Time-reversal-symmetry bounds on electromagnetic fields

For linear electromagnetic systems possessing time-reversal symmetry, we present an approach to bound ratios of internal fields excited from different ports, using only the scattering matrix (S matrix), improving upon previous related bounds by Sounas and Al\`u (2017) [Phys. Rev. Lett. 118, 154302 (2017)]. By reciprocity, emitted-wave amplitudes from internal dipole sources are bounded in a similar way. When applied to coupled-resonant systems, our method constrains ratios of resonant coupling/decay coefficients. We also obtain a relation for the relative phase of fields excited from the two ports and the ratio of field intensities in a two-port system. In addition, although lossy systems do not have time-reversal symmetry, we can still approximately bound loss-induced non-unitarity of the S matrix using only the lossless S matrix. We show numerical validations of the near-tightness of our bounds in various scattering systems.