Selfinduced moving and zerovelocity(ZV) gap solitons were studied in a resonantly absorbing Bragg reflector of finite atomic width. Numerical results showed that the existence of moving gapsoliton is in general not affected by the finite atomic width but the existence of the ZV gapsoliton is highly affected by the widths of the atomic layers. Thus the trapping of the photonic energy occurs only in very thin atomic layers arranged with Bragg periodicity.
Selfinduced moving and zerovelocity(ZV) gap solitons were studied in a resonantly absorbing Bragg reflector of finite atomic width. Numerical results showed that the existence of moving gapsoliton is in general not affected by the finite atomic width but the existence of the ZV gapsoliton is highly affected by the widths of the atomic layers. Thus the trapping of the photonic energy occurs only in very thin atomic layers arranged with Bragg periodicity.
We present hitherto unknown forms of soliton dynamics in the forbidden frequency gap of a Bragg reflector, modified by periodic layers of near-resonant two-level systems (TLS). Remarkably, even extremely low TLS densities create an allowed band within the forbidden gap. This spectrum gives rise, for any Bragg reflectivity, to a vast family of stable gap solitons, both standing and moving, having a unique analytic form, an arbitrary pulse area, and inelastic collision properties. These findings suggest new possibilities of transmission control, noise filtering, or ``dynamical cavities'' (self-traps) for both weak and strong signal pulses.
Summary form only given. In recent years, there has been considerable interest in nonlinear and quantum optics of photonic bandgap structures. Some of this attention has centered on the properties of gap solitary waves, which are light pulses tuned at a Bragg frequency within a forbidden bandgap of the periodic structure. These solitary waves may occur in a periodically modulated medium with a Kerr-like nonlinearity, and in the resonance grating as a two-wave soliton of self-induced transparency. In the later case, the coupled-mode Maxwell-Bloch equations which describe the on-resonance coherent interaction of the intense field with a periodic structure of thin layers of two-level atoms in the ground state, lead to an integrable sine-Gordon equation. In our study, we concentrate on the nonintegrable case, that is, amplification in a resonant Bragg structure by means of a comprehensive analysis that includes and numerical modelling of Dicke superradiance and coherent amplification.
A practical method of slowing and stopping an incident ultrashort light pulse with a resonantly absorbing Bragg reflector is demonstrated numerically. It is shown that an incident laser pulse with suitable pulse area evolves from a given pulse waveform into a stable, spatially-localized oscillating or standing gap soliton. We show that multiple gap solitons can be simultaneously spatially localized, resulting in efficient optical energy conversion and storage in the resonantly absorbing Bragg structure as atomically coherent states.
We theoretically show that a self-induced transparency (SIT) soliton and a Bragg soliton can coexist in a nonlinear photonic band gap (PBG) medium doped uniformly with inhomogeneous-broadening two-level atoms. The Maxwell-Bloch equations for the pulse propagating through such a uniformly doped PBG structure are derived first and further reduced to an effective nonlinear Schrödinger equation. This model describes an equivalent physical mechanism for a Bragg-soliton propagation resulting from the effective quadratic dispersion balancing with the effective third-order nonlinearity. Because the resonant atoms are taken into account, the original band gap can be shifted both by the dopants and the instantaneous nonlinearity response originating from an intense optical pulse. As a result, even if a SIT soliton with its central frequency deep inside the original forbidden band, it still can propagate through the resonant PBG medium as long as this SIT soliton satisfies the effective Bragg-soliton propagation. An approximate soliton solution describing such coexistence is found. We also show that the pulse width and group velocity of this soliton solution can be uniquely determined for given material parameters, atomic transition frequency, and input central frequency of the soliton. The numerical examples of the SIT soliton in a one-dimensional As2S3-based PBG structure doped uniformly with Lorentzian line-shape resonant atoms are shown. It is found that a SIT soliton with approximately 100-ps width in such a resonant PBG structure can travel with the velocity being two orders of magnitude slower than the light speed in an unprocessed host medium.
We derive the properties of self-induced transparency (SIT) solitary waves in a one-dimensional periodic structure doped uniformly with resonance two-level atoms. In our model, the electromagnetic field is treated classically and the dopant atoms are described quantum mechanically. The resulting solitary waves take the form of ultrashort (picosecond) laser pulses which propagate near the band edge of the nonlinear photonic band gap (PBG) material doped with rare-earth atoms such as erbium. Solitary wave formation involves the combined effects of group velocity dispersion (GVD), nonresonant Kerr nonlinearity, and resonant interaction with dopant atoms. We derive the general Maxwell-Bloch equations for a nonlinear PBG system and then demonstrate the existence of elementary solitary wave solutions for frequencies far outside the gap where GVD effects are negligible and for frequencies near the photonic band edge where GVD effects are crucial. We find two distinct new types of propagating SIT solitary wave pulses. Far from Bragg resonance, we recapture the usual McCall-Hahn soliton with hyperbolic secant profile when the nonlinear Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ However, when the host nonresonant Kerr coefficient is nonzero, we obtain the first new type of soliton. In this case, the optical soliton envelope function deviates from the hyperbolic secant profile and pulse propagation requires nontrivial phase modulation (chirping). We derive the dependence of the solitary wave structure on the Kerr coefficient ${\ensuremath{\chi}}^{(3)},$ the resonance impurity atom density, and the detuning of the average laser frequency from the atomic transition. When the laser frequency and the atomic transition frequencies are near the photonic band edge we obtain the second type of soliton. To illustrate the second type of soliton we consider two special cases. In the first case, GVD facilitates the propagation of an unchirped SIT-gap soliton moving at a velocity fixed by the material's parameters. The soliton structure changes dramatically as the laser frequency is tuned through the atomic resonance. In the second illustrative case we set the Kerr coefficient ${\ensuremath{\chi}}^{(3)}=0.$ In this case, the solution is a chirped pulse which arises from the balance between GVD and the resonance interaction with the dopant atoms. Finally, we show that under certain circumstances, these solitary wave solutions may persist even in the presence of (subpicosecond) dipolar dephasing of the dopant atoms and absorption losses of the host PBG material, provided that the system is incoherently pumped. These results may be relevant to the application of PBG materials as optical devices in fiber-optic networks.
We consider some new aspects of the formation of moving optical solitons in a medium of Bragg-type resonant grating doped with two-level atoms. For generality, account is taken of the local-field effect assisted by a sufficiently high density of resonant atoms. It is established analytically that there exists a family of soliton solutions to the two-wave Maxwell-Bloch system of equations, with these solitons exhibiting bistable properties. The existence of bistable solitons and their properties are confirmed by numerical simulations.