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Strongly chirped dissipative solitons in normal and anomalous dispersion regimes

V. L. Kalashnikov, A. Rudenkov, E. Sorokin, I. T. Sorokina

TL;DR

The paper develops an adiabatic theory for strongly chirped dissipative solitons in the cubic–quintic complex Ginzburg–Landau equation, deriving closed-form expressions for the spectrum, peak power, and energy across normal and anomalous dispersion regimes. It identifies two physical DS branches and demonstrates that dissipative-soliton resonance enables energy scaling on a scalable branch, offering a direct path to high-energy femtosecond oscillators without external amplification. A node-regularized spectral framework is introduced, and a Bose–Einstein condensation–like thermodynamic interpretation is proposed to quantify energy scalability limits and breakup conditions. Collectively, the results provide actionable laser-design guidance for energy-scalable, single-pulse operation and motivate a generalized, optics-based thermodynamic theory of strongly chirped DS with measurable proxies for entropy and temperature.

Abstract

We develop an adiabatic theory for strongly chirped dissipative solitons governed by the cubic-quintic complex Ginzburg-Landau equation and analyze their existence regions in both normal- and anomalous-dispersion regimes. Closed-form expressions for the spectrum, peak power, and energy allow a compact dimensionless parameterization of the dissipative soliton parametric space. The analysis reveals that dissipative-soliton resonance, i.e., chirp-driven temporal stretching with bounded peak power, naturally emerges on the scalable branch, providing a direct pathway to high-energy femtosecond oscillators without the need for external amplification. We establish a basis for interpreting these results within a thermodynamic framework that connects energy ``condensation'' in the soliton to a BEC-like metaphor, providing quantitative indicators for energy scalability limits and breakup onsets, and aligning with a recently formulated thermodynamic methodology for dissipative solitons. Beyond immediate laser design guidance, our approach suggests a generalized thermodynamic theory of strongly chirped dissipative solitons, including measurable entropy/temperature proxies and a phase diagram that delineates single- versus multi-soliton states. This unifies practical laser-engineering criteria with many-body concepts, pointing to optics-based, metaphorical simulations of condensate phenomena.

Strongly chirped dissipative solitons in normal and anomalous dispersion regimes

TL;DR

The paper develops an adiabatic theory for strongly chirped dissipative solitons in the cubic–quintic complex Ginzburg–Landau equation, deriving closed-form expressions for the spectrum, peak power, and energy across normal and anomalous dispersion regimes. It identifies two physical DS branches and demonstrates that dissipative-soliton resonance enables energy scaling on a scalable branch, offering a direct path to high-energy femtosecond oscillators without external amplification. A node-regularized spectral framework is introduced, and a Bose–Einstein condensation–like thermodynamic interpretation is proposed to quantify energy scalability limits and breakup conditions. Collectively, the results provide actionable laser-design guidance for energy-scalable, single-pulse operation and motivate a generalized, optics-based thermodynamic theory of strongly chirped DS with measurable proxies for entropy and temperature.

Abstract

We develop an adiabatic theory for strongly chirped dissipative solitons governed by the cubic-quintic complex Ginzburg-Landau equation and analyze their existence regions in both normal- and anomalous-dispersion regimes. Closed-form expressions for the spectrum, peak power, and energy allow a compact dimensionless parameterization of the dissipative soliton parametric space. The analysis reveals that dissipative-soliton resonance, i.e., chirp-driven temporal stretching with bounded peak power, naturally emerges on the scalable branch, providing a direct pathway to high-energy femtosecond oscillators without the need for external amplification. We establish a basis for interpreting these results within a thermodynamic framework that connects energy ``condensation'' in the soliton to a BEC-like metaphor, providing quantitative indicators for energy scalability limits and breakup onsets, and aligning with a recently formulated thermodynamic methodology for dissipative solitons. Beyond immediate laser design guidance, our approach suggests a generalized thermodynamic theory of strongly chirped dissipative solitons, including measurable entropy/temperature proxies and a phase diagram that delineates single- versus multi-soliton states. This unifies practical laser-engineering criteria with many-body concepts, pointing to optics-based, metaphorical simulations of condensate phenomena.

Paper Structure

This paper contains 13 sections, 92 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Adiabatic theory of strongly chirped DS
  3. Stationary-phase spectrum (SPA).
  4. Spectral power (envelope).
  5. (i) Linearized denominator ($A_{2}=0$): truncated–Lorentz, explicit $\arctan$.
  6. (ii) Quadratic denominator kept ($A_{2}\neq 0$): elementary closed form.
  7. Physically relevant solutions
  8. NGD, $C>0$ (A, Table \ref{['tbl1']})
  9. Case $\widetilde{\chi}>0$.
  10. Case $\widetilde{\chi}<0$.
  11. Two–sided limit $\widetilde{\chi}\to 0^{\pm}$.
  12. AGD, $C<0$ (C, Table \ref{['tbl1']})
  13. Conclusion

Figures (3)

  • Figure 1: The regions of the positive (a) and negative (b) branches of $\widetilde{\Delta}^2_{\pm}$ corresponding to the criterion A in Table \ref{['tbl1']}. The colored surfaces correspond to the different values of $\widetilde{\Delta}^2$. The scattered points fill the regions where the criterion of A in Table \ref{['tbl1']} is satisfied. The tildes are removed from axis labels intentionally.
  • Figure 2: Dependence of $\Delta_{\mp}^2$ on $\chi$ (tildes are removed, the $\Delta_{\mp}^2$-branches are illustrated by the different colors). $C=$0.5, $\Sigma=$0.1.
  • Figure 3: The same as in Fig. 1, but for the minus branch of $\tilde{\Delta}_{-}^{2}$ and the criterion C in Table 1. The shaded domain is the admissible AGD region satisfying Eq. \ref{['eq:AGDwindow']}.