Large field enhancement obtained by combining Fabry-Perot resonance and Rayleigh anomaly in photonic crystal slabs

© 2017 IOP Publishing Ltd. By applying the properties of Fabry-Perot resonance and Rayleigh anomaly, we have shown that a photonic crystal slab can scatter the light from an incident plane wave into a diffracted light with a very large reflection or transmission coefficient. The enhanced field is either a propagating diffracted wave (with a grazing angle of diffraction) or a weakly evanescent diffracted wave, so it can be particularly useful for applications requiring an enhanced propagating field (or an enhanced field with a low attenuation). An efficient effective medium technique is developed for the design of the resonant photonic crystal slabs. Numerical simulations have shown that photonic crystal slabs with low index contrast, such as the ones found in the cell wall of diatoms, can enhance the intensity of the incident light by four orders of magnitude

Doppler shift generated by a moving diffraction grating under incidence by polychromatic diffuse light

© 2016 Optical Society of America. We consider the spectral response of moving diffraction gratings, in which the incident light extends over a broad angular range and where the diffracted light is observed from a specific angle. We show that the dispersion relation between the frequency perceived by an observer who is looking at a moving grating and the incident frequency can exhibit some unique features, such as a flat band (i.e., a local minimum). An observer can see the light diffracted into a nonspecular diffraction order from a multitude of incident light rays, and the angle of incidence of each ray is frequency dependent; as a consequence, when the grating is moving, each incident ray experiences a Doppler shift in frequency that depends on its angle of incidence. We find that remarkable features appear near a Wood anomaly where the angle of incidence, for a given diffraction angle, can change very quickly with frequency. This means that light of multiple frequencies and incident from multiple angles can be mixed by the motion of the grating into the same diffracted ray and their frequencies can be compressed into a narrower range. The existence of a flat band means that a moving grating can be used as a device to increase the intensity of the perceived diffracted light due to spectral compression. The properties of a grating in motion in sunlight can also be relevant to the study of naturally occurring gratings which are typically in oscillatory motion

Effective impedance modeling of metamaterial structures

© 2016 Optical Society of America. We present methods for retrieving the effective impedance of metamaterials from the Fresnel reflection coefficients at the interface between two semi-infinite media. The derivation involves the projection of rigorous modal expansions onto the dominant modes of the two semi-infinite media. It is shown that the effective impedance can also be written as a ratio of averaged field quantities. Thus, a number of effective impedance formulas, previously obtained by field averaging techniques, can also be derived from the scattering-based formalism by an appropriate choice of projection. Within the effective medium limit, it is observed that a simple semianalytic modeling technique based on the effective impedance can be used to reliably compute the reflection coefficients of metamaterials over a wide range of incidence angles. We use this technique to model planar metamaterial waveguides or surface modes

Modeling waveguides in photonic woodpiles using the fictitious source superposition method

We extend the fictitious source superposition method in order to model linear defects in photonic woodpiles, and we use the method to model a waveguide that is created by changing either the radius or refractive index of a single rod of an infinite woodpile composed of chalcogenide glass cylinders. In one instance, a nearly constant dispersion was observed over a sizable kx interval, where kx is the Bloch vector in the waveguiding direction, making this a compelling geometry for slow-light waveguides. The principal advantage of the method is that it does not rely on a supercell, thus avoiding what is possibly the greatest source of inefficiency present in most of the other methods that are used for modeling these structures. Instead, the method proceeds by placing an artificial source inside each rod of the defect layer and then subsequently taking an appropriate field superposition to remove all but one of these sources. The remaining source can then be used to mimic the fields that would be produced by a defect rod. © 2011 Optical Society of America

Photonic-crystal surface modes found from impedances

We present a method for finding surface modes at interfaces between two-dimensional photonic crystals (PCs), in which the surface modes are represented as superpositions of the PCs' propagating and evanescent Bloch modes. We derive an existence condition for surface modes at an air-PC interface in terms of numerically calculated PC impedance matrices, and use the condition to find surface modes in the partial band gap of a PC. We also derive a condition for modes of a three-layer structure with two interfaces, and find both coupled surface modes and waveguide modes. We show that some waveguide modes cross the band edge and become coupled surface modes. © 2010 The American Physical Society

Efficient coupling into slow light photonic crystal waveguide without transition region: Role of evanescent modes

We show that efficient coupling between fast and slow photonic crystal waveguide modes is possible, provided that there exist strong evanescent modes to match the waveguide fields across the interface. Evanescent modes are required when the propagating modes have substantially different modal fields, which occurs, for example, when coupling an index-guided mode and a gap-guided mode. ©2009 Optical Society of America

Efficient slow-light coupling in a photonic crystal waveguide without transition region

We consider the coupling into a slow mode that appears near an inflection point in the band structure of a photonic crystal waveguide. Remarkably, the coupling into this slow mode, which has a group index ng > 1000, can be essentially perfect without any transition region. We show that this efficient coupling occurs thanks to an evanescent mode in the slow medium, which has appreciable amplitude and helps satisfy the boundary conditions but does not transport any energy. © 2008 Optical Society of America

Gap-edge asymptotics of defect modes in two-dimensional photonic crystals

We consider defect modes created in complete gaps of 2D photonic crystals by perturbing the dielectric constant in some region. We study their evolution from a band edge with increasing perturbation using an asymptotic method that approximates the Green function by its dominant component which is associated with the bulk mode at the band edge. From this, we derive a simple exponential law which links the frequency difference between the defect mode and the band edge to the relative change in the electric energy. We present numerical results which demonstrate the accuracy of the exponential law, for TE and TM polarizations, hexagonal and square arrays, and in each of the first and second band gaps. © 2007 Optical Society of America

A flexible Bloch mode method for computing complex band structures and impedances of two-dimensional photonic crystals

We present a flexible method that can calculate Bloch modes, complex band structures, and impedances of two-dimensional photonic crystals from scattering data produced by widely available numerical tools. The method generalizes previous work which relied on specialized multipole and finite element method (FEM) techniques underpinning transfer matrix methods. We describe the numerical technique for mode extraction, and apply it to calculate a complex band structure and to design two photonic crystal antireflection coatings. We do this for frequencies at which other methods fail, but which nevertheless are of significant practical interest. © 2012 American Institute of Physics

Engineering cavity modes in photonic crystal double-heterostructures

We present results from a new method that allows us to design the mode fields for 3D photonic crystal heterostructure cavities, in the domain where the perturbation used to create the cavity is weak. The method, based on a perturbation treatment from solid-state physics, enables the rapid computation of the main features of 3D cavity modes for an arbitrary perturbation and is several orders of magnitude faster than direct numerical methods. We use this method to study optimal confinement of resonant states in these structures. © 2010 Optical Society of America