By the combination of multimode interference and photonic crystals, a broad-band 1.3/1.55-µm demultiplexer can be realized with very compact structure. Simulation with the finite-difference time domain method verifies its excellent performance, greater than 20dB isolation ratio and less than 3 dB insertion loss over 100nm bandwidth at both wavelength bands.
© 2006 Optical Society of America
Integrated optical multiplexer/demultiplexers (MDMUXs) are often required for access networking applications for their low cost, compactness, and potential integration with the photonic and electronic components. For realizing the MDMUXs, multimode interference (MMI) based devices [1–3] are more attractive than the conventional directional couplers  and other structures [5, 6] because of having larger tolerance on fabrication fluctuation. To realize MDMUXs with MMI couplers, the device length is usually chosen to be the common multiple of the beat lengths for multiple wavelengths. Since the MMI effect is weakly wavelength-dependent, it usually requires a long device to meet the common multiple for far-apart wavelength bands, e.g., the 1.3- and 1.55-µm bands. Grating-assisted MMI waveguides were proposed to shorten the device [7, 8]. However, this type of device has narrow bandwidth due to the grating response. To improve the bandwidth, a novel design of 1.3/1.55-µm demultiplexers based on restricted type of MMI with embedded photonic crystals (PhCs) was proposed here. The same principle can be applied to general type of MMI couplers.
The broadband reflectivity and/or transmission provided by bandgap of PhCs can be utilized for realizing the multiplexing and demultiplexing functions. By introducing PhCs in a MMI demultiplexer, the total device length can be reduced. The characteristics of the device were verified by the simulation using the finite-difference time domain (FDTD) method. Less than 2 dB insertion loss and greater than 20 dB isolation ratio can be obtained. With the criteria of >20dB isolation ratio and <3 dB insertion loss, the demultiplexer can work over 100 nm of bandwidth at both 1.3 µm and 1.55 µm bands.
2. Design and analysis
In contrast with the grating assisted MMI [7, 8], PhCs of periodic air holes are introduced to replace the 1D grating in constructing the demultiplexer. The schematic of a PhCs-assisted MMI demultiplexer is depicted in Fig. 1. The device consists of four access ports and a MMI waveguide with PhCs. The width of the input and output access waveguides is set to 1 µm. And the slab of PhCs are formed on silicon substrate of dielectric constant (εr=11.6). The effective-index approximation was used to convert the 3D structure to 2D one for simplifying the analysis. The effective index is obtained as neff=2.88 for the slab waveguide. This method was justified to give similar results as full 3D calculations  while the slab height (t) is about 0.6 times of the lattice constants (a). Consequently, the device dimension is first optimized by using the modal expansion method; and the width of the MMI section is set to We=4µm. In our design, the device length Ld is chosen to pass the 1.3-µm light pass through the MMI, and the effective length Leff is designed for reflecting the 1.55-µm light to the opposite input end.
Because the operation of the MMI device is based on the self-imaging effect, the field evolution along the MMI section is given by a superposition of all guided modes :
where cm and ϕm denote the excitation coefficient and modal field of the m-th mode, respectively. Lπ is the beat length that is wavelength-dependent.
Nevertheless, the light of which the frequency falls inside the photonic bandgap is reflected by the PhCs. The transmission and reflection coefficients for the PhCs can be denoted as t(λ) and r(λ), respectively, assuming the same coefficients for all the guided modes. So that the forward propagating field Ψt(x,Ld) and backward propagating field Ψr(x,0) can be written as :
The second equality of Eq. (2) indicates the self imaging effect for the 1.3-µm transmitted field Ψt(x, Ld) when the coupler length is equal to the beat length of the 1.3-µm light, i.e., Ld=L π(1.3). Similarly, Eq. (3) reveals the self imaging effect for the 1.55-µm reflected field Ψr(x, 0) when Leff=L π(1.55)/2. Lπ(1.3) and L π(1.55) are the beat lengths for the 1.3-µm and 1.55-µm light, respectively. Eqs. (2) and (3) indicate the demultiplexing function for the 1.3- and 1.55-µm light can be achieved. The same design principle can be used for realizing devices for other wavelength bands.
3. Simulation and results
Air holes of radius r/a=0.26 were arranged in a hexagonal lattice. Such a PhC structure was found to have a bandgap in the spectral range 0.2412≤a/λ≤0.2827 for TM polarization (electric field in plane). The wavelength of 1.55-µm and 1.3-µm corresponds to a/λ=0.27 and 0.3219, respectively. Another section of PhCs of radius r/a=0.43 is introduced at Port 2 to enhance the isolation ratio. Figures 2(a) and 2(b) demonstrates the field evolution calculated by the FDTD approach for both the 1.3- and 1.55-µm wavelengths. The demultiplexing function can be clearly seen. The total length of the device is reduced to Ld=45 µm and Leff=18 µm.
The key parameters of a wavelength demultiplexer are isolation ratio and insertion loss, which are defined as 10log(Po,r/Po,w) and 10log(Po,r/Pi), respectively. Pi denotes the input power, while Po,r and Po,w denote the fractional powers in the right and wrong output ports. Figure 3 illustrates the simulated isolation ratio and insertion loss of the MMI demultiplexer as a function of the wavelength. The results indicate an insertion loss of 1.45 and 0.57 dB as well as an isolation ratio of 22.4 and 23.9 dB at the 1.3- and 1.55-µm wavelength, respectively, for the TM mode. For both wavelength bands, <2dB insertion loss and >20dB isolation ratio can be obtained over 100 nm of wavelength range. The insertion loss for 1.3-µm wavelength is relatively high due to the reflection at the input and output interfaces of the photonic crystals. The reflection can be reduced by modifying the photonic crystal layers at the interfaces for smooth transitions .
Figure 3(a) also shows >20 dB isolation ratio over 100 nm of bandwidth for TE mode at the 1.3-µm band. Though the insertion loss is larger for TE mode, it can still be kept below 3dB over 100 nm of wavelength range. The photonic bandgap of a PhCs is strongly polarization dependent. At the 1.55-µm band, both the insertion loss and isolation are not satisfactory for TE polarization since the wavelength does not fall in the photonic bandgap. Therefore, the demultiplexing function is polarization independent for 1.3-µm band, but only work for the TM mode in the 1.55-µm band. This type of characteristics can still be feasible for practical applications in passive optical networks (PONs). For example, the 1.55-µm laser of a transmitter in the center office can be integrated with the demultiplexer. Since the laser output has stable polarization that can be matched with the demultiplexer, polarization independency is not necessary for the 1.55-µm band. The device can also be designed for applications in the user end where the 1.3-µm laser is used for transmitting the upstream signals. In this case, the device dimension and the photonic crystals can be designed for passing the 1.55-µm light through but reflecting the 1.3-µm light by the PhCs.
By the FDTD numerical simulation, a broadband of PhCs-assisted MMI demultiplexer is designed to provide <3dB insertion loss and >20dB isolation ratio over 100nm of wavelength range at both 1.3- and 1.55-µm wavelength windows. By using the effect of photonic bandgap, the device can be very compact, 45 µm long and 4 µm wide for the design example, compared to the traditional MMI demultiplexer. We believe that such device can be more compactness if the access waveguide is narrow enough for supporting a single mode. Polarization independency can be obtained for one of the bands and can satisfy the requirement of applications in PONs.
This work was supported in part by Ministry of Economic Affairs, R.O.C. under contract No. 91-EC-17-A-07-S1-0011, and the National Science Council NSC94-2213-E011-016.
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