Electro-optic modulator response

The EO effect is a second-order nonlinear optical (NLO) effect. Only non-centrosymmetrical materials exhibit second-order NLO effects. This non-centrosymmetry is a condition, both at the macroscopic level of the bulk arrangement of the material and at the microscopic level of the individual molecule. All electro-optic modulators that are presently used by telecom operators are ferro-electric inorganic crystals. The optical nonlinearity in these materials is to a large fraction caused by the nuclear displacement in the applied electric field, and to a smaller fraction by the movement of the electrons. This limits the bandwidth of the modulator. The nonlinear response of organic materials is purely electronic and, therefore, inherently faster. 

Measurement of device bandwidths in the order of 100 GHz typically requires heterodyne detection and a stripline electrode configuration such as that illustrated in Fig. 31. The response of polymeric electro-optic modulators is typically flat to 100 GHz. Fall off above that frequency (Fig. 32) can be traced to resistive losses in millimeter wave transmission structures and in the metal electrodes. 

The strong interest in nonlinear optical (NLO) properties of organic materials in the past two decades is due to the electronic nature of the nonlinearity and the related fast response. Possible applications are for second-harmonic generation (SHG) and for electro-optic modulation due to the Pockels effect. The advantage of polymeric materials is easy processibility (especially to obtain thin films), which allow the realization of integrated optical elements and higher flexibility in molecular engineering [15,129]. 

Equations (2.27), (2.28), (2.29) and (2.30) show that nonlinear optical effects in organic r-conjugated molecules (i.e. electric field dependent polarizablity) are basically due to electronic rearrangements so it is expected that organic molecules exhibit extremely fast response times leading to the possibility of electro-optic modulation in frequency domains that are prohibited for inorganic crystals presently available in the market. 

A half-wave plate (HWP) and a polarizer (GLP) are positioned after the oscillator and are used to variably attenuate the laser output power to the desired input power required by specific experiments. Using a beam sampler (M ), a small portion of the laser beam is directed into a beam diagnostic unit (AC). In it, the laser pulse is characterized both in the time and frequency domains by employing an autocorrelator and a spectrometer. The laser beam is then expanded to match or overfill the back aperture of the objective lens. This is accomphshed using two positive lenses with the appropriate focal lengths. At the focal point of the first lens, a pinhole (SF) is carefully positioned to spatially filter the laser beam. An electro-mechanical shutter (S), used to control laser exposure times in the sample, is placed before this assembly. If exposure times shorter that a few milliseconds are required, faster response shutters such as acousto- or electro-optic modulators can be used. 

Fig. 4.26 Waveguide electro-optic modulators and their response characteristics (a) phase modulator (b) Mach-Zehnder interferometer (c) directional coupler.

Organic compounds with delocalized 7r-electron systems are leading candidates for nonlinear optical (NLO) materials, and interest in these materials has grown tremendously in the past decade [108-118]. Reliable structure-property relationships—where property here refers to first-order (linear) polarizability a, second-order polarizability and third-order polarizability y—are required for the rational design of optimized materials for photonic devices such as electro-optic modulators and all-optical switches. Here also, quantum-chemical calculations can contribute a great deal to the establishment of such relationships. In this section, we illustrate their usefulness in the description of the NLO response of donor-acceptor substituted polymethines, which are representative of an important class of organic NLO chromophores. We also show how much the nonlinear optical response depends on the interconnection between the geometric and electronic structures, as was the case of the properties discussed in the previous sections [ 119]. 

An LCD is a ubiquitous electronic display. Now, it is widely distributed among human daily life, like mobile phones, TV, and personal computers. The LCD has, however, a drawback, i.e., slower response than a plasma display or an electroluminescene display. Recently we have first succeeded in combination of a nanoparticle technology with the LCD technology, which realized fast response of the LCD [45,235,236]. Thus we have found a phenomenon, i.e., a frequency modulation of the LCD doped with metallic nanoparticles. Since the frequency modulation, or electro-optic property depends on the kind of metals, we have prepared AgPd bimetallic nanoparticles protected with a typical liquid crystal molecule, 4-cyano-4 -pentylbiphenyl (5CB) to investigate the electro-optic property [45,235,236]. 

Figure 9.12 Seed scattering at refractive index modulations induced by localized internal random fields via the electro-optic effect. The internal fields are also responsible for the formation of a rich ferroelectric domain structure. Here, a periodic sequence of domains with lengths A d is shown. Note, that the grating period of the refractive index modulation As is equal to the lengths of the ferroelectric domains.

Nonlinear optical activity reflects the nonlinear response of /r, (f- ) to electromagnetic radiation, which Eq. (7) shows to be governed by the first and second hyperpolarizabilities, p and y. A high level of such activity can have important applications in a variety of electro-optical devices,82,86,87 such as frequency converters, modulators, switches, etc. 

Recently, it was theoretically shown, on the basis of standard density-matrix formalism of nonlinear optics, that chiral isotropic media can possess an electrooptic response [174]. Such materials would be inherently stable and could therefore be extremely useful for the development of electro-optic devices. Contrary to usual electro-optic materials, index (absorption) modulation in such media is due to the imaginary (real) part of the electro-optic susceptibility. The response relies on the damping of the material response. 

Photocurrent with subband light to provide information on surface states" Optoelectric impedance (photopotential or current response to modulated illumination) or electro-optic impedance (photoresponse to potential modulation) for information on the contribution of minority, majority, and injected carriers in recombination and multiplication ... 

Detailed investigation on the optical characteristics, including the electro-optic phase modulation, electric hysteresis property, and thermo-optic coefficient, of transparent PMN-PT electro-optic ceramics have been conducted [229]. A polarization independent PMNT electro-optic switch by using s -shifted fiber Sagnac interferometer stmcture was constracted and analyzed experimentally. Some switch performances, including thermal characteristic and different switching frequency response, were also realized. 

Typical electro-optical responses of the suspensions of spherical particles (CS81), recorded by the scattered light intensity are presented in Fig. 2. They are detected for the crystal state of the systems and for different intensities and frequencies of the applied sine-wave electric pulses. The low-frequency responses are modulated they follow the field frequency at sufficiently low field intensity and exhibit a double frequency modulation at higher field intensity. Two different time scales are involved in the decay of the responses (10 " and 1 s), which can be both exponential and oscillatory. At higher field intensity or frequency the effects cannot be distinguished by the responses of anisotropic colloids. 

Figure 3 presents the frequency dependence of the electro-optical effects for suspensions of different volume fractions of spherical particles. The stock solution (8% sphere volume fraction) is highly deionized, and dilution is carried out with deionized water. Thus the highly dilute samples are in the liquid-phase state. Modulated responses are detected at low frequencies —- for highly dilute samples... 

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