Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Numerical investigation of a self-induced transparency soliton in a nonlinear photonic bandgap structure doped uniformly with two-level atoms

Boren Luo, Hong‐Yih Tseng, Sien Chi

Published Sep 1, 2003• 8 citations
Publisher

Abstract

We numerically study the characteristics of a nonlinear pulse that propagates through a one-dimensional photonic bandgap (PBG) structure uniformly doped with two-level atoms. The numerical model adopted is the coupled system of nonlinear coupled-mode equations and atomic Bloch equations. The simulation results show that a self-induced transparency (SIT) soliton and a gap soliton can coexist in a nonlinear PBG structure uniformly doped with resonant atoms. Although this mixed state, known as a SIT-gap soliton, near the PBG edge has been theoretically predicted, we numerically show that such a solitary wave still exists even if its central frequency is located deep inside the PBG. The propagating characteristics of the SIT-gap soliton are also discussed.

DOI
10.1364/josab.20.001866

Related papers

Coexistence of a self-induced transparency soliton and a Bragg soliton

Hong‐Yih Tseng, Sien Chi

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.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 20, 2002•8 citations

Self-induced transparency solitary waves in a doped nonlinear photonic band gap material

Neşet Aközbek, Sajeev John

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.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Sep 1, 1998•66 citations

SELF-INDUCED TRANSPARENCY BRAGG SOLITONS IN A NONLINEAR PHOTONIC BANDGAP STRUCTURE

P. Ramesh Babu, Krishnamoorthy Senthilnathan

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.

Optics and Photonics Letters•Jun 1, 2011•0 citations

Generation of self-induced-transparency gap solitons by modulational instability in uniformly doped fiber Bragg gratings

B. Kalithasan, Kuppusamy Porsezian, Krishnamoorthy Senthilnathan +1 more

We consider the continuous-wave (cw) propagation through a fiber Bragg grating that is uniformly doped with two-level resonant atoms. Wave propagation is governed by a system of nonlinear coupled-mode Maxwell-Bloch (NLCM-MB) equations. We identify modulational instability (MI) conditions required for the generation of ultrashort pulses in both anomalous and normal dispersion regimes. From a detailed linear stability analysis, we find that the atomic detuning frequency has a strong influence on the MI. That is, the atomic detuning frequency induces nonconventional MI sidebands at the photonic band gap (PBG) edges and near the PBG edges. Especially in the normal dispersion regime, MI occurs without any threshold condition, which is in contrast with that of conventional fiber Bragg gratings. We also perform a numerical analysis to solve the NLCM-MB equations. The numerical results of the prediction of both the optimum modulation wave number and the optimum gain agree well with that of the linear stability analysis. Another main result of the present work is the prediction of the existence of both bright and dark self-induced transparency gap solitons at the PBG edges.

Physical Review A•May 3, 2010•7 citations

Self-induced transparency and giant nonlinearity in doped photonic crystals

Gershon Kurizki, David Petrosyan, Tomáš Opatrný +2 more

Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.

arXiv:quant-ph/0204076•Journal of the Optical Society of America B•Sep 1, 2002•9 citations

Distortionless pulse-train propagation in a nonlinear photonic bandgap structure doped uniformly with inhomogeneously broadening two-level atoms

Hong‐Yih Tseng, Sien Chi

The pulse propagation in a one-dimensional nonlinear photonic bandgap (PBG) structure doped uniformly with inhomogeneously broadening two-level atoms is investigated. The Maxwell-Bloch equations describing pulse propagation in such a uniformly doped PBG structure are derived first and further reduced to effective nonlinear coupled-mode equations. An exact analytic pulse-train solution to these effective coupled-mode equations is obtained. Such a distortionless; pulse-train solution is given by sinusoidal functions with a DC background and a modulated phase. Numerical examples of the distortionless pulse train in a silica-based PBG structure doped uniformly with Lorentzian lineshape two-level atoms are shown.

IEEE Journal of Selected Topics in Quantum Electronics•May 1, 2002•3 citations
We numerically study the characteristics of a nonlinear pulse that propagates through a one-dimensional photonic bandgap (PBG) structure uniformly doped with two-level atoms. The numerical model adopted is the coupled system of nonlinear coupled-mode equations and atomic Bloch equations. The simulation results show that a self-induced transparency (SIT) soliton and a gap soliton can coexist in a nonlinear PBG structure uniformly doped with resonant atoms. Although this mixed state, known as a SIT-gap soliton, near the PBG edge has been theoretically predicted, we numerically show that such a solitary wave still exists even if its central frequency is located deep inside the PBG. The propagating characteristics of the SIT-gap soliton are also discussed.
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 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.
We consider the continuous-wave (cw) propagation through a fiber Bragg grating that is uniformly doped with two-level resonant atoms. Wave propagation is governed by a system of nonlinear coupled-mode Maxwell-Bloch (NLCM-MB) equations. We identify modulational instability (MI) conditions required for the generation of ultrashort pulses in both anomalous and normal dispersion regimes. From a detailed linear stability analysis, we find that the atomic detuning frequency has a strong influence on the MI. That is, the atomic detuning frequency induces nonconventional MI sidebands at the photonic band gap (PBG) edges and near the PBG edges. Especially in the normal dispersion regime, MI occurs without any threshold condition, which is in contrast with that of conventional fiber Bragg gratings. We also perform a numerical analysis to solve the NLCM-MB equations. The numerical results of the prediction of both the optimum modulation wave number and the optimum gain agree well with that of the linear stability analysis. Another main result of the present work is the prediction of the existence of both bright and dark self-induced transparency gap solitons at the PBG edges.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.
The pulse propagation in a one-dimensional nonlinear photonic bandgap (PBG) structure doped uniformly with inhomogeneously broadening two-level atoms is investigated. The Maxwell-Bloch equations describing pulse propagation in such a uniformly doped PBG structure are derived first and further reduced to effective nonlinear coupled-mode equations. An exact analytic pulse-train solution to these effective coupled-mode equations is obtained. Such a distortionless; pulse-train solution is given by sinusoidal functions with a DC background and a modulated phase. Numerical examples of the distortionless pulse train in a silica-based PBG structure doped uniformly with Lorentzian lineshape two-level atoms are shown.