Cavity Soliton formation in Fabry-Perot Resonators

Cavity Soliton formation in Fabry-Perot Resonators Krupamaya Panda1, 2, 3, Carlo Silvestri1, 2, Christelle Monat3, Christian Grillet3, C. Martijn de Sterke1, 2 , and Antoine F. J. Runge1, 2 1. Institute of Photonics and Optical Sciences, School of Physics, University of Sydney 2. ARC Centre of Excellence for Optical Microcombs for Breakthrough Science (COMBS) 3. Institut des Nanotechnologies de Lyon (INL), Ecole Centrale de Lyon Fabry-Perot cavities hold great potential in chip-scale frequency combs. Here, due to highly dispersive nature of Bragg gratings of the cavity, dispersion tuning is remarkably flexible. This work investigates inherent differences in Fabry-Perot and ring cavities by numerically solving Lugiato-Lefever equation. Moreover, we numerically show existence of pure-quartic cavity solitons in Fabry-Perot cavities. 5. Conclusions and Outlook ➢In this work we studied the cavity dynamics of a Fabry-Perot under anomalous quadratic dispersion. ➢In the Fabry-Perot consecutive excitement of turring rolls, chaotic modulation instability, and cavity solitons was observed similar to the ring case. ➢Having counterpropagating fields adds extra nonlinear phase shift to the system. ➢Assuming a continuous wave state numerical results suggest Fabry-Perot may have increase in nonlinearity by threefold compared to a ring cavity. ➢Furthermore, we also confirm the existence of dissipative pure-quartic solitons in Fabry-Perot. ➢Formation dynamics of these dissipative PQSs are currently under investigation. ➢Future studies will include design, fabrication, and characterization of an integrated Fabry-Perot cavity with anomalous quartic dispersion. References 1. Cole, Daniel C., et al. "Theory of Kerr frequency combs in Fabry-Perot resonators." Physical Review A 98.1 (2018): 013831. 2. Wildi, Thibault, et al. "Dissipative Kerr solitons in integrated Fabry–Perot microresonators." Optica 10.6 (2023): 650-656. 3. Tam, Kevin KK, et al. "Stationary and dynamical properties of pure-quartic solitons." Optics Letters 44.13 (2019): 3306-3309. 4. Taheri, Hossein, and Andrey B. Matsko. "Quartic dissipative solitons in optical Kerr cavities." Optics Letters 44.12 (2019): 3086-3089. Acknowledgments This work presented here was supported through the generous funding provided through the Australia France Network of Doctoral Excellence (AUFRANDE) which is a co-funded by the European Union’s research and innovation program under the Marie SkłodowskaCurie Grant No. 101081465; and the Australian Research Council (ARC) grants (Grant No. DE220100509, DP230102200, CE230100006). We sincerely appreciate the international collaboration enabled by these funding sources. 2. Numerical Simulations ➢LLE of Eq 1. was numerically solved through Split-Step Fourier Method for various values of detuning under anomalous quadratic dispersion ➢Like ring cavity case, in a Fabry-Perot turring rolls, modulation instability and cavity solitons also emerge consecutively. ➢Simulations suggest temporal pattern formation in Fabry-Perot and ring cavity are almost similar. (a) (b) (c) (d) Figure 2: Numerically simulated auxiliary field for 𝑘 = 2 in Eq. 1. (a) Spatial evolution of field against cavity detuning (b) cavity solitons (c) chaotic modulation instability and (d) turring rolls. 3. Nonlinear Dyanmics of Farby-Perot ➢Key differences between a Fabry-Perot and ring case are occurrence of modulation instability and cavity solitons toward larger detunings. ➢Numerical values of average cavity energy suggest Fabry-Perot experiences an effectively large nonlinearity compared to the ring due to the XPM term. ▪Experienced nonlinearity can be roughly a factor of three compared to ring given that the cavity is in either continuous wave or stable turring roll state. (a) (b) Figure 3: Simulated average cavity energies for 𝑘 = 2 in Eq. 1. (a) Fabry-Perot ( ) and ring ( ) (b) Comparison of Fabry-Perot and ring to a ring with 3 times large nonlinearity ( ). 4. Can Fabry-Perot sustain Pure-Quartic Cavity Solitons? ➢Dissipative Pure-Quartic Solitons form under the balance of anomalous quartic dispersion, nonlinearity, loss and gain. ➢Dissipative PQSs are also a stable solutions of the Eq. 1 for 𝑘 = 4. ➢Dissipative PQSs have relatively flatter spectra compared to quadratic case and can have larger pulse energy for same pulse width3. (a) (b) Figure 4: Conventional solitons (𝑘 = 2, 𝛽2= −0.02, 𝐹 = 20, 𝛼 = 16 ) and Pure-Quartic cavity solitons (𝑘 = 4, 𝛽4= −0.0003, 𝐹 = 20, 𝛼 = 16)4 (a) Along spatial coordinate (log scale) (b) spectrum Quadratic Cavity Soliton Pure-Quartic Cavity Soliton Email: kpan08[email protected].edu.au ➢A Fabry-Perot cavity consists of two reflectors separated by a distance 𝐿 where optical field continuously bounces off in between mirrors. ➢Fabry-Perot cavities can be used to generate frequency combs. Where cavity soliton formation can lead to coherent mode-locked comb states. ➢In Fabry-Perot two counterpropagating fields always exist and require two coupled equations for full description of cavity dynamics. ➢ Numerically solving these coupled equations is often a computational hassle. ➢Full cavity dynamics can be described with a special Lugiato-Lefever formalism for Fabry-Perot (FP-LLE). ➢FP-LLE is solved for an auxiliary field 𝜓, and includes an additional cross-phase modulation (XPM) term1. ▪Formalism is limited to only high-finesse cavities. ▪Physical fields can be reconstructed through 𝜓 as it contains all the information. ▪For a ring 𝜓 represents a physical field and the additional term vanishes. Figure 1: A conceptual illustration of two counterpropagating cavity solitons in an integrated FabryPerot cavity with chirped Bragg-gratings. 𝝏𝝍 𝝏𝝉 = − 𝟏 + 𝒊𝜶 𝝍 + 𝒊 𝝍 𝟐𝝍 + 𝒊𝜷𝒌 𝒌! 𝝏𝒌𝝍 𝝏𝜽𝒌+𝑭+𝟐𝒊𝝍 𝝍 𝟐 XPM Dispersion SPM Driving term detuning Where 𝒌 = 𝟐, 𝟒 (1) 1. LLE for Fabry-Perot