How to analyze thermal radiation in nonlinear photonics systems? Why is it challenging? 

Despite a long history of the separate fields of nonlinear optics and thermal radiation, their intersection remained unexplored primarily because of two reasons: 
1. Practical concern: Nonlinear interactions of photons/light fields are weak inside bulk materials, typically requiring high power laser light. Thermal radiation in most systems is low power. 
2. Theoretical concern: Addressing the thermodynamic implications of the nonlinear frequency mixing effects is challenging. e.g. Does it break the detailed balance of energy at thermal equilibrium? Does it make heat flow from a cold body to hot body violating second law of thermodynamics?  
In our recent works, we have overcome these challenges. It is now well-known that the nonlinear interactions can be significantly enhanced using various approaches (resonant systems, density of states, bound states in continuum, quantum-well engineering, inverse design etc.) to lower the power requirements. As the power requirements are scaled down, low power thermal fluctuations can exhibit interesting nonlinear effects. To explore these effects in engineered systems, we have developed tools and techniques ensuring that their description is consistent with thermodynamic laws. 
Opt. Exp. 2020    
Opt. Exp. 2017     
Phys. Rev. B 2015 
Appl. Phys. Lett. 2015

How to analyze thermal radiation from generic bianisotropic media

Radiative heat transport phenomena have been extensively studied using common isotropic materials. Very recently, other classes (which are computationally difficult to analyze) such as uni/biaxial anisotropic materials and gyroelectric materials are explored. Our goal is to develop tools and techniques to extend this exploration to many other unexplored classes of nontrivial materials like gyromagnetic, magnetoelectric, and other nontrivial materials that have not been explored yet.
In our recent works, we have found interesting 'photon-spin'-related phenomena using gyrotropic and magnetoelectric materials. See fundamenal prospects page. 
A universal look at thermal-radiation properties has also enabled us to discover new spin-resolved Kirchhoff's laws. We believe that this research direction will be promising in the long run. 
 New J. Phys. 2019 
New J. Phys. 2020

Gain-loss systems for controlling and enhancing near-field radiative heat flux

Thermal radiation and near-field heat transfer are described using fluctuational electrodynamic theory. We have generalized it to describe incoherent amplified spontaneous emission from gain media below lasing threshold.
We show that a combination of loss-compensation (using gain medium) and near-field interactions can be utilized to obtain and tailor giant (orders of magnitude enhanced) radiative heat flux at the nanoscale. Because of a large magnitude of heat flux (comparable to conductive flux rates), this finding will be important for nanoscale heat management.  
Phys. Rev. B. 2016

Spintronic approach for controllable nonreciprocity and spin-photonic applications

We propose a design (left schematic) which uses strong spin-orbit-coupling (SOC) of a narrow band-gap semiconductor InSb with ferromagnetic dopants. A combination of intrinsic SOC with gate-applied electric field leads to strong external Rashba spin-orbit-coupling. This makes the magnetically doped InSb thin film a gyromagnetic medium (non-symmetric permeability tensor). 
We then show photon-spin-dependent Purcell effect in the vicinity of this thin film which has gate-controllable nonreciprocity. As shown in the figure, a dipole (classical source or atomic/molecular transition) emitting right circularly polarized light experiences larger Purcell factor than that emitting left circularly polarized light. 
Phys. Rev. B. 2020