Reciprocity in EM

Radiation from a heated ratchet:

 

yellow ball "Near Field Propulsion Forces from Nonreciprocal Media," D. Gelbwaser-Klimovsky, N. Graham, M. Kardar, and Matthias Krüger,

Phys. Rev. Lett. 126, 170401 (2021).

greenarrowDispersion relation of photons (relevant at far fields):      

Reciprocity of electromagnetic field equations:            

"Nonreciprocal radiative heat transfer between two planar bodies," L. Fan, ..., C. Fan, Phys. Rev. B 101, 085407 (2020).

yellow ball The reciprocity condition can be broken in a number of ways, e.g. by magneto-optical couplings

  

yellow ball There is a motive force with non-reciprocal media, which can be used to construct a heat engine

As with heat transfer, the motive force is much larger in the near-field regime , where    is a characteristic material frequency.

Scaled motive force F (red diamonds), and heat transfer H (gray circles) for a SiC plate and one of n-InSb subject to a magnetic field along the x axis. The dots cor-respond to numeric calculations and the continuous lines to the small d asymptotes. Note that the force changes sign from +y to -y (dark red to light red diamond) at large separation. Inset: [f(ω)/h(ω)](ωd) for d= 1nm. Figures parameters: B= 10T, T1= 300K, T2= 270K.