Time-reversal symmetry in nonlinear optics

Abstract

The applicability of time-reversal symmetry to nonlinear optics is discussed, both from macroscopic (Maxwell equations) and microscopic (quantum theoretical) point of view. We find that only spatial operations can be applied for the symmetry classification of nonlinear optical processes in magnetic, in particular antiferromagnetic, materials. An example is given where both operations (time reversal and a spatial operation) can yield different results.Comment: To be published in Phys. Rev. B on Nov. 1, 200

Symmetry analysis of second-harmonic generation at surfaces of antiferromagnets

“…Instead, the behavior of χ (2ω) el with respect to the magnetic order parameter (which for ferromagnetic materials corresponds to the dependence of χ (2ω) el on magnetization) is fully taken into account by the considerations of the magnetic point group. At no stage of our consideration we invoke the notion of time reversal, consequently we do not apply the characterization of the susceptibility χ (2ω) as c-tensor (changing its sign in the time-reversal operation) or i-tensor (invariant under the time-reversal operation) [31].…”

“…However Tanabe et al neglected the dissipation in the process of SHG [30], which is a rather crude approximation. In general, taking into account the dissipation makes the χ (2ω) el tensor elements complex and invalidates their separation in purely real and imaginary ones [31].…”

Refraction-type sonic crystal junction diode

“…Nonlinearity is another means of facilitating non-reciprocity in optics. 22,23 Similarly, acoustic rectification is accomplished by incorporating nonlinear materials tandem to a one-dimensional (1D) crystal to achieve frequency conversion. [17][18][19] However, power consumption, low conversion efficiency, and narrow bandwidth in nonlinear acoustic devices hinder operation of such systems.…”

Acoustic transmission through asymmetric grating structures made of cylinders

“…[9][10][11][12][13][14] Essentially, the asymmetric optic transmission is closely connected with the breaking of time-or space-reversal symmetry. Two different ways have been utilized to break the timereversal symmetry.…”

“…One is based on the magnetic fieldinduced Faraday rotation of the polarization state, [9][10][11][12] and the other is introducing nonlinear ingredients into the structures. 13,14 With breaking the spatial inversion symmetry, grating structures with asymmetric geometries have also been employed to realize similar functionalities. [15][16][17][18][19] In parallel, the asymmetric transmission for acoustic waves should be also important in ultrasonic applications, such as in acoustic rectifying devices or sound diodes.…”