Special phase matching of second-harmonic generation in helical ferroelectric liquid crystal cells

Abstract

The helical structures in ferroelectric liquid crystals can be utilized to realize a special phase matching for second-harmonic generation (SHG) when two counter fundamental waves propagate along the helical axis and the wavelength of SHG is near the photonic (selective reflection) band edge. On the basis of the exact theory [Drevensek-Olenik and Copic, Phys. Rev. E 56, 581 (1997)], a simple analytical description is derived and some characteristic features of the special phase matching are shown. (1) Special phase matching is definitely achieved under particular combinations of polarization. (2) The SH spectrum is related to a subsidiary oscillating structure in the selective reflection spectrum. The maximum SH intensity is realized at the first dip of the oscillation near one of the edges in the selective reflection band. (3) The thickness (d) dependence of the maximum SH intensity is d4 in thick cells, while it is d2 for conventional phase matching. (4) The linewidth for the SH peak is d(-3) dependent, which is much narrower than in conventional phase matching.

Optical Activity Produced by Layer Chirality in Bent-Core Liquid Crystals

“…Spectacular Bragg reflection is produced by macroscopically helical chiral nematic and smectic C phases when the wavelength is commensurate with the helical pitch [1,2]. Lasing has been observed in these systems when doped with an appropriate dye [3].…”

Polar liquid crystals – ferro, antiferro, banana, and columnar –

“…Because of the helical structure, the unperturbed SmC * structure has no macroscopic polarization. Hence, SHG is not observed unless a special condition is used (special phase matching [7,8]). A single hysteresis roop and a single polarization switching current peak are observed, as observed by the triangular method ( Fig.…”

Second-harmonic generation in a laterally azo-bridged trimer ferroelectric liquid crystal: Phase matching in the presence of a helicoidal structure

“…In general the SHG light was found to be elliptically polarized for linearly polarized We now summarize the basic aspects of the theory for SHG in helicoidal structures [18,19]. Fig.…”

“…[19] give the results shown in This can be understood in terms of the relative proximity of 2ω to the band at 572 nm [16]. The sign of the index dispersion is assumed to be positive since at the fundamental and SHG wavelengths normal dispersion is expected.…”

“…The SHG process in helicoidal SmC* phases was theoretically analyzed some years ago [17][18][19]. In particular it was shown that the helicoidal structure provides some special possibilities to achieve phase matching (PM).…”