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A5.6: Modeling of Micro-Disk Resonator Arrays

Subproject Leader: Kurt Busch

Contributing Scientists:

Present: Richard Diehl, Jens Niegemann

 

Three-dimensional simulation of a pulse that travels in an optical fiber and couples to a real-world goblet-resonator.
Three-dimensional simulation of a pulse that travels in an optical fiber and couples to a real-world goblet-resonator.
Schematic representation of a slotted ring-resonator based 4-port device.
Schematic representation of a slotted ring-resonator based 4-port device.
Spectral response of a slotted ring-resonator based 4-port device.
Spectral response of a slotted ring-resonator based 4-port device.

Integrated Optics: Basic Functional Elements

Waveguides and resonators comprise the basic building blocks for the realization of an integrated optics. Loosely speaking, waveguides transport light between elements and resonators are used to “store” the light by means of constructive interference. This means that in a resonator light bounces back and forth between mirrors or, for our purposes equivalently, light runs around in loops. Efficient “trapping” can only occur for selected frequencies – the resonance frequencies that very sensitively depend on the resonator’s geometrical and material properties. Upon judiciously coupling such resonators with one or several waveguides one can thus realize a number of more complex functional elements.

For instance, one can functionalize the resonator’s surface in order to allow for the deposition of specific molecules or proteins. This added material will alter the resonator’s properties, for instance its resonance frequency. As frequencies – more precisely frequency shifts – can be detected with extremely high sensitivity this suggests that efficient and highly parallel sensing schemes may be constructed based on entire arrays of coupled waveguide-resonator systems.

Modeling Micro-Disk Resonator Arrays

The fabrication and experimental characterization of such resonator-based optical biosensors are pursued by Heinz Kalt’s group in subproject A5.4: Optical Biosensors on the Basis is Micro-Disk Resonators. For instance, they have introduced a novel class of polymer-based goblet-shaped resonators [1] with ultra-smooth surfaces that lends itself for the integration with micro-fluidic systems. For the equally challenging modeling of these structures, we pursue a dual strategy that will be able to deliver designs with optimized performance such as regarding sensitivity and/or frequency range of operation etc.

First, we have adapted our Discontinuous Galerkin Time-Domain (DGTD) approach to such systems [2]. In essence, the DGTD approach allows for a numerically exact analysis and delivers quantities such as coupling efficiencies between waveguide and resonator for a given setup. In view of the enormous size of typical resonators – in Ref. [1], the resonator has a diameter of 40 mm at an operation wavelength of 1.3 mm – we have improved the DGTD’s time-stepping capabilities [3]. Further improvements will result from multi-step approaches (in collaboration with M. Hochbruck, Dept. of Mathematics, KIT) and the use of GPUs.

In a second line of research, we develop approximate coupled-mode theoretical (CMT) approaches that sacrifice some degree of exactness of brute-force numerical approaches for a much more efficient treatment of coupled resonator-waveguide systems. Clearly, the CMT models have to be gauged against the (numerically exact) results of DGTD [3]. Then, the CMT models allow for the efficient optimization of experimentally relevant setups and the analysis of more complex resonator-waveguide systems and arrays thereof.

References

[1] T. Grossmann, M. Hauser, T. Beck, C. Gohn-Kreutz, M. Karl, H. Kalt, C. Vannahme, and T. Mappes, High-Q conical polymeric microcavities, Appl. Phys. Lett. 96, 013303 (2010)
[2] J. Niegemann, W. Pernice, and K. Busch, Simulation of Optical Resonators using DGTD and FDTD, J. Opt. A 11, 114015 (2009)
[3] R. Diehl, K. Busch, and J. Niegemann, Comparison of low-storage Runge-Kutta schemes for Discontinuous-Galerkin Time-Domain simulations of Maxwell’s Equations, J. Comput. Theor. Nanosci. 7, 1572 (2010)
[4] K.R. Hiremath, J. Niegemann, and K. Busch, Analysis of light propagation in slotted resonator based systems via coupled-mode theory, Opt. Express 19, 8641 (2011)

 

List of Publications 2006-2011 as PDF

Subproject Report 2006-2010 as PDF