This work is a response to a problem which was most clearly formulated by Wolf [Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, New York, 1973), p. 339] in this way: ``Attempts to generalize [the extinction theorem] within the framework of molecular optics encounters formidable difficulties.'' Here the method of integral equations is applied to an arbitrary nonlinear and anisotropic medium, taking into account quadrupole and magnetic-dipole radiation. Using the fundamental equations of molecular optics, we prove the extinction theorem in a general case, and its physical interpretation is elucidated. The question about structure of a surface layer that produces the reflected wave is clarified. A connection between the microscopic and macroscopic characteristics of nonlinear media is obtained. This advance was achieved by the implementation of the straightforward idea of variable substitution in the original integral equation. This substitution turns out to yield insight into the transition from a local to a Maxwellian field.
This work is a response to a problem which was most clearly formulated by Wolf [Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, New York, 1973), p. 339] in this way: ``Attempts to generalize [the extinction theorem] within the framework of molecular optics encounters formidable difficulties.'' Here the method of integral equations is applied to an arbitrary nonlinear and anisotropic medium, taking into account quadrupole and magnetic-dipole radiation. Using the fundamental equations of molecular optics, we prove the extinction theorem in a general case, and its physical interpretation is elucidated. The question about structure of a surface layer that produces the reflected wave is clarified. A connection between the microscopic and macroscopic characteristics of nonlinear media is obtained. This advance was achieved by the implementation of the straightforward idea of variable substitution in the original integral equation. This substitution turns out to yield insight into the transition from a local to a Maxwellian field.
A method of integro-differential equation associated with the optical loch equations is proposed to consider the problem of nonlinear transient reflection (refraction) of two laser noncomplanar pulses. It is a 3D boundary-value problem of a semiclassical nonlinear resonant transient optics for the phase memory effects exhibited by surface atoms in response to pulses of fields resolved in space and time. A generalized Lorentz- Lorenz formula and a theorem of extinction of nonlinear transient optics are used to investigate generalized reflection and refraction laws.
The method of characteristics is used to analyse the system of five nonlinear partial differential equations describing ultrashort optical pulse propagation through a medium of two-level atoms. Contrary to previous suggestions it is shown rigorously that the system is causal: no physical speeds exceed c. The method is well adapted to numerical integration. It can take full account of both back scattering and the effect of a surface to the dielectric. A number of new physical results obtained this way are briefly reported.
The optical extinction theorem due to P. P. Ewald, C. W. Oseen and C. G. Darwin is used completely to describe the action of a dielectric slab as a Fabry-Perot interferometer. The analysis is very comparable to that given by Born and Wolf. It is then shown that by generalising the optical extinction theorem to the nonlinear regime essentially the same Fabry-Perot cavity action is regained but in this case the refractive index and hence the cavity tuning depends on the input intensity. This way a multistable output/input relation is derived. It is shown further how the extinction theorem will also handle the problem of 'standing waves' in the cavity. The possibility of optical turbulence in a Fabry-Perot cavity is briefly mentioned.
Based on the separability with respect to position variables of the susceptibility for a finite system, we have developed a formulation which solves Schri:idinger and Maxwell equations selfconsistently. The case of linear response is' described in detail. As a manifes tation of the selfconsistency between the two equations, the appearance of radiative damping rate with correct magnitude has been demonstrated for a two-level atom in vacuum. The interaction of electromagnetic (EM) radiation with matter has been studied in various aspects for quite a long time. The relevant phenomena range, in the scale of wavelength, from rf wave (NMR, for example) to gamma ray (Mossbauer effect): They are related with the absorption, reflection, transmission, propagation, refrac tion, scattering, diffraction, emission, etc. of EM wave in linear and nonlinear manner. For the theoretical treatment of these phenomena, we need Schrodinger equation for the description of matter and Maxwell equations in classical or quantized form for radiation field. When the Maxwell equations are treated in classical form, this is called semiclassical treatment of radiation-matter interaction. Though it has a certain limitation, the semiclassical treatment can be appliedto most of the phenom ena mentioned above. For the treatment of the interaction of EM radiation with solids, it is usual to employ a susceptibility function to describe the solid, and solve the Maxwell equa tions containing that susceptibility as an integral kernel. In doing so, we must consider the boundary conditions (BC) arising from the shape of the sample in question. However, we do not consider BC's in treating microscopic systems such as an atom or small molecule. This would mean that the use of BC(s is in general not compulsory, although we are so much accustomed to it. In this respect, there has been a long debated problem of additional boundary condition (ABC) in relation with exciton polaritons in semiconductors or insulators, where the nonlocal nature of the medium allows the existence of two or more eigenmodes of the coupled exciton-EM radiation. After the long history of the ABC problem,r>- 4 > we now have a recipe to derive the appropriate form(s) of ABC(s) from a microscopic model of the medium including the details of the surface. 5 >-s> Another form of the microscopic solution of the ABC problem has been given as an ABC-free formulation, 9 >-n> where one needs
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.
Wysin et al1 suggested that the local field enhancement near a metal surface which occurs if surface plasmons are excited in a metal film, can be useful for observing optical bistability arising from the nonlinearity of the Kerr medium. Other geometrical arrangements2 have also been suggested. These studies assume plane waves in the nonlinear medium and use the Fresnel formulae for reflection and refraction from a layered medium but with linear refractive index replaced by the nonlinear refractive index. This assumes that the fields in the medium are homogeneous. However if surface plasmons are excited, then the fields are inhomogeneous and one has the problem of reflection and refraction from an inhomogeneous layered medium. The inhomogeneity is to be determined self consistently. Thus a proper treatment of optical bistability with surface plasmons should use the nonlinear solutions of the wave equation in Kerr medium. This is what we do in this paper.