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A Deeper Look at the Fundamentals of Heterodyne Detection Requirements

Chandrasekhar Roychoudhuri, Narasimha S. Prasad

Published Jul 8, 2007• 2 citations
OpenAlex

Abstract

We generally accept the experimentally observed criteria for heterodyne detections that the two waves that are mixed must (i) be collinear, (ii) have matched wave fronts and (iii) cannot be orthogonally polarized. We have not found in the literature adequate physical explanations for these requirements. The purpose of this paper is to find deeper physical understanding of the coherent heterodyne detection processes that could lead to better coherent laser radar system designs1. We find that there are a number of unresolved paradoxes in classical and quantum optics regarding the definitions and understanding of the "interference" and "coherence" properties of light, which are attributed as essentially due to inherent properties of the EM waves. A deeper exploration indicates that it is the various quantum mechanical properties of the detecting material dipoles that make light detectable (visible, or measurable) to us. Accordingly, all the properties that we generally attribute to only light, are in reality manifestations of collective properties of dipole-light interactions. "Interference" and "coherence" can be better understood in terms of this mutual interaction, followed by energy absorption by the dipoles from EM wave fields, manifesting in some measurable transformation of the detecting dipoles. Light beams do not interfere by themselves. The superposition effects due to light beams become manifest through the response characteristics of the detecting dipoles. In this paper, we will show some preliminary expe rimental results that clearly demonstrate that the heterodyning wave fronts have quantitative degradation in signal generation as the angle between them deviates from perfect collinearity. Subsequently, we will propose a hypothesis for this behavior. We will present experimental data establishing that the so called incoherent light can be detected through heterodyne mixing as long as the pulse length contained in the "incoherent" light is longer than the response time of the detector. We will also present a correspondingly better interpretation of two distinguishable coherence properties, temporal coherence and spectral coherence. Our investigation provides a deeper insight into how to rela x various system requirements for heterodyne detection and accordingly develop systems that are simpler, more reliable and lower in cost. Also, we believe that engineering of detector architecture by appropriately modifying dipole behavior using emerging nanotechnology to optimize heterodyne efficiency will be advantageous.

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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.

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IEEE Journal of Quantum Electronics•Aug 1, 1975•7 citations
We generally accept the experimentally observed criteria for heterodyne detections that the two waves that are mixed must (i) be collinear, (ii) have matched wave fronts and (iii) cannot be orthogonally polarized. We have not found in the literature adequate physical explanations for these requirements. The purpose of this paper is to find deeper physical understanding of the coherent heterodyne detection processes that could lead to better coherent laser radar system designs1. We find that there are a number of unresolved paradoxes in classical and quantum optics regarding the definitions and understanding of the "interference" and "coherence" properties of light, which are attributed as essentially due to inherent properties of the EM waves. A deeper exploration indicates that it is the various quantum mechanical properties of the detecting material dipoles that make light detectable (visible, or measurable) to us. Accordingly, all the properties that we generally attribute to only light, are in reality manifestations of collective properties of dipole-light interactions. "Interference" and "coherence" can be better understood in terms of this mutual interaction, followed by energy absorption by the dipoles from EM wave fields, manifesting in some measurable transformation of the detecting dipoles. Light beams do not interfere by themselves. The superposition effects due to light beams become manifest through the response characteristics of the detecting dipoles. In this paper, we will show some preliminary expe rimental results that clearly demonstrate that the heterodyning wave fronts have quantitative degradation in signal generation as the angle between them deviates from perfect collinearity. Subsequently, we will propose a hypothesis for this behavior. We will present experimental data establishing that the so called incoherent light can be detected through heterodyne mixing as long as the pulse length contained in the "incoherent" light is longer than the response time of the detector. We will also present a correspondingly better interpretation of two distinguishable coherence properties, temporal coherence and spectral coherence. Our investigation provides a deeper insight into how to rela x various system requirements for heterodyne detection and accordingly develop systems that are simpler, more reliable and lower in cost. Also, we believe that engineering of detector architecture by appropriately modifying dipole behavior using emerging nanotechnology to optimize heterodyne efficiency will be advantageous.
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.
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.
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.
All two-beam interferometry eventually reduces to quantitative measurement of the effective fringe visibility (or degree of coherence) in some form. We present generalized analytical and experimental results of visibility for the cases of two beam Poynting vectors both collinear (scanning fringe mode) and non-collinear (spatial fringe mode) with different polarizations and frequencies. This leads to a much broader and deeper understanding of the roles of material dipoles (beam splitters & detectors; both classical and quantum) in measured coherence effects that are not explicitly addressed in the traditional coherence theory. Coherence theory should be presented as correlation between sensing dipole undulations that are simultaneously induced by superposed light beams rather than as correlation between the optical fields. This generalized understanding of the physical processes behind coherence phenomenon will open up (i) better understanding of the nature of light and (ii) many more innovative approaches to quantitative interferometry.
T hink about coherent systems, and odds are that the first example to cross your mind will be a laser: a device that emits monochromatic light homogenized so that the photons propagate with their phase in lockstep. The well-defined wavefront of the laser beam makes it possible to focus the light to spot sizes on the order of the wavelength of the light without the aberrations usually observed with the random wavefront of incoherent light. The well-defined phase also provides a medium capable of storing and carrying information more efficiently than the intensity-modulated signals typical of incoherent sources. These useful properties of coherence have made lasers almost ubiquitous in science and technology, and that “almost” is shrinking by the day. In general, coherence comes about when individual components of a system act in unison, either in phase or with a fixed phase difference between the components. More accurately, the system can be described as a local oscillator whose wavefunction contains phase and amplitude terms that define how the system evolves in space and time. The collection of articles in this special issue describes the recent progress and developments of coherence in optical, atomic, and semiconductor systems, and how manipulating that coherence may lead to useful applications and to experimental systems for studying the elements of quantum mechanics. Since the first demonstration of the laser in 1960, progress in improving the extent of the spatial and temporal coherence of laser light has been steady. Psaltis (p. [1359][1]) reviews developments in optical coherence and highlights examples of the key role coherence has played in applications in imaging, communication, and information processing and storage. Just as lasers revolutionized the field of optics, many researchers have high expectations that other coherent systems will provide similar advances in their respective fields. Exploiting the fundamental tenet of quantum mechanics whereby particles have the properties of waves, Kasevich (p. [1363][2]) reviews coherence effects in collections of cold atoms and describes how the shorter wavelengths associated with atoms and the recent accessibility of bright coherent atom sources may lead to precision measurements beyond anything currently available to the optical regime. For integration and potential applications, the ideal system would be based in semiconductors. Snoke (p. [1368][3]) describes recent work toward the formation of coherent semiconductor systems. With coherence in the atomic and optical systems generally comprising macroscopic systems, Mabuchi and Doherty (p. [1372][4]) look at coherence effects at the quantum limit, probing the interactions between single atoms and single photons confined to high-quality cavities. In addition to providing invaluable information on the limits of quantum mechanics, such effects might also shed new light on information science in the quantum regime. The section opens with a pair of News features by staff writers Charles Seife and Robert Service. Seife presents a smattering of common applications that scientists and engineers have found for coherent waves, whether in light, sound, or subatomic particles. Service describes efforts to create new coherent sources of the type of radiation known as “hard” x-rays—a long-sought range of high frequencies with enormous potential for scientific research, technology, and medicine. [1]: /lookup/doi/10.1126/science.1078823 [2]: /lookup/doi/10.1126/science.1079430 [3]: /lookup/doi/10.1126/science.1078082 [4]: /lookup/doi/10.1126/science.1078446
After reviewing recent work on multiphoton direct detection and single-photon heterodyne detection, we examine the behavior of a multiphoton absorption heterodyne receiver. Expressions are obtained for the detector response, signal-to-noise ratio (SNR), and minimum detectable power for a number of cases of interest. Receiver performance is found to depend on the higher order correlation functions of the radiation field and on the local oscillator (LO) irradiance. Although performance similar to that of the single-photon heterodyne receiver can theoretically be achieved, practical problems would appear to make this difficult. A physical interpretation of the process in terms of the absorption of monochromatic and nonmonochromatic photons is given. The double-quantum case is treated in particular detail; the results of a preliminary experiment are presented and suggestions for future experiments are provided.