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Optics and Spectroscopy

On the relation between retarded and advanced arrival of a pulse at the output of an optical system

Nikolai S. Bukhman

Published Apr 23, 2004• 10 citations
Publisher

Abstract

It is shown that the possibility of negative delay time of a pulse at the output of an optical system (compared to the pulse at its input) is a necessary consequence of the possibility of positive delay time of the pulse and the superposition principle. In particular, two optical systems with different positive delay times are sufficient for creating an optical system with a negative delay time. The negative delay time of a pulse can be considered as a spline extrapolation of its time dependence resulting from the interference of several copies of the pulse with different delays. It is shown that a negative delay time of a pulse arises necessarily in any interferometer in an area of destructive interference of two copies of the initial pulse that are similar in amplitude and undergo different delay times.

DOI
10.1134/1.1719154

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It is shown that the possibility of negative delay time of a pulse at the output of an optical system (compared to the pulse at its input) is a necessary consequence of the possibility of positive delay time of the pulse and the superposition principle. In particular, two optical systems with different positive delay times are sufficient for creating an optical system with a negative delay time. The negative delay time of a pulse can be considered as a spline extrapolation of its time dependence resulting from the interference of several copies of the pulse with different delays. It is shown that a negative delay time of a pulse arises necessarily in any interferometer in an area of destructive interference of two copies of the initial pulse that are similar in amplitude and undergo different delay times.
The arrival time of a light pulse at a point in space is defined using a time expectation integral over the Poynting vector. The delay between pulse arrival times at two distinct points is shown to consist of two parts: a spectral superposition of group delays (inverse of group velocity) and a delay due to spectral reshaping via absorption or amplification. The result provides a context wherein group velocity is always meaningful even for broad band pulses and when the group velocity is superluminal or negative. The result imposes luminality on sharply defined pulses.
Recent manifestations of apparently faster-than-light effects confirmed our predictions that the group velocity in transparent optical media can exceed c. Special relativity is not violated by these phenomena. Moreover, in the electronic domain, the causality principle does not forbid negative group delays of analytic signals in electronic circuits, in which the peak of an output pulse leaves the exit port of a circuit before the peak of the input pulse enters the input port. Furthermore, pulse distortion for these 'superluminal' analytic signal scan be negligible in both the optical and electronic domains. Here we suggest an extension of these ideas to the microelectronic domain. The underlying principle is that negative feedback can be used to produce negative group delays. Such negative group delay scan be used to cancel out the positive group delays due to 'transistor latency' as well as the 'propagation delays' due to the interconnects between transistors. Using this principle, it is possible to speed up computer systems.
We present a simple electronic circuit that produces negative delays. When a pulse is sent to the circuit as input, the output is a pulse with a similar wave form that is shifted forward in time. The advance time or negative delay can be increased to the order of seconds so that we can observe the advance with the naked eye by observing two light emitting diodes that are connected to the input and the output. The negative group delay in the electronic circuit shares the same mechanism with superluminal light propagation, where the group velocity exceeds the speed of light or even becomes negative.
We have theoretically investigated the time delay of a chirped light pulse,defined as the temporal difference of peaks of the output and input light pulses after transmitting a Fabry-Perot interferometer.The results show that for an interferometer of known parameters,the chirp of the light pulse makes the time delaly become intensively smaller.The mismatch between the central frequency of the light pulse and the resonance frequency of the interferometer also has an influence on the time delay.Under some circumstances,this mismatch will induce a time delay smaller than t0 that is defined as the one-way traverse time of the light inside the interferometer.
We have theoretically investigated the time delay of a chirped light pulse, defined as the temporal difference of peaks of the output and input light pulses after transmitting a Fabry-Perot interferometer. The results show that for an interferometer of known parameters, the chirp of the light pulse makes the time delay become intensively smaller. The mismatch between the central frequency of the light pulse and the resonance frequency of the interferometer also has an influence on the time delay. Under some circumstances, this mismatch will induce a time delay smaller than t0 that is defined as the one-way traverse time of the light inside the interferometer.