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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Reality of superposition principle and autocorrelation function for short pulses

Chandrasekhar Roychoudhuri

Published Feb 9, 2006• 13 citations
Publisher

Abstract

We "see" light only when some material detectors (dipoles) respond to the incident EM field. EM fields do not operate on each other to make themselves visible to us. Superposition of multiple fields becomes manifest only when the intrinsic properties of these dipoles allow them to respond to all the superposed fields simultaneously and thereby summing the effects of all the fields. Accordingly, depending upon the different intrinsic properties of the detectors and the physical conditions of measurements (integration times, etc.) the manifestation of the "coherence" properties for the same set of superposed fields could be different. It is then prudent to represent the autocorrelation function for superposed fields in terms of the dipole undulation of the detectors rather than the fields themselves. Then the physics of the detectors and the measurement conditions automatically becomes an inherent part of the discussion on coherence. We illustrate our premise by presenting the analysis to understand the behavior of beam splitters, two-beam interferometers and an N-beam grating "interferometer" in terms of the autocorrelation functions due to a short pulse as would be experienced by the material dipoles of the beam splitters and detectors. Our approach reveals that superposition effects to become manifest the multiple fields must be physically superposed simultaneously on the detecting dipoles and hence the process is causal.

DOI
10.1117/12.670412

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We "see" light only when some material detectors (dipoles) respond to the incident EM field. EM fields do not operate on each other to make themselves visible to us. Superposition of multiple fields becomes manifest only when the intrinsic properties of these dipoles allow them to respond to all the superposed fields simultaneously and thereby summing the effects of all the fields. Accordingly, depending upon the different intrinsic properties of the detectors and the physical conditions of measurements (integration times, etc.) the manifestation of the "coherence" properties for the same set of superposed fields could be different. It is then prudent to represent the autocorrelation function for superposed fields in terms of the dipole undulation of the detectors rather than the fields themselves. Then the physics of the detectors and the measurement conditions automatically becomes an inherent part of the discussion on coherence. We illustrate our premise by presenting the analysis to understand the behavior of beam splitters, two-beam interferometers and an N-beam grating "interferometer" in terms of the autocorrelation functions due to a short pulse as would be experienced by the material dipoles of the beam splitters and detectors. Our approach reveals that superposition effects to become manifest the multiple fields must be physically superposed simultaneously on the detecting dipoles and hence the process is causal.
The intention of this paper is to underscore that to understand fundamentally new properties of light beams, we must first find the limits of semi classical model to explain optical interference phenomena. We claim that we have not yet reached that limit. Careful analysis of the processes behind detecting fringes indicate that the effect of superposition of multiple optical beams can become manifest only through the mediation of the detecting dipoles. Since the detectors are quantum mechanical, (i) the observed effects are different for different detectors for the same superposed light beams, and further, (ii) they are only capable of registering discrete number of "clicks", whose rate will vary with the incident intensity. A reduced rate of "clicks" at very low intensity does not prove that light consists of indivisible packets of energy. We have also experimentally demonstrated that (i) neither Fourier synthesis, nor, (ii) Fourier decomposition actually model the behavior of EM fields under all possible circumstances. Superposed light beams of different frequencies do not synthesize a new average optical frequency. A pure amplitude modulated pulse does not contain any of the mathematical, Fourier analyzed frequencies. The QED definition of photon being a Fourier mode in the vacuum, it necessarily becomes non-local. Since we have demonstrated that the Fourier theorem has various limitations in classical physics, its indiscriminate use in quantum mechanics should also be critically reviewed.
When two electromagnetic fields of different frequencies are physically superposed, the linear superposition equation implies that the fields readjust themselves into a new mean frequency whose common amplitude undulates at half their difference frequency. Neither of these mathematical frequencies are measurable quantities. We present a set of experiments underscoring that optical fields do not interfere with each other or modify themselves into a new frequency even when they are physically superposed. The multi-frequency interference effects are manifest only in materials with broad absorption bands as their constituent diploes attempt to respond collectively and simultaneously to all the optical frequencies of the superposed fields. Interference is causal and real since the dipoles carry out the operation of summation dictated by their quantum mechanical properties.
This chapter explains the basic mathematical framework behind the emergence of the superposition effect as experienced by detectors when simultaneously stimulated by more than one EM wave by modeling the light–matter interaction process in view of the Non-Interaction of Waves property. The growing field of quantum optics does treat the atoms and molecules as quantum dipoles and EM waves mostly as classical waves. The summation of amplitudes implied by the superposition principle is actually carried out by the oscillating dipoles as their single conjoint dipolar stimulation, while constrained by their intrinsic quantum properties. The measurable superposition effects, which are always reported by detectors, are colored by their own unique response characteristics. Thus, one can generate different types of measurable superposition effects simply by changing the quantum characteristics of the detectors.
The physical interaction processes behind the emergence of dark and bright fringes registered by the detectors at the output of optical interferometers is explained. This knowledge should be helpful to interferometrists to make better physical interpretations of their data. The belief in mysterious “interference of single indivisible photon” will disappear once we recognize that the spatial or temporal energy re-distributions are generated by the physical transformation experienced by the detecting molecules drawing energy from all the light beams. The molecules could be photodetectors at the interferometer output, or the beam combining dielectric boundary. The superposition principle (SP), represented by the linear mathematical sum of two or more wave amplitudes, does not represent an observable phenomenon. The superposition effect (SE), represented by the non-linear square modulus of the joint dipolar stimulation of the detectors by all the superposed waves, is observable. We present two laboratory experiments to clarify these points. Both classical beam combiners and quantum detectors are capable of generating superposition fringes of intensity variations. The logic of “quantumness” of light is narrowly relevant only when a quantum detector deciphers the fringes; it is not valid for classical beam combiners. We will also discuss “entanglement” based on these experiments.
Any superposition effect as measured (SEM) by us is the summation of simultaneous stimulations experienced by a detector due to the presence of multiple copies of a detectee each carrying different values of the same parameter. We discus the cases with light beams carrying same frequency for both diffraction and multiple beam Fabry-Perot interferometer and also a case where the two superposed light beams carry different frequencies. Our key argument is that if light really consists of indivisible elementary particle, photon, then it cannot by itself create superposition effect since the state vector of an elementary particle cannot carry more than one values of any parameter at the same time. Fortunately, semiclassical model explains all light induced interactions using quantized atoms and classical EM wave packet. Classical physics, with its deeper commitment to Reality Ontology, was better prepared to nurture the emergence of Quantum Mechanics and still can provide guidance to explore nature deeper if we pay careful attention to successful classical formulations like Huygens-Fresnel diffraction integral.
Comparing the radio and the light wave detection processes, this paper clarifies that what we normally call "interference" of EM waves, is actually the summation of the field induced signals carried out by the detectors. We have also presented a generalized definition of the superposition effects as measured (SEM) due to multiple physical steps behind any detection process. Thus the manipulation of the various physical properties of the detectors to various parameters of the EM waves can yield different "interference" effects for the same set of superposed waves. If EM waves interfered by themselves, such manipulation would not have been possible. We also give simple examples of visibility degradations due to rotation of the states of polarization and underscore that such degradation should not be assigned to degradation of coherence properties of the EM waves. It is due to the change in the stimulating amplitude, reduced by Malus'cosθ law, which is accessible to the uniaxial dipole like response of the detecting molecules.