Electric optical rectification

DC electric fields. DC generation is known as optical rectification. The actual phenomena that will be observed depend on the experimental conditions and whether or not phase matching has been achieved. Three-wave mixing processes in which two beams interact to generate a third beam require the mixing medium to have a non-zero In an isotropic medium, reversal of the... 

Here Xo (2w), x (wiiw2) and Xo (O) are the non-resonant values of the hyperpolarisabilities. Thus second harmonic generation is resonantly enhanced at both the fundamental and the harmonic of the optical transition, sum and difference frequency generation at the fundamentals and the sum and difference frequencies, and the rarely observed optical rectification only at the fundamental frequency. The term 3 in the expansion gives rise to effects such as third harmonic generation, x(3) -3oj oj, oj,u>), electric field induced second harmonic generation, x(3) (- 2w 0,w, oj), the optical Kerr effect, x(3) (-oj oj, oj, -cj), etc. that will display resonances at oj, 2oj and 3u>. 

Another application of noncentrosymmetric materials is generation of T Hz electric pulses, impossible to obtain by using classical electric circuitry. This can be done either by linear optical rectification effect with susceptibility or... 

Y(0 , - , 0) dc-Optical Rectification dc-OR Electric Field Induced Optical Rectification (EFIOR)... 

The tensors and 7 constitute the molecular origin of the second-and third-order nonlinear optical phenomena such as electro-optic Pock-els effect (EOPE), optical rectification (OR), third harmonic generation (THG), electric field induced second harmonic generation (EFI-SHG), intensity dependent refractive index (IDRI), optical Kerr effect (OKE), electric field induced optical rectification (EFI-OR). To save space we do not indicate the full expressions for and 7 related to the different second and third order processes but we introduce the notations —(Ajy,ui,cj2) and 7(—a , o i,W2,W3), where the frequency relations to be used for the various non-linear optical processes which can be obtained in the case of both static and oscillating monochromatic fields are reported in Table 1.7. 

P( P(-o> w,0) P(0 -fa>,w) Y( - Y(-2(i) (i>,tD,0) Y(-o) (i>,0,0) Second harmonic generation (SHG) Electrooptic Pockels effect Optical rectification Third harmonic generation DC electric-field-induced SHG Intensity-dependent refractive index Optical Kerr effect Coherent anti-Stokes Raman pSHG pEOPE pOR. yTHG. EFISH oj DC-SHG. JlDRI or. yOKE. yCARS... 

In Eqs. 1 and 2. the indices i, j. k. and I refer to the coordinate system of the bulk material and molecule, respectively. Illustrated in Fig. 1 are the linear and nonlinear polarizations with respect to electric field. The Fourier decomposition of this nonlinear polarization comprising components of zero frequency, the fundamental frequency, the second-harmonic frequency, the third-harmonic frequency, etc., is shown in Fig. 2. The effects up to the second order, which are easily observed experimentally, are called the optical rectification. P(0) linear electro-optic effect P((u) second-harmonic generation P(2a>), and third-harmonic generation P(3co). 

Furthermore, they examined the performance of different density functionals, including a local-density approximation and a generalized-gradient approximation as well as the functional of van Leeuwen and Baerends that has been constructed to have the correct asymptotic behaviour. Moreover, they considered different frequency-dependent processes, including third-harmonic generation [THG, corresponding to y( 3electric-field-induced second harmonic generation (EFISH, y( 2electro-optic Kerr effect [EOKO, y(—ft> optical rectification [OR, /S(0 [Pg.161]

The static and dynamic linear responses, a(0 0) and a( co co), correspond to the so-called static and dynamic polarizabilities, respectively. At second order in the fields, the responses are named first hyperpolarizabilities whereas second hyperpolarizabilities correspond to the third-order responses. Different phenomena can be distinguished as a function of the combination of optical frequencies. So, p(0 0,0), p(—co co,0), p(0 o), — ea), and p(— 2co co,co) are associated with the static, dc-Pockels (dc-P), optical rectification (OR), and second harmonic generation (SHG) processes whereas y(0 0,0,0), y(- ( ( ,0,0), y( 2co co,( ,0), y( co co, — ca, ), and y(— 3 , , ) describe the static, dc-Kerr, electric-field-induced second harmonic generation (EFISHG), degenerate four-wave mixing (DFWM),... 

Various combinations of these frequencies give rise to different NLO phenomena for instance, at second order, (0 0, 0), 0 -w, a>, 0), (0 a>, -a>), and P —2co CO, ) define the static, dc-Pockels, optical rectification, and second harmonic generation (SHG) responses, respectively. According to Eq. (8.1), the first hyperpolarizabilities can be formally expressed as the second-order derivatives of the dipole moment with respect to electric fields, or, alternatively, as the third-order derivatives of the total energy E. 

Thus, if an intense light beam passes through a second-order nonlinear optical material, light at twice the input frequency will be produced as well as a static electric field. The first process is called a second-harmonic generation (SHG) and the second is called an optical rectification. 

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. 

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