Theory Of Self-induced Transparency Research Articles

Two-component pulse in uniaxial media

A theory of self-induced transparency (SIT) for the two-component pulse in anisotropic uniaxial media is developed. The system of equations of SIT for extraordinary wave in uniaxial media by means of generalized reduction perturbation method is reduced to the coupled nonlinear Schrodinger equations for auxiliary functions. It is shown that in the theory of SIT, the second derivatives play a significant role that leads to the formation of a vector 0π pulse oscillating with the sum and difference of the frequencies. Explicit analytical expressions for the profile and parameters of the two-component nonlinear wave are presented. It is obtained along with scalar 2π pulse, the vector 0π pulse is also the basic pulse of SIT. The conditions for existence of the nonlinear extraordinary wave depend on the direction of propagation.

Polarisation effects in the formation of optical breathers at the inhomogeneously broadened J = 0 → J = 1 quantum transition

The formation and collisions of breathers excited by laser radiation at the inhomogeneously broadened J = 0 → J = 1 quantum transition are studied by numerical simulations in the slowly varying envelope approximation. Conditions are obtained under which laser pulses with the initial shape quite simply realised in experiments can be transformed into elliptically polarised breathers in the medium, each of the components of their field being a breather described by the theory of self-induced transparency at a nondegenerate quantum transition. It is shown that the collision of such breathers is not elastic in the general case and leads to the appearance of more general types of resonance breather-like pulses. Taking into account relaxation processes, the possibility of the formation of a breather at the 6p2 3P0 → 6p7s 3P1 transition in the 208Pb isotope is investigated. It is found that relaxation in some case not only causes the pulse decay but also changes the eccentricity of its polarisation ellipse.

Optical solitons in semiconductor quantum dot waveguides

A theory of self-induced transparency for a TM-mode propagating in a planar semiconductor waveguide sandwiched between two dielectric media is developed. A transition layer between the waveguide and one of the connected media is described using a model of a two-dimensional sheet of quantum dots. Explicit analytical expressions for the optical soliton in the presence of single-excitonic and biexcitonic transitions are obtained with realistic parameters which can be reached in current experiments.

Integrable models of the dynamics of longitudinal-transverse acoustic pulses in a paramagnetic crystal

We study the interaction between longitudinal-transverse acoustic pulses and a system of paramagnetic impurities with the effective spin S = 1 in a statically deformed crystal. We show that the dynamics of a pulse propagating at an arbitrary angle to the static-deformation direction and of the effective spins satisfy the modified reduced Maxwell-Bloch equations and, if the spectrum of the acoustic pulse overlaps the quantum transitions between spin sublevels, the modified sine-Gordon equation. These equations generalize the well-known models in the theory of the inverse scattering method and in the theory of self-induced transparency and also belong to the class of integrable equations. Analyzing soliton solutions shows that the pulse-medium interaction reveals some qualitatively new features in these models compared with the cases of purely transverse or purely longitudinal acoustic fields.

Peculiarities of the evolution of a precursor pulse in the shaping of quasi-resonance self-induced transparency pulses

The results of a numerical simulation of the evolution of a precursor pulse are presented. This pulse exists at the stage of the conversion of a quasi-resonance input pulse into a 2π pulse considered in the theory of self-induced transparency. Calculations have shown that the efficiency of precursor-pulse formation increases as the input laser pulse shortens and its area approaches π. The results of a numerical analysis of the known experiments on the observation of a precursor pulse in ruby crystals are also presented. In one of the cases considered, the calculation results cast some doubt on the interpretation of the experiment adopted earlier.

Domain theory of self-induced transparency in a semiconductor superlattice

A self-consistent description of the electrodynamics of a semiconductor superlattice interacting with electromagnetic field of arbitrary frequency and strength is presented. Central to the present formalism is a recasting of the proper boundary conditions for the Maxwell problem that enables a speedy and straightforward solution for the distribution of the internal field in the active superlattice medium. On application of the self-consistent approach we found a self-induced transparency region in the superlattice layer which takes the form of a domain. The propagation and evolution of such a domain, which can contain a coherent train of Bloch oscillations, dominate the electron dynamics of the superlattice. The important properties of the self-induced transparency domain are also discussed here.

Stochastic theory of self-induced transparency: linearized approach

Making use of c-number stochastic theory and soliton perturbation theory, we study the quantum fluctuations of a self-induced transparency (SIT) soliton propagating through a lossless two-level medium. Considering the fluctuations as small corrections to the classical soliton, we are able to construct and solve four stochastic equations that govern the evolution of four soliton parameters: photon number (intensity), phase, timing, and momentum (frequency). We find excellent agreement between our stochastic theory of SIT solitons and the second-quantized theory of Lai and Haus [Phys. Rev. A 42, 2925 (1990)].

Hamiltonian formulation of self-induced transparency theory without slowly varying envelope approximation

It was shown that the propagation of an ultrashort light pulse in resonance absorbing medium under self-induced transparency conditions can be described by the theory which allows Hamiltonian formulation where corresponding Poisson brackets are non-ultralocal and the restrictions of a slowly varying envelope approximation are lifted. By employing the representation of zero curvature, a compact form of fundamental Poisson brackets for a monodromy matrix was found to satisfy the requirements of the generalized Hamiltonian formulation of completely integrable systems. An explicit form of PB amongst monodromy matrix elements, canonical variables of an angle-action type and integrals of motion can then be derived by a standard procedure. Semi-classical quantization of this model can also be done. The model considered extends the list of completely integrable non-ultralocal models.

Quantum theory of self-induced transparency

It is known that classical electromagnetic radiation at a frequency in resonance with energy splittings of atoms in a dielectric medium can be described using the classical sine-Gordon theory. In this paper we quantize the electromagnetic field and compute some quantum effects by using known results from the sine-Gordon quantum field theory. In particular, we compute the intensity of spontaneously emitted radiation using the thermodynamic Bethe ansatz with boundary interactions.

Theory of self-induced transparency in a Kerr host medium beyond the slowly-varying-envelope approximation.

The self-induced transparency in the Kerr host medium has been studied beyond the slowly-varying-envelope approximation. An analytic solution is obtained. There exists a hyperbolic-secant soliton whose power, pulse width, group velocity, and propagation constant are uniquely determined for given parameters of the medium. The reductions of the group velocities of the solitons by the self-induced-transparency effect in the resonant medium with homogeneous and inhomogeneous broadening are also studied. It is found that there is negative dispersion induced by the self-induced transparency, which is not predicted by the theory with the slowly-varying-envelope approximation. The amount of the induced dispersion is determined by the total dispersion of the system required to be compensated by the Kerr effect. Numerical examples of the self-induced transparency in an erbium-doped fiber are shown. In a typical erbium-doped fiber, the soliton solution has not been found because the inhomogeneous-broadening linewidth of the medium is too large.

Theory of self-induced transparency without the SVEA and RWA

An approximate solution to the complete semiclassical Maxwell-Bloch equations for the sharp-line case has been found making use of the coupling constant as a small parameter. This approach confirms results obtained through the reduced Maxwell-Bloch equations. The solution describes coherent propagation of an optical pulse more generally than the theory using the slowly varying envelope approximation (SVEA) and the rotating-wave approximation (RWA). Conditions for resonant propagation, taking into account the Bloch-Siegert shift, have been found and discussed in detail.

Gauge relation between self-induced transparency theory and principal chiral models

The gauge relations between generalised reduced Maxwell-Bloch equations and field equations of some principal chiral models are established. One-photon resonance in two-level and three-level media and also two-photon resonance are considered.

The soliton of the Rayleigh wave

A theory of self-induced transparency is constructed for the Rayleigh wave in a system which consists of a thin resonance transitional layer on a solid surface. The solution is obtained in the form of a soliton (2π-pulse of McCall and Hanh) for the Rayleigh wave. It is shown that characteristic parameters of the soliton depend on the transverse-mode profile.

Self-induced transparency for love waves

A theory of self-induced transparency is constructed for the Love wave in a system which consists of a film lying on a semispace in the presence of paramagnetic impurities. The solution is obtained in the form of the 2π-pulse of McCall and Hahn for the Love wave. It is shown that the characteristic parameters of the nonlinear Love wave depend on the transverse-mode profile.

Polarization effects in self-induced transparency theory

Bloch-Maxwell equations, describing the interaction between two-level atoms and the electromagnetic field, are generalized in the case of an atom with degenerate transition 0 ⇄ 1. The degenerate Bloch-Maxwell model has additional discrete degrees of freedom and makes it possible to investigate the polarization properties of resonance optical phenomena. It is shown that the model is completely integrable. The theory of self-induced transparency for pulses whose polarization is a function of space-time variables is developed.

Rigorous theory of self-induced transparency in the case of a double resonance in a three-level medium

A study is made of steady-state ultrashort electromagnetic radiation pulses of two different wavelengths propagating at the same velocity in a three-level medium under exact resonance conditions. It is shown that such pulses (simultons) correspond to the soliton solutions of the corresponding generalized reduced Maxwell–Bloch equations which thus represent a new example of a system of evolution equations that can be solved exactly by the inverse scattering method. A full characterization of a simulton requires the knowledge of its duration and phase and also of a two-dimensional vector (called the internal polarization vector) with the components equal to the relative amplitudes of the pulses forming a simulton. Collision of two different simultons generally changes their polarizations. An expression is obtained for the angle of rotation of the polarization vectors as a function of the simulton amplitudes and their initial polarizations.

Theory of self-induced transparency without the approximation of slowly varying amplitudes and phases

An analysis is made of the propagation of an ultrashort optical radiation pulse under conditions of inhomogeneous broadening of a resonance line. By dispensing with the approximation of a slowly varying complex pulse envelope, constraints on the duration are removed and any phase modulation is automatically taken into account. It is shown that if the boundary conditions determining the attenuation of the pulse at its leading edges are defined, the appropriate reduced Maxwell–Bloch equations can be integrated using the method of the inverse problem of scattering theory. Higher conservation laws, whose existence has been doubted, are found.

Scattering of light by an intense saturating pulse in a resonance medium

A linear response of a resonant medium to a weak electromagnetic field is studied in the case when a medium is a gas of three-level atoms subjected to a strong saturating pulse. A noncoherent intense pulse and a coherent 2π pulse (of the kind encountered in the theory of self-induced transparency) are considered. The expressions obtained are used to study the problem of the spectrum of the reflection of light by a pulse moving in a medium. An analysis is made of the possibility of using the Doppler effect, which occurs when light is reflected by a moving pulse, in an investigation of the characteristics of pulse propagation, determination of its parameters, and study of the nonlinear characteristics of the medium itself. Possibilities of experimental observation of the predicted effects are discussed, particularly the possibility of conversion of an electromagnetic radiation spectrum.

Self-induced transparency in waveguides

A theory of self-induced transparency (SIT) in waveguides, covered by thin films (thickness d ⪡ λ = 2π/ cω) of a resonant substance, has been developed. The shape of a waveguiding soliton (waveguiding “2π”-pulse) has been determined, and its velocity as a function of the film thickness and other characteristics of the resonant layer has been investigated.

A general theory of self-induced transparency

We summarize a theory of self-induced transparency (SIT) which exhibits so-called ‘soliton’ solutions of the underlying equations, as the natural description of pulse evolution and break up. The theory is in remarkable agreement with recently published experimental work on87Rb vapour where transparent2Nπ pulses appear to break up into a train of 2π pulses.