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• Abstract

SECTION 1

## INTRODUCTION

When waveguides are crossed, guided waves suddenly expand due to the lack of confinement in the lateral direction. This results in coupling into the intersecting waveguides in addition to radiation and scattering losses. Ultra-low crosstalk between intersecting waveguides is required in optical integrated circuits in order to minimize the required area to produce multiple optical devices on the same chip. Low crosstalk is also beneficial for improving bit rate in optical communications systems. Recent work has shown that crosstalk between photonic devices can be reduced to a much smaller degree than that between their electronic counterparts [1]. However, the low crosstalk essentially relies on designing innovative photonic structures. More recently, a number of structures have been proposed and investigated to eliminate crosstalk [2], [3], [4], [5], [6], [7]. One method that has attracted great attention is based on cavity coupling that can achieve low crosstalk over a wide spectrum [3], [4], [5], [6], [7]. The key idea is to excite modes orthogonal to each other at the intersection area. Johnson et al. [3] proposed a resonant cavity that supported two orthogonal modes at the intersection area of two line-defect waveguides in a two-dimensional (2-D) square lattice photonic crystal (PC) structure, which was composed of periodic cylindrical rods in air. In the work of Johnson et al. [3], as the quality factor (Q-factor) of the cavity increased by adding more rods next to the defect rod, crosstalk could be reduced. As a result of the Q-factor change, both the output bandwidth spectrum and crosstalk are controlled. Based on a similar structure, Liu et al. [4] reported crosstalk reduction by using two single-mode coupled resonator optical waveguides that had a nonoverlapping photonic band gap (PBG). Their results are very attractive and promising. Furthermore, all-optical transistors can potentially be achieved based on the PC cross-waveguide geometry [8]. However, in both works of Johnson et al. [3] and Liu et al. [4] the structures had an infinite thickness and light was guided in air, or void PBG waveguides, instead of dielectric waveguides. As a result, the structures are only ideal 2-D models that cannot be experimentally realized.

In order to experimentally demonstrate the structure proposed by Johnson et al. [3], Roh et al. [5] used two aluminum metal plates to insure confinement in the out-of-plane direction. One plate was placed on the top, and the other was placed at the bottom of the cylindrical alumina rods in air. Crosstalk reduction as large as −30 dB was experimentally achieved at the resonant frequency. However, this metallic-cladding structure can not be scaled down for telecom wavelengths. To work for the telecom wavelengths, Teo et al. [6] fabricated a structure that was composed of 13-$\mu\hbox{m}$-high silicon rods in air, which are too high to provide effective out-of-plane field confinement. For practical applications, a widely used way is to convert a 2-D structure into a planar structure. Unfortunately, in a planar structure light cannot be confined in void PBG waveguides without out-of-plane confinement on light propagation.

In our previous work [7], we proposed transverse mode planar structures in a square lattice of silicon pillars for telecom wavelengths. We replaced the void PBG waveguides in the structures proposed by Johnson et al. [1] with dielectric strip waveguides to achieve out-of-plane field confinement. Herein, we propose transverse electric (TE) planar structures in a square lattice of air-holes in silicon for telecom wavelengths. The slab waveguide achieves the out-of-plane confinement by total internal reflection. To illustrate the effectiveness of our design, we performed a series of simulations. First, the Q-factor of the cavity was increased by adding more air-holes next to the defect air-hole. Then, the optimized devices were fabricated on silicon-on-insulator (SOI) wafers. The fabrication process details and experimental results are described.

SECTION 2

## INTERSECTION DESIGN

In order to achieve low crosstalk for TE modes, we propose a 2-D square lattice PC structure composed of square air-holes in silicon of a width of $0.8a$ ($a$ is the lattice constant of the PCs). The TE PBG of the structures is between $0.34(a/\lambda)$ and $0.41(a/\lambda)$ as shown in Fig. 1(c). Two intersecting line-defect waveguides are created by replacing a row and a column of air-holes with a slab waveguide, as shown in Fig. 1(a) and (b). The slab waveguides have a width of $0.8a$ as that of the bulk air-holes. The resonant cavity at the center of the intersection is introduced by creating a defect air-hole of a width of $0.6a$ that has a resonant frequency of about $0.4(a/\lambda)$, as shown in Fig. 1(c). Fig. 1(d) shows the mode excited in a square lattice PC along the horizontal axis. Another orthogonal mode can be excited along the vertical axis. The Q-factor of the cavity is increased by increasing the number of air-holes next to the defect. The following names are given to the structures that are shown in Fig. 1 to denote the number of airholes that form the cavity: “7 × 7” and “3 × 3” for the structures that have seven air-holes and three air-holes along the row or column of the intersection area, respectively.

Fig. 1. Two-dimensional photonic crystal structures of square air-holes in silicon for the following cavity sizes: (a) “7 × 7” cavity size and (b) “3 × 3” cavity size. (c) TE band diagram. (d) Field pattern inside the cavity.
SECTION 3

## NUMERICAL RESULTS

The 2-D finite-difference time-domain method is used to analyze all the structures introduced in this paper. Each structure is terminated by a perfectly matched layer in order to reduce the back reflection from the waveguide ends. A broadband TE Gaussian pulse is used as a light source. Two detectors are used to measure the forward (throughput) and crosstalk coupling powers, as shown in Fig. 1(a). The measured power is plotted as a function of frequency. A linear scale is used for the forward power measurement while a log scale is used for the crosstalk measurement.

The cavity size is changed by increasing the number of air-holes that form the cavity. As shown in Fig. 2, we found that the measured throughput values for the “7 × 7,” “3 × 3,” and “1 × 1” structures are 85%, 82%, and 34%, while the crosstalk values at resonance are −40, −22, and −10 dB, respectively. The Q-factor for the “7 × 7,” “3 × 3,” and “1 × 1” structures are 250, 30, and 5, respectively. As the Q-factor increases, both the throughput spectrum and crosstalk decrease.

Fig. 2. Comparison of the (a) throughput and (b) crosstalk for the “7 × 7,” “3 × 3,” and “1 × 1” structures of cubic air-holes in silicon.
SECTION 4

## FABRICATION PROCESS AND EXPERIMENTAL RESULTS

We fabricated the optimized “7 × 7” and “3 × 3” structures on SOI platform using e-beam lithography. The scanning electron microscope (SEM) image of the fabricated “7 × 7” structures is shown in Fig. 3. According to three-dimensional simulations, we found that in order to have a band gap centered at 1480 nm, the height of the air-hole should be 250 nm, and the lattice constant should be 560 nm. To fabricate the optimized devices, the SOI wafer was spun coated with a negative resist (XR-1541). Then, the e-beam was used to transfer the pattern on the negative resist. Next, the unexposed areas of the resist were removed by developing the wafer in AZ® 300 MIF (metal-ion-free) developer for 4 minutes. The exposed resist acted as a mask during the etching process. Chlorine plasma, which consists of $\hbox{Cl}_{2}$ and $\hbox{BCl}_{3}$, was used to etch the unprotected silicon. The mask was not removed after etching silicon because it acted as silicon oxide. Finally, the buried oxide under the air-holes was etched using a buffered oxide etchant solution for 10 minutes. In order to be able to test the PC cavity a testing platform was fabricated at the same time. It is made of a holder to carry the PC device, a J-coupler [9] to couple the light effectively from an optical fiber into the PC and three waveguides to couple the light out of the device.

Fig. 3. SEM image of the fabricated “7 × 7” PC structure. (a) PC structure and the testing platform, which consists of a J-coupler and three waveguides. (b) Close-up image of the “7 × 7” PC cavity.

We tested the fabricated “7 × 7” and “3 × 3” TE devices. The experimental measurement set up was as follows: the light from a tunable laser with spectral range from 1260 nm to 1520 nm propagated through a polarization controller to allow TE-like modes to couple into a 10- $\mu\hbox{m}$ silicon waveguide. Coupling into and out of the silicon waveguides was achieved using tapered micro-lens fibers with a spot diameter of 2.5 ± 0.5 $\mu$m. A J-coupler was fabricated and used to couple light from the 10-$\mu\hbox{m}$ silicon waveguide into the 448-nm PC line-defect waveguide. Translational stages were used to align the input and output fibers to the device under testing. An infrared camera mounted on a microscope was used to capture the vertically scattered light from the waveguides. The output power was measured using an infrared detector and recorded using a power meter. A microscopic image of a cavity at resonance is shown in Fig. 4.

Fig. 4. Microscopic image of the cavity at resonance.

A comparison between the experimental and simulation results of the “7 × 7” and “3 × 3” structures are shown in Fig. 5. The Fabry Perot oscillations are formed by the reflection from the end-facets of the waveguides and the cavity. In our simulations, the light source, the output detector, and the crosstalk detector are all placed inside the PC line-defect waveguides. In our experiment, the light source and detector are out of the SOI chip. To be able to compare the simulation with the experiment, both results should be normalized to one. Also, the resonant frequency in both results should match. As expected from simulation and theory, as the size of the cavity increases, the Q-factor and the crosstalk decreases. The Q-factor and crosstalk value for the fabricated “7 × 7” structure [see Fig. 5(a) and (c)] is 168 and −20 dB and that of the “3 × 3” structure [see Fig. 5(b) and (c)] is 54 and −10 dB. The measured Q-factors and crosstalk values are slightly different from that resulted from the numerical simulations. This is due to fabrication errors. From the plots in Fig. 5, it is clear that the resonance frequency is shifted for the experimental results from that predicted by the simulation results. Based on the 2-D simulation results, to get a shift in the resonance frequency from 1480 nm to 1345 nm requires that the widths of the fabricated square air-holes and defect be wider than that used in the simulation by about 5% (i.e., lattice constant is still the same (i.e., $a = 560\ \hbox{nm}$), square air-holes of a width of 0.842a, and a defect Air-hole of a width of $0.642a$). However, based on the measured values using the SEM for the tested “7 × 7” device [see Fig. 5(d)], the measured widths of the bulk square air-holes and cavity defect are wider than that predicted by simulation by about 5% (i.e., lattice constant is still the same (i.e., $a = 560\ \hbox{nm}$), square air-holes of a width of $0.884a$, and a defect air-hole of a width of $0.688a$). The difference between the simulation and the measured values is because we did a 2-D simulation which does not take into consideration the out-of-plane effect. The measured spectrum of the throughput for the “7 × 7” cavity matches very well the simulation data, taking into account the shift of the resonance frequency, as shown in Fig. 5(a). The measured spectrum of the throughput for the “3 × 3” cavity has the bandpass in the same range of frequencies but exhibited a narrower spectrum, a higher Q [as shown in Fig. 5(b)]. This is very well expected because of the sensitivity of the devices due to any fabrication tolerance. However, the fabrication error is not the same for both the defect air-hole and the bulk air-holes. As a result of that, the Q-factor of the fabricated “3 × 3” is higher than that of simulation which is evident in its narrower spectrum. Practically speaking the throughputs of the devices were quite close to the simulation predictions. The crosstalk experimental curves show consistently that the “7 × 7” cavity has lower crosstalk values than that of the “3 × 3” as predicted by the simulation data. The crosstalk simulation results show stronger wavelength dependence than the experimental results, Fig. 5(c), which is might be due in the major part to the low sensitivity and narrow dynamic range of the photodetector used in the experiment.

Fig. 5. Comparison of experimental results with simulation results of (a) throughput “7 × 7” structure and (b) throughput “3 × 3” structure. The inset shows the unfiltered transmission measurements. (c) Crosstalk “7 × 7” and “3 × 3” structures. (d) SEM image of the tested “7 × 7” structure that shows the measured widths of the bulk crystals and defect.
SECTION 5

## CONCLUSION

We designed, fabricated, and experimentally demonstrated two intersecting waveguides formed in a square lattice PC structure. The proposed structures provide index guiding and confinement in the vertical direction. We have fabricated several different variations of the devices where the waveguides are separated by a different number of air-holes to improve the coupling efficiency and reduce the crosstalk. We experimentally showed that the crosstalk reduction of the “7 × 7” and “3 × 3” air-hole structures is about −20 dB and −10 dB, respectively. The experimental results exhibited similar performance to those predicted by the numerical simulations.

## Footnotes

First published Online Corresponding author: Z. Lu (e-mail: zxleen@rit.edu).

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