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CRC Press eBooks

Quantum Theory of Optical Parametric Processes

Carson L. Tang, L.K. Cheng

Published Nov 19, 2020• 0 citations
Publisher

Abstract

This chapter outlines the noise source on the basis of a quantum theory. A quantum theory is, however, needed for a rigorous analysis of the spontaneous parametric scattering process and a clear understanding of the spontaneous parametric process is important for a number of reasons. First, since the frequency and phase-matching conditions for the spontaneous emission are the same as those for the corresponding stimulated parametric process, the tuning characteristics of optical parametric oscillators and amplifiers can be determined from the spontaneous parametric emission prior to the construction of an actual oscillator or amplifier. It is, however, far from clear whether such an amplifier can be made practical, although there are interesting fundamental issues related to squeezing in optical parametric processes that have attracted a great deal of attention. For optical parametric processes, one is usually interested in the transparent region of the optical media.

DOI
10.1201/9781003072843-3

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This chapter outlines the noise source on the basis of a quantum theory. A quantum theory is, however, needed for a rigorous analysis of the spontaneous parametric scattering process and a clear understanding of the spontaneous parametric process is important for a number of reasons. First, since the frequency and phase-matching conditions for the spontaneous emission are the same as those for the corresponding stimulated parametric process, the tuning characteristics of optical parametric oscillators and amplifiers can be determined from the spontaneous parametric emission prior to the construction of an actual oscillator or amplifier. It is, however, far from clear whether such an amplifier can be made practical, although there are interesting fundamental issues related to squeezing in optical parametric processes that have attracted a great deal of attention. For optical parametric processes, one is usually interested in the transparent region of the optical media.
A quantum theory is developed for the spontaneous optical parametric process in nonlinear, anisotropic, and dispersive media; the process is treated directly as a scattering problem rather than a problem involving equivalent coupled oscillators. Following the general procedure in quantum field theory, a general expression is obtained for the differential extinction coefficient, which contains all the information on the intensity of the spontaneous emission in the parametric scattering process. The tuning characteristics, beam divergence, and spectral properties of the spontaneous emission for colinear and noncolinear interactions are described in detail and illustrated with numerical examples on such standard nonlinear optical crystals as LiNbO3{\mathrm{O}}_{3}O3​, NH4{\mathrm{H}}_{4}H4​H2{\mathrm{H}}_{2}H2​PO4{\mathrm{O}}_{4}O4​, and KH2{\mathrm{H}}_{2}H2​PO4{\mathrm{O}}_{4}O4​ under various pumping conditions. Explicit formulas for the intensity of the spontaneous emission are also obtained. The spontaneous intensity calculated using the formulas given is shown to be in complete agreement with known experimental data on NH4{\mathrm{H}}_{4}H4​H2{\mathrm{H}}_{2}H2​PO4{\mathrm{O}}_{4}O4​ pumped at 3472 \AA{}.
Chapter 6 begins by transforming the optical wave itself into a quantized form, and the full implications of the wave‐particle duality of Chapter 2 become clear. The electric field may be pictured as an infinite ladder of discrete states and this structure allows optical interactions to be described photon by photon. The origin of spontaneous emission emerges from this treatment as a transition process that is stimulated by electric field fluctuations of the vacuum, and Weisskopf–Wigner theory explains why it is irreversible. The subject of coherent states is introduced and intriguing possibilities outlined regarding the noise properties of components of these states that form different quadratures in terms of the optical phase. Next, statistical analysis of light fields is considered to serve as a basis for more quantitative comparisons of fields and their noise properties. Methods of calculating the first and second degrees of coherence are presented, and the ranges of values corresponding to “classical” versus “quantum” light sources are discussed. The reduced density matrix is developed to justify analysis that focuses on only certain aspects of optical dynamics while ignoring others, as an important tool for simplifying complex problems. Finally, in view of its historical importance, the problem of calculating the fluorescence spectrum of resonantly excited two‐level atoms is considered using both a method of moments and dressed atom theory.
Introduction Most of the lightwave transmission systems operating today benefit fully from extensive deployment of optical amplifiers (OA). These components perform the amplification of optical intensity directly in the optical domain, without resorting to any electrical-domain regeneration. Optical amplifiers increase the average number of output photons per unit time by several orders of magnitude compared with the incoming signal intensity. However, as with every amplifying process, optical amplification cannot be achieved without paying back for the unavoidable noise power added to the signal intensity. As we will see in detail in Chapter 6, the optical amplification process comes with optical noise generated by spontaneous emission inside the active medium. The intensity of the optical signal is represented by the flux of the signal photon population. Conversely, the photons generated by the spontaneous emission process inside the optical cavity represent the noise photon population. The fundamental phenomenon supporting optical amplification is stimulated emission. The basic property of stimulated emission, making the great difference from spontaneous emission and enabling optical amplification, is the coherent nature of the photon generation process. Accordingly, both signal and noise photons go through the same multiplication process by means of stimulated emission. Unless the optical cavity where the stimulated emission takes place (the active cavity) presents selective features for enhancing the signal photon population relative to the spontaneous one, there is no way to avoid noise photons going through stimulated emission, filling most of the cavity population. As a consequence, both photon populations increase, leading respectively to amplified signal intensity and to amplified spontaneous emission intensity. It should be apparent that every noise photon can create a new identical noise photon as a result of stimulated emission, effectively increasing the noise intensity in the active optical cavity. This is the well-known mechanism of amplified spontaneous emission (ASE) noise in optical amplification. Any improvement in the optical amplifier structure devoted to increasing stimulated over spontaneous emission will probably increase the optical signal-to-noise ratio (OSNR) at the cavity output. The spectrum of gain characteristic of the optical active medium is usually wide enough to support an efficient amplification of the broadband spontaneous emission spectrum, leading to the broadband ASE noise power spectral density.