As a light beam is produced by an amplification of modes of the zero point field in its source, this field cannot be distinguished; consequently a nonlinear optical effect is a function of the total field. However, we generally prefer to use a conventional field which excludes the zero point field; for a low conventional field, the total field may be developed to the first order, so that the effect appears linear. This nearly trivial remark allows a correct computation of the signal of a photocell used for photon counting and shows that the "impulsive stimulated Raman scattering" (ISRS), a nonlinear, without threshold effect, which shifts the frequencies, becomes linear at low light levels, so that the shifted spectra are not distorted.
As a light beam is produced by an amplification of modes of the zero point field in its source, this field cannot be distinguished; consequently a nonlinear optical effect is a function of the total field. However, we generally prefer to use a conventional field which excludes the zero point field; for a low conventional field, the total field may be developed to the first order, so that the effect appears linear. This nearly trivial remark allows a correct computation of the signal of a photocell used for photon counting and shows that the "impulsive stimulated Raman scattering" (ISRS), a nonlinear, without threshold effect, which shifts the frequencies, becomes linear at low light levels, so that the shifted spectra are not distorted.
Nonlinear optics is the study of the response of dielectric media to strong optical fields. The fields are sufficiently strong that the response of the medium is, as its name implies, nonlinear. That is, the polarization, which is the dipole moment per unit volume in the medium, is not a linear function of the applied electric field. In the equation for the polarization, there is a linear term, but, in addition, there are terms containing higher powers of the electric field. This leads to significant new types of behavior, one of the most notable being that frequencies different from that of the incident electromagnetic wave, such as harmonics or subharmonics, can be generated. Linear media do not change the frequency of light incident upon them. The first observation of a nonlinear optical effect was, in fact, second-harmonic generation – a laser beam entering a nonlinear medium produced a second beam at twice the frequency of the original. Another type of behavior that becomes possible in nonlinear media is that the index of refraction, rather than being a constant, is a function of the intensity of the light. For a light beam with a nonuniform intensity profile, this can lead to self-focusing of the beam. Most nonlinear optical effects can be described using classical electromagnetic fields, and, in fact, the initial theory of nonlinear optics was formulated assuming the fields were classical. When the fields are quantized, however, a number of new effects emerge. Quantized fields are necessary if we want to describe fields that originate from spontaneous emission. For example, in a process known as spontaneous parametric down-conversion, a beam of light at one frequency, the pump, produces a beam at half the original frequency, the signal. This second beam is a result of spontaneous emission.
The existence of the zero point electromagnetic field in the dark is a trivial property of classical electromagnetism. Splitting the total, genuine electromagnetic field into the sum of a conventional field and a zero point field is physically meaningless. If a receiver attenuates the genuine field down to a zero conventional field, it remains a zero point field having the coherence and the phase of the conventional field, and vice-versa for the amplification of the zero point field by a source. Nonlinear optical effects must be written using the genuine field, so that at low light levels they become linear in relation to the conventional field. The result of the interpretation of all observations, even at low light levels, is exactly the same in quantum electrodynamics and in the semi-classical theory. The zero point field is stochastic only far from the sources and the receivers; elsewhere, it is shaped by matter, it may be studied through fields visible before an absorption or after an amplification. Two examples are given : the computation of fourth order interferences and the use of the impulsive stimulated Raman scattering with ordinary incoherent light in astrophysics.
In the classical theory, an electromagnetic field obeying Maxwell's equations cannot be absorbed quickly by matter, so that it remains a zero point field. Splitting the total, genuine electromagnetic field into the sum of a conventional field and a zero point field is physically meaningless until a receiver attenuates the genuine field down to the zero point field, or studying the amplification of the zero point field by a source. In classical optics all optical effects must be written using the genuine field, so that at low light levels the nonlinear effects become linear in relation to the conventional field. The result of the interpretation of all observations, even at low light levels, is exactly the same in quantum electrodynamics and in the semi- classical theory. The zero point field is stochastic only far from the sources and the receivers; elsewhere, it is shaped by matter, it may be studied through fields visible before an absorption or after an amplification. A classical study of the reduction of the wave packet extends the domain of equivalence of the classical and quantum zero point field; using both interpretations of this field makes the results more reliable, because the traps are different.
Introduction We have already encountered situations in which light of one frequency falling on an atomic system gives rise to light of different frequencies (cf. Section 15.6). The atom may here be considered to play the role of a (noisy) nonlinear transducer for the incident field. Even stronger nonlinear effects arise when one is dealing with a large number of atoms, or a nonlinear medium . Under these circumstances it is sometimes permissible to ignore the atomic structure and to treat the medium as a continuum, as in Maxwell's electromagnetic theory. The subject of the interaction of the incident field with the nonlinear medium is usually known as nonlinear optics. The subject had its beginnings in an experiment in which a strong beam of red light (wavelength 6943 Å) from a ruby laser was allowed to fall on a quartz crystal, and a faint beam of blue light at a wavelength of 3472 Å, the first harmonic of the red, was produced (Franken, Hill, Peters and Weinreich, 1961). The development of the subject of nonlinear optics into a mature field is due largely to the work of Bloembergen and his collaborators. In the following we shall consider only a few simple illustrative examples of phenomena in nonlinear optics. More topics and more detail can be found in the books by Bloembergen and others (Bloembergen, 1965; Yariv, 1967, Chap. 21; Shen, 1984; Schubert and Wilhelmi, 1986; Butcher and Cotter, 1990; Boyd, 1992).
Impulsive stimulated Raman scattering (ISRS) plays a key role in coherent control of low-energy rotational resonances. Femtosecond laser pulses are widely employed to utilize ISRS because they are broadband and can cover the needed frequencies in a single pulse. Here, we show theoretically that the ISRS process is expressed as a linear response to the instantaneous Stokes parameters (ISPs) of the laser pulse. These IPSs expressed in rotational coordinates are then shown to be responsible for the angular momentum transfer from light to matter. These relationships have led to the designs of spectral profiles and polarization states of light pulses that should selectively excite particular rotational modes.
Abstract The book so far is almost entirely concerned with linear optical processes, where the response of a material to incident light is described by its linear susceptibility and the rates of optical processes are proportional to the incident intensity. However, examples of nonlinear behaviour occur in the saturation of atomic transitions, discussed in §1.7, and in the power-broadened susceptibility, derived in eqn (2.8.6). Atomic saturation is also an important component in the laser theory of§§t.10 and 7.3. The expressions derived in these examples contain the electromagnetic energy density or photon number in denominators whose expansions include terms proportional to all positive powers of the optical energy. The higherorder, or nonlinear, terms are normally much smaller than the linear term for conventional light sources but their influence is often significant in experiments that use laser sources. The present chapter treats the effects of the nonlinear terms in modifying the properties of incident light beams.