Electrooptic phase modulators using

Rickard, M. Nakata, M. Takezoe, FI. Watanabe, J. Clark, N. A. Electronic electrooptic phase modulation using bent-core Uquid crystals. Appl. Phys. Lett. 2005, 87, 261115. 

In an electrooptic material the phase retardation angle is controlled by altering birefringence, which is in turn controlled by the potential of an apphed electric field. An electrooptic device thus acts as a variable phase optical retardation plate, and can be used to modulate the wavelength or intensity of an incident beam. 

Thus, the applied field, E2, changes the effective linear susceptibility (i.e. the dependence of the polarization on the light field, Eft. Since the linear susceptibility is related to the refractive index, the refractive index of the material is also changed by the applied field. This is known as the linear electrooptic (EO) or Pockels effect and can be used to modulate the polarization or phase of light by changing the applied voltage. 

For second harmonic generation (SHG), the tensor is y(2)(—2co co, co) (useful for frequency doubling and parametric down-conversion) while for the linear electrooptic or Pockels71 effect the tensor is y(2)(— co co, 0) (useful for Q-switching of lasers, for phase or amplitude modulators, and for beam deflectors) for optical rectification the tensor is y 2>(0 00, —co) for frequency mixing the tensor is y(2)(— co3 oolr co2) (useful for frequency up-converters, optical parametric oscillators, and spectroscopy). 

In contrast, the nonlinearities in bulk materials are due to the response of electrons not associated with individual sites, as it occurs in metals or semiconductors. In these materials, the nonlinear response is caused by effects of band structure or other mechanisms that are determined by the electronic response of the bulk medium. The first nonlinear materials that were applied successfully in the fabrication of passive and active photonic devices were in fact ferroelectric inorganic crystals, such as the potassium dihydrogen phosphate (KDP) crystal or the lithium niobate (LiNbO,) [20-22]. In the present, potassium dihydrogen phosphate crystal is broadly used as a laser frequency doubler, while the lithium niobate is the main material for optical electrooptic modulators that operate in the near-infrared spectral range. Another ferroelectric inorganic crystal, barium titanate (BaTiOj), is currently used in phase-conjugation applications [23]. 

Nematic materials are only one member of a large family of a variety of structurally different compounds forming liquid crystalline mesophases. Although only nematics have yet found really widespread use, mostly for display applications, some structurally highly diverse smectic phases also have unique electrooptical characteristics, for example ferroelectricity or antiferroelectricity, which can be modulated by selective fluorination [5, 51]. For 20 years intensive effort has been devoted to making practical use of these phenomena. 

Figure 71. Electrooptic modulation due to the field-controlled position of the optic axis between crossed polarizers. I) The optic axis is swinging around Pq=0 giving an optical signal with double frequency compared to the input signal. II) The linear regime. When the optic axis is swinging around f o=22.5°, the variation of the transmitted intensity is proportional to 0. For a liquid crystal X/2 cell with quasi-bookshelf (QBS) structure, it follows from Eq. (311) that the intensity / varies linearly with if is small (///o l/2+2

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