200 femtosecond impulse response of a Fabry–Pérot etalon with the spectral ballistic imaging technique
TL;DR: In this article, the spectral ballistic imaging technique was used to measure the impulse response of a Fabry-Perot etalon with less than 0.2 ps temporal resolution and the results show excellent agreement with the theoretical predictions and negligible noise.
Abstract: We use the spectral ballistic imaging technique to measure the impulse response of a Fabry–Perot etalon with less than 0.2 ps temporal resolution. The results show excellent agreement with the theoretical predictions and negligible noise. Comparison to the Kramers–Kronig method along with its limitations is also presented.
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TL;DR: In this paper, the Kramers-Kronig (KK) algorithm is applied to reconstruct the impulse response of a diffusive medium, and it is demonstrated by a simulation of a 1D scattering medium with realistic parameters that its impulse response can be generated from the KK method with high accuracy.
Abstract: The Kramers-Kronig (KK) algorithm, useful for retrieving the phase of a spectrum based on the known spectral amplitude, is applied to reconstruct the impulse response of a diffusive medium. It is demonstrated by a simulation of a 1D scattering medium with realistic parameters that its impulse response can be generated from the KK method with high accuracy.
13 citations
TL;DR: It is shown that by averaging the temporal optical field response of a diffusive medium (as opposed to the optical intensity response) the signal-to-noise ratio of the object's reflection can be improved considerably.
Abstract: We measure the sub-picosecond optical impulse response of a system consisting of a varying 1D diffusive medium and a stationary hidden object. It is shown that by averaging the temporal optical field response of a diffusive medium (as opposed to the optical intensity response) the signal-to-noise ratio of the object’s reflection can be improved considerably. The Spectral-Ballistic-Imaging technique is used to reconstruct the optical-field impulse response with a 200fs temporal resolution.
7 citations
TL;DR: In this paper, the phase spectrum is reconstructed from the amplitude spectrum in a finite spectral range with the aid of one or more phase-anchoring values using spectral ballistic imaging to partially mitigate the finite-range effects.
Abstract: The differential multiply subtractive Kramers-Kronig (DMSKK) method is utilized for deriving the optical spectral response of a 1D scattering medium The technique is based on the multiply subtractive Kramers-Kronig technique, where the phase spectrum is reconstructed from the amplitude spectrum in a finite spectral range with the aid of one or more phase-anchoring values We employ a new phase-anchoring technique in the DMSKK method to partially mitigate the finite-range effects This method incorporates spectral ballistic imaging to anchor the phase difference (instead of the phase directly) at one or more reference wavelengths The simplicity of phase derivative measurements and its utilization in the DMSKK method are emphasized by a simple experiment
5 citations
TL;DR: An efficient digital signal processing algorithm is suggested, which includes several fast Fourier transforms, to efficiently reconstruct the impulse response of a diffusive medium from its amplitude spectrum.
Abstract: We suggest adopting an efficient digital signal processing algorithm, which includes several fast Fourier transforms, to efficiently reconstruct the impulse response of a diffusive medium from its amplitude spectrum. It is also demonstrated that the singularities, which appear in the phase spectrum reconstruction, can be easily eliminated through the implementation of at least two types of data padding.
4 citations
TL;DR: In this paper, the authors apply the multiply subtractive anchoring method for phase spectrum retrieval, which is based on the fast Fourier transform and Lagrange polynomials.
Abstract: We apply the multiply subtractive anchoring method for efficient phase spectrum retrieval, which is based on the fast Fourier transform and Lagrange polynomials. Because the polynomials eventually diverge, choosing the optimum anchoring points is crucial. It is demonstrated that, if more than two anchoring points are chosen, the algorithm’s performance can easily deteriorate.
2 citations
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TL;DR: In this article, a general formula for the index of refraction in terms of the atomic absorption coefficient α and the critical frequencies is given, from the condition, experimentally verified, that the electrons in the atom for impressed frequencies, large compared to their natural frequencies, shall act like free electrons as far as the index is concerned, a relation is obtained for α.
Abstract: After a brief summary of the ideas underlying the quantum theory of dispersion it is shown that it can be applied to the refraction of x-rays, although the assumption that the number of atoms in a wave length cube is large is no longer satisfied. A general formula for the index of refraction in terms of the atomic absorption coefficient α and the critical frequencies is given. From the condition, experimentally verified, that the electrons in the atom for impressed frequencies, large compared to their natural frequencies, shall act like free electrons as far as the index of refraction is concerned, a relation is obtained for α. From the failure of this relation when applied to the groups of electrons separately, conclusions are drawn as to the coupling of the groups. Some considerations on the origin of the Compton shifted radiation are added, from which it appears that in the wave description this radiation must be regarded as coming from all the atoms and as being coherent with the incident waves; a result suited to stress the difficulty of harmonizing the wave picture with that of quantum processes in the atoms.1
1,531 citations
TL;DR: A rigorous proof is given of the logical equivalence of strict causality ("no output before the input") and the validity of a dispersion relation, e.g., the relation expressing the real part of a generalized scattering amplitude as an integral involving the imaginary part.
Abstract: "Strict causality" is the assumption that no signal whatsoever can be transmitted over a space-like interval in space-time, or that no signal can travel faster than the velocity of light in vacuo. In this paper a rigorous proof is given of the logical equivalence of strict causality ("no output before the input") and the validity of a dispersion relation, e.g., the relation expressing the real part of a generalized scattering amplitude as an integral involving the imaginary part. This proof applies to a general linear system with a time-independent connection between the output and a freely variable input and has the advantage over previous work that no tacit assumptions are made about the analytic behavior or single-valuedness of the amplitude, but, on the contrary, strict causality is shown to imply that the generalized scattering amplitude is analytic in the upper half of the complex frequency plane. The dispersion relations are given first as a relation between the real and imaginary parts of the generalized scattering amplitude and then in terms of the complex phase shift.
819 citations
TL;DR: In this article, a sinusoidally modulated fight beam undergoes phase shift when traveling along a fiber when its wavelength is changed, which allows simple and accurate measurements of chromatic dispersion in optical fibers.
Abstract: A sinusoidal technique is reported, which allows simple and accurate measurements of chromatic dispersion in optical fibers. It is based on the phase shift which a sinusoidally modulated fight beam undergoes while traveling along a fiber when its wavelength is changed. The choice of a multiple LED's source permits the continuous spectral covering from 750 to 1600 nm;easily available instrumentation and devices are needed for the measurement setup. The technique is reported in detail by showing results obtained in multimode fibers; statistical evaluation of its accuracy and a comparison with conventional methods are carried out. An accuracy of a few picoseconds in relative delay and of ∓1 ps/nm . km in chromatic dispersion are demonstrated, that compare very favorably with the existing techniques.
181 citations
TL;DR: Direct measurements of the frequency dependence of the optical group delay for a number of optical components commonly used in femtosecond optics are reported, obtaining measurement accuracy of about ±1 fsec over the spectral range of 400–750 nm.
Abstract: We report direct measurements of the frequency dependence of the optical group delay for a number of optical components commonly used in femtosecond optics. We have investigated the group-delay errors that occur on reflection from metal and dielectric mirrors under various conditions and passage through devices that introduce angular dispersion. We obtain measurement accuracy of about ±1 fsec over the spectral range of 400–750 nm.
131 citations
TL;DR: In this paper, dispersion inequalities are presented to check for the selfconsistency of experimentally obtained complex moduli, such as the complex dielectric constant, magnetic permeability, and complex bulk and shear moduli of viscoelastic materials.
Abstract: Dispersion inequalities are presented to check for the self-consistency of experimentally obtained complex moduli, such as the complex dielectric constant, magnetic permeability, and complex bulk and shear moduli of viscoelastic materials. Unlike the Kramers-Kronig dispersion relations, they only require measurements over a finite frequency range. They can provide highly accurate interpolation formulas for the real part, given its value at a few selected frequencies and given the imaginary part over a range of frequencies.
100 citations