Optical Harmonics and Nonlinear Phenomena

Franken, P. A.; Ward, John F.

doi:10.1103/revmodphys.35.23

Cited by 593 publications

(235 citation statements)

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“…Large optical fields are required to alter the index of refraction of conventional bulk materials because a strong nonlinear response can only be induced if the electric field of the light beam acting on the electrons is comparable to the field of the nucleus. As a result, early experimental observations of nonlinear optical phenomena, such as frequencydoubling or sum-frequency generation 9 , were achievable only after the development of powerful lasers.…”

Section: The Challenge Of Making Photons Interactmentioning

confidence: 99%

Quantum nonlinear optics — photon by photon

2014

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other. This linearity in light propagation, in combination with the high frequency and hence large bandwidth provided by waves at optical frequencies, has made optical signals the preferred method for communicating information over long distances. In contrast, the processing of information requires some form of interaction between signals. In the case of light, such interactions can be enabled by nonlinear optical processes. These processes, which are now found ubiquitously throughout science and technology, include optical modulation and switching, nonlinear spectroscopy and frequency conversion 1 , and have applications across both the physical 2 and biological 3,4 sciences.A long-standing goal in optical science has been the implementation of nonlinear effects at progressively lower light powers or pulse energies. The ultimate limit may be termed 'quantum nonlinear optics' (Box 1) -the regime where individual photons interact so strongly with one another that the propagation of light pulses containing one, two or more photons varies substantially with photon number. Although this domain is difficult to reach owing to the small nonlinear coefficients of bulk optical materials, the potential payoff is significant. The realization of quantum nonlinear optics could improve the performance of classical nonlinear devices, enabling, for example, fast energy-efficient optical transistors that avoid Ohmic heating 5 . Furthermore, nonlinear switches activated by single photons could enable optical quantum information processing and communication 6 , as well as other applications that rely on the generation and manipulation of non-classical light fields 7,8 . The challenge of making photons interactAt low optical powers, most optical materials exhibit only linear optical phenomena, such as refraction and absorption, which can be described by a complex index of refraction. However, a sufficiently intense light beam can modify a material's index of refraction, such that the light propagation becomes power-dependent. This is the essence of classical nonlinear optics (Box 1). Large optical fields are required to alter the index of refraction of conventional bulk materials because a strong nonlinear response can only be induced if the electric field of the light beam acting on the electrons is comparable to the field of the nucleus. As a result, early experimental observations of nonlinear optical phenomena, such as frequencydoubling or sum-frequency generation 9 , were achievable only after the development of powerful lasers. Advances in nonlinear optics over the past four decades have resulted in progressively more efficient nonlinear processes 10 , thus enabling the observation of nonlinear processes at lower and lower light levels. It is natural to inquire if and how these nonlinear interactions can be made so strong that they become important even at the level of individual quanta of radiation. Although this question was addressed in early theoretical studies [11][12][13] , it has become more pressing with the advent of...

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Section: The Challenge Of Making Photons Interactmentioning

confidence: 99%

Quantum nonlinear optics — photon by photon

2014

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“…However, for moderately small electric fields observed in actual experiments (|αE| ≪ 1), the chosen dependence D(E) correctly describes dielectric properties of certain media with accuracy up to terms of order E 2 inclusively. Since even powers of E are present in the series expansion of D, the medium for which the dependence ε(E) is approximated by function (3) does not possess a center of inversion [7]. This is inherent in, e.g., uniaxial pyroelectric and ferroelectric crystals, provided that the z axis is aligned with the crystallographic symmetry axis.…”

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confidence: 99%

“…The value of α can be obtained, for example, in experiments on microwave frequency doubling in ferroelectric crystals [8,9]. Along with the medium properties, another factor leading to lack of a center of inversion can be the presence of a strong external electric field [7]. For example, let an isotropic medium in which [4], be placed in a uniform static electric field E = E 0ẑ0 .…”

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Exact Axisymmetric Solutions of the Maxwell Equations in a Nonlinear Nondispersive Medium

Petrov

Kudrin

2010

Phys. Rev. Lett.

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The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium. Wave propagation in nonlinear media is a fundamental and wide-ranging problem in physics [1, 2]. The possible self-steepening and formation of shock discontinuities in large-amplitude pressure waves is well known in fluid mechanics, being a typical nonlinear phenomenon. A similar phenomenon (formation of surfaces of discontinuity for the electric and magnetic fields) can also be observed during propagation of intense electromagnetic waves in certain media, and there is an elegant physical analogy between the fluid mechanics and electrodynamics in this case. The discovery of materials with well-pronounced nonlinearity of electromagnetic properties (for example, ferrites and ferroelectrics) has attracted considerable attention to essentially nonlinear electromagnetic phenomena, and some important advances have been made [3,4]. Further theoretical progress, however, has met serious difficulties because such phenomena cannot be described satisfactorily by perturbation theory, and rigorous solutions of field equations are required in order to get theoretical predictions. In view of the above, finding new, physically important exact solutions of nonlinear partial differential equations (PDEs) that describe the behavior of waves in nonlinear media is very topical [5,6]. In most papers on the subject, plane nonlinear waves are considered. At the same time, features of propagation of nonlinear cylindrical and spherical waves, as well as the properties of the related nonlinear PDEs in the corresponding curvilinear coordinates, remain poorly studied.In what follows, we present a new method for constructing exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium. It is assumed that the medium considered lacks a center of inversion and the dependence of the electric displacement on the electric field can be approximated by an exponential function.Consider electromagnetic fields in a loss-free nonmagnetic medium. With a view to analyzing uniaxial crystals, we assume that the medium possesses an axis of symmetry, hereafter taken as the z axis of a cylindrical coordinate system (r, φ, z). If the fields are independent of φ and z, the Maxwell equations admit solutions in which only the E z and H φ components are nonzero (E wav...

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“…The technique was suggested in 60's [4,21], but started to be commercially available a couple of years ago.…”

Section: Modeling Of the Cavity Geometry Bandwidthmentioning

confidence: 99%