Optical frequency mixing

The summation runs over repeated indices, /r, is the i-th component of the induced electric dipole moment and , are components of the applied electro-magnetic field. The coefficients aij, Pijic and Yijki are components of the linear polarizability, the first hyperpolarizability, and the second hyperpolarizability tensor, respectively. The first term on the right hand side of eq. (12) describes the linear response of the incident electric field, whereas the other terms describe the nonhnear response. The ft tensor is responsible for second order nonlinear optical effects such as second harmonic generation (SHG, frequency AotAAin, frequency mixing, optical rectification and the electro-optic effect. The ft tensor vanishes in a centrosymmetric envirorunent, so that most second-order nonlinear optical materials that have been studied so far consists of non-centrosyrmnetric, one-dimensional charge-transfer molecules. At the macroscopic level, observation of the nonlinear optical susceptibility requires that the molecular non-symmetry is preserved over the physical dimensions of the bulk stmcture. 

The nonlinear optical teclmiques of up- and down-conversion are based on mixing optical beams in a suitable crystal (BBO, LiNbO, KDP, etc) witli tire generation of new optical frequencies tire physical principle is as follows. If two beams having optical frequencies cOp CO2 and wavevectors k, are mixed in a nonlinear optical crystal at tire appropriate angle, a new optical frequency co can be coherently generated witli tire following conditions satisfied ... 

Materials for Frequency Doubling. Second-order NLO materials can be used to generate new frequencies through second harmonic generation (SHG), sum and difference frequency mixing, and optical parametric oscillation (OPO). The first, SHG, is given in equation 3. 

Finally, some liquid-crystalline elastomers exhibit interesting photonic effects [200,201]. Of particular importance are non-linear optical properties. These involve interactions of light with the elastomer in a way that some of the characteristics of the incident light change, specifically its phase or frequency (including frequency doubling or frequency mixing) [202,203]. 

Quadratic NLO effects arising from (3 and x(2) include SHG, the electro-optic (EO, Pockels) effect and frequency mixing (parametric amplification). SHG is actually just a special case of a three-wave... 

Figure 9.3 Schematic illustration of second-order nonlinear optical effects, (a) Second-harmonic generation. Two light fields at frequency go are incident on medium with nonvanishing / 2. Nonlinear interaction with medium creates new field at frequency 2 go. (b) Frequency mixing. One light field at frequency GO and one at frequency go2 is incident on nonlinear medium. Nonlinear interaction with medium creates new field at frequency goi + go2. (c) electro-optic effect. Static electric field E (0) applied over nonlinear medium changes phase of an incoming light field.

The proportionality constants a and (> are the linear polarizability and the second-order polarizability (or first hyperpolarizability), and x(1) and x<2) are the first- and second-order susceptibility. The quadratic terms (> and x<2) are related by x(2) = (V/(P) and are responsible for second-order nonlinear optical (NLO) effects such as frequency doubling (or second-harmonic generation), frequency mixing, and the electro-optic effect (or Pockels effect). These effects are schematically illustrated in Figure 9.3. In the remainder of this chapter, we will primarily focus on the process of second-harmonic generation (SHG). 

We believe that our model can be extended even further to accurately describe other nonlinear optical interactions such as sum and difference frequency mixing, as well as higher-order harmonics generation. 

The double-beam transient absorption spectrometer utilized in this work is described in detail elsewhere [3]. Briefly, the output from a 1 kHz Ti Sapphire laser is frequency quadrupled to generate the 200 nm photolysis pulses. The probe pulses are generated by frequency doubling the output of an optical parametric amplifier (OPA) pumped at 400 nm or by sum-frequency mixing of the OPA output with 400 nm and 800 nm pulses. The sample consisted of a 0.1 mm jet of aqueous KNO3 solution. The acidity of the solutions was adjusted by addition of HN03(aq). 

Figure 6. Instrumental schematic for vacuum UV photofragmentation-laser induced fluorescence measurement of ammonia SHGC, second harmonic generation crystal SFMC, sum frequency mixing crystal BS, beam splitter BD, beam dump TP, turning prism CL, cylindrical lens R, reflector TD, trigger diode OSC, oscillator cell AMP, amplifier cell BE, beam expander G, grating OC, output coupler M, mirror BC, beam combiner L, lens A, aperture PD, photodiode SC, sample cell RC, reference cell FP, filter pack SAM.PMT, sample cell photomultiplier REF.PMT, reference cell photomultiplier PP, additional photomultiplier port EX, exhaust and CGI, calibration gas inlet to flow line. (Reproduced with permission from reference 15. Copyright 1990 Optical Society of America.)...

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). 

Figure 1 The setup used to generate intense ultrastable IR pulses. In a first frequency conversion step in a BBO optical parametrical amplifier, 800 nm pulses from a Ti sapphire amplifier are split into signal and idler pulse, which subsequently are difference frequency mixed in a AgGaS2 crystal.

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