Arkady Kurnosov,¹ Lucas J. Fernández-Alcázar,^2,3 Alba Ramos,^2,3 Boris Shapiro,⁴ and Tsampikos Kottos¹

¹ Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, CT-06459, USA
² Institute for Modeling and Innovative Technology, IMIT (CONICET – UNNE), Corrientes W3404AAS, Argentina
³ Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina, Corrientes W3404AAS, Argentina
⁴ Technion – Israel Institute of Technology, Technion City, Haifa, 3200, Israel

Recent experimental developments in multimode nonlinear photonic circuits (MMNPC), have motivated the development of an optical thermodynamic theory that describes the equilibrium properties of an initial beam excitation [1,2]. However, a non-equilibrium transport theory for these systems is still terra incognita when they are in contact with thermal reservoirs [3]. Here, by combining Landauer and kinematics formalisms we develop a universal one-parameter scaling theory that describes the whole transport behavior from the ballistic to the diffusive regime, including both positive and negative optical temperature scenarios. We also derive a photonic version of the Wiedemann-Franz law that connects the thermal and power conductivities. Our work paves the way toward a fundamental understanding of the transport properties of MMNPC and may be useful for the design of all-optical cooling protocols.

References:
[1] L. G. Wright, D. N. Christodoulides, F. W. Wise, Control lable spatiotemporal nonlinear effects in multimode fibres, Nat. Photonics 9, 306 (2015)
[2] A. Ramos, L. Fernandez-Alcazar, Tsampikos Kottos, B. Shapiro, Optical Phase Transitions in Photonic Networks: a Spin-System Formulation, Phys. Rev. X 10, 031024 (2020)
[3] M. Lian,Y.-J. Chen, Y. Geng, Y. Chen, J.-T. Lü, Violation of the Wiedemann-Franz law in coupled thermal and power transport of optical waveguide arrays, arXiv:2307.16529v1