Stress modeling helps designers reduce PDL in AWGs
The dramatic downturn of the fiberoptic market, more than ever before, puts the onus on optical- component manufacturers to reduce component pricing. Components based on planar waveguide technology are manufactured using processes and equipment very similar to those used in the integrated circuit (IC) industry. Because these processes are suitable for high-volume manufacturing, planar-waveguide technology can dramatically cut the manufacturing costs of optical components.
However, one of the bottlenecks for the widespread application of planar-waveguide circuits is polarization-dependent loss (PDL). An important source of PDL is stress in the waveguide layers in the circuit, built up during manufacturing or device operation. This stress causes an anisotropic change of the refractive index of the waveguide material; in other words, the refractive index depends on the polarization of the light coupled into the planar waveguide. This anisotropy is likely to cause the planar-waveguide circuit to exhibit PDL. Stress-induced PDL significantly reduces yield for many different planar-waveguide technologies.
Consider, for example, the well-known arrayed waveguide grating (AWG), often used as a wavelength multiplexer/demultiplexer at high channel counts. The stress built up in the waveguide layers during the manufacturing process causes the propagation constant in the waveguide to be dependent on the polarization. Since the demultiplexing principle of this component is based on the wavelength dependence of the propagation constant; by the same principle, a polarization-dependent propagation constant results in a shift of the spectral response with input polarization (see Fig. 1). Since these components must satisfy strict PDL requirements within the entire "clear window" centered at the ITU frequency, a minor polarization-dependent shift can kill the PDL specification.1 If special precautions aren't taken with respect to the stress effect during design and manufacturing, PDL of many dBs can result.
To minimize PDL, design engineers must have a good quantitative understanding of stress distributions in planar waveguides and their affects on the optical properties of components. A dedicated stress-simulation module allows users to perform such simulations within a software platform.
Although the stresses built up in the planar waveguide depend on the exact technology used, the impact on optical properties can be generalized, as is often the case with the photoelastic properties of the material. The photoelastic effect is described analytically by a fourth-rank strain-optic tensor, Pijkρ, which couples the strain tensor, εkρ, to the indicatrix (1/n2)ij, with n index of refraction, as:
This formula states that the change in the indicatrix is directly proportional to the strain. Exploiting the symmetry of both the indicatrix and strain tensor, the formula can also be written as:
if the following subscript contraction is used:
Initially, we assume that isotropic materials, like fused silica, are used. Restricted in this way, most of the 6 × 6 array of elements of the strain-optic tensor are related to each other or zero:
Where * = (•–º)/2. So, in fact, only two independent elements remain.
Although waveguide stress depends on fabrication technology, two distinct categories can be identified: stress built up during the actual manufacturing of the component, and stress induced when operating the component.
First, we can calculate the stress buildup during cooling to room temperature at the end of the manufacturing process, as the result of different expansion coefficients between waveguide layers and substrate. Second, we can calculate the stress induced when operating a thermally activated device (such as a variable optical attenuator or optical switch to exploit the thermo-optic effect). In the latter, the material below the heater electrode expands or shrinks depending on the voltage applied to the electrode. The result is additional stress buildup underneath the electrode causing the PDL to depend on the operating point of the component.
In both cases, stress solvers were developed using relatively standard finite-element techniques. For thermally induced stress, the required thermal input distribution is calculated using a multigrid finite difference solver that we developed. The polarization-dependent refractive-index perturbation can be added as an overlay to the background refractive-index distribution. Subsequently, operators can perform many optical simulations using various optical simulation modules.
Given that the current stress-modeling solvers assume the structure is invariant in the propagation direction of the waveguide, typically an eigenmode calculation for the two polarizations would be performed. A designer can use the scripting facilities within the software platform to automate these steps.
A typical silica-on-silicon substrate waveguide structure has been previously analyzed with core and upper cladding layers deposited using the flame-hydrolysis method (see Fig. 2).2 Differences in the thermal expansion coefficient of silica-based glass and the silicon substrate cause large stress in the waveguide layers because of the high temperature at which the glass layers are sintered. When cooling to room temperature, the thick silicon substrate with its higher coefficient of expansion compresses the glass layer. The consequence is a nonzero transverse-electric/transverse-magnetic (TE/TM) spectral shift for any interferometric component (AWG or Mach-Zehnder-based mux/demux) fabricated using this technology. However, adjusting the doping levels of the cladding to increase its thermal expansion coefficient can minimize the stresses involved, arriving at net-zero birefringence.
The simulated net birefringence is a function of the cladding thermal-expansion coefficient, tce, which confirms that net-zero birefringence can be achieved with a top-cladding expansion coefficient of roughly 3.7 × 10–6 1/K (see Fig. 3). This is only slightly higher than the optimum birefringence of 3.5 × 10–6 1/K predicted before. Note that in the previous work the average refractive-index change is taken into account only in the core region, whereas the more rigorous calculations presented here take into account the full refractive-index perturbation.
Martin Amersfoort is vice president of product management at C2V, PO Box 318, 7500 AH, Enschede, The Netherlands. He can be reached at info@C2V.nl.
- M. Volanthan et al., white paper: http://www.alcatel.com/telecom/optronics/products/whitepaper/4-pbp/awg.pdf.
- A. Kilian et al., J. Lightwave Tech. 18, 193 (2000).