Identification of the absorption processes in periodic plasmonic structures using energy absorption interferometry.

Power dissipation in electromagnetic absorbers is a quadratic function of the incident fields. To characterize an absorber, one needs to deal with the coupling that may occur between different excitations. Energy absorption interferometry (EAI) is a technique that highlights the independent degrees of freedom through which a structure can absorb energy: the natural absorption modes of the structure. The coupling between these modes vanishes. In this paper, we use the EAI formalism to analyze different kinds of plasmonic periodic absorbers while rigorously accounting for the coupling: resonant golden patches on a grounded dielectric slab, parallel free-standing silver wires, and a silver slab of finite thickness. The EAI formalism is used to identify the physical processes that mediate absorption in the near and far field. First, we demonstrate that the angular absorption, which is classically used to characterize periodic absorbers in the far field and which neglects the coupling between different plane waves, is only valid under stringent conditions (subwavelength periodicity, far-field excitation, and negligible coupling between the two possible polarizations). Using EAI, we show how the dominant absorption channels can be identified through the signature of the absorption modes of the structure, while rigorously accounting for the coupling. We then exploit these channels to improve absorption. We show that long-range processes can be exploited to enhance the spatial selectivity, while short-range processes can be exploited to improve absorptivity over wide angles of incidence. Finally, we show that by simply adding scatterers with the proper periodicity on top of the absorber, the absorption can be increased by more than 1 order of magnitude.

Characterization of power absorption response of periodic three-dimensional structures to partially coherent fields.

In many applications of absorbing structures it is important to understand their spatial response to incident fields, for example in thermal solar panels, bolometric imaging, and controlling radiative heat transfer. In practice, the illuminating field often originates from thermal sources and is only partially spatially coherent when it reaches the absorbing device. In this paper, we present a method to fully characterize the way a structure can absorb such partially coherent fields. The method is presented for any three-dimensional material and accounts for the partial coherence and partial polarization of the incident light. This characterization can be achieved numerically using simulation results or experimentally using the energy absorption interferometry that has been described previously in the literature. The absorbing structure is characterized through a set of absorbing functions onto which any partially coherent field can be projected. This set is compact for any structure of finite extent, and the absorbing function is discrete for periodic structures.

Characteristic functions describing the power absorption response of periodic structures to partially coherent fields.

Periodic thin-film structures are widely used as absorptive structures for electromagnetic radiation. We show that the absorption behavior for partially coherent illumination can be fully characterized by a set of characteristic functions in wavenumber space. We discuss the prediction of these functions using electromagnetic solvers based on periodic boundary conditions, and their measurement experimentally using Energy Absorption Interferometry (EAI). The theory is developed here for the case of 2D absorbers with TE illumination and arbitrary material properties in the plane of the problem, except for the resistivity, which is assumed isotropic. Numerical examples are given for the case of absorbing strips printed on a semi-infinite substrate. We derive rules for the convergence of the representation as a function of the number of characteristic functions used, as well as conditions for sampling in EAI experiments.

Optical modeling techniques for multimode horn-coupled power detectors for submillimeter and far-infrared astronomy.

An important class of detectors for the submillimeter and far-infrared uses a multimode horn to couple incident radiation into an absorbing film made from a thin conductor. We consider how to model the full, partially coherent, optical behavior of these multimode detectors using extensions of mode-matching techniques. We validate modeling the absorber as a resistive sheet, and demonstrate the equivalence of mode-matching and Green's function methods for calculating the scattering matrix representation of the film. Finally, we show how the scattering matrix of the film can be cascaded with those of the other components, as determined by mode matching, so as to calculate the overall optical response of the detector. Simulations are presented of the optical behavior of a square absorbing film in a circular waveguide.

Analysis of far-infrared horns, lightpipes, and cavities containing patterned conductive films.

A scheme is described for calculating the scattering parameters of patterned conductive films in waveguide. The films can have non-uniform, non-isotropic, and non-local sheet impedances. Once the scattering parameters are known, they can be combined with the scattering parameters of paths, dielectric slabs, and waveguide steps to build up models of complicated components comprising patterned films in profiled lightpipes and cavities. It is then straightforward to calculate the Stokes fields of the total reception pattern, the natural optical modes to which the component is sensitive, the Stokes fields of the individual natural modes, and the spatial state of coherence. The method is demonstrated by modeling an absorbing pixel in a length of shorted multimode waveguide. The natural optical modes change from being those of the waveguide to those of a free-space pixel as the size of the absorber is reduced.

Modeling the intensity and polarization response of planar bolometric detectors.

Far-infrared bolometric detectors are used extensively in ground-based and space-borne astronomy, and thus it is important to understand their optical behavior precisely. We have studied the intensity and polarization response of free-space bolometers and shown that when the size of the absorber is reduced below a wavelength, the response changes from being that of a classical optical detector to that of a few-mode antenna. We have calculated the modal content of the reception patterns and found that for any volumetric detector having a side length of less than a wavelength, three magnetic and three electric dipoles characterize the behavior. The size of the absorber merely determines the relative strengths of the contributions. The same formalism can be applied to thin-film absorbers, where the induced current is forced to flow in a plane. In this case, one magnetic and two electric dipoles characterize the behavior. The ability to model easily the intensity, polarization, and straylight characteristics of electrically small detectors will be of great value when designing high-performance polarimetric imaging arrays.

Optical theory of partially coherent thin-film energy-absorbing structures for power detectors and imaging arrays.

Free-space power detectors often have energy absorbing structures comprising multilayer systems of patterned thin films. We show that for any system of interacting resistive films, the expectation value of the absorbed power is given by the contraction of two tensor fields: one describes the spatial state of coherence of the incoming radiation, the other the state of coherence to which the detector is sensitive. Equivalently, the natural modes of the optical field scatter power into the natural modes of the detector. We describe a procedure for determining the amplitude, phase, and polarization patterns of a detector's optical modes and their relative responsivities. The procedure gives the state of coherence of the currents flowing in the system and leads to important conceptual insights into the way the pixels of an imaging array interact and extract information from an optical field.

Simulations of astronomical imaging phased arrays.

We describe a theoretical procedure for analyzing astronomical phased arrays with overlapping beams and apply the procedure to simulate a simple example. We demonstrate the effect of overlapping beams on the number of degrees of freedom of the array and on the ability of the array to recover a source. We show that the best images are obtained using overlapping beams, contrary to common practice, and show how the dynamic range of a phased array directly affects the image quality.

Coupled-mode theory for infrared and submillimeter wave detectors.

We present a comprehensive, spatiotemporal, modal theory of submillimeter-wave and far-infrared power detectors. The theory is based on the contraction of the coherence tensor of the light with another coherence tensor that incorporates all of the physics of the detector. The theory is extremely general and applies to detectors of any bandwidth, with light in any state of polarization and spatiotemporal coherence. The theory applies equally to quasi-monochromatic and pulsed systems. We show that the tensor associated with the detector is a measureable quantity and outline a procedure for its experimental determination. We derive expressions for the statistical properties of a detector's output, including the correlations between the outputs of different detectors, say, in an array or interferometer. The theory provides a clear conceptual understanding of how any general detector couples to the modes of an optical system and thereby provides a powerful and flexible way of modeling the behavior of detectors and instruments.

Scattering coherent and partially coherent space-time pulses through few-mode optical systems.

We consider the spatiotemporal behavior of coherent and partially coherent, pulsed, few-mode optical systems. It is shown that there is some set of orthogonal space-time pulses at the input reference surface that maps in one-to-one correspondence with some set of orthogonal space-time pulses at the output reference surface; we call these pulses eigenfields. The spectrum of the coupling coefficients determines the amount of information that can be transmitted within a given period of time. The eigenfields are unique for a given system and can be used to propagate a field that is in any state of spatial and temporal coherence. They can also be used to account for the spatial and temporal coherence of internally generated noise and to calculate the powers, fluctuations, and correlations that would be recorded by multimode detectors. Our technique is ideal for modeling the behavior of pulsed imaging arrays and interferometers.

Partially coherent analysis of imaging and interferometric phased arrays: noise, correlations, and fluctuations.

Phased arrays are of considerable importance for far-infrared, submillimeter-wave, and microwave astronomy; they are also being developed for areas as diverse as optical switching, radar, and radio communications. We present a discretized, modal theory of imaging and interferometric phased arrays. It is shown that the average powers, field correlations, power fluctuations, and correlations between power fluctuations at the output ports of an imaging, or interferometric, phased array can be determined for a source in any state of spatial coherence and polarization, once the synthesized beam patterns are known. It is not necessary to know anything about the internal construction of the beam-forming networks; indeed, the beam patterns can be taken from experimental data. The synthesized beams can be nonorthogonal and even linearly dependent. Our theory leads to many conceptual insights and opens the way to a range of new design and simulation techniques.

Quantum-statistical analysis of multimode far-infrared and submillimeter-wave astronomical interferometers.

We present a detailed quantum-statistical model of multimode far-infrared and submillimeter-wave astronomical interferometers. The scheme identifies explicitly the optical modes associated with each telescope and uses these to trace the quantum-statistical properties of the field from a source through the telescopes, through the beam combiners, and onto the detectors. The scheme can be used with any optical configuration, and elegant expressions result for the average rate at which photons are detected by the pixels of an imaging array, the mean-square fluctuations in the rates, and the correlations between the fluctuations in the rates of different pixels. Numerous extensions to the basic technique are possible.

Modal analysis of astronomical bolometric interferometers.

A procedure is described for modeling the behavior of astronomical bolometric interferometers. The scheme is based on the notion of eigenfields. The input and output eigenfields are those field distributions on the sky and at the detector to which the individual telescopes of an interferometer can couple. Eigenfields are more fundamental than eigenmodes and provide, regardless of optical configuration, an orthogonal basis for propagating the second-order statistical properties of a field from a source through the telescopes, through the beam combiners, and onto the detectors. With our scheme, it is possible to calculate the power coupled into coherent, partially coherent, and incoherent imaging arrays and to include the spatially distributed noise sources of the telescopes themselves.

Terahertz astronomical telescopes and instrumentation.

The terahertz (THz) region of the electromagnetic spectrum is of great importance for astrophysics. In fact, it is central to the whole field of experimental cosmology. This paper outlines the range of astrophysical problems that can be answered by observing at THz frequencies, describes some of the major THz astronomical telescopes that are being constructed, and gives a vision of the way in which the technological development of superconducting very-large-scale integration circuit technology and solid-state source technology will lead to major advances in the subject.

General approach for representing and propagating partially coherent terahertz fields with application to Gabor basis sets.

We discuss a general theoretical framework for representing and propagating fully coherent, fully incoherent, and the intermediate regime of partially coherent submillimeter-wave fields by means of general sampled basis functions, which may have any degree of completeness. Partially coherent fields arise when finite-throughput systems induce coherence on incoherent fields. This powerful extension to traditional modal analysis methods by using undercomplete Gaussian-Hermite modes can be employed to analyze and optimize such Gaussian quasi-optical techniques. We focus on one particular basis set, the Gabor basis, which consists of overlapping translated and modulated Gaussian beams. We present high-accuracy numerical results from field reconstructions and propagations. In particular, we perform one-dimensional analyses illustrating the Van Cittert-Zernike theorem and then extend our simulations to two dimensions, including simple models of horn and bolometer arrays. Our methods and results are of practical importance as a method for analyzing terahertz fields, which are often partially coherent and diffraction limited so that ray tracing is inaccurate and physical optics computationally prohibitive.

Representing the behavior of partially coherent optical systems by using overcomplete basis sets.

A technique is described for representing the behavior of partially coherent optical systems by using overcomplete basis sets. The scheme is closely related to Gabor function theory. Through singular-value decomposition it is shown that if E is a matrix containing the sampled basis functions, then all of the information needed for optical calculations is contained in S = EE(dagger) and R = E(dagger)E. For overcomplete sets, S can be inverted to give a dual basis set, E = S(-1)E, which can be used to find the correlation matrix elements A of a sampled bimodal expansion of the spatial coherence function. Overcomplete correlation matrices can be scattered easily at optical components. They can be used to determine (i) the natural modes of a field; (ii) the total power in a field, Pt = Tr[RA]; (iii) the power coupled between two fields, A and B, that are in different states of coherence, Pc = Tr[RARB]; and (iv) the entropy of a field, Q = Tr[Zsigmar(I-Z)r/r], where Z = RA/Tr[RA].

Analyzing the power coupled between partially coherent waveguide fields in different states of coherence.

A procedure is described for calculating the power coupled between partially coherent waveguide fields that are in different states of coherence. The method becomes important when it is necessary to calculate the power transferred from a distributed source S to a distributed load L through a length of multimode metallic, or dielectric, waveguide. It is shown that if the correlations between the transverse components of the electric and magnetic fields of S and L are described by coherence matrices M and M', respectively, then the normalized average power coupled between them is (eta) = Tr[MM']/Tr[M]Tr[M'], where Tr denotes the trace. When the modal impedances are equal, this expression for the coupled power reduces to an equation derived in a previous paper [J. Opt. Soc. Am. A 18, 3061 (2001)], by use of thermodynamic arguments, for the power coupled between partially coherent free-space beams.