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 Alù [D. L. Sounas and A. Alù, 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 and 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 nonunitarity 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.

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• Electromagnetic field calculations
• Nanophotonics
• Near-field optics
• Classical electromagnetism
• Electromagnetic wave theory
• Methods in electromagnetism