Electromagnetic waves in a waveguide with a space-time multiperiodic dielectric filling

On the Electrodinamics of Space-Time Periodic Mediums in a Waveguide of Arbitrary Cross Section

“…Let the permittivity and permeability of the filling of the waveguide with help of pump wave are modulated in space and time under the periodic law ( Fig.1.1) [23,25] ( ) propagates in a similar waveguide along their axis in the positive direction. Suppose that the signal wave doesn't change the quantities of ε and μ .…”

“…These components satisfy to partial differential equations with variable coefficients which are obtained from the Maxwell equations taking into account that the charge density and the current density are equal to zero. These wave equations have a form [23][24][25] and to pass to the new variables ξ and η according to the formulas [22] ()() and taking into account that permittivity and permeability of the filling change by the harmonic law (1.1) the above received differential equations (1.14) and (1.15) on variables ξ and η are transformed to the differential equations with periodic coefficients of Mathie-Hill type [32]. In the first approximation on small modulation indexes they have a form [23] ( ) () The solutions of the equations (1.18) and (1.19) we look for the form…”

“…As in my earlier works (see, e.g., [23], [31], [34][35][36][37]), transverse electric (ТЕ) and transverse magnetic (TM) waves in the waveguide will be described through the longitudinal components of the magnetic ( z H ) and electric ( z E ) field. Then, bearing in mind that It is easy to check in this case that the transverse components of the ТЕ and TM fields can be expressed in terms of (1.6) as:…”

“…Solving (2.17) by the method developed in [23], [31], [34][35][36][37] and discarding the terms proportional to the modulation indices in the first power, we obtain the following expressions for the ТЕ and TM field in the frequency domain defined by formulas (2.18): [38] for the TE wave is the frequency near which the strong interaction takes place, and plays a significant role in this domain. Note in conclusion that the results obtained here turn into those reported in [37] in the limit 1 0 m → ; in the limit 0 u → , one arrives at results for a waveguide with an inhomogeneous but stationary anisotropic insert.…”