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Self-Induced Transparency Solitons in Nanophotonic Waveguides

Andreas Pusch

Published Jan 1, 2012• 0 citations
Publisher

Abstract

This thesis explores the existence and properties of self-induced transparency (SIT) solitons in nanophotonic waveguides. SIT solitons are shape-preserving solutions of the semi-classical Maxwell-Bloch equations, a system of nonlinearly coupled differential equations. In a first investigation, collisions of counterpropagating simultons (SIT solitons in absorbing three-level systems) are studied numerically in the plane-wave approximation and a polarisation- and group-velocity dependent soliton birth is uncovered. Apart from their fundamental interest, such light-light interaction effects may be of use for optical computing applications if they can be transferred to tightly confined light pulses. Confining light is usually achieved by using dielectric waveguides that exhibit group velocity dispersion leading to chirped pulses, which experience absorption when entering an absorbing medium. If the chirp is strong enough and the pulse intense enough, they can even completely invert an absorber. When investigating chirped pulse propagation through a dense ensemble of two-level system it is found that the chirped pulses dynamically reshape into unchirped pulses experiencing transparency. Furthermore, the conditions on the waveguide geometry to enable SIT are analysed, identifying a nanophotonic slot waveguide with a low-index gap, exhibiting high electric field enhancement and a homogeneous field profile, as the ideal candidate system for guided SIT solitons. This analysis is supported by two-dimensional numerical calculations that show the solitary character is maintained during propagation if the absorber density is high enough to ensure a slow-down of the pulse and to thus counteract the waveguide dispersion. Finally, the soliton birth due to simulton collisions and optical memory schemes proposed for plane-wave SIT are investigated in the two-dimensional slot waveguide and found to also be possible in this geometry.

DOI
10.25560/10533

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This thesis explores the existence and properties of self-induced transparency (SIT) solitons in nanophotonic waveguides. SIT solitons are shape-preserving solutions of the semi-classical Maxwell-Bloch equations, a system of nonlinearly coupled differential equations. In a first investigation, collisions of counterpropagating simultons (SIT solitons in absorbing three-level systems) are studied numerically in the plane-wave approximation and a polarisation- and group-velocity dependent soliton birth is uncovered. Apart from their fundamental interest, such light-light interaction effects may be of use for optical computing applications if they can be transferred to tightly confined light pulses. Confining light is usually achieved by using dielectric waveguides that exhibit group velocity dispersion leading to chirped pulses, which experience absorption when entering an absorbing medium. If the chirp is strong enough and the pulse intense enough, they can even completely invert an absorber. When investigating chirped pulse propagation through a dense ensemble of two-level system it is found that the chirped pulses dynamically reshape into unchirped pulses experiencing transparency. Furthermore, the conditions on the waveguide geometry to enable SIT are analysed, identifying a nanophotonic slot waveguide with a low-index gap, exhibiting high electric field enhancement and a homogeneous field profile, as the ideal candidate system for guided SIT solitons. This analysis is supported by two-dimensional numerical calculations that show the solitary character is maintained during propagation if the absorber density is high enough to ensure a slow-down of the pulse and to thus counteract the waveguide dispersion. Finally, the soliton birth due to simulton collisions and optical memory schemes proposed for plane-wave SIT are investigated in the two-dimensional slot waveguide and found to also be possible in this geometry.
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.
This thesis presents theoretical models and results of numerical simulations describing the propagation of optical pulses through dense, thermal atomic vapours. In particular we investigate the nonlinear effects of optical solitons due to self-induced transparency (SIT) in two-level systems, optical simultons in V-type three-level systems and electromagnetically induced transparency (EIT) in Λ-type systems, including the storage and retrieval of dark-state polaritons. An investigation is made into two-photon excitation of the 5D states of rubidium in a high-intensity beam including the hyperfine structure of the relevant atomic levels. Decay from these states to the 6P manifolds is ruled out as a cause of experimentally observed fluorescence due to the amount of power broadening associated with intensities necessary to provide any significant level of population in these highly excited states. We combine the nonlinear effects of optical solitons and EIT to explain experimentally observed steepened pulses in a V-type system in a micron-length cell. We explain the behaviour as the early formation of a simulton pulse drawn from a CW probe field by a strong coupling pulse, due to coherent population trapping. We predict that in a longer cell it may be possible to facilitate propagation of matched pulses, even when the transitions in the system have different propagation coefficients, as long as decoherence from collision broadening can be controlled. The fact that weak pulses can propagate with this scheme suggests an approach to achieving transparent propagation of single or few photon pulses distinct from, but related to, both SIT and EIT.
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.
Formation of optical solitons in self-induced transparency (SIT) regime, where light pulses propagate virtually without loss in nominally strongly absorbing medium, is one of the most striking coherent transient phenomena in optics. Here we study experimentally and by numeric simulations how a square shape pulse gradually transforms into a smooth sech shape pulse of well-defined pulse area, depending on the parameters such as the pulse amplitude, duration, propagation distance etc. The SIT experiments for circularly polarized light are performed in the R1−3∕2) line of a 30 ppm ruby (α-Al2O3:Cr3+) at 1.7 K in a magnetic field of BIIc = 4.5 T, which corresponds to effective absorption coefficient, αL =14.5. In such a magnetic field and temperature range, a 30 ppm ruby is in the so-called superhyperfine limit resulting in a very long decoherence (phase memory) time, TM = 50 μs. We show, in good quantitative agreement with the simulations, how SIT soliton is formatted and how this results in extremely slow pulse peak propagation velocity of ∼300 m∕s, which is to date, the slowest pulse propagation ever observed in a SIT experiment. We also show that for accurate quantitative description of the observed SIT and soliton pulse shapes, the simulations need to account for variation of the incident pulse amplitude across the beam spatial profile. Potential implications of the SIT effect on classical- and quantum information storage will be discussed.
The possibility of observing a self-induced transparency (SIT) in an erbium-doped optical fiber is investigated. A general equation that includes the SIT, the group-velocity dispersion (GVD) of the fiber, and the nonlinear refractive index is discussed. It is shown that for one particular value of waveguide parameters the nonlinear index can balance the GVD, that is, the nonlinear Schr\"odinger equation (NLS), while maintaining a SIT soliton. This is called a SIT-NLS soliton. The phase change of the SIT-NLS soliton is governed solely by the NLS component, and the pulse delay due to resonance is determined solely by the SIT component when the detuning is zero. Practical parameters for silica-based fibers do not allow the coexistence of a mixed soliton state. A simple derivation of a condition for a SIT-NLS soliton is also presented. The SIT-NLS soliton is computer-run, and it is shown that a stable 2\ensuremath{\pi}/N=1 SIT-NLS soliton exists. However, high-order SIT-NLS solitons always split into multiple 2\ensuremath{\pi}/N=1 solitons. The NLS property can be preserved when Zsp{\mathit{Z}}_{\mathrm{sp}}Zsp​\ensuremath{\ll}Labs.{\mathit{L}}_{\mathrm{abs}.}Labs.​ Finally, the NLS soliton that interacts coherently with erbium ions is studied, and the coherent pulsation that produces multiple narrow pulses is described.
We consider an optical pulse propagation in a one-dimensional nonlinear periodic structure doped uniformly with inhomogeneously broadening two-level atoms wherein the pulse propagation is governed by the nonlinear coupled mode-Maxwell Bloch equations. We investigate the pulse-train like periodic waves as well as bright and dark solitons near the photonic bandgap structure under the influence of self-induced transparency (SIT) effect. Further, we demonstrate that the resulting bright and dark SIT Bragg solitons may be realized both in anomalous and normal dispersion regimes, and this novel concept is ultimately the crux of this paper.