Two theorems for the group velocity in dispersive media

Bolda, Eric L.; Chiao, Raymond Y.; Garrison, J. C.

doi:10.1103/physreva.48.3890

Cited by 146 publications

(71 citation statements)

References 7 publications

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“…The exponential suppression of (5.7) near q + , where the weak value is maximal in magnitude, is generic of the phenomenon of Fourier superoscillations [40,41,42,43,47], exhibited by the amplitude n 2 ; j|e iĴzq |n 1 ; j near q + . This suppression imposes a "robustness" condition on the prior distribution in q if one is to measure eccentric weak values near q + : not only must the prior distribution be "sharp" around q = q + , but additionally it must show a sufficiently fast fall-off to overcome the exponential rise in likelihood.…”

Section: Illustration Of the Qavw Frameworkmentioning

confidence: 99%

Quantum averages of weak values

2005

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We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a definite mechanical effect on a measuring probe specifically designed to minimize the back-reaction on the measured system. We then present a new framework for general measurement conditions (where the back-reaction on the system may not be negligible) in which the measurement outcomes can still be interpreted as quantum averages of weak values. We show that in the classical limit, there is a direct correspondence between quantum averages of weak values and posterior expectation values of classical dynamical properties according to the classical inference framework.

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Section: Illustration Of the Qavw Frameworkmentioning

confidence: 99%

Quantum averages of weak values

2005

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“…In a series of papers [7,18,19,[22][23][24][25][26], Chiao and coworkers showed theoretically that anomalous dispersion can occur inside a transparent material, particularly on the DC side of a single gain line. It was predicted that by using a gain doublet [22], it is possible to obtain a transparent anomalous dispersion region where the group velocity of a light pulse exceeds c with almost no pulse distortion.…”

Section: Pacs Number(s)mentioning

confidence: 99%

“…More recently, it has been considered [7][8][9][10][11][13][14][15][16][17][18][19][21][22][23][24]] to use various schemes including the anomalous dispersion near an absorption line [8][9][10][11], nonlinear [13] and linear gain lines [14][15][16][17][18][19][22][23][24], active plasma medium [17,21], or in a tunneling barrier [25,26] to observe these effects. Sometimes it is applied [9][10][11]25,26] to observe superluminal propagation of light pulses.…”

Section: Pacs Number(s)mentioning

confidence: 99%

Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity

Dogariu¹,

Kuzmich²,

Wang³

2001

Phys. Rev. A

301

175

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Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light pulse propagation can be observed even at a negative group velocity through a transparent medium with almost no pulse distortion. Consequently, a negative transit time is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the rephasing process owing to the wave nature of light and is not at odds with either causality or Einstein's theory of special relativity.

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“…The emphasis is on the content of the time constant because without the , NGD is not exhibited. This, however, does not violate the causality since the initial transient pulse is still limited to the front velocity, which will never exceed the speed of light [1], [2].…”

Section: Introductionmentioning

confidence: 99%

“…Since NGD occurs at the range of frequencies where the absorption or the attenuation is maximum [2], conventionally, in the microwave regime, bandstop structures are used to realize NGD circuitry. Based on either series or shunt resonators, many active and passive NGD circuitries have been proposed and demonstrated with or without tunability [6]- [11].…”

Section: Introductionmentioning

confidence: 99%

Maximally Flat Negative Group-Delay Circuit: A Microwave Transversal Filter Approach

Itoh

2014

IEEE Trans. Microwave Theory Techn.

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Abstract-A comprehensive method to synthesize negative group delay (NGD) in the microwave regime with a maximally flat response is proposed in this paper. This method is based on transversal-filter topologies; it will be shown that by choosing proper coupling coefficients of each tap of a transversal filter, we can realize NGDs with maximally flat characteristics at the output of the transversal filter. The desired coefficients to realize maximally flat NGDs with various amount of group delay are analytically derived and tabulated in this paper. Furthermore, the results are verified experimentally through microwave transversal-filter approaches in both passive and active ways using multi-section asymmetric directional couplers and distributed amplifiers.

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Two theorems for the group velocity in dispersive media

Cited by 146 publications

References 7 publications

Quantum averages of weak values

Quantum averages of weak values

Transparent anomalous dispersion and superluminal light-pulse propagation at a negative group velocity

Maximally Flat Negative Group-Delay Circuit: A Microwave Transversal Filter Approach

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