Reciprocity in EM

Radiation from a heated ratchet:

 

yellow ball "Near Field Propulsion Forces from Nonreciprocal Media," D. Gelbwaser, N. Graham, M. Kardar, M. 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, PRB 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

Both heat transfer andmotive force are 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 correspond 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.

(Figure parameters: B= 10T, T1= 300K, T2= 270K.)