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PT-symmetry and EP are nontrivial non-Hermitian physics - Coggle Diagram
PT-symmetry and EP are nontrivial non-Hermitian physics
They have been extensively studied in waveguides , periodic structures and WGM-supporting resonators = i.e. structures >> wavelength, but not for dipolar resonators
but in these resonators large radiative decay is present, so if we just take eps = eps' \pm ieps'', that is not going to work out.
In order to find the conditions for PT symmetry regime and EP, we study the system analytically using the coupled dipole method.
Here we have the coupled dipole matrix, where a0 is Lorenz-Mie coeff. and H0 Hankel function describes the scattered waves.
Kernel vectors of this matrix describe eigenstates, and complex eigenfrequencies are determined by det(matrix) = 0. We can rewrite it as follows:
If we plot left and right parts of the equation, we can observe that the only point that corresponds to the coalescence of eigenvalues is the tangentiality point of the two planes, marked by the triangle.
To make sure that this is an exceptional point, we find and plot the eigenfrequencies around it. The eigenfrequency surfaces demonstrate this special topology which resembles the Riemann surface of a square root function, characteristic to exceptional points.
Now we consider the PT symmetry regime: if we start at the EP and decrease the gain/loss contrast, we get PT symmetry. If we increase it, we get broken PT symmetry.
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Here is how the mode field distribution at the EP looks like:
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We also make use of the mapping n' + in'' -> scattering pole
