Mutual action of optical activity effect and linear electro-optic effect in periodically poled “gyroelectric” crystal Guoliang Zheng a,b,n , Zhengbiao Ouyang a,b , Shixiang Xu a,b a College of Electronic Science and Technology, Shenzhen University, Shenzhen 518060, China b Shenzhen Key Laboratory of Micro-Nano Photonic InformationTechnology, Shenzhen 518060, China article info Article history: Received 23 April 2010 Received in revised form 3 November 2013 Accepted 27 November 2013 Available online 16 December 2013 Keywords: Linear electro-optic effect Activity effect Quasi-phase-matched Mutual action abstract The wave coupling theory for the mutual action of optical activity (OA) effect and linear electro-optic (EO) effect in quasi-phase matched (QPM) materials is developed, and some relevant numerical results in periodically poled 5PbO  3GeO 2 are given. The QPM linear EO effect in “gyroelectric” crystal exhibits quite different phenomena from that in normal QPM materials, since the QPM condition of OA effect coincides with that of linear EO effect. The OA effect cannot be ignored when studying the QPM linear EO effect in QPM crystals with optical activity even although the light wave deviates from the optical axis. The mutual action of QPM linear EO effect and QPM OA effect can find its application in optical filtering and switching. In addition, our study may inspire people to study further about the mutual action of QPM OA effect and other second-order nonlinear optics process, which is helpful to know the molecular chirality of OA materials and the essential role it plays in nonlinear optics processes. & 2013 Elsevier B.V. All rights reserved. 1. Introduction The “quasi-phase matching” proposed by Armstrong and Bloembergen in 1962 provides an efficient method to match a nonlinear process in phase [1]. Thanks to the quasi-phase- matched (QPM) technology, the nonlinear frequency conversions in the periodic-, quasi-periodic- and random-poled ferroelectric have been extensively studied in recent years [2–6]. In addition to nonlinear frequency conversions, the QPM technology is also valid in linear electro-optic (EO) effect [1,7]. The QPM EO effect has received more and more attentions for its novel characteristics and potential applications [8–15]. One of the most important applica- tions is EO Solc-type filter, whose central transmitting wavelength can be tuned thermally, electrically, or by UV-light illumination [8–13]. On the other hand, some important EO crystals, such as quartz and La 3 Ga 5 SiO 14 (LGS), are optically active. For example, LGS can be used in a pulse off EO Q-switch for it is not hygroscopic in the air and has high optical damage threshold [16–18]. From a traditional point of view, it is difficult to design EO devices by the use of EO crystals possessing optical activity. Therefore, we studied the mutual action of the optical activity and the electro- optic effect in single-domain bulk crystals, and gave the optimal design for EO device in EO crystals with optical activity [19]. Unfortunately, the study about mutual action in QPM materials, to the best of our knowledge, has not been reported yet. In our previous work, we have successfully derived the wave coupling theory for QPM linear EO effect and QPM OA effect, respectively [20,21]. Considering linear EO effect and OA effect are both from second-order susceptibility, we take QPM linear EO effect and QPM OA effect as a mutual action, and obtain the corresponding wave coupling theory. Finally, we give some numerical results about mutual action in periodically poled 5PbO  3GeO 2 and dis- cuss the potential applications in optical devices. 2. Theory and calculation In general, there exist two independent plane wave compo- nents for a monochromatic light wave with frequency ω propa- gating in a birefringent crystal, i.e., E ω ¼ E ω 1 þ E ω 2 ¼ E 1 ðrÞexp ðik 1 rÞþ E 2 ðrÞexp ðik 2 rÞ; ð1Þ where E ω 1 and E ω 2 denote two cross components when k 1 ¼ k 2 , or two independent components experiencing different refractive indices when k 1 ak 2 . Let E 1 ðrÞ¼ ffiffiffiffiffiffiffiffiffiffiffi ω=n 1 p A 1 ðrÞa; E 2 ðrÞ¼ ffiffiffiffiffiffiffiffiffiffiffi ω=n 2 p A 2 ðrÞb; ð2Þ where a and b are the two unit vectors and a U b ¼ 0, A 1 (r) and A 2 (r) are the normalized amplitudes of the two components, n 1 and n 2 are the unperturbed refractive indices corresponding to the two components, respectively. Since both OA effect and linear EO effect Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optcom Optics Communications 0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.11.054 n Corresponding author at: College of Electronic Science and Technology, Shenzhen University, Shenzhen 518060, China. Tel.: þ86 755 26534860; fax: þ86 755 26534624. E-mail address: zhgl@szu.edu.cn (G. Zheng). Optics Communications 316 (2014) 217–219