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Non-Hermitian systems with parity-time symmetry have been found to exhibitreal spectra of eigenvalues, indicating a balance between the loss and gain.However, such a balance is not only dependent on the magnitude of loss andgain, but also easily broken due to external disturbance. Here, the authorspropose a transformation-optics approach to construct a unique class ofnon-Hermitian systems with robustly balanced loss and gain, irrespective of themagnitude of loss/gain and the environmental disturbance. Throughtransformation-optics operators like space folding and stretching, loss andgain can be generated and separated in the real space. While in the virtualspace, the loss and gain are still combined to each other, rendering a balanceof energy that is far more robust than other non-Hermitian systems. Thisamazing feature is verified by finite-element simulations. This work reveals aclass of non-Hermitian systems in which loss and gain are balanced robustly,thereby denoted as pseudo-Hermitian systems.

Pseudo-Hermitian Systems Constructed by Transformation Optics with Robustly Balanced Loss and Gain