Christopher N. Thomas

Experimental Demonstration of an Interferometric Technique for Characterizing the Full Optical Behavior of Multi-Mode Power Detectors

An experimental method is presented for characterizing the full optical behavior of few-mode power detectors. The technique involves illuminating the detector with a pair of coherent sources. When the phase of one source is rotated relative to the other, the detector output displays a fringe. Measurement of the complex amplitude of this fringe allows an element of a two-point optical response function to be recovered. By repeating the process for different source positions and orientations, the full two-point response function can be mapped out. From this function it is possible to obtain the full spatial form of each of the modes of the field in which the detector is incoherently sensitive to power, along with the responsivity to the power carried by each of these modes. We describe a scanning system assembled for performing such measurements at frequencies in the range 195-270 GHz. Results will be presented for measurements made on a detector that was stopped down to simulate and a few-mode planar absorber.

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 detectors 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.

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.

Electrothermal model of kinetic inductance detectors

An electrothermal model of Kinetic Inductance Detectors (KIDs) is described. The non-equilibrium state of the resonators quasiparticle system is characterized by an effective temperature, which because of readout-power heating is higher than that of the bath. By balancing the flow of energy into the quasiparticle system, it is possible to calculate the steady-state large-signal, small-signal and noise behaviour. Resonance-curve distortion and hysteretic switching appear naturally within the framework. It is shown that an electrothermal feedback process exists, which affects all aspects of behaviour. It is also shown that generation-recombination noise can be interpreted in terms of the thermal fluctuation noise in the effective thermal conductance that links the quasiparticle and phonon systems of the resonator. Because the scheme is based on electrothermal considerations, multiple elements can be added to simulate the behaviour of complex devices, such as resonators on membranes, again taking into account readout power heating.

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 Greens 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.

Probing the dynamical behavior of surface dipoles through energy-absorption interferometry

Spatial interferometry, based on the measurement of total absorbed power, can be used to determine the state of coherence of the electromagnetic field to which any energy-absorbing structure is sensitive. The measured coherence tensor can be diagonalized to give the amplitude, phase, polarization patterns, and responsivities of the individual electromagnetic modes through which the structure can absorb energy. Because the electromagnetic modes are intimately related to dynamical modes of the system, information about collective excitations can be found. We present simulations, based on the Discrete Dipole Approximation (DDA), showing how the dynamical modes of systems of surface dipoles can be recovered. Interactions are taken into consideration, leading to long-range coherent phenomena, which are revealed by the method. The use of DDA enables the interferometric response of a wide variety of objects to be modeled, from patterned photonic films to biological macromolecules.

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.

Ultra-low-noise transition edge sensors for far infrared wavelengths: optical design, measurement and stray light control

Ultra-low-noise Transition Edge Sensors (TESs) have been selected for the far-infrared Fourier transform spectrometer SAFARI on the space telescope SPICA, now under study as an M5 mission, operating in three wavelength bands: S-band from 34-60 μm, M-band from 60-110 μm and L-band from 110-210 μm. We report the fabrication and optical characterisation of a linear TES array for the SAFARI M-band, integrated with micromachined reflective backshorts and profiled pyramidal optical feedhorns. The design and construction of the cryogenic optical test facility used to illuminate the devices under test are described, featuring a variable temperature blackbody load, band-defining filters and an optical aperture. We observe effective numbers of optical modes, Nef f = 0.41 ± 0.03, and near-unity optical efficiencies in TES-backshort assemblies, with some loss of efficiency in the presence of horns. Stray light control measures are discussed in the context of a significant reduction achieved in long wavelength stray light detected by these devices.

Thermal elastic-wave attenuation in low-dimensional SiNx bars at low temperatures

At low temperatures,  400 μm, it is known that the conductance scales as 1/L, where L is the length, but for short bars, 1 μm < L < 400 μm, the length dependence is poorly known. Although it is assumed that the transport must exhibit a diffusive to ballistic transition, the functional form of the transition and the scale size over which the transition occurs have not, to our knowledge, been measured. In this paper, we use ultra-low-noise superconducting Transition Edge Sensors to measure the heat flux through a set of SiNx bars to establish the characteristic scale size of the ballistic to diffusive transition. For bars supporting 6 to 7 modes, we measure a thermal elastic-wave attenuation length of 20 μm. The measurement is important because it sheds light on the scattering processes, which in turn are closely related to t...

Dynamical behaviour of superconducting microresonators with readout-power heating

We consider the effects of quasiparticle heating on the dynamical behaviour of superconducting microresonators operating with high readout powers. It is seen that resonance-curve distortion and hysteretic switching are an inevitable consequence of the forms of the quasiparticle heating and cooling functions. The model uses a diagrammatic representation of dynamical behaviour to gain an insight into how the instantaneous operating point moves in response to step changes in readout power, signal power, bath temperature, and frequency. The coupling quality factor has a marked effect on non-linear behaviour. The model is used to calculate the waveforms generated when a device switches between hysteretic states. The work suggests that measured response times need not be representative of intrinsic quasiparticle relaxation rates.