1. Introduction

Photonic crystal (PhC) structures have been the subject of intensive research in recent years [1]. This research was essentially motivated by the miniaturization perspectives they offer to further scale down the size of optical lightwave circuits. Such a miniaturization is possible because of the tight confinement of light provided by photonic bandgap effects. However this is not the only potential advantage of the photonic crystal technology. Other interesting functionalities, that exploit unusual refractive behaviors of photonic crystals and/or slow light effects, have also attracted much attention. One particular example is the “superprism” (SP) effect [2-4], related to the group velocity dispersion. A large change in the deflection angle of a light beam within the photonic crystal is achieved for a slight change of the wavelength or of the incident angle, when operating within the sharp corner regions of the PhC dispersion diagram (Fig. 1(a)).

Despite the apparent simplicity of the SP idea, its implementation for practical applications faced with problems overlooked at the initial stage of the superprism studies [2]. The major issue is related to the beam divergence determined by its width. While the direction of the wave vector changes rapidly when operating in the vicinity of a sharp corner, the distribution of the perpendicular component of the wave vector leads at the same time to a large spread-out of the group-velocity directions (Fig. 1(b)) [3]. The beam broadening results in a higher cross-talk level and negatively impacts the wavelength resolution of a demultiplexer using the SP effect.

 

Fig. 1. (a). Variation of the group velocity direction with the wavelength in the vicinity of a sharp equi-frequency curve corner. (b) Spread-out of the group-velocity directions for a beam of tangential wave vector width Δk‖.

Download Full Size | PDF

The second issue, while less critical, is related to the insertion losses of such a demutiplexer. These losses are due to the group index mismatch on the slab/PhC interface as well as to the radiation losses when operating above the light cone. A number of solutions were proposed to reduce the PhC insertion losses from slab waveguides by using adiabatic transitions [5], multilayered gratings [6] or antireflection layers [7,8].

The essential of the deployed efforts were oriented to solve the problem of the wavelength resolution. One of the proposed solutions is to use phase-velocity dispersion variation instead of group-velocity dispersion [9,10]. This approach does not however have experienced a great development. While the beam divergence is lower, the angular dispersion is reduced at the same time and thus mitigates the wavelength resolution.

Other solutions proposed to circumvent the problem consisted to compensate the beam broadening by its refocusing. The beam deflection and focusing can be performed either separately by means of a photonic crystal slab superlens that collects the light deflected in the SP area [11], or simultaneously by combination of the SP effect and diffraction compensation within the same PhC structure [12]. The later approach allowed the experimental demonstration of a four channel demultiplexer with a channel spacing of 8 nm and -6.5 dB cross-talk level obtained using a PhC structure of 4500 µm² [13]. However, the drawback of this approach is that it requires a long beam preconditioning region of 1 mm length which is hardly compatible with miniaturization requirements.

Another solution consists to use a superprism that would exhibit a simultaneous beam collimation. This approach relying on the use of a SP with optimal dispersion/broadening ratio was theoretically investigated for square and triangular lattices [14].

In the present work, we aim to implement this approach for the realization of coarse WDM demultiplexing. To achieve optimal balance between the dispersion and collimating properties, the use of a rhombohedral PhC lattice (Fig. 2(a)) is proposed and experimentally realized.

2. Design of the PhC structure with optimized beam collimation and angular dispersion

The choice of such a structure is motivated by the following considerations. The minimum of the beam divergence occurs when the equi-frequency curves (EFC) are maximally flat for a wide range of the wave vector values. Such flat zones for the EFC are easy to be obtained in square lattice PhC structures [15]. On the other hand the hexagonal lattice structures are known to provide high wavelength dependent angular dispersion. It is reasonably to expect that the rhombohedral lattice structure with a sharp angle of 75° would display an efficient balance between the beam collimation and the angular deflection properties.

Dispersion diagrams and EFC have been calculated using the MIT 3D Photonic band program [16]. Beam broadening p=∂θ _r /∂θ _in and dispersion q=∂θ _r /∂(a/λ) factors have been systematically calculated using the same expressions as in [17]. Here θ_in is the incidence angle on the PhC interface and θ_r is the refraction angle within the PhC area.

 

Fig. 2. (a). Rhombohedral lattice PhC structure (b) Equi-frequency-curves of the first quasi TE modes. Regions of band structure with different properties are marked in: blue for low beam divergence (|p|< 2); red for strong superprism effect (|q|>35); green where blue and red regions overlap; gray for regions that cannot be excited from the input slab waveguide.

Download Full Size | PDF

In the presented context we are searching for the regions in k-space where p≈0 in order to obtain a high beam collimation. We are also looking for the regions with strong enough dispersion where |q|≫1. The structure considered for the modeling is a 220 nm thick Silicon-On-Insulator (SOI) film with air holes. We concentrate our attention on the properties of the first (quasi-TE) band. This allows operating below the light cone and avoiding the coupling with radiation modes. The EFC for the normalized frequencies lying in the interval 0.05<a/λ<0.23 are drawn on the Fig. 2(b). Different zones in blue, red, green, and grey colors correspond to: low beam divergence (|p|<2); strong SP effect (|q|>35); both previous conditions; and non-accessible regions within zero order k|| wave vector, respectively.

As it is evident from the Fig. 2(b), the regions with strong dispersion (red zones) occupy significant areas. Regions simultaneously exhibiting strong dispersion and good collimation properties also occur (green zones), though with greatly reduced areas because of the additionally imposed constraints. These areas are of particular interest since they can potentially present high q/p ratio, which is a factor of merit to obtain high wavelength resolution. The next step is then to find the equi-incident-angle path (EIAP) that crosses a green region and allows obtaining a high q/p ratio in the most wide spectral range. This is important to assure a large extent of the refraction angle variation. The final condition to be satisfied is that the EFC along the equi-incident-angle path should be as flat as possible for a maximum extent of the wave vector values.

The above-described procedure was applied to find the optimal EIAP, the period length and the air-hole diameter for the considered rhombohedral lattice PhC structure. In the wavelength region around 1.55 µm, efficient collimation and SP effects were obtained for a PhC structure with a lattice constant of 300 nm and a hole diameter of 155 nm. The structure is operated under an incident angle θ_in=-50° on the slab/PhC interface. The EIAP for θ_in=-50° is plotted as solid bold line on the Fig. 2(b). It crosses the green region in the area centered near (k_x=-0.45, k_z=0.2).

Figures 3(a), 3(b) shows the logarithmic scale color maps for the p, q factors which characterize the beam divergence and the angular dispersion, respectively. The solid bold line is the optimal EIAP. It is important to mention that for the wavelength near 1.55 µm (a/λ=0.194), the EIAP crosses a blue color zone where p≈0. This corresponds to a near perfect collimation. Figure 3(d) shows that at the same time, |q|≈35, which means a wavelength dependent angular deviation around 0.25 °/nm.

 

Fig. 3. (a). q and (b) p factors for the first quasi TE band. The bold solid curve is the EIAP for an incident angle θ_in=-50°. (c) Refraction angle (dashed line) and 3D-FDTD PhC insertion power. (d) p and q (dashed line) factors along the EIAP at θ_in=-50°.

Download Full Size | PDF

The resulting refraction angle variation is from -60° to 60° for a wavelength span from 1.40 µm to 1.67 µm, as shown in Fig. 3(c). This is one of the largest values reported so far for a wavelength-dependant superprism effect in planar 2D PhCs. The inserted power at the PhC interface has been calculated using 3D Finite Difference Time Domain (FDTD) modeling. The simulated transmission normalized to the input power is better than -1 dB from 1.48 µm to 1.67 µm as shown in Fig. 3(c). The actual device operation was limited to this spectral range.

3. Device fabrication

The fabricated system consists of a rhombohedral lattice PhC of circular air holes etched in a SOI wafer with a 220 nm thick top silicon film separated from the Si substrate by a 1 µm S_iO₂ layer. Refractive slab waveguides were defined using a RAITH 150 electron beam lithography process using negative resist. The PhC structure was separately insolated by means of a lithography process with positive resist. The photoresist patterns were transferred to the 150 nm thick top silica cladding layer using a reactive ion etching system. This layer served as mask to etch the silicon film through a SF₆/O₂ anisotropic etching process.

Figure 4 shows a scanning electron microscope (SEM) view of the experimental device. The PhC area is limited to a 100 µm length with an overall surface of 2800 µm². The 9 µm wide input waveguide provides a reasonably small beam divergence (≈3°) for the light incident on the PhC interface. A tapered transition from a 400 nm wide single mode waveguide is used to insure fundamental mode operation of the input waveguide. This point is especially critical since for a 9 µm width, the waveguide is intrinsically multimode. The light transmitted through the PhC area is collected by 4 output waveguides of different width ranging from 7 µm to 14 µm. Each output waveguide width was adapted to optimize the transmission uniformity across the different channels. In order to reduce the insertion loss, the diameter of the few first rows of holes was gradually reduced [5], as shown on the two upper insets.

 

Fig. 4. SEM view of the fabricated demultiplexing structure. Details of the PhC structure are shown on the insets.

Download Full Size | PDF

4. CWDM demultiplexer modeling and characterization results

The 2D FDTD modeling combined with effective index method was performed to determine the demultiplexing properties of the designed structure. Figure 5(a) shows the modeling results for the different output channels optical power transmission. The cross-talk level given by modeling is around -12/-15 dB.

The experimental characterization is based on a set-up using a tunable semiconductor laser in the spectral range between 1450 nm and 1650 nm. A linearly polarized light beam is coupled into an input waveguide using a polarization maintaining lensed fiber. The output light is collected by a 40× objective and is measured with a small area IR detector.

 

Fig. 5. (a). 2D-FDTD transmission results for the four output channels normalized with respect to the input power. (b) Experimental transmission of the four output channels normalized with respect to the maximum of transmitted power.

Download Full Size | PDF

The experimental results showing the spectral transmission of the output channels are displayed on the Fig. 5(b). They are in good agreement with modeling. Furthermore, the experimental cross-talk level of -16/-20 dB is even lower as compared to the modeling. This result is however not so surprising because of the limited accuracy inherent to the 2D calculations. The minimum of insertion losses is less than 2 dB. These losses were normalized with respect to the losses of a dedicated test structure in which the silicon slab superprism region does not include any etched PhC. The non-uniformity of transmission level between the different channels is below 5 dB. These are one of the best results reported so far for a SP demultiplexer for the insertion losses as well as the cross-talk level.

The further reduction of the cross-talk level might not only depend on the improvement of the technological process but also would require a more refined design for the PhC structure. The implementation of a chirped PhC design would allow improving the handling of the beam divergence for a wider wavelength range.

5. Summary

We have presented the experimental demonstration of a compact PhC wavelength demultiplexer based on a SP effect. The particularity of the developed approach is to target a moderate angular dispersion while keeping a large span of the refraction angle variation with a limited beam divergence. For this we investigated a rhombohedral lattice that presents an efficient balance between the beam collimation and the angular deflection properties.

The experimental results show a four optical channels demultiplexer with a 25 nm channel spacing and -16 dB cross-talk with insertion losses of less than 2 dB. The investigated structure presents a significant potential for the further improvement of performances. The actual PhC area of the demonstrator was limited to 2800 µm². The exploited refraction angle variation is currently using only a half of the available angular span. This opens promising perspectives toward PhC devices for practical applications.