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Energy-leaky modes in partially measured scattering matrices of disordered media

We investigate energy-leaky modes induced by incomplete measurements of the scattering matrices of complex media. Due to the limited numerical apertures of an optical system, it is experimentally challenging to access theoretically predicted perfect transmission channels in the diffusive regime. By conducting numerical simulations on scattering matrices, we demonstrate that leaky modes contributed from uncollected transmission in the TM provides an energy transmission that is more enhanced than that predicted by measurement. On the other hand, a leaky mode originating from the uncollected reflection in the partial measurement of a RM strongly suppresses the energy transmission through a zero-reflection channel, restricting the transmission enhancement to no more than a 5-fold enhancement in limited optical systems. Our study provides useful insights into the effective control of energy delivery through scattering media and its ultimate limitation in practical schemes.