1. Introduction

In an all-optical planar light wave circuits (PLCs), it is necessary to be able to optically tune the high power laser beam to the devices. Conventional planar dielectric optical waveguides cannot be used for this purpose, since they suffer from absorption and nonlinear effects. The hollow core waveguides have become progressively important in the role to transfer the signals to the device to be tuned optically. Numerous types of the hollow waveguides have been developed such as anti-resonant reflecting optical waveguides (ARROWs) [1], teflon light pipes [2], and semiconductor hollow waveguide formed by omni-directional reflector [3–6]. For the dielectric waveguides on silicon-on-insulator, the optical loss of 90° dent waveguides has been reported [7–12]. The bending radius can be as small as 2 µm. However, the optical properties of the 90o bent hollow waveguides mentioned above have not yet been investigated. In this paper, we proposed a novel hollow waveguides composed of DBR structure. The DBR consists of ten pairs of alternatively stacked silicon nitride and silicon oxide. The maximum reflectance of DBR is designed at the wavelength of 1550nm. The optical loss of the 90° bent hollow waveguide is studied.

2. Simulation

Figure 1(a) shows the cross-sectional view of the air-core hollow waveguide composed of DBR structure. The guiding material of the hollow waveguide is air. In the DBR structure, ten multilayer pairs of Si₃N₄/SiO₂ were coated on the Si substrate. The refractive indices of Si₃N₄ and SiO₂ were 2.00 and 1.48, respectively. The thickness of the Si₃N₄ and SiO₂ are 194nm and 262nm, respectively, to be quarter wavelength of 1550nm. Figure 1(b) shows the photonic band structure of Si₃N₄/SiO₂ multilayer stacks. Since the index difference between Si₃N₄ and SiO₂ is low, no complete bandgap is can be observed. As the propagation constant K_y of the light which can be guided in a waveguide is low, the complete bandgap is not necessary. Only partial bandgap of the DBR is required to achieve the guiding in the hollow waveguide. From our experience, the operating wavelength is 1550nm (λ) and the period of the multilayer (a) is 456nm, the normalized operating frequency (a/λ) is chosen to be 0.29.

 

Fig. 1. (a) Diagram of DBR structure (n₁ and n₂ are the index of refraction for Si₃N₄ and SiO₂, respectively.) (b) Projected band structure of a multilayer film. The black lines indicate the light line. The partial band gap for operating frequency is indicated by dotted line.

Download Full Size | PDF

In this work, two types of 90o bent hollow waveguide (arc-type and cut-type) are studied as shown in Figs. 2. The radius of the arc and the cut length of the 45°-cut is denoted as R and X, respectively. The width of the air-core waveguide is 12µm. Ten pairs of multilayer are attached on the air-core. (Only four pairs of multilayer are shown in Fig. 2.) Two-dimensional (2-D) finite-difference time-domain (FDTD) method is used to calculate the bending loss of these structures. In Figs. 3(a) and 3(b), solid lines show the simulation results of the single arc- and cut-type bent waveguides for different radii and cut lengths, respectively. For the arc-type waveguides, the bending loss can be reduced with larger bending radii. On the other hand, for the cut-type waveguides, the bending loss can be reduced with larger cut length. Within these results, the minimum loss is for arc- and cut-type is 0.013 and 0.03dB, respectively for the TE mode. In the most cases shown in Fig. 3, the loss for the TM mode is larger than that for the TE mode. This is attributed to the fact that the maximum K_y in Fig. 1(b) is 0.248 for TE which is larger than that of the TM mode, 0.201.

 

Fig. 2. Schematic structures of bent waveguide of (a) arc-type bend and (b) cut-type bend.

Download Full Size | PDF

 

Fig. 3. Simulated(solid lines) and experimented(dot lines) bending loss for different (a) radii of arc-type bending waveguide and (b) cut lengths of cut-type bending waveguide.

Download Full Size | PDF

3. Sample preparation

The air-core hollow waveguides in our studies are embedded by two multilayer stacks. The multilayer stacks are formed by ten pairs of Si₃N₄/SiO₂. The photoresist SU8 is used as the sacrificial material. To fabricate the air-core hollow waveguides, the bottom multilayer stack was first deposited by plasma enhanced chemical vapor deposition (PECVD) on silicon wafer. The SU8 photoresist is coated and patterned on the bottom multilayer stacks by conventional photolithography process. The thickness and the width of SU8 photoresist is 5 and 12µm, respectively. Straight waveguides and bent waveguides are formed in the SU8 photoresist. Each bent waveguide consists of 2 arc-type bends or 2 cut-type bends as illustrated in Fig. 3 forming an “S” waveguide. After the photolithography process, the top multilayer structure was deposited on the sample by PECVD. Afterwards, the sample is covered by a 4-µm-thick Si₃N₄ layer to strengthen the multilayer structure. The sample edges are cleaved so that the sacrificial material of the waveguide ends is bare. The sacrificial material is removed by SU8 remover producing the air-core hollow waveguide. Figure 4(a) shows the cross-sectional view of hollow waveguide.

 

Fig. 4. (a). SEM picture of the cross-sectional of device. (b) Far-field image of output side of device.

Download Full Size | PDF

4. Results and discussion

To characterize the transmission of our air-core hollow bent waveguides, a laser at the wavelength of 1550nm is directly coupled into the hollow waveguide. The polarization of the incident light is controlled by the polarization controller (Agilent 8169A). Figure 4(b) shows the output field captured by an infrared charge coupled device (IR CCD). The light is clearly confined inside the air core. The propagation loss of hollow waveguides is obtained using cut-back method to be 1.2 and 1.1 dB/mm for the TE and TM modes, respectively. The propagation loss is higher than that of SHOW-ODR reported by our group [3–6]. This is attributed to the fact that the index difference between Si₃N₄ and SiO₂ is lower than that between Si and SiO₂ which are used in SHOW-ODR leading to lower reflection from DBR for higher order modes.

In Figs. 3(a) and 3(b), dot lines show the experimental bending loss of single arc- and cut-type bend for different bending radii and cut lengths, respectively. In the arc-type bent waveguide, the bending loss is higher for the TM mode than the TE mode. The bending loss is reduced as the arc radius increases. The measurement results are consistent with the simulation results. No obvious loss reduction is observed as the arc radius is larger than 6µm. This may be attributed to the fact that a larger radius could induce an additional propagation loss of waveguide bending because of the propagation distance increase with the radius. The minimum bending loss of the arc-type bent waveguide is 3.5dB.

The minimum bending loss of single cut-type bending waveguide was 0.8dB. As the cut-length increases from 5 to 13 micrometers, the bending loss decreases. This result is also consistent with the simulation result. The incident angle of guided light of the straight waveguide to the DBR at cut-type bending corner is 45°. However, for the arc-type hollow waveguide, the incident angle includes from 0° to 90°. Therefore, the minimum bending loss of arc-type hollow waveguide is larger than that of cut-type hollow waveguide. According to the simulation result, the DBR structure exhibits a partial band gap when the propagation constant K_y is below 0.248 for TE mode and 0.201 for TM mode. The corresponding incident angle for the TM mode (43.1°) is lower than that for the TE mode (57.5°). Therefore, the bending loss is higher for the TM mode than that of the TE mode.

In Fig. 4(a), we can observe that the thin film thickness on the top of the hollow waveguide is thicker than that of the side wall of the hollow waveguide. This phenomenon implies that the reflectivity of the side wall of the hollow waveguide is different from the simulation. As the incident angle is 45°, the reflectivity of the thin films on the top of the hollow waveguide is 98% and 56% for the TE and TM modes, respectively. If the thin film thickness of the side wall of the hollow waveguide is 90% thinner than that on the top of the hollow waveguide, the corresponding 45° reflectivity of the side wall of the hollow waveguide is reduced to be 78% and 48% for the TE and TM modes, respectively. This non-uniform thin film deposition between the top and the side wall of the waveguide induces the discrepancy of the bending loss between the simulation and experimental results. By enlarging the refraction index contrast between the two thin films (for example, using Si and SiO₂ thin films), the forbidden band gap can be wider leading to reduce the reflectivity variation due to non-uniform thin film deposition between the top and the side wall of the waveguide.

5. Conclusion

In this work, we have studied the optical properties of the hollow waveguide formed by DBR. Two different bending types with different bending radius and cut length have been demonstrated experimentally and numerically. For cut-type bent waveguide, the minimum bending loss is 1.0dB and 0.8dB for the TE and the TM modes, respectively. For the arc-type bent waveguide, the minimum bending loss is 3.9dB and 6.4dB for the TE and the TM modes, respectively. The difference of the bending loss between the simulation and the experimental results is attributed to the non-uniform thin film deposition between the top and the side wall of the hollow waveguide leading to different thin film reflectivity. This discrepancy can be improved by using the thin film materials with larger refraction index contrast. The bent hollow waveguides could provide the design variety for the potential applications to the optical sensing [1, 13], the study of slow-light [14], and the micro optical communication devices [3, 15, 16]. The cores of the hollow waveguides presented in this work can be filled with liquid or gaseous materials inside and let the wave propagate in those. The photoluminescence of liquid or gas can be done by launching a pumped light source into the waveguide. The excited light can be confined in the hollow waveguide and detected from the end of the waveguide. This method may enable researchers to collect more photoluminescence signal than those of conventional methods even using high numerical aperture objective. The hollow waveguides might open the new applications of interaction between propagating waves and materials, filled inside the hollow waveguides.