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We report on the realization and characterization of highly efficient waveguide bends in photonic crystals made of materials with a low in-plane index contrast. By applying an appropriate bend design photonic crystal bends with a transmission of app. 75 % per bend were fabricated.
©2003 Optical Society of America
1. Introduction
During the past several years photonic crystals (PCs) have attracted much interest as miniaturized devices, where the flow of photons can be controlled. Some emphasis was on the optimization of sharp waveguide bends, which are required for a future all-optical integration. Until recently most experimental investigations on PCs were performed on semiconductors with large in-plane index contrasts (>3:1). Here, photonic crystal waveguide (PCWG) bends with a transmission of up to 77% were realized [1–3]. However, semiconductor based PCs also revealed some drawbacks. For single mode operation very small waveguide areas are required, which results in high coupling losses, usually larger than 20 dB. Operating semiconductor heterostructures PCs above the light cone evokes high propagation losses, mainly because of out-of-plane scattering at the air holes (cf. [10], 10 dB/mm [4] and more [5,6,7] for a W3-PCWG, where three rows of holes are removed in ΓK-direction). An alternative approach of realizing PCs consists in using materials with a much lower index contrast (2.1:1). These materials have the advantage of being transparent in a wider spectral range and thus the potential for fabricating PCs, which can be operated in the visible. Moreover, a lower refractive index implies larger feature sizes and, hence, lower coupling losses.
Very recently, we reported on the fabrication of low-loss PCWGs in that low-index material [8]. Here, we proceed with the evaluation of its potential for low-loss PCWG bends.
The Letter is organized as follows. First, we discuss the design for PC waveguides and bends, where various bends are evaluated by means of 3D finite-difference time-domain (FDTD) calculations. After concisely introducing the fabrication process we discuss the experimental results.
2. Design of the slab system
We realized PC slabs (a two-dimensional lattice etched into a layered structure) by using the glass-like materials Niobium Pentoxide (Nb2O5, n=2.1) and silica (SiO2, n=1.43). An Nb2O5 waveguiding layer (thickness of 500nm) was sandwiched between an SiO2 cladding (thickness of 300nm and an SiO2 buffer (thickness of 2000nm). The buffer layer separates the waveguiding layer from the Si-substrate, which is needed for cleaved optical facets for sample characterization. The selected Nb2O5 waveguiding layer ensures single mode guiding in the vertical direction of the unstructured slab for 1.5 µm wavelength. The structure is symmetrized by the SiO2 cladding, which helps preventing TE-TM-mixing.
Fig. 1. 3D band structure of the PC slab system (left) and a 2D effective index band structure calculation for the W3-PCWG (right). The diameter of the holes is 374 nm at a lattice pitch of 595 nm.
The photonic crystal itself consists of a hexagonal pattern of air holes with a diameter of 370nm at a lattice pitch of 595nm. This structure was designed by means of 3D band structure calculations using preconditioned conjugate-gradient minimization of the block Rayleigh quotient in a plane wave basis, using a freely available software package [12], which show that for TE-like polarization a band gap around 1550 nm with a gap-to-midgap ratio of 13% exists (see Fig. 1).
It is important to note that, although the in-plane index contrast is relatively low (2.1:1), the vertical index contrast between Nb2O5 and SiO2 is fairly high (Δ=(-)/2=0.27) compared to semiconductor heterostructures PC slab systems (e.g. GaAs to AlGaAs, Δ=0.1 [1,2,6]). The confinement of light inside the PCWGs strongly depends on the vertical index contrast and on the hole depth. Theoretical calculations predict that for the present slab system with an index contrast of Δ=0.27 a minimal hole depth of only 1100nm (aspect ratio of 1:3) is required.
3. Design of photonic crystal waveguide bends
Usually, integrated optics prefers single mode waveguides with low losses. However, single-mode W1-PCWGs, operating above the light cone, are known to be very lossy. Intrinsic PCWG losses (not taking into account the material absorption and material scattering) were determined to be in the range of 100 – 300dB/mm [9]. Thus, to avoid such losses we preferred W3-PCWGs.
Fig. 2. Transmission of a W3-PCWG double bend (3D-FDTD calculations, TE polarized excitation) for three different bend designs (unaltered bend, three holes shifted and three extra holes inserted at the bend).
A W3-PC waveguide is formed by omitting three rows of holes in the ΓK (nearest neighbor) direction. The band structure of the W3-PCWG was obtained by means of a 2D effective index calculation, which is applicable because of the low dispersion in the frequency window of the band gap [11] (in Fig. 1 the white area between the two shaded regions). The calculations yield three modes, besides the fundamental mode one even and one odd mode can be observed. Here even and odd refers to the parity of the modes with respect to the plane perpendicular to the layers and parallel to the waveguide. This is the only rigorously defined symmetry property.
The bends were formed inside the PC connecting two W3-PCWG along the ΓK directions. Two of these 60°-bends were arranged consecutively to define a PC double bend with an overall length of 60µm. We performed 3D-FDTD calculations (computational window 60µm×20µm×2µm) of this double bend for three different bend designs (unaltered, three additional holes, three holes moved), where the PC-structure was of the same size as the samples used in the experiments. By calculating double bend transmissions we can also properly account for the Fabry-Pérot resonances, introduced by the reflections at the two consecutive bends (see Fig. 2). For wavelengths exceeding 1.52 µm, the peak transmissions of the three designs are comparable. Below 1.5 µm the transmissions of the altered bends are considerably higher. Since the bends, where three extra holes are inserted into the PCWG, exhibit the highest maximum transmission this type of bends were fabricated. Fig. 3 shows a 3D FDTD simulation of this bend excited at 1509 nm, where the maximum transmission of ~80% per bend could be observed.
Fig. 3. (left: 1.45MB, right: 1.74MB) 3D-FDTD simulation of a 60° double bend excited at 1509 nm, where a high transmission of ~ 80% per bend are observed (cross section at the center of waveguiding layer, left original computing window, right blow-up of lower bend). Alternatively animations of higher quality can be obtained, (2.58 MB) and (3.38 MB).
4. Fabrication
The PCs were fabricated using e-beam lithography. Since Nb2O5 is much more resistant than SiO2, and to realize steep holes in the Nb2O5 layer a three-layers resist (a thick polymer layer, chromium layer and a resist layer at the top) was used for contrast enhancement. After e-beam exposure the topmost resist layer is developed and used as an etching mask to transfer the pattern into the underlying chromium layer by reactive ion etching.
Fig. 4. SEM images of the fabricated W3-PCWG consisting of holes with a diameter of 370 nm and a depth of 1100 nm (aspect ratio of 1:3) in a hexagonal lattice of period 595 nm. The wall angle in the holes amounts to 85°.
To generate the etching mask for the slab system the 700nm thick polymer layer underneath is structured with reactive ion beam etching in a second etching step. Then, in a final etching step the slab system itself is etched, also with reactive ion beam etching. After etching, the sample is cleaved to obtain optical facets for characterization. SEM images show holes of 1100nm depth and an average diameter of 374nm with a separation of 595nm. Wall angles amount to 85°, and an aspect ratio of 1:3 is achieved (see Fig. 4).
Three rows of holes in the ΓK (nearest neighbor) direction were omitted during the e-beam exposure to form a W3 waveguide (see Fig. 4). Two types of PCWGs were realized, viz. very long PCWGs with an overall length of 10mm and much shorter PCWGs with a length of 60µm. For easier handling of these PCWGs ridge waveguide tapers were used for coupling. Furthermore, based on the FDTD transmission calculations PCWG double bends with two different designs (unaltered and three extra holes inserted, Fig. 5) were fabricated. The 60µm long PCWGs were used for transmission normalization purposes.
5. Results and discussion
5.1. Propagation losses in straight photonic crystal waveguides
The PCWG and bends were characterized in a direct transmission set up. The coupling of the input (tunable laser diode) and output beams of the PCWGs was performed by using two microscope objectives (NA=0.95, NA=0.85). First, the near field distributions at the output facets of the W3-PCWG were determined. After a propagation distance of 60µm the W3-PCWG shows a multi-mode profile in accordance with band structure calculations. However, after a propagation distance of 0.8mm only one mode can be observed, i.e., after a sufficiently large propagation distance the W3 is effectively single mode. This is because of higher order modes penetrate deeper into the crystal and thus experience high out-of-plane scattering losses.
Fig. 5. SEM-images of the W3-PCWG double bend with the optimized (top left, right) and with the unaltered bend (bottom left). The PC consists of holes with a diameter of 360nm and a depth of 1.1 µm at a lattice pitch of 595 nm.
The propagation loss of W3-PCWGs is another important property. It was determined for the fundamental mode of the W3 by means of the cutback method. In this way a linear fit of the transmissions (in dB) yields both the overall coupling and the propagation loss. Besides a coupling loss of ~12dB, a propagation loss of 8.5dB/mm was determined for the W3-PCWG, which is in accordance with the theoretical limit obtained from 3D-FDTD calculations. To our knowledge this is the lowest loss reported so far for a W3-PCWG.
5.2. Photonic crystal waveguide bends
After establishing that the W3-PCWG has a very low loss, the W3 bend transmission for different designs was measured. To obtain the bend transmission (efficiency) of a single bend the square root of the double bend transmission normalized in terms of the straight PCWG was calculated. As mentioned above, ridge waveguide tapers were used to couple into these much shorter PCWGs and bends. By doing so the overall coupling loss could be decreased to ~9dB.
For an unaltered PCWG bend (Fig. 5, bottom left) with an average hole diameter of 374nm, a period of 595 nm and a hole depth of 1100nm, a transmission of 36%/bend (at 1490nm) was obtained. For the optimized PCWG bend (three additional holes) (Fig. 5, top left) we determined a maximum transmission of 75%/bend at 1515 nm for TE polarization (see Fig. 6). By monitoring the near field distribution at this wavelength, we could observe that the bend also supports one higher order mode, depending on how the PCWG leading to the bend was excited. Under optimized coupling conditions only the fundamental mode could be observed.
A 73nm bandwidth with transmissions exceeding 35%/bend in the range 1501nm – 1574nm was found. Although some deviations between the experimental data and the FDTD-simulations exist, both the maximum transmission per bend and the position of this peak are in very good agreement with theoretical predictions.
The deviations are caused by fabrication induced variations (due to the proximity effect) of the hole diameter and wavelength dependent losses at the ridge waveguide taper-PCWG interface due to the non-optimized coupling between ridge waveguide and PCWG. Numerical simulations (3D-FDTD) show that for an optimized coupling the transmission is wavelength independent and above 90%.
6. Conclusion
To conclude effectively single mode W3 PCWG with low losses (8.5 dB/mm) and highly efficient PCWG-bends (75% transmission/bend) have been fabricated in a slab system with a low in-plane index contrast. This high efficiency has been obtained by optimizing the bend structure. Both figures for the W3-PCWG, waveguide losses and bend efficiency, are comparable to the best values reported so far for semiconductor heterostructure PCs. By investigating the near field distribution of the W3-PCWGs it could be shown, that after a certain length (<0.8mm) the W3 is effectively single mode. Hence, low index amorphous materials can perform as well as semiconductors. Since the investigated materials are transparent in a much wider spectral domain they are promising candidates to realize PCs in the visible.
This work has been partly funded by the Bundesministrium für Bildung und Forschung (BMBF) and the Deutsche Forschungsgemeinschaft (DFG).
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