Photonic crystals: straightening out light.
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Biomedical subjects
David A B Miller
Publications and source records attributed to David A B Miller.
Strong quantum-confined Stark effect in germanium quantum-well structures on silicon.
Silicon is the dominant semiconductor for electronics, but there is now a growing need to integrate such components with optoelectronics for telecommunications and computer interconnections. Silicon-based optical modulators have recently been successfully demonstrated; but because the light modulation mechanisms in silicon are relatively weak, long (for example, several millimetres) devices or sophisticated high-quality-factor resonators have been necessary. Thin quantum-well structures made from III-V semiconductors such as GaAs, InP and their alloys exhibit the much stronger quantum-confined Stark effect (QCSE) mechanism, which allows modulator structures with only micrometres of optical path length. Such III-V materials are unfortunately difficult to integrate with silicon electronic devices. Germanium is routinely integrated with silicon in electronics, but previous silicon-germanium structures have also not shown strong modulation effects. Here we report the discovery of the QCSE, at room temperature, in thin germanium quantum-well structures grown on silicon. The QCSE here has strengths comparable to that in III-V materials. Its clarity and strength are particularly surprising because germanium is an indirect gap semiconductor; such semiconductors often display much weaker optical effects than direct gap materials (such as the III-V materials typically used for optoelectronics). This discovery is very promising for small, high-speed, low-power optical output devices fully compatible with silicon electronics manufacture.
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Relationship between the superprism effect in one-dimensional photonic crystals and spatial dispersion in nonperiodic thin-film stacks.
We derive that, in all-pass (unity amplitude transmittance or reflectance) one-dimensional layered structures, the tangent of the group-propagation angle, the group delay, and the stored energy are approximately proportional. Thus photonic crystal superprisms and spatial dispersion in nonperiodic photonic nanostructures are generally related to wavelength-dependent stored energy in the stack.
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Limits on the performance of dispersive thin-film stacks.
Dispersive thin-film stacks are interesting as compact, cost-effective devices for temporal dispersion compensation and wavelength multiplexing. Their performance depends on the total group delay or spatial shift that can be achieved. For general multilayer stacks, no analytic model exists relating the performance to the stack parameters such as the refractive indices and the number of layers. We develop an empirical model by designing and analyzing 623 thin-film stacks with constant dispersion. From this analysis we conclude that, for given stack parameters, the maximum constant dispersion value is inversely proportional to the wavelength range over which the dispersion is achieved. This is equivalent to saying that, for constant dispersion, there is a maximum possible spatial shift (or group delay) that can be achieved for a given material system and number of layers. This empirical model is useful to judge the feasibility of dispersive photonic nanostructures and photonic crystal superprism devices and serves as a first step in the search for an analytic performance model. We predict that an 8-channel wavelength multiplexer can be realized with a single 21-microm-thick SiO2-Ta2O5 thin-film stack.
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Photonic crystal device sensitivity analysis with Wannier basis gradients.
We present a powerful sensitivity analysis method for devices in a photonic crystal. The method is based on a Wannier basis field expansion and efficient matrix analysis techniques for finding eigenvalue and transmission gradients with respect to the perturbation. The method permits fast analysis of a large number of dielectric perturbation situations for multiple devices in a photonic crystal. We verify the method with finite-difference time-domain and plane-wave expansion calculations.
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Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator.
We present a powerful design and optimization method for devices in a photonic crystal. The method is based on a Wannier basis field expansion and efficient matrix analysis techniques for searching through a vast number of designs. The method permits the design of many compact optical devices with complex and novel functions. We present a design example of a very compact mode separator that is 8.2 microm x 13.3 microm in size that demultiplexes the three modes of an input photonic crystal multimode waveguide into three single-mode output waveguides. We verify the method with finite-difference time-domain calculations.
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Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method.
We use Hamiltonian optics to design and analyze beam propagation in two-dimensional (2D) periodic structures with slowly varying nonuniformities. We extend a conventional Hamiltonian method, adding equations for calculating the width of a beam propagating in such structures, and quantify the range of validity of the extended Hamiltonian equations. For calculating the beam width, the equations are more than 10(3) times faster than finite difference time domain (FDTD) simulations. We perform FDTD simulations of beam propagation in large 2D periodic structures with slowly varying nonuniformities to validate our method. Beam path and beam width calculated using the extended Hamiltonian method show good agreement with FDTD simulations. By contrasting the method with ray tracing of the bundle of rays, we highlight and explain the limitations of the extended Hamiltonian method. Finally, we use a frequency demultiplexing device optimization example to demonstrate the potential applications of the method.
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Multilayer thin-film structures with high spatial dispersion.
We demonstrate how to design thin-film multilayer structures that separate multiple wavelength channels with a single stack by spatial dispersion, thus allowing compact manufacturable wavelength multiplexers and demultiplexers and possibly beam-steering or dispersion-control devices. We discuss four types of structure--periodic one-dimensional photonic crystal superprism structures, double-chirped structures exploiting wavelength-dependent penetration depth, coupled-cavity structures with dispersion that is due to stored energy, and numerically optimized nonperiodic structures utilizing a mixture of the other dispersion effects. We experimentally test the spatial dispersion of a 200-layer periodic structure and a 66-layer nonperiodic structure. Probably because of its greater design freedom, the nonperiodic structure can give both a linear shift with wavelength and a larger usable shift than the thicker periodic structure gives.
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