Magnus Olsson
Multiphysics modeling, the modeling of coupled-field phenomena, has become a standard research and design tool in industry and academia. Multiphysics effects are well known in optics and photonics work. Electro-optical effects, for example, have long been used in sensors and modulators. Stress-optical and thermo-optical effects, although sometimes used in sensors, are frequently unwanted side effects to be controlled.
Lasers, for their part, are multiphysics devices. During the laser design process, designers must account for electromagnetic, quantum, and thermal effects. Yet, until recently, efficient modeling and virtual prototyping of such multiphysics effects eluded designers. Now, advances in computational hardware and software algorithms have made multiphysics analyses of such effects a reality.
COMSOL has seen a rapid, growing interest in applying multiphysics software to optics and photonics design, and we are aware of several hundred projects with connections to optics, photonics, or lasers—fundamental research, low-volume production of highly sophisticated devices, and even optimizing the engineering design process for standard optical components. Many applications coupled classical engineering fields such as light propagation, electrostatics, heat transfer, and structural mechanics. The modeling goals just as often sought to leverage multiphysics effects as to reduce them. Engineers and researchers use multiphysics modeling in many situations to streamline and improve their optics and photonics design work.
The work of Winnie N. Ye and colleagues at Carleton University (Ottawa, Canada) offers a typical example of multiphysics modeling for stress-optical effects.1 The group used multiphysics software to eliminate polarization-dependent spectral shifts in silicon-on-insulator arrayed-waveguide grating demultiplexers. They used a prestressed silicon dioxide (SiO2) cladding to control the stress in the waveguide core and prevent the spectral shift, as experiments confirmed. The team then conducted structural analysis of the model using two methods: a generalized plain strain model that was more accurate and a normalized plain strain model that was accurate enough but the computational cost was significantly less.
Another example of multiphysics software is the modeling of electro-optical effects. Researchers at the Institute for Photonics and Nanotechnology (Rome, Italy) have used multiphysics modeling in the design of an electro-optic Bragg amplitude modulator.2 Their design was based on using the electro-optical effect in lithium niobate to tune the spectral response of a Bragg grating to modulate the amplitude of a transmitted signal. The device had the advantage of having shorter electrodes than the standard Mach-Zehnder modulator and hence a lower radio-frequency capacitance and a wider signal band. Their main analysis involved multiphysics modeling of the electro-optical effect but they also modeled the diffusion process used in the manufacturing of the device.
The thermo-optical effect is another case investigated using multiphysics software, in silicon-on-insulator waveguide arrays, by Francesca Magno and colleagues at Politecnico di Bari, Italy.3 They focused on finding the effective thermo-optic coefficient for an entire waveguide structure, accounting for the non-uniform temperature and optical field distributions. Their work relates to the design of optical switches and resonators.
Thermal management
A very common multiphysics coupling is that between current conduction and thermal management in high-power devices like lasers and light-emitting diodes (LEDs). This is perhaps the most fundamental industrial design optimization problem and, regardless of what industry segment we are looking at, we find people involved in multiphysics modeling and simulation. A good example of this is Professor Te-yuan Chung at the National Central University (Jhongli City, Taiwan), who uses multiphysics simulations to improve the electric and thermal management of high-brightness LEDs.4 Excessive heating due to current crowding limits the efficiency and expected lifetime of these LEDs. For a typical high-volume/low-cost application like this, even minor design improvements have short pay-back times.
A rather typical engineering LED design was investigated at Osram Opto Semiconductors (Regensburg, Germany).5 Elmar Baur and associates modeled the current-density distribution across an LED chip using a two-domain approach for the n- and p-layers with an effective current-voltage characteristic for the p-n junction. Output from the model is the current-voltage-characteristic, the current distribution within the active layer, and the voltage drop on the contact grid. They report good agreement between simulated and experimental results and have used the model to optimize the current distribution in the active region of an LED chip. The modeling results in images of two alternative LED chip designs.
Mikhail Kisin at the Stony Brook University, Stony Brook, NY, performs work on quantum-well and cascade semiconductor lasers using an eight-band Schrö dinger and Poisson equation system.6 Kisin‘s model allows him to analyze heavily strained gallium antimonide based quantum-well mid-infrared lasers as well as tunable interband and quantum-cascade lasers. Researchers like Kisin typically gain from multiphysics software the ability to include their own, nonstandard submodels within the multiphysics framework. Here, it is the quantum mechanics that Kisin typed into the multiphysics interface as his own set of user-defined equations. Frequently, researchers do this in combination or coupled with some of the predefined standard physics formulations found in the software, typically electrostatics or diffusion. Instead of creating their simulation entirely from scratch in C or FORTRAN, they gain greatly from the tools that are available within the program for analyzing multiphysics behavior: coupling equations and solving them simultaneously, a suite of solvers, and the ability to easily change the underlying mathematical equations. They also save time, as other key elements like geometry definition, meshing, and post-processing tools are available directly without additional low-level coding.
These are just some representative samples of how scientists and engineers use multiphysics modeling. Combined with the fact that computational methods and hardware are improving at a breakneck pace with the industry‘s trend toward smaller, faster, and more densely packed devices, it is likely that multiphysics modeling will continue to be one of the fastest growing technologies in photonics design.
REFERENCES
- W. N. Ye et al., J. of Lightwave Tech. 23, 3 (March 2005).
- A. Secchi et al., Proc. COMSOL Users Conf. 2006, Milan, Italy.
- F. Magno et al., Proc. COMSOL Users Conf. 2006, Milan, Italy.
- 4. T.-Y. Chung, Proc. COMSOL Users Conf. 2006, Taipei, Taiwan.
- E. Baur et al., Proc. COMSOL Users Conf. 2007, Grenoble, France.
- M. V. Kisin, Proc. COMSOL Users Conf. 2007, Boston, USA.
MAGNUS OLSSON is product manager of Electromagnetic Simulation, COMSOL, Tegné rgatan 23, SE-111 40 Stockholm, Sweden; e-mail: [email protected]; www.comsol.com.