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Roadmap on transformation optics

Transformation optics asks, using Maxwell's equations, what kind of electromagnetic medium recreates some smooth deformation of space? The guiding principle is Einstein's principle of covariance: that any physical theory must take the same form in any coordinate system. This requirement fixes very precisely the required electromagnetic medium. The impact of this insight cannot be overestimated. Many practitioners were used to thinking that only a few analytic solutions to Maxwell's equations existed, such as the monochromatic plane wave in a homogeneous, isotropic medium. At a stroke, transformation optics increases that landscape from 'few' to 'infinity', and to each of the infinitude of analytic solutions dreamt up by the researcher, there corresponds an electromagnetic medium capable of reproducing that solution precisely. The most striking example is the electromagnetic cloak, thought to be an unreachable dream of science fiction writers, but realised in the laboratory a few months after the papers proposing the possibility were published. But the practical challenges are considerable, requiring meta-media that are at once electrically and magnetically inhomogeneous and anisotropic. How far have we come since the first demonstrations over a decade ago? And what does the future hold? If the wizardry of perfect macroscopic optical invisibility still eludes us in practice, then what compromises still enable us to create interesting, useful, devices? While three-dimensional (3D) cloaking remains a significant technical challenge, much progress has been made in two dimensions. Carpet cloaking, wherein an object is hidden under a surface that appears optically flat, relaxes the constraints of extreme electromagnetic parameters. Surface wave cloaking guides sub-wavelength surface waves, making uneven surfaces appear flat. Two dimensions is also the setting in which conformal and complex coordinate transformations are realisable, and the possibilities in this restricted domain do not appear to have been exhausted yet. Beyond cloaking, the enhanced electromagnetic landscape provided by transformation optics has shown how fully analytic solutions can be found to a number of physical scenarios such as plasmonic systems used in electron energy loss spectroscopy and cathodoluminescence. Are there further fields to be enriched? A new twist to transformation optics was the extension to the spacetime domain. By applying transformations to spacetime, rather than just space, it was shown that events rather than objects could be hidden from view; transformation optics had provided a means of effectively redacting events from history. The hype quickly settled into serious nonlinear optical experiments that demonstrated the soundness of the idea, and it is now possible to consider the practical implications, particularly in optical signal processing, of having an 'interrupt-without-interrupt' facility that the so-called temporal cloak provides. Inevitable issues of dispersion in actual systems have only begun to be addressed. Now that time is included in the programme of transformation optics, it is natural to ask what role ideas from general relativity can play in shaping the future of transformation optics. Indeed, one of the earliest papers on transformation optics was provocatively titled 'General Relativity in Electrical Engineering'. The answer that curvature does not enter directly into transformation optics merely encourages us to speculate on the role of transformation optics in defining laboratory analogues. Quite why Maxwell's theory defines a 'perfect' transformation theory, while other areas of physics such as acoustics are not apparently quite so amenable, is a deep question whose precise, mathematical answer will help inform us of the extent to which similar ideas can be extended to other fields. Here, the contributors to this Roadmap, who are all renowned practitioners or inventors of transformation optics, will give their perspectives into the field's status and future development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Procedures for dealing with certain types of noise and systematic errors common to many Hadamard transform optical systems

Sources of noise and error correcting procedures characteristic of Hadamard transform optical systems were investigated. Reduction of spectral noise due to noise spikes in the data, the effect of random errors, the relative performance of Fourier and Hadamard transform spectrometers operated under identical detector-noise-limited conditions, and systematic means for dealing with mask defects are among the topics discussed. The distortion in Hadamard transform optical instruments caused by moving Masks, incorrect mask alignment, missing measurements, and diffraction is analyzed and techniques for reducing or eliminating this distortion are described.

Harwit, M.↗

Systematic errors in Hadamard transform optics

Error sources encountered in Hadamard transform optical instruments are discussed. Such errors are caused by factors including moving masks, incorrect mask alignment, defects in mask fabrication, missing data, drifts in background level, and diffraction. Techniques for error reduction and/or elimination are described for each of the cases considered. It is noted that the errors described occur in singly encoded spectrometers and imagers.

Sloane, N. J. A.↗

Production of Airy-related beams by an Airy transform optical system

Based on the process of Huygens–Fresnel diffraction integral, we investigate theoretically the characteristics of fields generated by diffracted controllable dark-hollow beams (CDHBs) through an Airy transform optical system. It is shown that the CDHB is transformed into Airy-related beams and the dark central spot is converted into peak intensity. The effects of the incident CDHB parameters such as the mode number N, central spot width w{sub 0} and ε as well as the phase pattern parameters of Airy transform optical system on the generated beam are analyzed in detail with numerical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Propagation properties of finite cosh-Airy beams through an Airy Transform Optical System

In this paper, we have derived the analytical expression for a diffracted finite cosh-Airy beam by an Airy Transform Optical System (ATOS). The obtained output field is expressed as a superposition of finite Airy modes with different weights and decay factors. Numerical examples were performed to illustrate the influence of the scale factor, the parameter associated with cosh-function, in addition to the parameters of the finite Airy mode and the parameters of the ATOS on the generated beam. It is shown that the resulting beam possesses more manipulation degrees of freedom than that corresponding to finite Airy or Gaussian-Airy beams. This investigation is also extended to the cos-Airy beams. The obtained results are consistent with those previously obtained for fundamental Gaussian and Airy beams, and the present study provides a more generalized investigation on the conversion of related Airy beams by an ATOS.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Contributions to workload of rotational optical transformations

An investigation of visuomotor adaptation to optical rotation and optical inversion was conducted. Experiment 1 examined the visuomotor adaptability of subjects to an optically rotating visual world with a univariate repeated measures design. Experiment 1A tested one major prediction of a model of adaptation put forth by Welch who predicted that the aversive drive state that triggers adaptation would be habituated to fairly rapidly. Experiment 2 was conducted to investigate the role of motor activity in adaptation to optical rotation. Specifically, this experiment contrasted the reafference hypothesis and the proprioceptive change hypothesis. Experiment 3 examined the role of cognition, error-corrective feedback, and proprioceptive and/or reafferent feedback in visuomotor adaptation to optical inversion. Implications for research and implications for practice were suggested for all experiments.

Atkinson, R. P.↗

Fourier-transform optical microsystems

The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.

NASA Discipline Environmental Health↗

Shape-Selective Optical Transformations of CdSe Nanoplatelets Driven by Halide Ion Ligand Exchange

Treatment of CdSe nanoplatelets with halide salts induces a bathochromic shift in the absorption resonances that does not occur in quasi-spherical quantum dots of the same composition. The optical shifts are not strongly sensitive to the cation moiety, which may be organic or inorganic. The magnitude of the energy shift is largest for thinner nanoplatelets, with bathochromic shifts as large as 240 meV observed for 3 monolayer nanoplatelets. This effect is driven by a tetragonal distortion of the zinc blende lattice in response to ligand exchange. In conclusion, the expansion of the lattice in the shortest nanoplatelet axis results in the observed red-shifts due primarily to relaxation of quantum confinement, with secondary contributions from strain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Broadband Fourier-Transform Optical Photothermal Infrared Spectroscopy and Imaging

Infrared (IR) spectroscopy is a powerful method for mapping chemical heterogeneity on the microscale. Synchrotron IR radiation uniquely provides a high brightness and broad bandwidth to further extend the capabilities of IR spectroscopic imaging. However, the diffraction-limited spatial resolution of IR spectroscopy is insufficient for studies requiring submicrometer spatial differentiation. Optical photothermal IR (O-PTIR) microscopy is a powerful, emerging method that overcomes the IR diffraction limit in IR hyperspectral imaging by employing a modulated IR beam and a visible probe laser beam to detect local temperature-induced modulation at the visible diffraction limit. In this work, we extend the spectral range of photothermal infrared measurements by incorporating a synchrotron IR source, demonstrating a combined synchrotron-based O-PTIR modality that enables high spatial resolution far-field chemical imaging spanning the entire mid-IR range. Both optical- and fluorescence-detected photothermal modalities were performed using a step-scan interferometer, demonstrating improved spectral range (541-4000 cm-1) when compared to optical photothermal microscopy with commercial laser sources (800-1800 cm-1 for this particular source) and improved spatial resolution, when compared to synchrotron microspectroscopy measurements. Following these initial validation studies, synchrotron Fourier-transform fluorescence-detected photothermal IR spectroscopy in combination with synchrotron microspectroscopy measurements was used to differentiate cells in mouse brain tissue sections, which requires submicron spatial resolutions beyond those accessible by IR spectroscopy alone.

Razumtcev, Aleksandr↗

Photoisomerization Dynamics in a Densely Packed Optically Transformable Azobenzene Monolayer

Molecular monolayers that can be reconfigured through the use of external stimuli promise to enable the creation of interfaces with precisely selected dynamically adjustable physical and electronic properties with potential impact ranging from electronics to energy storage. Azobenzene-containing molecular monolayers have multiple stable molecular conformations but face a challenging nanoscale problem associated with understanding the basic mechanisms of reconfiguration. Time-resolved X-ray reflectivity studies show that the reconfiguration of a densely packed rhenium–azobenzene monolayer occurs in a period of many seconds. Finally, the degree of reconfiguration from trans to cis forms depends on the integrated UV fluence and has kinetics that are consistent with a mechanism in which the transformation occurs through the nucleation and growth of nanoscale two-dimensional regions of the cis isomer.

36 MATERIALS SCIENCE↗

Masks for Hadamard transform optics, and weighing designs

This paper gives a brief survey of the design of masks for Hadamard spectrometers and image scanners. Three different criteria are described for judging a mask, as well as techniques for choosing masks that are not too far from the optimum.

Sloane, N. J. A.↗

High-speed joint-transform optical image correlator using GaAs/AlGaAs semi-insulating multiple quantum wells and diode lasers

We demonstrate a compact real-time optical image correlator using diode lasers and a semi-insulating GaAs/AlGaAs multiple-quantum-well (SI-MQW) device as the holographic element. With only 3 mW of power incident upon the SI-MQW device, the correlation is obtained in 1 microsec and can be erased in as fast as 2 microsec, which presents the possibility of a system capable of 3 x 10 exp 5 correlations/s. We also show that images can be stored for a controllable length of time (2-25 microsec), which presents possibilities for the use of the SI-MQW device as a data or image buffer memory.

Partovi, A.↗

Reconfigurable unitary transformations of optical beam arrays

Spatial transformations of light are ubiquitous in optics, with examples ranging from simple imaging with a lens to quantum and classical information processing in waveguide meshes. Multi-plane light converter (MPLC) systems have emerged as a platform that promises completely general spatial transformations, i.e., a universal unitary. However, until now, MPLC systems have demonstrated transformations that are far from general, e.g., converting from a Gaussian to Laguerre-Gauss mode. Here, we demonstrate the promise of an MLPC, the ability to impose an arbitrary unitary transformation that can be reconfigured dynamically. Specifically, we consider transformations on superpositions of parallel free-space beams arranged in an array, which is a common information encoding in photonics. We experimentally test the full gamut of unitary transformations for a system of two parallel beams and make a map of their fidelity. We obtain an average transformation fidelity of 0.85 ± 0.03. This high-fidelity suggests that MPLCs are a useful tool for implementing the unitary transformations that comprise quantum and classical information processing.

47 OTHER INSTRUMENTATION↗

Transformation of double-half inverse Gaussian hollow beams into superposition of finite Airy beams using an optical Airy transform

In the present work, we investigate theoretically the transformation of a double-half inverse Gaussian hollow (DHIGH) beam into a superposition of finite Airy beams by using an optical Airy transform system. The analytical expression of the generated finite Airy beam is derived by means of the generalized Huygens–Fresnel integral diffraction. Numerical calculations show that the optical Airy transform system converts the central dark spot of the hollow incident beam into peak intensity. It is demonstrated that the characteristics of the transverse intensity distribution of the output finite Airy beam are determined by the phase pattern’s constants of the Airy transform system and the radius size of the incident DHIGH beam. Moreover, it is shown that the profile of the central peak intensity of the generated beam can be controlled by means of the radius size of the incident hollow DHIGH beam.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optical joint transform correlation on the DMD

Initial experimental investigation of the deformable mirror device (DMD) in a joint optical transform correlation is reported. The inverted cloverleaf version of the DMD, in which form the DMD is phase-mostly but of limited phase range, is used. Binarized joint Fourier transforms were calculated for similar and dissimilar objects and written onto the DMD. Inverse Fourier transform was done in a diffraction order for which the DMD shows phase-mostly modulation. Matched test objects produced sharp correlation, distinct objects did not. Further studies are warranted and they are outlined.

Knopp, Jerome↗