Phenomenon Of Self-induced Transparency Research Articles

Emergence of solitons from many-body photon bound states in quantum nonlinear media

Solitons are known to occur in the context of atom-light interaction via the well-known semi-classical phenomenon of self-induced transparency (SIT). Separately, in the regime where both light and atoms are fully treated quantum mechanically, quantum few-photon bound states are known to be a ubiquitous phenomenon that arises in different systems such as atoms coupled to chiral or bidirectional waveguides, and in Rydberg atomic media. In the specific case of two-level atoms coupled to a chiral waveguide, a recent analysis based on Bethe ansatz has established that SIT emerges from the quantum realm as a superposition of quantum many-photon bound states. Beyond this case, however, the nature of any connection between the full quantum many-body regime and semi-classical behavior has not been established. Here, we employ a general spin-model formulation of quantum atom-light interfaces to numerically investigate this problem, taking advantage of the fact that this approach readily allows for powerful many-body simulations based on matrix product states (MPS). We first analytically derive the two-photon bound state dispersion relation for a variety of atom-light interfaces, and then proceed to numerically investigate the multi-excitation bound states dynamics. Interestingly, for all the specific systems studied, we find that the large-photon number limit always coincides with the soliton phenomenon of self-induced transparency or immediate generalizations thereof.

Dissipative aspects of extreme nonlinear optics

Studies of extreme nonlinear optical effects, in which dissipative factors such as absorption and amplification of light in a medium play a fundamental role, are reviewed. The generation of pulses with extremely short duration down to unipolar ones is analysed by tracking the development of ideas related to the self-induced transparency phenomenon, whose practical application becomes real for extremely short pulses in lasers and laser media. Extreme radiation structuring is achieved in dissipative (laser) solitons characterised by a complex topology of phase and polarisation singularities, which is of interest for coding information.

Mechanisms of stationary converted waves and their complexes in the multi-component AB system

Under investigation in this article is a multi-component AB system which models the self-induced transparency phenomenon. By using the modified Darboux transformation, we present the breather solutions of such system. We study the subtle mechanism that converts the breathing state into the solitary and periodic ones, through which we obtain various stationary nonlinear excitations such as the multi-peak solitons, (quasi) periodic waves, (quasi) anti-dark solitons, W-shaped solitons and M-shaped solitons which exhibit stationary feature. According to the analysis of the group velocity difference, we give the corresponding conversion rule and present the explicit correspondence of phase diagram of wave numbers for various converted waves, by which we show the gradient relation among these converted waves. Further, by separating the converted waves into the solitary wave as well as the periodic wave, we classify different kinds of nonlinear waves and indicate the difference of the superposition mechanism among them. We show that the breather and various converted waves are formed by different superposition modes between the solitary wave components with different localities and periodic wave components with different frequencies. By virtue of the second-order solutions, we consider all possible superposition situations of two nonlinear waves and present the corresponding nonlinear wave complexes. In particular, for the hybrid structure made of a breather and a nonlinear wave with variable velocity, we then discover that the nonlinear wave does not change its state under the conversion condition, leading to that an additional breathing structure or a dark structure is contained in the converted waves. Finally, we unveil the underlying relationship between the conversion and modulation instability.

Ultrashort Optical Pulses and Their Generation in Resonant Media (Scientific Summary)

Our recent studies of methods for obtaining ultrashort light pulses and analysis of the impact of ultrashort optical pulses on classical and quantum micro-objects with the identification of the determining role of the degree of unipolarity of pulses (maximum for strictly unipolar pulses) in the efficiency of direct laser acceleration of charged particles and excitation of atoms and molecules have been reviewed. Special attention has been paid to the coherent mode locking regime in lasers, which is implemented when the laser pulse duration is less than the relaxation time of the working transition in media with resonance amplification and absorption (laser analog of the phenomenon of self-induced transparency). Experimental data on coherent mode locking in a titanium-sapphire laser with a cell with rubidium vapor at self-induced transparency in rubidium have been presented. The interaction of ultrashort pulses in resonant media has also been analyzed.

Dynamical behaviour of rogue wave solutions in a multi-component AB system

With the aid of a 3 × 3 matrix spectral problem, we propose a multi-component AB system to describe self-induced transparency phenomenon. Based on the gauge transformation between the spectral problems, a one-fold Darboux transformation of this system can be given directly. The compact determinant forms of the n-fold classical Darboux transformation of the multi-component AB system are obtained by iterating the one-fold Darboux transformation and solving a linear algebraic system. Furthermore, an N-fold generalized Darboux transformation of the multi-component AB system is generated by utilizing the limit technique and Taylor expansion. As applications of the generalized Darboux transformation, all kinds of solutions for the multi-component AB system can be obtained, including Ma breather solutions, Akhmediev breather solutions and rogue wave solutions. In addition, the dynamical behaviours of all types of rogue wave solutions, such as four-peaked, four-petalled, triangular and ring, are discussed in detail by using the generalized Darboux transformation.

Double degeneration on second-order breather solutions of Maxwell–Bloch equation

The breather solutions of the Maxwell–Bloch equations in a two-level resonant system associated with the self-induced transparency phenomenon are constructed by the Darboux transformation. After constructing the formulas of the second-order breather solutions, the double degeneration and hybrid solutions are studied by the analytical form as well as figures. Our results might be helpful in such application or prevention of the rogue waves from breather solution interactions and degeneration in the nonlinear optical systems associated with the Maxwell–Bloch equations.

Bulk plasmon-polariton gap solitons in defective metamaterial photonic superlattices.

We show the existence of a defect mode within the plasmon-polariton gap in 1D defective photonic superlattices, composed by alternating layers of conventional dielectric (A) and negative refractive (B) material slabs with a dielectric defective layer (D), which, in the nonlinear regime, can be tuned by means of the incident field intensity. Also, we have shown that the self-induced transparency phenomena can be only observed when gap-soliton modes, coupled through the defective layer, are excited in both mirror systems around the defective slab.

Self-induced terahertz-wave transmissivity of waveguides with finite-length layered superconductors

We predict and study theoretically a new nonlinear electromagnetic phenomenon in a sample of layered superconductor of finite length placed in a waveguide with ideal walls. Two geometries are considered here: when the superconducting layers are parallel or perpendicular to the waveguide axis. We show that the transmittance of the superconductor slab can vary over a wide range, from nearly zero to one, when changing the amplitude of the incident wave. Thus, one can induce the total transmission or reflection of the incident wave by just changing its amplitude. Moreover, the dependence of the superconductor transmittance on the incident wave amplitude has a hysteretic behavior with jumps. The considered phenomenon of self-induced transparency can be observed even at small amplitudes, if the wave frequency $\omega$ is close to the cutoff frequency for linear Josephson plasma waves.

Self-induced transparency of circularly polarized femtosecond pulses

The phenomenon of self-induced transparency in a two-level medium is studied using a new integrable set of evolution equations for the optical pulses with a duration on the order of the energy-transition oscillation period. A mathematical apparatus is developed for the inverse scattering problem and used to obtain solitonic solutions to the model. The characteristics of linearly and circularly polarized pulses are compared with each other.

Vibrational self-induced transparency and phonon squeezing

It is shown that the phenomenon of self-induced transparency can occur when a coherently excited propagating phonon mode has a frequency that is equal to the difference between the frequencies of two flat phonon branches. The nonlinear coupling is due to cubic anharmonicity. Using a quantum kinetic-type approach, the Maxwell-Bloch equations are derived for such systems. Including third-order correlations in this approach, the intrinsic damping of parametrically excited two-phonon oscillations is investigated, that lead to phonon squeezing. In addition, we analyze the resonant interaction of a coherently driven phonon mode with one flat branch of the phonon dispersion relation.

Self-Induced Transparency Phenomena of Single-Mode Pulse Laser Propagating in a Thick Ytterbium Vapor Column

The variations in pulse shape of a single-mode pulse laser propagating through ytterbium (Yb) atomic medium were investigated experimentally. The laser pulse shape was changed as a function of pulse area and it could be explained well using the area theorem. When the pulse area was close to 2π, the pulse shape was transformed to a hyperbolic secant function after transmission. The transmission curve of the propagating laser vs. the pulse area demonstrated self-induced transparency phenomena well. However, the transmission was markedly reduced when the atomic density was increased above ∼4×1010 atoms/cm3. Several causes; such as collision-induced polarization relaxation, Doppler broadening, laser incoherence, and power broadening, which could induce reduced transmission, were examined. It was the incoherence of the laser that caused reduced transmission because the laser line width was broader than the Fourier-transform limit, and the absorbed energy dissipated through spontaneous emission.

The competition between nonlinearity, dispersion and randomness in signal propagation

The phenomenon of self-induced transparency (SIT) is reinterpreted in the context of competition between randomness, nonlinearity and dispersion, and furthermore the problem is recast to show that it is isomorphic to a problem of the nonlinear Schroedinger (NLS) type with a random potential in which the randomness is manifested spatially. It is shown that, under mild assumptions, the SIT result continues to hold when we replace the uniform medium of inhomogeneously broadened two-level atoms by a series of intervals in each of which the frequency mismatch is randomly chosen from some distribution. The exact solution of this problem confirms and reveals the reason for the fact that nonlinearity can help improve the transparency of the medium. Also, the small-amplitude, almost monochromatic limit of SIT is taken and results in a complex envelope equation which turns out to be an exactly integrable combination of NLS and a modified SIT equation. Finally, some generalizations are made to describe a broad class of integrable systems which combine randomness, nonlinearity and dispersion.

Self-induced transparency for ultrashort pulses propagating in a multilevel quantum medium

We study theoretically the phenomenon of self-induced transparency for ultrashort pulses (videopulses) propagating in a multilevel quantum medium under conditions in which the method of slowly varying amplitudes and phases breaks down and the pulse spectrum substantially overlaps the quantum transitions. A special class of transitions with one common level is considered. We find that the dynamics of the videopulses in such a medium is described by a double sine-Gordon equation. We establish the conditions under which steady-state traveling 0π-, 2π-, and 4π-videosolitons are formed. It is found that 4π-videosolitons can propagate both in equilibrium media and in some nonequilibrium media, while 0π-videosolitons can propagate only in nonequilibrium media. We study amplification processes in highly nonequilibrium systems and show that, depending on the initial state of the medium, 2π-and qπ-pulses (0<q<1) with increasing amplitudes may be formed. We conclude that the amplification of an ultrashort pulse occurs due to an increase in the photon number density and to an increase in the frequency of each photon. Finally, we study the possibility of an electromagnetic autosoliton being formed in a nonequilibrium dissipative medium.

Transient pulse propagation and pulse break-up phenomena in III–V semiconductors

The coherent radition-semiconductor interaction model based upon the time-dependent perturbation technique has been employed for the analytical study of transient pulse propagation and pulse break-up in directgap semiconductors. In order to check the validity of our model, we have applied our analysis initially to the Rubidium atomic vapor system duly irradiated with pulsed ruby laser. Numerical estimation of the change in transient transmitted intensity reveals good agreement between the present results and the experimental observations in Rb vapor system. Finally, we have analyzed pulse propagation in an important direct-gap crystal, namely InSb duly irradiated by ultrafast infrared dye laser operating in the 3.9-9.4 μm wavelength range. Pulse break-up and pulse peak shifts can be noticed from the results. The pulse velocity is also found to reduce by at least a factor of 100. These features are analogous to the phenomenon of self-induced transparency where the pulse area theorem is usually employed.

EXCITONIC SELF-INDUCED TRANSPARENCY IN SEMICONDUCTORS

The form invariant coherent pulse propagation in semiconductors excited at 1s-exciton resonance is studied analytically using the reduced semiconductor Maxwell-Bloch equations. The sech-shaped pulse solution for excitonic self-induced transparency (SIT) is presented, showing significant difference in comparison with the well known SIT solution for non-interacting two-level systems. In contrast to 2π pulses in atomic systems, the phenomenon of SIT of interacting excitons in semiconductors occurs for the pulses of area 1.07π. Possible applications of the SIT solitons in semiconductor all-optical switching devices are discussed.

Spatial distortions of laser pulses in coherent on-resonance propagation: Small-scale self-focusing.

When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a ${\mathrm{Tm}}^{169}$ vapor.

Spatial distortions of laser pulses in coherent on-resonance propagation: Large-scale self-focusing.

When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a ${\mathrm{Tm}}^{169}$ vapor.

Self-Induced Transparency in a Ferromagnetic System Under a Bias Magnetic Field

The phenomenon of self-induced transparency is shown to exist in a ferromagnetic system under a bias magnetic field.

Numerical study of fast oscillating breathers in the self-induced transparency phenomenon

A numerical analysis of the dynamics of an oscillatory modulated input signal has been carried out to detect a frequency modulation band when the initial profile spreads almost unaffected along a resonant sample or, on the contrary, rapidly evolves to a classic breather. It is shown that only waves whose modulation period is less than a specific time of medium response to the driving radiation have a chance to survive. The simulation has been undertaken on the basis of the sine-Gordon model, degenerated two-level and three-level systems for simultons. Nonlinear steady waves has been recently observed in numerical experiments on resonant medium excitation by a sequence of ultrashort pulses.

Self-induced transparency in an atomic medium with degenerate transitions in the presence of a strong magnetic field

We found the new physical conditions under whivh self-induced transparency phenomena in two-level systems exist.