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In this work we establish universal ensemble independent bounds on the mean and variance of the mutual information and channel capacity for imaging through a complex medium. Both upper and lower bounds are derived and are solely dependent on the mean transmittance of the medium and the number of degrees of freedom N. In the asymptotic limit of large N, upper bounds on the channel capacity are shown to be well approximated by that of a bimodal channel with independent identically Bernoulli distributed transmission eigenvalues. Reflection based imaging modalities are also considered and permitted regions in the transmission-reflection information plane defined. Numerical examples drawn from the circular and DMPK random matrix ensembles are used to illustrate the validity of the derived bounds. Finally, although the mutual information and channel capacity are shown to be non-linear statistics of the transmission eigenvalues, the existence of central limit theorems is demonstrated and discussed. [ABSTRACT FROM AUTHOR]

Optimization of polarimeters has historically been achieved using an assortment of performance metrics. Selection of an optimization parameter is, however, frequently made on an ad hoc basis. We rigorously demonstrate that optimization strategies in Stokes polarimetry based on three common metrics, namely the Frobenius condition number of the instrument matrix, the determinant of the associated Gram matrix, or the equally weighted variance, are frequently formally equivalent. In particular, using each metric, we derive the same set of constraints on the measurement states, correcting a previously reported proof, and show that these can be satisfied using spherical 2 designs. Discussion of scenarios in which equivalence between the metrics breaks down is also given. Our conclusions are equally applicable to optimization of the illumination states in Mueller matrix polarimetry. [ABSTRACT FROM AUTHOR]

Complete determination of the polarization state of light requires at least four distinct projective measurements of the associated Stokes vector. Stability of state reconstruction, however, hinges on the condition number k of the corresponding instrument matrix. Optimization of redundant measurement frames with an arbitrary number of analysis states, m, is considered in this Letter in the sense of minimization of k. The minimum achievable k is analytically found and shown to be independent of m, except for m = 5 where this minimum is unachievable. Distribution of the optimal analysis states over the Poincare sphere is found to be described by spherical 2 designs, including the Platonic solids as special cases. Higher order polarization properties also play a key role in nonlinear, stochastic, and quantum processes. Optimal measurement schemes for nonlinear measurands of degree t are hence also considered and found to correspond to spherical 21 designs, thereby constituting a generalization of the concept of mutually unbiased bases. [ABSTRACT FROM AUTHOR]

In this work, we theoretically and experimentally investigate the thermal response of whispering gallery mode microresonators operating in an aqueous glycerol medium. Thermal stabilisation of the resonance wavelength is realised by appropriate choice of the resonator radius and glycerol concentration, with a 60 fold reduction in thermal sensitivity demonstrated. Finally, we employ our stabilised system to determine the thermal dependence of the molecular polarisability of adsorbed bovine serum albumin molecules and the refractive index of dextran and poly(diallyldimethylammonium chloride) coatings. [ABSTRACT FROM AUTHOR]

In this Letter we propose the use of whispering gallery mode resonance tracking as a label-free optical means to monitor diffusion kinetics in glassy polymer microspheres. Approximate solutions to the governing diffusion equations are derived for the case of slow relaxation and small Stefan number. Transduction of physical changes in the polymer, including formation of a rubbery layer, swelling, and dissolution, into detectable resonance shifts are described using a perturbative approach. Concrete examples of poly(methyl methacrylate) and polystyrene spheres in water are considered. [ABSTRACT FROM AUTHOR]

Biosensing relies on the detection of molecules and their specific interactions. It is therefore highly desirable to develop transducers exhibiting ultimate detection limits. Microcavities are an exemplary candidate technology for demonstrating such a capability in the optical domain and in a label-free fashion. Additional sensitivity gains, achievable by exploiting plasmon resonances, promise biosensing down to the single-molecule level. Here, we introduce a biosensing platform using optical microcavity-based sensors that exhibits single-molecule sensitivity and is selective to specific single binding events. Whispering gallery modes in glass microspheres are used to leverage plasmonic enhancements in gold nanorods for the specific detection of nucleic acid hybridization, down to single 8-mer oligonucleotides. Detection of single intercalating small molecules confirms the observation of single-molecule hybridization. Matched and mismatched strands are discriminated by their interaction kinetics. Our platform allows us to monitor specific molecular interactions transiently, hence mitigating the need for high binding affinity and avoiding permanent binding of target molecules to the receptors. Sensor lifetime is therefore increased, allowing interaction kinetics to be statistically analysed. [ABSTRACT FROM AUTHOR]

Shifts of the resonance frequency of high Q whispering gallery modes (WGMs) in spherical dielectric microresonators by plasmonic nanoparticles can be greater than the WGM line width, such that the perturbation theory commonly used for describing resonance shifts by dielectric nanoparticles (Teraoka and Arnold 2006 J. Opt. Soc. Am. B 23 1381) is no longer applicable. This paper therefore reports on an analytic framework, based on generalized Lorenz-Mie theory, capable of describing resonance shifts by metallic nanoparticles supporting plasmon oscillations. Generalization to nanoparticles of arbitrary geometry is presented by employing the extended boundary condition method. Within this framework, hybrid resonance conditions for coupled spherical photonic and plasmonic resonators are established and shown to simplify for small plasmonic nanoparticles. Approximate analytic formulae are derived for the shift and broadening of the isolated WGM and plasmon resonances, from which either apparent resonance shifts or mode splitting are shown to follow. Tuning of plasmon resonances using, for example, core-shell nanoparticles to attain a large spectral overlap between WGM and plasmon resonances is demonstrated to significantly enhance the magnitude of resonance shifts, with a 60-fold enhancement achieved without any optimization. Hybridization of photonic-plasmonic resonances is furthermore demonstrated (in addition to hybridization of transverse electric-transverse magnetic WGMs) and the associated level repulsion illustrated. Finally, the dependence of WGM resonance shifts on the orientation of silver nanorods is theoretically investigated and found to be strong by virtue of the asymmetry of the nanorod. [ABSTRACT FROM AUTHOR]

A significant number of areal surface topography measuring instruments, largely based on optical techniques, are commercially available. However, implementation of optical instrumentation into production is currently difficult due to the lack of understanding of the complex interaction between the light and the component surface. Studying the optical transfer function of the instrument can help address this issue. Here a review is given of techniques for the measurement of optical transfer functions. Starting from the basis of a spatially coherent, monochromatic confocal scanning imaging system, the theory of optical transfer functions in three-dimensional (3D) imaging is presented. Further generalizations are reviewed allowing the extension of the theory to the description of conventional and interferometric 3D imaging systems. Polychromatic transfer functions and surface topography measurements are also discussed. Following presentation of theoretical results, experimental methods to measure the optical transfer function of each class of system are presented, with a focus on suitable methods for the establishment of calibration standards in 3D imaging and surface topography measurements. [ABSTRACT FROM AUTHOR]

Near-field enhancements of the electric field at the center of spheroidal multilayer metallic nanoparticles (NPs) are investigated when illuminated by focused beams of arbitrary field structure (i.e., amplitude, phase, and polarization distributions). Employing a Mie-type representation, the enhancement at the center of such NPs (such as a core-shell geometry) is analytically shown to be independent of the field structure of the illumination beam for both on- and off-axis NPs. Furthermore, it is shown that, to leading order, the average field enhancement in the near field of these NPs is also approximately illumination independent. [ABSTRACT FROM AUTHOR]

Directionality inherent in the polarization of light affords the means of performing robust dynamic orientational measurements of molecules and asymmetric scatterers. In this paper, the precision with which measurements of this kind can be made is quantified for a number of common polarizationbased measurement architectures using a metric derived from Fisher information. Specifically, a fundamental limit of 0.5 radian per detected photon (on average) is found, thus highlighting the importance of maximizing photon numbers by correct fluorophore selection. Informational dips, whereby measurement precision is degraded, are shown to arise in many realistic measurement scenarios, particularly for inference from null readings. The severity of these precision losses is therefore considered, and it is shown to decrease with increased system redundancy. Contamination of measured data from coherently and incoherently radiating extraneous sources, furthermore, causes a loss of precision. Analytic and numerical results are hence also presented in this vein. [ABSTRACT FROM AUTHOR]

Rigorous, closed form expressions are derived for non-paraxial imaging of sources of multipole radiation from which conservation of angular momentum (AM) flux is established. Coupling of spin and orbital optical AM flux is also quantitatively investigated, highlighting the importance of spin-orbit interactions in high numerical aperture imaging. [ABSTRACT FROM AUTHOR]

In the search for higher resolution, modern day imaging systems frequently employ objective lenses with a high numerical aperture. Propagation of light through such lenses introduces a spatial variation in the polarisation across the beam profile, whilst the inherently large propagation angles also necessitates inclusion of additional transverse and axial electric field components in modelling. A full treatment of polarisation effects including such considerations has implications at all stages in the image formation process, namely; illumination, scattering from the sample, imaging and detection. This tutorial review considers each stage in turn and details the theories required for rigorous modelling and analysis. In particular a generalisation of the well known Jones calculus and ray tracing methods are shown to conveniently and accurately allow rigorous studies of high numerical aperture confocal and conventional polarised light microscopes, imaging samples of arbitrary complexity. Generalisation of the illumination to partially coherent, partially polarised systems is also briefly given. Whilst rigorous modelling techniques can prove time consuming a number of simplifications and approximations can be adopted, allowing computational gains to be achieved. Discussion in this vein is hence also presented. [ABSTRACT FROM AUTHOR]

Brillouin microscopy is an emerging imaging modality that provides fundamental information about mechanical properties of media in a non-contact manner. To date, low numerical aperture (NA) optics have been used, due to noticeable angular broadening of the Brillouin spectrum at higher NAs. In this work, we investigate theoretically and experimentally the dependence of spectral broadening effects in Brillouin imaging on system NA, for both 90° and 180° scattering geometries. Lineshape deformations and broadening are found to be minimised in a backscattering geometry, hence paving the way for high resolution in-vivo mechanical imaging. [ABSTRACT FROM AUTHOR]

Abstract: We report on measurements and characterization of polarization properties of Second Harmonic (SH) signals using a four-channel photon counting based Stokes polarimeter. In this way, the critical polarization parameters can be obtained concurrently without the need of repeated image acquisition. The critical polarization parameters, including the degree of polarization (DOP), the degree of linear polarization (DOLP), and the degree of circular polarization (DOCP), are extracted from the reconstructed Stokes vector based SH images in a pixel-by-pixel manner. The measurements are further extended by varying the polarization states of the incident light and recording the resulting Stokes parameters of the SH signal. In turn this allows the molecular structure and orientation of the samples to be determined. Use of Stokes polarimetry is critical in determination of the full polarization state of light, and enables discrimination of material properties not possible with conventional crossed-polarized detection schemes. The combination of SHG microscopy and Stokes polarimeter hence makes a powerful tool to investigate the structural order of targeted specimens. [Copyright &y& Elsevier]

Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises, for example, in optical scattering or electron transport, typically necessitates cascading of multiple random matrices drawn from an underlying ensemble for thin media, greatly increasing the computational burden. Here we propose a dual pool based bootstrapping approach to speed up statistical studies of scattering in thick random media. We examine how potential matrix reuse in a pool based approach can impact statistical estimates of population averages. Specifically, we discuss how both bias and additional variance in the sample mean estimator are introduced through bootstrapping. In the diffusive scattering regime, the extra estimator variance is shown to originate from samples in which cascaded transfer matrices are permuted matrix products. Through analysis of the combinatorics and cycle structure of permutations we quantify the resulting correlations. Proofs of several analytic formulas enumerating the frequency with which correlations of different strengths occur are derived. Extension to the ballistic regime is briefly considered.

We report sensing of single nanoparticles using disordered metallic nanoisland substrates supporting surface plasmon polaritons (SPPs). Speckle patterns arising from leakage radiation of elastically scattered SPPs provide a unique fingerprint of the scattering microstructure at the sensor surface. Experimental measurements of the speckle decorrelation are presented and shown to enable detection of sorption of individual gold nanoparticles and polystyrene beads. Our approach is verified through bright-field and fluorescence imaging of particles adhering to the nanoisland substrate., (Creative Commons Attribution license.)

Small perturbations in the dielectric environment around resonant dielectric structures usually lead to a frequency shift of the resonator modes directly proportional to the polarizability of the perturbation. Here, we report experimental observations of strong frequency shifts that can oppose and even exceed the contribution of the perturbations' polarizability. We show in particular how the mode frequencies of a lithium niobate whispering-gallery-mode resonator are shifted by planar substrates-of refractive indices ranging from 1.50 to 4.22-contacting the resonator rim. Both blue- and redshifts are observed, as well as an increase in mode linewidth, when substrates are moved into the evanescent field of the whispering gallery mode. We compare the experimental results to a theoretical model by Foreman et al. [J. Opt. Soc. Am. B33, 2177 (2016)JOBPDE0740-322410.1364/JOSAB.33.002177] and provide an additional intuitive explanation based on the Goos-Hänchen shift for the optical domain, with applications to dielectric structures ranging from meta-surfaces to photonic crystal cavities.

Polarimetric imaging can provide valuable information about biological samples in a wide range of applications. Detrimental tissue scattering and depolarization however currently hamper in vivo polarization imaging. In this work, single pixel imaging is investigated as a means of reconstructing polarimetric images through scattering media. A theoretical imaging model is presented, and the recovery of the spatially resolved Mueller matrix of a test object behind a scattering phantom is demonstrated experimentally.

Brillouin spectroscopy can suffer from low signal-to-noise ratios (SNRs). Such low SNRs can render common data analysis protocols unreliable, especially for SNRs below ∼10. In this work we exploit two denoising algorithms, namely maximum entropy reconstruction (MER) and wavelet analysis (WA), to improve the accuracy and precision in determination of Brillouin shifts and linewidth. Algorithm performance is quantified using Monte-Carlo simulations and benchmarked against the Cramér-Rao lower bound. Superior estimation results are demonstrated even at low SNRs (≥ 1). Denoising is furthermore applied to experimental Brillouin spectra of distilled water at room temperature, allowing the speed of sound in water to be extracted. Experimental and theoretical values were found to be consistent to within ±1% at unity SNR., Competing Interests: The authors declare that there are no conflicts of interest., (Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.)

Interactions between whispering gallery modes (WGMs) and small nanoparticles are commonly modeled by treating the particle as a point dipole scatterer. This approach is assumed to be accurate as long as the nanoparticle radius, a, is small compared to the WGM wavelength λ. In this Letter, however, we show that the large field gradients associated with the evanescent decay of a WGM causes the dipole theory to significantly underestimate the interaction strength and, hence, the induced WGM resonance shift, even for particles as small as a∼λ/10. To mitigate this issue, we employ a renormalized Born approximation to more accurately determine nanoparticle-induced resonance shifts and, hence, enable improved particle sizing. The domain of validity of this approximation is investigated, and supporting experimental results are presented.

Plasmonic metasurfaces enable simultaneous control of the phase, momentum, amplitude and polarization of light and hence promise great utility in realization of compact photonic devices. In this paper, we demonstrate a novel chip-scale device suitable for simultaneous polarization and spectral measurements through use of six integrated plasmonic metasurfaces (IPMs), which diffract light with a given polarization state and spectral component into well-defined spatial domains. Full calibration and characterization of our device is presented, whereby good spectral resolution and polarization accuracy over a wavelength range of 500-700 nm is shown. Functionality of our device in a Müller matrix modality is demonstrated through determination of the polarization properties of a commercially available variable waveplate. Our proposed IPM is robust, compact and can be fabricated with a single photolithography step, promising many applications in polarization imaging, quantum communication and quantitative sensing.

We present a comprehensive overview of sensor technology exploiting optical whispering gallery mode (WGM) resonances. After a short introduction we begin by detailing the fundamental principles and theory of WGMs in optical microcavities and the transduction mechanisms frequently employed for sensing purposes. Key recent theoretical contributions to the modeling and analysis of WGM systems are highlighted. Subsequently we review the state of the art of WGM sensors by outlining efforts made to date to improve current detection limits. Proposals in this vein are numerous and range, for example, from plasmonic enhancements and active cavities to hybrid optomechanical sensors, which are already working in the shot noise limited regime. In parallel to furthering WGM sensitivity, efforts to improve the time resolution are beginning to emerge. We therefore summarize the techniques being pursued in this vein. Ultimately WGM sensors aim for real-world applications, such as measurements of force and temperature, or alternatively gas and biosensing. Each such application is thus reviewed in turn, and important achievements are discussed. Finally, we adopt a more forward-looking perspective and discuss the outlook of WGM sensors within both a physical and biological context and consider how they may yet push the detection envelope further.

A theoretical analysis of detection limits in swept-frequency whispering gallery mode biosensing modalities is presented based on application of the Cramér-Rao lower bound. Measurement acuity factors are derived assuming the presence of uncoloured and 1/ f Gaussian technical noise. Frequency fluctuations, for example arising from laser jitter or thermorefractive noise, are also considered. Determination of acuity factors for arbitrary coloured noise by means of the asymptotic Fisher information matrix is highlighted. Quantification and comparison of detection sensitivity for both resonance shift and broadening sensing modalities are subsequently given. Optimal cavity and coupling geometries are furthermore identified, whereby it is found that slightly under-coupled cavities outperform critically and over coupled ones.