZI device incorporating a finwaveguide on one arm, the fin-waveguide having = 450 nm, fill-factor = 0.5, m = 0, 0.25, 0.5. In all of the measured devices the length of the fin-waveguide PhC section was 500 µm long, however, as quasi-TE to quasi-TM conversion relies on bandgap stopping and not adiabatic coupling, mode-beating or selfimaging techniques, and conversion is therefore not dependent on waveguide/device length, the length of the waveguide can be reduced to several µm if desired, massively decreasing device footprint.

Photonic Bandgap Closing
The simplest experimental demonstration of the phenomenon observed in simulation (Figure 4) is the effect of low-energy PBG shrinking as m → 0.5. This is observed in fin-waveguide design = 450 nm, fill-factor = 0.5. The spectra for these devices are shown in Figure 7. Grating coupler efficiency was measured to be 7 dB/GC at λ = 1,525 nm. The m = 0 fin-waveguide has a PBG width (PBG width ) ∼ 59.94 nm and as m → 0.5 this PBG width decreases roughly linearly to 9.98 nm at m = 0.5. Due to the imperfection of the fabrication the PBG does not close completely.

Straight Waveguide Transverse Magnetic Propagation
High-energy quasi-TE propagation when m = 0, and quasi-TM propagation when m = 0.5, is demonstrated experimentally in a fin-waveguide with = 350 nm, fill-factor = 0.5, which is presented in Figure 8. Figure 8 shows the transmission spectrum (black line) for m = 0 (Ai) and m = 0.5 (Bi). The red to blue lines overlaid onto the transmission spectrum are Gaussian apodizations of the raw spectrum centered at points between λ = 1,540-1,605 nm at 5 nm intervals. The Fourier transform of these normalized spectra produce the λ dependent free-spectral range (λ FSR ) of that particular section of the spectrum, (Aii) and (Bii) for m = 0 and m = 0.5, respectively. Figure 8Aii for m = 0 exhibits two λ FSR peaks, one narrow and "clean" at λ FSR = 0.255 nm, the other broad and noisy at λ FSR = 0.4-0.7 nm. These peaks can be identified as originating from the GC/GC cavity FPR and the GC/fin-waveguide cavity FPR, respectively. The GC/GC cavity λ FSR spectrum is narrow because reflection from the Bragg mirror-like GCs occurs in a narrowly defined space (∼15 µm per GC). The λ FSR also exhibits a linear dependency on λ. The following equations can be used to extract n eff from λ FSR in the case of a cavity with consistent n eff (Equation 2) and in the case of a cavity with different n eff fin components (Equation 3): Where L cavity is the length of the cavity, n eff fin is the effective refractive index of the fin-waveguide, n eff taper is the refractive  index of the taper, L taper is the length of the taper, and L fin is the length of the fin-waveguide. Due to the fabrication non-uniformity, the finwaveguide/wire-waveguide interface is not operating as a single reflection point, therefore the λ FSR is broadened. The broad λ FSR spectrum peaks in Figure 8Aii at λ FSR = 0.6 nm indicate a n eff = 3.94 in the 500 µm taper-waveguide (Equation 2). Using n eff taper = 3.94, L taper = 1 mm, L fin = 250 µm, we can calculate n eff fin = 3.17. This is only an approximate value as there is large uncertainty in λ FSR .

Figure 8Bi
shows that with m = 0.5 the spectrum pattern is altered significantly in the high-energy region. Figure 8Bii shows two λ FSR peaks that are not present in (Aii). The major peak occurs at λ FSR = 3.33 nm for Gaussian apodization centered on 1,540 nm. Using Equation (3) this gives a n eff fin = 1.42. The minor peak occurs at λ FSR = 1.7 nm for Gaussian apodization also centered on 1,540 nm. Using Equation (3) this gives a n eff fin = 2.79. This implies that at high-energy this particular mismatched fin-waveguide is multi-mode, supporting a dominant quasi-TM slot-mode (indicated by the large λ FSR = 3.33 nm peak) as well as a less dominant quasi-TE strip-mode. The fact that large λ FSR amplitude peaks are present indicates that the coupling between the strip-waveguide/fin-waveguide is poor, and a large proportion of the light is being reflected. However, despite this, the clear λ FSR = 3.33 nm peak associated with quasi-TM cavity FPR demonstrates that a 10 nm slot-mode has been induced by the application of m = 0.5, and the n eff fin = 1.42.

Mach-Zehnder Interferometer
Transverse Magnetic Propagation Figure 9 shows the transmission spectra, Fourier transform calculated λ FSR (λ), and n eff (λ) for three asymmetric MZI devices ( L arm = 542 µm) with different 500 µm long waveguide designs on one arm; (Ai-iv) is a strip-waveguide reference device with a strip-waveguide on both arms, (Bi-iv), is a fin-waveguide reference device with a m = 0.0 fin-waveguide on one arm, and (Ci-iv) is an MZI incorporating a m = 0.5 fin-waveguide on one arm. Figure 9Ai shows a typical MZI transmission spectrum with λ FSR (λ) linearly increasing from 0.92 to 1.03 nm from λ = 1,535-1,600 nm (Aii and Aiii). This corresponds to n eff decreasing linearly from 2.37 to 2.29 (Aiv). The linear decrease in n eff and lack of sharp discontinuity across λ indicates that the same mode (quasi-TE) is propagating across the spectrum. Similarly, (Bi) shows a typical MZI transmission spectrum with λ FSR (λ) linearly increasing from 0.99 to 1.14 nm from λ = 1,535-1,600 nm (Bii and Biii) which corresponds to n eff decreasing linearly from 2.2 to 2.08 (Biv). This indicates that the m = 0.0 fin-waveguide is operating in quasi-TE mode, irrespective of λ.
If the propagating mode changes from quasi-TE to quasi-TM as a function of λ within the 500 µm long waveguide on one of the arms, we expect to see a change in the λ FSR (λ), and therefore a change in the n eff (λ). This is indeed what we can observe in the transmission data for the asymmetric MZI device incorporating a fin-waveguide ( = 450 nm, fill-factor = 0.5, m = 0.5) (Figure 9Ci). Because of the high-loss associated with m = 0.5 devices the transmission spectrum exhibits high noise, the λ FSR peaks extracted from the Gaussian-apodized spectrum are broader than those extracted from the reference data. However, λ FSR can still be identified in Figure 9Cii, particularly for λ = 1,555-1,600 nm, with a linear increase in λ FSR from 0.95 → 1.2 nm. λ FSR can also be identified for Gaussian-normalizations centered on lower wavelengths, most notably for λ = 1,535 nm, where λ FSR = 1.37. Figure 9Cii shows that for Gaussianapodization centered on 1,540, 1,545, and 1,550 nm, λ FSR = 1.35, 1.33, 1.11 nm, respectively. λ FSR as a function of centered λ therefore begins at λ FSR = 1.37 nm, decreases with a sharp discontinuity to 0.95 nm as λ increases, and then increases linearly as a function of λ. Figure 9Ciii shows the effect on n eff (λ).Between λ = 1,535-1,545 nm n eff = 1.57-1.65, and at λ = 1,555 nm n eff = 2.34. Despite the fact that the transmission and λ FSR spectra exhibit high noise, this is clear evidence that the n eff (Ciii) is highly dependent on λ in a discontinuous, non-linear way. This is explained by the dominance of the 10 nm slot quasi-TM mode propagation within the mismatched fin-waveguide at low λ, and standard quasi-TE mode propagation at higher λ.

CONCLUSION
In this paper we have experimentally demonstrated quasi-TE to quasi-TM mode conversion through the introduction of a lateral mismatch to an asymmetric fin-waveguide PhC.
Transmission spectra demonstrate non-linear dependence of λ on n eff for two mismatched fin-waveguide devices, with n eff being calculated to be between 1.37-1.42 at low-λ and 2.75-3.94 at high-λ. n eff = 1.37-1.42 at low-λ is evidence of quasi-TM propagation within the 10 nm thick horizontal oxide slot region. This is the narrowest oxide-slot TM propagation currently reported in literature. 3D FDTD simulations predict that as m → 0.5, the TE 1 − band splits within the Brillouin zone, whilst the TM 1 + remains robust and unaffected. The loss associated with mismatched fin-waveguides is currently high, but once the fabrication process is optimized, these devices will be useful in sensing, light-amplification, modulation, and other telecommunication applications requiring very narrow TM slot-mode propagation. TE/TM dispersion relation engineering through the utilization of a lateral mismatch in an asymmetric geometry can also be developed, based on these proof-ofconcept designs and demonstrations, to explore new ways of manipulating light, adding a new degree of freedom to PhC design.

DATA AVAILABILITY STATEMENT
The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found at: https://doi.org/10.5258/ SOTON/D1607.

AUTHOR CONTRIBUTIONS
JB conceived of the idea with the help of ideas presented by HA and wrote the manuscript. MS contributed the simulation code, which JB implemented. JB, MH, and KK fabricated the devices. KD took the SEM image. Devices were measured in optical measurement labs setup and maintained by DT and GR. MC provided the guidance. SS provided the significant guidance during design, fabrication, analysis, and manuscript writing. JH provided the help with manuscript preparation. All authors were involved in the revision of the manuscript.