[Paper Review] Optical Solitons in Periodic Media with Resonant and Off-Resonant Nonlinearities

Gershon Kurizki, A. Kozhekin+2 more|ArXiv.org|Jul 8, 2000

Nonlinear Photonic Systems58 references13 citations

TL;DR

This paper proposes a resonantly absorbing Bragg reflector (RABR) with periodic thin layers of two-level systems (TLS) as a platform for stable optical solitons. By leveraging resonant nonlinearities in a periodic dielectric structure, it demonstrates the existence of both stable bright and dark gap solitons—unlike prior models—offering a robust, experimentally feasible system for ultrafast all-optical signal processing with soliton lifetimes up to microseconds.

ABSTRACT

The properties of optical solitons in periodic nonlinear media are reviewed. The emphasis is on solitons in periodically refractive media (Bragg gratings) incorporating a periodic set of thin layers of two-level systems resonantly interacting with the field. Such media support a variety of bright and dark `gap solitons' propagating in the band gaps of the Bragg gratings, as well as their multi - dimensional analogs (light bullets). These novel gap solitons differ substantially from their counterparts in periodic media with either cubic or quadratic off-resonant nonlinearities.

Motivation & Objective

• To identify a physical platform capable of supporting stable optical solitons in periodic media with both resonant and off-resonant nonlinearities.
• To overcome the instability limitations of Kerr-nonlinear and second-harmonic-generation Bragg grating models by introducing a resonantly absorbing Bragg reflector (RABR).
• To demonstrate the coexistence of stable bright and dark solitons under the same parameter conditions, a feature not previously realized in nonlinear optical systems.
• To provide a feasible experimental pathway for realizing these solitons using quantum wells or rare-earth-doped superlattices under cryogenic conditions.

Proposed method

• Modeling the system using a periodic array of thin two-level systems (TLS) embedded in a dielectric medium with alternating refractive indices, forming a resonant Bragg reflector (RABR).
• Deriving coupled nonlinear equations for the field envelope and atomic polarization, incorporating resonant absorption and nonlinear response via the Rabi frequency and detuning parameters.
• Applying the slowly varying envelope approximation (SVEA) to reduce the full Maxwell-Bloch equations to a set of coupled nonlinear Schrödinger-type equations for the optical field and atomic populations.
• Using numerical simulations to evolve the system from initial soliton profiles (zero-width and finite-width corrected) under realistic parameters, including dephasing and deexcitation effects.
• Evaluating soliton stability and lifetime by tracking temporal and spatial evolution over time scales up to τ ≈ 50 in dimensionless units.
• Assessing experimental feasibility by estimating required material parameters such as absorption length, dephasing time, and laser intensity (10⁶–10⁷ W/cm²), and device dimensions (~1 mm to 1 cm).

Experimental results

Research questions

• RQ1 Can stable bright and dark solitons coexist in the same nonlinear optical medium under identical parameters, particularly in a periodic structure with resonant nonlinearity?
• RQ2 How does the periodic arrangement of resonant two-level systems (TLS) in a Bragg reflector enable the formation of gap solitons with arbitrary pulse area, unlike in uniform media?
• RQ3 What are the conditions under which solitons in a resonantly absorbing Bragg reflector (RABR) remain stable despite the presence of dephasing and spontaneous emission?
• RQ4 Can the RABR structure support solitons with lifetimes on the order of microseconds, making them experimentally viable for all-optical signal processing?
• RQ5 What material parameters (e.g., TLS density, layer thickness, dephasing time) are required to realize stable solitons in a RABR using quantum wells or rare-earth-doped superlattices?

Key findings

• The RABR structure supports a vast family of stable bright and dark gap solitons, including both moving and standing solitons, with stable dark solitons existing over a large parameter range.
• Stable bright and dark solitons coexist for the same system parameters, a feature not previously observed in nonlinear optical systems, particularly in contrast to conventional second-harmonic generation media.
• Soliton lifetimes in the RABR can reach up to ~1 μs, limited primarily by exciton dephasing time (~10⁻¹³ s), which is feasible for experimental observation in cryogenically cooled systems.
• Numerical simulations show that both zero-width and finite-width dark soliton solutions evolve regularly over τ ≈ 50 (dimensionless time), with significant distortion only after τ ≈ 10, indicating robustness.
• The required laser intensities for soliton formation are in the range of 10⁶–10⁷ W/cm², achievable with current laser technology, and device sizes of ~1 mm to 1 cm are feasible with ~10³–10⁴ unit cells.
• The system remains stable under dephasing and deexcitation effects when modeled with damping terms (Γ₁, Γ₂), preserving soliton characteristics on the time scale ττ₀ < 1/Γ₁,₂.