The effective permittivity in the complex plane and a simple estimation method for leaky wave slowness

The well-known effective permittivity function is defined for complex values of slowness, using the procedure of analytical continuation from the real axis of slowness. An approximate estimation for a complex-value leaky wave slowness is given. Both parts of the slowness are expressed in terms of the real and imaginary parts of effective permittivity and the derivatives of them, which are calculated on the real axis only. This estimation may be as a simple indicator of possible existence of leaky waves. Lithium tetraborate and lithium niobate crystals are considered