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We describe NumBAT, an open-source software tool for modelling stimulated Brillouin scattering in waveguides of arbitrary cross-section. It provides rapid calculation of optical and elastic dispersion relations, field profiles and gain with an easy-to-use Python front end. Additionally, we provide an open and extensible set of standard problems and reference materials to facilitate the bench-marking of NumBAT against subsequent tools. Such a resource is needed to help settle discrepancies between existing formulations and implementations, and to facilitate comparison between results in the literature. The resulting standardised testing framework will allow the community to gain confidence in new algorithms and will provide a common tool for the comparison of experimental designs of opto-acoustic waveguides., Comment: 17 pages, 18 figures

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 diffraction order (with a grazing angle of diffraction) or a weakly evanescent order, 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.

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 non-specular 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.

The perfect absorption of light in subwavelength thickness layers generally relies on exotic materials, metamaterials or thick metallic gratings. Here we demonstrate that total light absorption can be achieved in ultra-thin gratings composed of conventional materials, including relatively weakly-absorbing semiconductors, which are compatible with optoelectronic applications such as photodetectors and optical modulators. We fabricate a 41 nm thick antimony sulphide grating structure that has a measured absorptance of A = 99.3% at a visible wavelength of 591 nm, in excellent agreement with theory. We infer that the absorption within the grating is A = 98.7%, with only A = 0.6% within the silver mirror. A planar reference sample absorbs A = 7.7% at this wavelength.

A finite element-based modal formulation of diffraction of a plane wave by an absorbing photonic crystal slab of arbitrary geometry is developed for photovoltaic applications. The semi-analytic approach allows efficient and accurate calculation of the absorption of an array with a complex unit cell. This approach gives direct physical insight into the absorption mechanism in such structures, which can be used to enhance the absorption. The verification and validation of this approach is applied to a silicon nanowire array and the efficiency and accuracy of the method is demonstrated. The method is ideally suited to studying the manner in which spectral properties (e.g., absorption) vary with the thickness of the array, and we demonstrate this with efficient calculations which can identify an optimal geometry., Comment: Accepted by Journal of the Optical Society of America A

Diffraction gratings are famous for their ability to exhibit, near a Wood anomaly, an arbitrarily large angular dispersion, e.g., with respect to the incidence angle or wavelength. For a diffraction grating under incidence by a plane wave at a fixed frequency, by rotating the incidence angle at a given angular velocity, the field propagated by a nonzero diffraction order will rotate at increasingly fast angular velocity as the incidence angle approaches the angle where Wood anomaly occurs. Such a fast rotating diffracted field has the potential to generate a substantial Doppler shift. Indeed, under the assumption of a grating with infinite extent, the expression for the instantaneous frequency shift perceived by an observer, who is looking into the light radiated by the diffraction order, is derived and it is in full agreement with the prediction from an interpretation based on the Doppler shift generated by a rotation of light sources. In particular the classical (non-relativistic) Doppler shift can take arbitrarily high values as the incidence angle approaches a Wood anomaly. It is also found that gratings of a finite size can have a similar property. In order to have a physically detectable frequency shift, it is important to use a grating which can maintain a significant reflectance into higher diffraction orders near their Wood anomaly cut-off. Interestingly, we have found that the geometry of the nanostructures of a \emph{Morpho} butterfly wing scale is aptly suited for such a function because it can strongly reflect into higher diffraction orders while minimising the reflection into the specular order., Comment: This paper has been withdrawn by the author because it has become obsolete after the publication of new articles: arXiv:1608.04166 and arXiv:1603.01329

Nanowire arrays exhibit efficient light coupling and strong light trapping, making them well suited to solar cell applications. The processes that contribute to their absorption are interrelated and highly dispersive, so the only current method of optimizing the absorption is by intensive numerical calculations. We present an efficient alternative which depends solely on the wavelength-dependent refractive indices of the constituent materials. We choose each array parameter such that the number of modes propagating away from the absorber is minimized while the number of resonant modes within the absorber is maximized. From this we develop a semi-analytic method that quantitatively identifies the small range of parameters where arrays achieve maximum short circuit currents. This provides a fast route to optimizing NW array cell efficiencies by greatly reducing the geometries to study with full device models. Our approach is general and applies to a variety of materials and to a large range of array thicknesses., Comment: Accepted by ACS Photonics

Solar cell designs based on disordered nanostructures tend to have higher efficiencies than structures with uniform absorbers, though the reason is poorly understood. To resolve this, we use a semi-analytic approach to determine the physical mechanism leading to enhanced efficiency in arrays containing nanowires with a variety of radii. We use our findings to systematically design arrays that outperform randomly composed structures. An ultimate efficiency of 23.75% is achieved with an array containing 30% silicon, an increase of almost 10% over a homogeneous film of equal thickness., Comment: The following article appeared in Appl. Phys. Lett. Copyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics

Aperiodic Nanowire (NW) arrays have higher absorption than equivalent periodic arrays, making them of interest for photovoltaic applications. An inevitable property of aperiodic arrays is the clustering of some NWs into closer proximity than in the equivalent periodic array. We focus on the modes of such clusters and show that the reduced symmetry associated with cluster formation allows external coupling into modes which are dark in periodic arrays, thus increasing absorption. To exploit such modes fully, arrays must include tightly clustered NWs that are unlikely to arise from fabrication variations but must be created intentionally., Comment: Accepted by Optics Express

We derive a frequency-domain-based approach for radiation (FAR) from double-heterostructure cavity (DHC) modes. We use this to compute the quality factors and radiation patterns of DHC modes. The semi-analytic nature of our method enables us to provide a general relationship between the radiation pattern of the cavity and its geometry. We use this to provide general designs for ultrahigh quality factor DHCs with radiation patterns that are engineered to emit vertically.

We present a semi-analytical formulation for calculating the supermodes and corresponding Bloch factors of light in hexagonal lattice photonic crystal waveguide arrays. We then use this formulation to easily calculate dispersion curves and predict propagation in systems too large to calculate using standard numerical methods., Comment: Accepted by J. Opt. Soc. Am. B, DocID:160522. http://www.opticsinfobase.org/abstract.cfm?msid=160522

We present a first-principles method to compute radiation properties of ultra-high quality factor photonic crystal cavities. Our Frequency-domain Approach for Radiation (FAR) can compute the far-field radiation pattern and quality factor of cavity modes $\sim 100$ times more rapidly than conventional finite-difference time domain calculations. It also provides a simple rule for engineering the cavity's far-field radiation pattern.

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 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., Comment: 9 pages, 4 figures. Source code available at https://launchpad.net/blochcode . The following article appeared in J. Appl. Phys. and may be found at http://link.aip.org/link/doi/10.1063/1.3674281 . Copyright 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics

We demonstrate that the spatial profiles of both propagating and evanescent Bloch-modes in a periodic structure can be extracted from a single measurement of electric field at the specified optical wavelength. We develop a systematic extraction procedure by extending the concepts of high-resolution spectral methods previously developed for temporal data series to take into account the symmetry properties of Bloch-modes simultaneously at all spatial locations. We apply our method to a photonic crystal waveguide interface and confirm its robustness in the presence of noise., Comment: 3 pages, 3 figures