Study of Optical Properties of Noninteger Dimensional Nonlinear Medium

Abstract

Study of the optical characteristics of materials, objects and geome tries has wider role and applications in science and engineering. Reflection and transmission coefficients are used to study the opti cal properties of planar geometries and usually S and P-polarized electromagnetic waves are used. Primary aim of the presented work is to study the reflection and transmission of second harmonic gen eration in non-integer dimensional environment. Three types of planar interface geometries are considered one by one in order of increasing complexity. First is nonlinear dielectric magnetic–linear dielectric magnetic noninteger dimensional (NID) planar interface. The second one, linear dielectric magnetic–nonlinear dielectric mag netic NID planar interface and the last is linear dielectric magnetic NID–nonlinear dielectric magnetic NID planar interface. Special cases are also produced taking negative values of the permittivity and/or permeability. Nonlinear materials considered in the study are of second harmonic generation type, hence only second order reflection and transmission characteristics are noted and analyzed. Slowly varying amplitude approximation is used to obtain the so lution of the nonlinear wave equation. Furthermore, all the NID materials taken in this study have noninteger dimension in only one direction which is normal to the planar interface. Impact of the presence and absence of non-linearity and/or NID on the behavior of the coefficients is noted. It is noticed that im pact of non-linearity on the coefficients is dependent on how the NID environment is used in a particular geometry. For instance, in case of a linear ordinary–nonlinear NID interface, S-polarized coefficients increases with increase of the non-linearity. Whereas, anti-reflection property is achieved for S-polarization excitation for linear NID–nonlinear NID medium interface. On the other hand, for linear ordinary–nonlinear NID interface, amplitude of the P polarized transmission (reflection) coefficient increases (decreases) as the value of nonlinear permittivity increases. For both excita tion polarizations, amplitude of the coefficients increases by taking smaller values of the noninteger dimension in all cases. It is also studied that dimension of the NID medium, nonlinear permittivity and nonlinear permeability are used to control the behavior of the coefficients