Article

# Designing for beam propagation in periodic and nonperiodic photonic nanostructures: extended Hamiltonian method.

Ginzton Laboratory, Stanford University, Stanford, California 94305-4088, USA.

Physical Review E (Impact Factor: 2.33). 10/2004; 70(3 Pt 2):036612. DOI: 10.1103/PhysRevE.70.036612 Source: PubMed

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**ABSTRACT:**The dispersive properties of planar photonic crystals (PhCs) have been envisaged for years. In particular, the superprism effect has been considered to obtain a strong influence of input beam conditions (e.g. wavelength or input angle) on the light group velocity direction, enabling the design and fabrication of on-chip infra-red spectrometers and integrated optical demultiplexers. We extend here the properties of PhCs to the study of graded photonic crystals (GPhCs) made of a two-dimensional chirp of lattice parameters and show that GPhCs enable solving several drawbacks of dispersive PhCs like the beam divergence issues or the need of long preconditioning regions to precompensate beam diffraction effects. The proposed approach is applied to a square lattice air-hole PhC with a gradual filling factor that was fabricated using ebeam lithography and ICP etching techniques. A nearly-constant 0.25μm/nm spatial dispersion is demonstrated for a 60μm square GPhC structure in the 1470-1600nm spectral range without noticeable spatial or spectral spreading. Moreover, contrary to PhC superprism structures, a linear dispersion is obtained in the considered wavelength range.Proceedings of SPIE - The International Society for Optical Engineering 11/2012; · 0.20 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We show that the effective gauge field for photons provides a versatile platform for controlling the flow of light. As an example we consider a photonic resonator lattice where the coupling strength between nearest neighbor resonators are harmonically modulated. By choosing different spatial distributions of the modulation phases, and hence imposing different inhomogeneous effective magnetic field configurations, we numerically demonstrate a wide variety of propagation effects including negative refraction, one-way mirror, and on- and off-axis focusing. Since the effective gauge field is imposed dynamically after a structure is constructed, our work points to the importance of the temporal degree of freedom for controlling the spatial flow of light.Physical Review Letters 11/2013; 111(20):203901. · 7.73 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We design an all-dielectric L\"uneburg lens as an adiabatic space-variant lattice explicitly accounting for finite film thickness. We describe an all-analytical approach to compensate for the finite height of subwavelength dielectric structures in the pass-band regime. This method calculates the effective refractive index of the infinite-height lattice from effective medium theory, then embeds a medium of the same effective index into a slab waveguide of finite height and uses the waveguide dispersion diagram to calculate a new effective index. The results are compared with the conventional numerical treatment - a direct band diagram calculation, using a modified three-dimensional lattice with the superstrate and substrate included in the cell geometry. We show that the analytical results are in good agreement with the numerical ones, and the performance of the thin-film L\"uneburg lens is quite different than the estimates obtained assuming infinite height.11/2011;

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