1. Introduction

Silicon photonics based on the silicon-on-insulator (SOI) technology is a promising platform for the future development of integrated photonics. With SOI waveguides, it is possible to integrate different microphotonic components such as waveguides, lasers, modulators and detectors on a same silicon substrate with microelectronic circuits using CMOS (complementary metal oxide semiconductor) compatible processes. The CMOS compatibility will enable some critical applications in semiconductor industry, such as chip-scale optical interconnects or all-optical signal processing. Because of high refractive index between silicon and silicon dioxide (SiO₂), silicon nanophotonic waveguides can have a cross section of several hundred nanometers and a bend radius of a few micrometers, which make high density photonic integration possible.

However, the intrinsic physical properties of silicon make it difficult to use silicon for some active optical devices, including light emission and high speed modulation. The slot waveguide configuration has emerged recently as a possible solution to these problems [1]. In this waveguide structure, a high percentage of light is confined in a sub-wavelength slot region with low refractive index and sandwiched by two strips (vertical slot waveguide) or slabs (horizontal slot waveguide) of a high refractive index material such as silicon. By introducing active optical materials like nanocrystal [2], erbium doped silicon dioxide [3], or nonlinear optical materials [4] into the slot region, hybrid silicon lasers, amplifiers, detectors and modulators can be constructed. Kerr nonlinearity in the incorporated materials is amplified due to much higher optical power density in the slot than inside a conventional strip or ridge waveguide, making it possible to realize ultra-fast all-optical computation at the power level of typical telecom laser diodes [5]. Strong optical confinement in the low refractive index medium also makes the slot waveguide an attractive technology for optical sensors [6-7].

Compared with the standard silicon strip waveguide, mode conversion of the slot waveguide poses some unique challenges. The main peak of the mode in the slot region is as narrow as several tens of nanometers. The shape of the fundamental mode of a slot waveguide does not have the smooth Gaussion-shaped single-peak distribution of a single mode optical fiber. Large mode size mismatch leads to high coupling loss in and out of the silicon slot waveguides, which might prevent the practical applications of this technology. For optical modulators with electro-optical materials in the slot, the two silicon strips need to be electrically isolated. Two types of fiber coupling techniques have been applied in conventional silicon waveguides: inverted tapers for butt coupling [8–10] and diffraction gratings for out-of-plane coupling [11-12]. Compared with grating couplers, taper couplers have the advantages of being insensitive to optical wavelength, low polarization dependence and possibility of passive fiber alignment with V-groove structure. Similar fiber couplers have been proposed for horizontal slot waveguides [13-14]. But up to now, no fiber coupling techniques for vertical slot waveguides have been reported. Several designs of efficient strip to slot waveguide couplers have been proposed and demonstrated [15–17], but they don’t directly address the fiber coupling issue and an additional fiber coupler for the strip waveguide may be required. This letter presents design, fabrication and measurements of an efficient mode size converter for fiber coupling with vertical silicon slot waveguides.

2. Design and simulations

In our design shown in Fig. 1(a) , the widths of two silicon strips are reduced gradually to a point that the silicon slot waveguide loses optical confinement, and the increasing evanescent light from the tapers are captured by a rectangular waveguide made of materials of lower refractive index than the index of silicon to expand the optical mode to a size comparable to that of a fiber. To work as an efficient fiber coupler, losses from three sources need to be minimized: 1) mode mismatch and reflection between the optical fiber and the low-index waveguide; 2) mode mismatch and reflection loss at the taper tips; 3) mode conversion along the tapered section. The main factors that affect these losses include modal profiles of the silicon slot waveguide, optical fiber, and low-index waveguide at the end facet and at the taper tips, length of the taper section, as well as positions of the two taper tips inside the low-index waveguide. In this work the effects of these factors were studied with computer simulations at the optical wavelength of 1550 nm to obtain an optimized design used for experimental demonstration.

 

Fig. 1 Schematics of the proposed mode size converter. (a) 3D view of the structure. (b) Profile of the silicon slot waveguide and its optical mode for TE polarization.

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Optical modes of the waveguide structures were analyzed with a three dimensional (3D) mode solver based on the film mode matching method (FMM) suitable for waveguide structures of high index contrast and subwavelength geometry (FIMMWAVE, Photon Design). Two silicon strips of the silicon slot waveguide are 220 nm thick and 270 nm wide, and the width of the slot is 100 nm [Fig. 1(b)]. Refractive indices of silicon and SiO₂ are 3.48 and 1.46, respectively, at the telecom wavelength of 1550 nm. We used SU8 (MicroChem) polymer as the cladding material covering the silicon slot waveguide and the core material of the low-index waveguide, which has a refractive index of 1.565. Confinement factors in the slot region of the silicon slot waveguide are calculated to be 34.6% for the transverse electric polarization (TE) and 2.7% for the transverse magnetic polarization (TM), while the confinement factors inside the silicon strips are 55.0% for TE and 21.1% for TM.

Mode mismatch losses at the waveguide interfaces were calculated with a 3D optical propagation tool using the eigenmode expansion method (EME) (FIMMPROP, Photon Design). The propagation simulation results of EME method are verified with the overlap integral of optical fields of the waveguide modes obtained from FMM mode solver. Dimensions of the SU8 polymer waveguide are 2 × 2 μm. The fundamental modes of optical fibers were estimated with Gaussian modes. Mode mismatch losses of the optical fiber with the silicon slot waveguide and the polymer waveguide are plotted as functions of the mode field diameter (MFD) of the fiber [Fig. 2(a) ]. A minimum mode mismatch loss of 0.5 dB from the fiber to the polymer waveguide for both polarizations occurs at fiber MFD of 1.875 μm. This level of MFD is possible with a lensed/tapered fiber [18]. The minimum mode mismatch loss between the silicon slot waveguide and fiber, however, requires the fiber to have a MFD smaller than 1 μm (0.8 dB for TE and MFD ≈0.6 μm, and 0.6 dB for TM and MFD ≈ 0.9 μm), which is difficult to be realized with a tapered fiber. For a MFD of 10 μm, which is typical for a cleaved standard single mode fiber, the mode mismatch loss is 4.8 dB at TE and 4.9 dB at TM for the polymer waveguide at both polarizations, and it is 13.3 dB at TE and 10.4 dB at TM for the silicon slot waveguide. Additionally, lower refractive index of polymer than that of silicon also reduces reflection loss at the waveguide end face (0.18 dB than 0.36 (TM) to 0.52 dB (TE)). Thus with an ideal mode size converter, we could expect to reduce the coupling loss of the silicon slot waveguide to an optical fiber with MFD of 10 μm at most by 8.8 dB for TE and 5.8 dB for TM per coupling.

 

Fig. 2 Simulation results of the mode size converter. (a) Mode mismatch loss from an optical fiber to the silicon slot waveguide and polymer waveguide vs. MFD of the fiber. (b) Mode mismatch loss at the taper tips vs. taper tip width. (c) Conversion efficiency along the taper section vs. taper length.

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Ideally the taper tip widths should be zero and there are no mode and refractive index mismatch losses at the tips. In reality due to the limitations in the lithography resolution the taper ends have a blunt tip of nonzero widths and a discontinuity of the waveguide profile is introduced. Studies using the above-mentioned propagation tool indicate that the mode mismatch loss increased with the taper tip width and decreased with the spacing between two taper tips [Fig. 2(b)]. This should be attributed to larger modal distribution changes for wider taper tips and taper tips closer to the polymer waveguide center. A 30 nm or smaller taper tip width, which is achievable with electron beam lithography (EBL), provides a mode mismatch loss lower than 0.1 dB for any tip spacing between 0 and 1.6 μm. For a 1.6 μm tip spacing, taper with tips wider than 100 nm, which allows the use of deep ultraviolet (DUV) lithography process, can still have a loss well below 0.2 dB. Simulations also show that reflection loss at the taper tips due to refractive index mismatch is much smaller than 0.1 dB even for a taper tip width of over 150 nm, so we can neglect its contributions to the total loss.

For straight tapers (the center of the tip is on the center line of the silicon strip) of 30 nm tip width, we have simulated conversion efficiency along the taper section as a function of taper length with the EME method [Fig. 2(c)]. The adiabatic limit, or the minimum length for lossless conversion, is approximately 50 μm for both TE and TM polarizations with optimal conversion efficiency of over 98% (conversion loss < 0.1 dB). Here propagation loss due to material absorption and surface scattering was not included, because it is normally very small over the relatively short length of the taper.

3. Fabrication and measurements

Samples with optimized design were fabricated on SOI wafers with 220 nm thick p-type top silicon on a 2 μm buried oxide layer. Each sample consists of 20 silicon slot waveguides next to each other, terminated with linearly tapered mode size converters at the both ends (Fig. 3 ). The waveguide profile is the same as shown in Fig. 1(b). A 90° bend of 100 μm radius was introduced in each waveguide to avoid direct irradiation of unguided light from the input fiber to detectors. The 100 μm bend radius is large enough to avoid additional bending loss, which become significant only when bend radius is on the order of 10 μm or below. The length of the two straight waveguide sections outside the bend starts with zero and increases with an increment of 600 μm. This allows the waveguide propagation loss and coupling loss to be separable, similar to the waveguide cut-back loss measurement method. Straight tapers with 30 nm tip width and 250 μm taper length have been used to guarantee an adiabatic conversion in the mode size converters. The silicon waveguides and tapers were defined with a 100 keV EBL system (JEOL 9300) and inductively coupled reactive ion etching. The wafer was then coated with 2 μm SU8-2002 polymer and patterned with contact photolithography to form the polymer waveguides. Samples were cleaved at the polymer waveguides close to the silicon taper tips so that the propagation loss of the polymer waveguide is negligible.

 

Fig. 3 Layout of the samples (not drawn in scale). 20 silicon slot waveguides with 90° bends are terminated at both ends with the mode size converters.

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To characterize the transmission property of the samples, 1550 nm light from a fiber laser source, after passing through a polarization controller, was coupled to one end of the waveguides with a standard cleaved optical fiber (Corning SMF-28). The output from the other end of the waveguides was lens (magnification/numerical aperture = 20/0.5) coupled on a photo-detector (HP 81521B). A polarizer was located behind the lens to select TE or TM light. Polarization state of the input light was set by adjusting the polarization controller to maximize the output intensity of the predetermined polarization. Alignment between the fiber and polymer waveguides was achieved with a computer closed-loop alignment system and piezoelectric actuators.

After insertion losses of each waveguide is measured, the sample was cleaved again to remove the mode size converters at the input side to measure insertion losses when fiber is directly coupled to the silicon slot waveguides. The same lens out-coupling was used for both measurements. Insertion losses of waveguides with and without input converters are presented in Fig. 4 . The slope and y-axis intercept of linear fitting of insertion loss as function of waveguide length gives the waveguide propagation loss and total coupling loss (of both input and output ends), respectively. The propagation loss of the silicon slot waveguide is 14.3 dB/cm for TE and 7.8 dB/cm for TM. Insertion loss contributed by a single converter is about 4.6 dB for both TE and TM, whereas fiber coupling loss to the silicon slot waveguide is 12.6 dB for TE and 9.9 dB for TM. The power gain is 8 dB for TE and 5.2 dB for TM by using the mode size converter, which is in good agreement with the simulations. Here we have neglected the loss from the 90° bend, which is much smaller than the coupling loss. We also assumed that the lens could capture all the output light from the waveguides, i.e. output coupling is lossless. Such assumptions make the above figures of coupling losses to be more conservative, and don’t affect the power gain results. Although the data presented in this paper is based on slot waveguide of 100nm slot and 270 nm ridges, slot waveguide of different slot width (from 100 to 130 nm) and silicon ridge width (from 220 to 270 nm) were also fabricated and tested and their results showed the same level of improvement in fiber coupling within measurement error. The results suggest that coupling design is not sensitive to slot waveguide geometries as long as the taper provides a smooth mode transition.

 

Fig. 4 Measured insertion loss of silicon slot waveguides with and without input taper couplers. (a) is for TE and (b) is for TM polarization.

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4. Conclusion

We have developed a mode size converter for low loss coupling of silicon slot waveguides to optical fibers. Simulations based on FMM and EME algorithms at the 1550 nm wavelength suggest that a tapers width smaller than 30 nm and taper length larger than 50 μm could confine the total conversion loss below 0.2 dB. To accommodate lower resolution lithography process, 100 nm or wider taper tip could be used if the two taper tips have larger spacing. Samples with optimized design were fabricated on a SOI wafer, and computer simulation results were experimentally confirmed. This work provides a practical and efficient solution for fiber coupling of future devices based on vertical silicon slot waveguides.