Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

A thermal light-emitting source, such as a black body or the incandescent filament of a light bulb, is often presented as a typical example of an incoherent source and is in marked contrast to a laser. Whereas a laser is highly monochromatic and very directional, a thermal source has a broad spectrum and is usually quasi-isotropic. However, as is the case with many systems, different behaviour can be expected on a microscopic scale. It has been shown recently that the field emitted by a thermal source made of a polar material is enhanced by more than four orders of magnitude and is partially coherent at a distance of the order of 10 to 100nm. Here we demonstrate that by introducing a periodic microstructure into such a polar material (SiC) a thermal infrared source can be fabricated that is coherent over large distances (many wavelengths) and radiates in well defined directions. Narrow angular emission lobes similar to antenna lobes are observed and the emission spectra of the source depends on the observation angle--the so-called Wolf effect. The origin of the coherent emission lies in the diffraction of surface-phonon polaritons by the grating.

Coherent emission of light by thermal sources

We present a theory of the Fano resonance for optical resonators, based on a temporal coupled-mode formalism. This theory is applicable to the general scheme of a single optical resonance coupled with multiple input and output ports. We show that the coupling constants in such a theory are strongly constrained by energy-conservation and time-reversal symmetry considerations. In particular, for a two-port symmetric structure, Fano-resonant line shape can be derived by using only these symmetry considerations. We validate the analysis by comparing the theoretical predictions with three-dimensional finite-difference time-domain simulations of guided resonance in photonic crystal slabs. Such a theory may prove to be useful for response-function synthesis in filter and sensor applications.

/pdf/temporal-coupled-mode-theory-for-the-fano-resonance-in-2okwo9a7sx.pdf

Temporal coupled-mode theory for the Fano resonance in optical resonators

The recent reformulation of the coupled-wave method by Lalanne and Morris [ J. Opt. Soc. Am. A13, 779 ( 1996)] and by Granet and Guizal [ J. Opt. Soc. Am. A13, 1019 ( 1996)], which dramatically improves the convergence of the method for metallic gratings in TM polarization, is given a firm mathematical foundation in this paper. The new formulation converges faster because it uniformly satisfies the boundary conditions in the grating region, whereas the old formulations do so only nonuniformly. Mathematical theorems that govern the factorization of the Fourier coefficients of products of functions having jump discontinuities are given. The results of this paper are applicable to any numerical work that requires the Fourier analysis of products of discontinuous periodic functions.

https://mcgrating.com/references/ref11.pdf

Use of Fourier series in the analysis of discontinuous periodic structures

A key goal of metalens research is to achieve wavefront shaping of light using optical elements with thicknesses on the order of the wavelength. Such miniaturization is expected to lead to compact, nanoscale optical devices with applications in cameras, lighting, displays and wearable optics. However, retaining functionality while reducing device size has proven particularly challenging. For example, so far there has been no demonstration of broadband achromatic metalenses covering the entire visible spectrum. Here, we show that by judicious design of nanofins on a surface, it is possible to simultaneously control the phase, group delay and group delay dispersion of light, thereby achieving a transmissive achromatic metalens with large bandwidth. We demonstrate diffraction-limited achromatic focusing and achromatic imaging from 470 to 670 nm. Our metalens comprises only a single layer of nanostructures whose thickness is on the order of the wavelength, and does not involve spatial multiplexing or cascading. While this initial design (numerical aperture of 0.2) has an efficiency of about 20% at 500 nm, we discuss ways in which our approach may be further optimized to meet the demand of future applications. Controlling the geometry of each dielectric element of a nanostructured surface enables frequency-dependent group delay and group delay dispersion engineering, and the fabrication of an achromatic metalens for imaging in the visible in transmission.

/pdf/a-broadband-achromatic-metalens-for-focusing-and-imaging-in-1jmcuho99u.pdf

A broadband achromatic metalens for focusing and imaging in the visible.

The coupled-wave method formulated by Moharam and Gaylord [ J. Opt. Soc. Am.73, 451 ( 1983)] is known to be slowly converging, especially for TM polarization of metallic lamellar gratings. The slow convergence rate has been analyzed in detail by Li and Haggans [ J. Opt. Soc. Am. A10, 1184 ( 1993)], who made clear that special care must be taken when coupled-wave methods are used for TM polarization. By reformulating the eigenproblem of the coupled-wave method, we provide numerical evidence and argue that highly improved convergence rates similar to the TE polarization case can be obtained. The discussion includes both nonconical and conical mountings.

https://mcgrating.com/references/ref10.pdf

Highly improved convergence of the coupled-wave method for TM polarization

We describe subwavelength surfaces etched into silicon wafers that exhibit antireflection characteristics for visible light. The wafers are fabricated by holographically recording a crossed-grating in a photoresist mask followed by reactive-ion etching to transfer the primary mask onto the silicon substrate. The dependence of reflectivity on the wavelength and angle of incidence is measured. The overall antireflection performance of the corrugated silicon wafers is compared with that of standard thin-film stacks, and is interpreted with the effective medium theory and with simulation results obtained from rigorous computations.

https://iopscience.iop.org/article/10.1088/0957-4484/8/2/002/pdf

Antireflection behavior of silicon subwavelength periodic structures for visible light

Diffractive lenses have been traditionally designed with the first diffracted order. The spectral characteristics of diffractive lenses operating in higher diffracted orders differ significantly from the first-order case. Multiorder diffractive lenses offer a new degree of freedom in the design of broadband and multispectral optical systems that include diffractive optical elements. It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets. The wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses. Experiments that illustrate lens performance in two spectral bands are described, and the results show excellent agreement with the theoretical predictions.

/pdf/spectral-properties-of-multiorder-diffractive-lenses-5gagz5blax.pdf

Spectral properties of multiorder diffractive lenses

A theoretical investigation of resonant scattering from two-dimensional gratings is presented. Abrupt changes of diffraction efficiency over a small parameter range have been observed by rigorous coupled-wave analysis. The peak reflection or transmission efficiencies can approach unity. This phenomenon is explained in terms of the coupling between the incident plane wave and guided modes that can be supported by the two-dimensional-grating waveguide structure. Because of the double periodicity, the incident field can be coupled into any direction in the grating plane. The guided modes supported by two-dimensional gratings are found by rigorous solution of the homogeneous problem associated with the scattering (inhomogeneous) problem. The complex propagation constants for the guided modes provide estimates of both the resonance angle and width. In addition, to illustrate the implication of the radical change in the phase and amplitude of the propagating waves, we report a study of finite-beam diffraction in the resonant scattering region. Applications for the structures include polarization-independent narrow-band filters and bandwidth-tunable filters. It is shown that, because of the double resonance, the polarization-independent narrow-band filters have a large angular tolerance.

Resonant scattering from two-dimensional gratings

Resonant effects in diffraction from two-dimensional dielectric gratings is demonstrated experimentally. A two-layer structure, which consists of a uniform guiding layer and a grating layer, yielded symmetric, low-sideband resonance that is suitable for narrow-band filter applications. Excellent agreement between measured and calculated spectral and angular dependence is obtained.

G. Michael Morris

Papers

Highly improved convergence of the coupled-wave method for TM polarization

Antireflection behavior of silicon subwavelength periodic structures for visible light

Spectral properties of multiorder diffractive lenses

Resonant scattering from two-dimensional gratings

Experimental demonstration of resonant anomalies in diffraction from two-dimensional gratings.