Linear electrooptic modulation

Bridges, W.B. and Schaffiner, J.H. 1995. Distortion in linearized electrooptic modulators. IEEE Trans. Micro. Theory Tech. 43 2184-2197. 

The applied voltage in effect changes the linear susceptibility and thus the refractive index of the material. This effect, known as the linear electrooptic (LEO) or Pockels effect, modulates light as a function of applied voltage. At the atomic level, the applied voltage is anisotropically distorting the electron density within the material. Thus, application of a voltage to the material causes the optical beam to "see" a different... 

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). 

The measurement of optical activity in Raman spectra is most often done by measuring the circular intensity difference (CID) and the circular intensity sum (CIS). Using this technique the linearly polarized la.ser beam used for excitation is modulated with a KD P electrooptical modulator resulting in an excitating beam which changes its state of polarization from left to right circularly polarized at a frequency of about 1/3 Hz. The Raman intensities are then collected separately and the dimensionless Raman CID calculated using ... 

The linear electrooptic effect is tlie change in the index of refraction of a medium due to the presence of a dc or low-frequency electric field, in such a manner that the change in the index of refraction depends linearly in the strength of the low-frequency electric field. The linear electrooptic effect is tlie mechanism behind optical intensity modulators that are used in optical switching and fiber-optics communications, where the optical signal is modulated at high frequencies (out to 110 GHz) [7-9],... 

Becker, R.A. 1984. Broad-band guided-wave electrooptic modulators. IEEE J. Quan. Elec. QE-20 723-727. Bertelsmeier, M. and Zschunke, W. 1984. Linearization of broadband optical transmission systems by adaptive predistortion. Frequenz 38 206-212. 

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

We report the largest known useful microscopic NLO susceptibilities for the linear and quadratic electrooptic effects. The QEO susceptibility of 9 might be large enough to explore simple primitive QEO modulation experiments, though perhaps is not nearly large enough to be of commercial importance. 

Non-linear optics (NO) has a great practical importance in electrooptics, in optical switches and modulators.107-109 The discovery of lasers has provided the ideal tool to study non-linear optical phenomena in molecules and polymers experimentally. 

As shown in previous sections of this chapter, when an external perturbation is applied to the polymer film (such as irradiation), the ATR guided modes shift their angular positions and the reflectivity is modulated (Fig. 31b). These angular shifts are very small in the case of electrooptic experiments they correspond to refractive index variations of the order of 10 . One has then to modulate the measuring electric field at a low frequency Q( = cos fit) and to detect the modulated signal with lock-in amplifiers. The lock-in signals detected at the modulation frequency and its second harmonic give, respectively, the linear (or Pockels) and the quadratic (or Kerr) electrooptic effects. The amplitude of the modulation of the thickness and the refractive indices is evaluated by a computer fit, and allows the determination of Pockels (r) and Kerr (s) coefficients (Eqs. 28) ... 

Lipscomb, G. F., Garito, A. F., and Narang, R. S., An exceptionally large linear electro-optic effect in the organic solid MNA, J. Chem. Phys., 75, 1509 (1981). Sigelle, M, and Hierle, R., Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique, J. Appl. Phys., 52, 4199 (1981). 

---