1x3 beam splitter for TE polarization based on self-imaging phenomena in photonic crystal waveguides

: Based on inspiration from multi-mode interference self-imaging and theoretical FDTD simulations, a 1x3 beam splitter was designed, fabricated and characterized. Measurements show that for TE-polarized incident light the power is distributed equally between the output ports within 1dB in the range from 1541nm to 1552nm, and the total transmission of the 1x3 splitter is equal to the corresponding length of a single-line-defect PhCW within the measurement uncertainty.


Introduction
Large-scale Photonic Integrated Circuits (PICs), possess significant advantages by simplifying the optical system design, improving its reliability and reducing the space and power consumption [1]. Some of the most successful PIC structures are made from slab Photonic Crystals (PhCs) due to the ease of fabrication by using well-known lithographic techniques [2]. In such Photonic Crystal Waveguides (PhCWs), the optical field is confined, horizontally, by a photonic band-gap (PBG) provided by the PhC and, vertically, by total internal reflection due to the refractive index differences between different layers. Beam splitters are one of the central building blocks among the integrated components in PICs. These have been made by slab PhC [3][4][5][6][7][8][9][10][11], including Y-junctions [9][10][11], T-junctions [5,6] and directional couplers [3,4]. Until now, most of the work has focused on the performance of single-mode PhCW, but introducing multi-mode interference regions in the PhCWs provides new extraordinary characteristics [12] and some 1x2 components that use multimode interference have been proposed [7,8].
In recent years, there has been a growing trend in the application of multimode interference (MMI) effects in integrated optics. Several components have been investigated theoretically including: a wavelength de-multiplexer based on self-imaging phenomena in PhCWs [13], the operation of a terahertz switch based on the self-imaging principle in silicon triangular PhCW [7,14], TE and TM polarization splitters based on the simulation using selfimaging phenomena in PhCW [15] and a 1x2 splitter based on self-imaging phenomena in PhCWs [8]. The 2D simulation of Yu et al. [4,16] indicated that the self-imaging phenomena also occurs in PhCWs between every second line defect in devices with many defect lines allowing the realization of 1xN (N≥2) splitters. Components based on every-other line-defect PhCWs are ultra-compact. The beat-length in the MMI region is much shorter than in the MMI region of conventional photonic waveguides. Moreover, in the latter the adjacent output waveguides have to be separated far enough to minimize coupling between them, and generally a rather wide multi-mode section is required. The every-other line-pattern in the former also facilitates the multi-mode field distribution [16]. The layout of rod slabs was adapted in Yu et al.'s research, but high transmittance can be obtained only for very long rods, increasing the fabrication difficulty. In contrast, thin air-slab PhCW devices with high transmittance can be easily fabricated and integrated with other PIC building blocks. Standard SOI wafers and e-beam lithography provide our fabrication platform. Here we report the theoretical and experimental results of a 1x3 beam splitter based on self-imaging in the 340nm top silicon layer of a SOI wafer.

Self-imaging principle and theoretical simulation
Bryngdahl et al. were the first suggesting the possibility of achieving self-imaging in slab waveguides [17] and Urich et al. explained the principle in detail [18]. Self-imaging is a property of multi-mode waveguides by which an input field profile is reproduced in single or multiple images at periodic intervals along the propagation direction [12,19]. The 2D PhC is formed by a triangular configuration with lattice pitch of Λ=380 nm and air hole diameter of D=222nm. This PhC structure defined in silicon (refractive index n=3.476) gives rise to high transmittance and a photonic band-gap (PBG) at near-infrared wavelength. The PBGs are disallowed bands in which the wavelengths are unable to pass through the PhC. Using a line-defect PhCW, light that propagates in the waveguide with a wavelength within the band-gap of the crystal is confined to the defect, and can be directed along the defect from one location to another. A W1 waveguide is obtained by removing exactly one single row of air-holes in the Γ-K direction of the lattice. Our proposed slab PhCW 1x3 beam splitter is shown in Fig. 1. It consists of three sections: a single-mode input, the MMI region, and three single-mode outputs all along the Γ-K direction. The lengths of the input and output ports are fixed in our theoretical design. The length L n of the MMI region needs to be optimized and corresponds to the length of n lattices in MMI region (n must be an integer to preserve the crystal structure). The interference between adjacent output ports can be ignored because they are short and separated by three rows of air holes. Only TE polarization was calculated in the simulation, considered as TE-like in 3D simulation. The TE-like modes are even (symmetric) and odd (anti-symmetric) about the mirror-symmetry plane(x = 0). The symmetric interference is adopted based on the principle of symmetry matching [19].  Figure 2 presents the in-plane normalized dispersion diagrams for single-and multi-mode PhCWs calculated by 3D plane wave expansion (PWE) method with the grid spacing of Λ/16. Super-cells are depicted as inserts. Single-mode W1 PhCWs support one even mode (Fig. 2a) and multi-mode PhCWs support five and three even modes ( Fig. 2b and Fig. 2c) in MMI region and output region. The bottom of the single-mode frequency span is very close to that of the multi-mode counterpart in the output region. This means that a 1x3 beam splitter is conceivable in this slab design near the normalized frequency of 0.241 (Λ/λ) in order to obtaining high transmittance [11,21]. Figure 3 shows the transverse profile of the magnetic field H y for these even modes of the supercells at kΛ/2π=0.5, calculated by 2D PWE method. All the even multi-modes are symmetric through the x=0 plane. Only the modes corresponding to the identical frequency can be excited (see the pink line in Fig. 2). However, it is possible to excite a superposition of modes at the excitation frequency.
The configuration of Fig. 1 is directly used in 3D FDTD modeling with the grid spacing of Λ/24. Different L n 's were simulated numerically. The simulations show that the components with L n =10Λ and 11Λ split the input power equally and exhibit vey good transmittance. This means that theoretically the first 3-fold images are obtained due to MMI, between 10Λ and 11Λ. The net normalized transmittance is obtained by the net transmittance through the theoretical sensors in the right ridge waveguides divided by that through the input sensor in the left waveguide. These transmittances for the W1 PhCW and the 1x3 splitter with L n =11Λ are shown in Fig. 4a. From the FDTD simulation, the optimum wavelength is 1567.4 nm and the total normalized transmittance is close to that for a W1 PhCW. A H y field distribution at 1567.4 nm through the same 1x3 splitter is depicted in Fig. 4b. The dispersion properties of a very similar W1 PhCW have been discussed by L.H. Frandsen [21]. The even PBG mode is seen from Fig. 2a to be flat from k z =0.35 to 0.5. The variation approaches zero in this range, addressed as the slow-light regime. The even semislow PBG mode penetrates into the photonic crystal cladding; and is therefore especially sensitive to the presence of the adjacent two rows of holes. In our devices, the structures of the input and each of output ports still maintain the character of the W1 PhCW. The input field is well matched to the PhCW and only guided modes will be excited in the component based on symmetric interference [19]. The second line is removed in the MMI region to permit self-imaging, so the modal field can distribute at every-other line-defect (Fig. 3b) and form maxima at the end of the MMI region. The distribution of the modal field in MMI region depends on the position and input frequency introduced from the single-mode port. After the coupling into the MMI region, the modal field around 1567.4 nm is distributed equally after propagating approximately 11Λ leading to the first three-fold imaging (Fig. 4b).

Fabrication and characterization
The designed splitters with different L n have been fabricated using e-beam lithography (JEOL-JBX9300FS) and inductively coupled plasma etching (ICP). In this way the desired design was defined into a 340-nm silicon layer. A SEM micrograph of the splitter with L n =11Λ is shown in Fig. 5a. The air holes have a diameter of 220 +/− 5nm. The width of the ridge waveguides connected to/from the splitters is 0.53µm. The upper and lower output waveguides are separated from the central output waveguide using cosine bends after 5µm length in order to avoid coupling between the adjacent ridge waveguides (shown in Fig. 5b). Straight tapers expand the waveguides to/from 4µm diameter into and out of the PhCWs.
The device under test (DUT) has been characterized with the setup illustrated in Fig. 5c. Light is generated with an Agilent 83437A Broadband (LED) Source, and lensed fibers are used to focus the light into and out of the DUT. Finally, the light was detected by an ANDO AQ6315 Optical Spectrum Analyzer using a resolution of 2nm.
The normalized transmittance spectra for TE polarization from 1480 to 1580 nm are characterized. The 1x3 splitters with L n from 10Λ to 13Λ can divide the incident light into three output channels in some wavelength span. Among them, the splitter with L n =11Λ is the best. The normalized 11Λ TE-polarized spectra are shown in Fig. 6a. The input power after the splitter is divided equally into three parts between 1541 and 1552 nm, with a maximum difference below 1dB. The experimental result is consistent with that of the numerical modeling. The small difference is attributed to the finite grid and omission of the native oxide in the modeling and fabrication errors. The total output of the 1x3 splitter is close to a W1 PhCW with the same length. Especially for the wavelength below 1550nm, the loss compared to W1 PhCW is within the measurement uncertainty. When the L n =11Λ splitter is reversed, it works as a 3x1 combiner. The incident light reaches the component from the side with three output ports. Figure 6b shows the normalized transmittance spectra through each port. Because the total power is induced separately from each port, the total input power is around 4.8dB higher than the total output power. Since two of the spectra are almost identical, it illustrates the possibility for realizing further multiple functionality.

Conclusion
In conclusion, we have presented a 1x3 splitter with excellent performance for TE polarization. It splits the input power equally into three output ports within a ~10nm range near 1550nm. The reversed performance as a 3x1 combiner is consistent with the former. If the 1x3 and 3x1 functions are used together, more functions can be obtained, for instance the 3x3 function for qutrit, which is in progress in our group.