Phase retrieval of reflection and transmission coefficients from Kramers–Kronig relations

Gralak, Boris; Lequime, Michel; Zerrad, Myriam; Amra, Claude

doi:10.1364/josaa.32.000456

Cited by 15 publications

(13 citation statements)

References 22 publications

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“…For the linear Lorentz oscillator model and an incident pulse, an exact analytic solution is available in integral form involving Green's functions, inverse Fourier and Laplace transforms. However it is difficult to extract useful design information from these complicated formulas; this requires either asymptotic analysis or various simplifying assumptions [12,13]. In our study, we combine scattering theory, Fourier, traveling wave and asymptotic analyses together with one-dimensional finite-difference time-domain (FDTD) numerical simulations [3,14,15] to provide interesting and practically useful scattering properties of thin films.…”

Section: Introductionmentioning

confidence: 99%

Scattering of a short electromagnetic pulse from a Lorentz–Duffing film: Theoretical and numerical analysis

et al. 2019

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We combine scattering theory, Fourier, traveling wave and asymptotic analyses together with numerical simulations to present interesting and practically useful properties of femtosecond pulse interaction with thin films. The dispersive material is described by a single resonance Lorentz model and its nonlinear extension with a cubic Duffing-type nonlinearity. A key feature of the Lorentz dielectric function is that its real part becomes negative between its zero and its pole, generating a forbidden region. We illustrate numerically the linear interaction of the pulse with the film using both scattering theory and Fourier analysis. Outside this region we show the generation of a sequence of pulses separated by round trips in the Fabry-Perot cavity due to multiple reflections. When the pulse spectrum is inside the forbidden region, we observe total reflection. Near the pole of the dielectric function, we demonstrate the slowing down of the pulse (group velocity tending to zero) in the medium that behaves as a high-Q cavity. We use the combination of analysis and simulations in the linear regime to validate the delta function approximation of the thin layer; this collapses the forbidden region to a single resonant point of the spectrum. We also study the single cycle pulse interaction with a thin film and show three distinct types of reflection: half-pulse, sinusoidal wave train and cosine wavelet. Finally we analyze the influence of a strong nonlinearity and observe that the film switches from reflecting to trasparent.

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Section: Introductionmentioning

confidence: 99%

Scattering of a short electromagnetic pulse from a Lorentz–Duffing film: Theoretical and numerical analysis

et al. 2019

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“…The problems of obtaining homogenized medium properties from emergent quantities using parameter retrieval methods for anisotropic media with aribitrarily oriented axes [31] and even bianisotropic metamaterials [32][33][34][35] have been addressed. Aspects of causality in such retrieval methods have been discussed [36,37]. Usually, magneto-dielectric coupling or bianisotropy is not very strong in most metamaterials, although it is present in many, and most of the models do not explicitly include bianisotropy [38].…”

Section: Effective Medium Theorymentioning

confidence: 99%

Properties of waveguides filled with anisotropic metamaterials

Bhardwaj¹,

Pratap²,

Semple³

et al. 2021

Comptes Rendus. Physique

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“…When such a sensor is probed with light, in addition to a change in transmission, the electromagnetic field undergoes a corresponding change in phase. This leads to a phase spectrum, φ(λ), whose relation to the transmission spectrum is governed by the Kramer-Kronig relations [31,32]. A change of the external physical quantity of interest, n, leads to a change in both the amplitude and phase of the probing light due to a shift of both the transmission and phase spectra [33][34][35][36], as shown in figure 1 To study the behavior and characteristic response of a sensor, we define the sensitivity as the inverse of the uncertainty in the estimation of the physical quantity of interest, ∆ 2 n , based on the estimation of a given parameter X [9,37]:…”

Section: Optical Resonance Sensing Schemesmentioning

confidence: 99%

“…where λ 0 is the resonance wavelength, ∆L is the half-width-at-half-maximum (HWHM), and i = √ −1. Since we only consider sensors with a linear response, their transmission and phase responses are related through the Kramers-Kronig relations [31,32]. As we show in B, for arbitrary values of T res and T off , the transmission and phase transfer functions for a Lorentzian lineshape are given by…”

Section: Quantum-enhanced Sensitivity Of Resonance Sensorsmentioning

confidence: 99%

Fundamental Sensitivity Bounds for Quantum Enhanced Optical Resonance Sensors Based on Transmission and Phase Estimation

Dowran,

Woodworth,

Kumar

et al. 2021

Preprint

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Quantum states of light can enable sensing configurations with sensitivities beyond the shotnoise limit (SNL). In order to better take advantage of available quantum resources and obtain the maximum possible sensitivity, it is necessary to determine fundamental sensitivity limits for different possible configurations for a given sensing system. Here, due to their wide applicability, we focus on optical resonance sensors, which detect a change in a parameter of interest through a resonance shift. We compare their fundamental sensitivity limits set by the quantum Cramér-Rao bound (QCRB) based on the estimation of changes in transmission or phase of a probing bright twomode squeezed state (bTMSS) of light. We show that the fundamental sensitivity results from an interplay between the QCRB and the transfer function of the system. As a result, for a resonance sensor with a Lorentzian lineshape a phase-based scheme outperforms a transmission-based one for most of the parameter space; however, this is not the case for lineshapes with steeper slopes, such as higher order Butterworth lineshapes. Furthermore, such an interplay results in conditions under which the phase-based scheme provides a higher sensitivity than the transmission-based one but a smaller degree of quantum enhancement. We also study the effect of losses external to the sensor on the degree of quantum enhancement and show that for certain conditions probing with a classical state can provide a higher sensitivity than probing with a bTMSS. Finally, we discuss detection schemes, namely optimized intensity-difference and optimized homodyne detection, that can achieve the fundamental sensitivity limits even in the presence of external losses.

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Phase retrieval of reflection and transmission coefficients from Kramers–Kronig relations

Cited by 15 publications

References 22 publications

Scattering of a short electromagnetic pulse from a Lorentz–Duffing film: Theoretical and numerical analysis

Scattering of a short electromagnetic pulse from a Lorentz–Duffing film: Theoretical and numerical analysis

Properties of waveguides filled with anisotropic metamaterials

Fundamental Sensitivity Bounds for Quantum Enhanced Optical Resonance Sensors Based on Transmission and Phase Estimation

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