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arXiv:2301.11035

Electromagnetic pulse transparency in coupled cavity arrays through dispersion management

Zoran M. Ivić, Željko Pržulj, Dalibor Čevizović, Giorgos P. Tsironis

Published Jan 26, 2023• 0 citations
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Abstract

We theoretically demonstrated the possible emergence of slow-light self-induced transparency solitons in the infinite one-dimensional coupled cavity array, with each cavity containing a single qubit. We have predicted a substantial dependence of pulse transparency on its dimensionless width $τ_0$. In particular, short pulses whose widths range from $τ_0\ll 1$ to $τ_0\lesssim 1$ exhibit simple, almost linear dispersion law with a finite frequency gap of the order of the cavity array photonic band gap. That is, the medium is opaque for very short pulses with carrier wave frequency below the photonic gap. When the pulse width exceeds the critical one, a twin transparency window separated by a finite band gap appears in the soliton pulse dispersion law. Observation of predicted effects within the proposed setup would be of interest for understanding the properties of self-induced transparency effect in general and future applications in the design of quantum technological devices.

DOI
10.48550/arxiv.2301.11035

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We theoretically demonstrated the possible emergence of slow-light self-induced transparency solitons in the infinite one-dimensional coupled cavity array, with each cavity containing a single qubit. We have predicted a substantial dependence of pulse transparency on its dimensionless width τ0τ_0τ0​. In particular, short pulses whose widths range from τ0≪1τ_0\ll 1τ0​≪1 to τ0≲1τ_0\lesssim 1τ0​≲1 exhibit simple, almost linear dispersion law with a finite frequency gap of the order of the cavity array photonic band gap. That is, the medium is opaque for very short pulses with carrier wave frequency below the photonic gap. When the pulse width exceeds the critical one, a twin transparency window separated by a finite band gap appears in the soliton pulse dispersion law. Observation of predicted effects within the proposed setup would be of interest for understanding the properties of self-induced transparency effect in general and future applications in the design of quantum technological devices.
We present a theoretical prediction of a novel, nonEIT, mechanism for the achievement of a transparency window. It relies on an intrinsically nonlinear (soliton type) mechanism which may be exploited for the production of slow light, which may appear in a photonic band-gap structure: the infinite coupled cavity array (CCA), filled with two-level systems - qubits. Each cavity contains a single qubit. The most important prediction is substantial dependence of the pulse transparency on its width. In particular, the medium is opaque for very short pulses with carrier wave frequency below the photonic gap. When the pulse width exceeds the critical one, a twin transparency window separated by a finite band gap appears in the SIT pulse dispersion law. Both low-frequency TW and the SIT pulse band gap lie entirely within the polaritonic band gap.
We examine theoretically the transparency of electromagnetic pulses through an infinite one-dimensional array of coupled optical microcavities uniformly filled with superconducting qubits-one per cavity. Two types of hybrid matter-light waves, i.e., polaritons and self-induced transparency solitons, govern the transparency of electromagnetic radiation in these media. The spectrum of linear excitations, i.e., polaritons, consists of two branches separated by a relatively wide forbidden band. In the nonlinear regime, the dispersion relation of the carrier wave is determined by soliton width that is controlled by the reciprocal qubit frequency. The separate dispersion curves lie within the polariton forbidden band. Soliton transparency requires that the carrier wave frequency exceeds a threshold value; the latter depends strongly on the pulse width. We find that for pulses with widths ranging from ultrashort to an intermediate limit, the threshold is of the order of the gap frequency value in the photon spectrum. For wider pulses, the threshold frequency gradually decreases to values that are toward the edge of the polariton lower band, provided the soliton width is larger than a critical value. In the overcritical regime, the bandgap appears in the spectrum of the soliton carrier wave, while a twin transparency window appears in the soliton pulse dispersion law. A possible experimental observation of the predicted effects within the proposed setup would be of interest in understanding the properties of self-induced transparency in general and applications in the design of quantum technological devices.
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 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 study the effects of dispersion in carrier waves on the properties of soliton self--induced transparency (SIT) in two level media. We found substantial impact of dispersion effects on typical SIT soliton features. For example, the degree of SIT pulse velocity slowing down (acceleration) is determined by the ratio of the incoming pulse frequency over atomic transition frequency - x=ω/ω0x=ω/ω_0x=ω/ω0​. Specifically, an immediate pulse stopping is predicted for absorbing media when pulse duration time exceeds some critical value. In the sharp line limit stopping may emerge only for frequency ratio above unity, while for the inhomogeneously broadened systems it appears irrespective of the value of xxx. Analysis performed on the basis of Mcall\& Hahn \textit{Area theorem} implies that pulse stopping is achieved when Ber's absorption coefficient approaches infinity, that is, pulse energy is fully absorbed in the medium. In the case of amplifying media super-luminal motion is predicted as in the case of resonance. However, there is a lowest value in the frequency ratio below which the pulse velocity tends to the sub-luminal region. These new features of the SIT phenomenon open novel ways on how it may be exploited for the control of electromagnetic wave radiation in two-level media. This may be achieved by varying frequency ratio.
We determine the dispersion law of the carrier wave of an exciton-photon pulse which propagates as a solitary wave. For short pulses, four branches $\ensuremath{\Omega}=\ensuremath{\Omega}$ ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$) appear: a branch which goes through the intersection point $\ensuremath{\hbar}cK={E}_{o}+\frac{{\ensuremath{\hbar}}^{2}{K}^{2}}{2M}$ of the uncoupled modes of the free exciton and the free light field, two polaritonlike branches and an excitonlike branch. The polaritonlike branches have a normal dispersion, whereas the branch which goes through the intersection point of the free modes has an anomalous dispersion for sufficiently short pulse width. This branch contains the solution of McCall and Hahn as a special case. For very short pulses the branch with anomalous dispersion continues into the two polaritonlike branches. For increasing pulse width a forbidden energy gap appears at $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}=0$. For long pulses, only the two polaritonlike solutions exist.