Second-Harmonic Generation And Detection Of Nonlinear Optical Materials By Using One-and Two-beam Techniques

In this thesis, we mainly investigate the second-order nonlinear suscepbitibility tensor of organic thin film, which belongs to C_∞ν symmetry, based on single- andtwo-beam second-harmonic generation (SHG). In addition, due to the advantages of two-beam SHG techinique, we also investigate the multipolar responses of centrosymmetric materials. This thesis is divided into three parts.â… : nonvanishing independent susceptibility tensor components and expansion coefficients based on single- and two-beam SHG for C_∞ν symmetry material. Firstly, by analyzing the structural properties of the material with C_∞ν symmetry and manipulating the proper symmetry operations, we can determine thenonvainishing independent tensor components of achiral molecule:χ_zzz⁽²⁾,χ_zxx⁽²⁾ =χ_zyy⁽²⁾ andχ_xxz⁽²⁾=χ_yyz⁽²⁾ =χ_xzx⁽²⁾ =χ_yzy⁽²⁾. Secondly, regardless of the spatial symmetry of the nonlinear surface layer, a SH field generated from the nonlinear layer in a collinear single-beam and noncollinear two-beam geometries can be described as the following, respectively,(?) (1)and(?) (2)where the subscript j=p, s denots the polarization of the second-harmonic signal irradiated from nonlinear thin film layer, f_j,g_j,h_j and k_j are expansioncoefficients, which are linear combination of tensor components and are directly accessible in an experiment, and E_p,s(ω), A_p,s(ω) and B_p,s(ω) are the p- ands-polarized components of the fundamental beam at frequencyω. Depending on the symmetry of the surface, some of the expansion coefficients in Eqs.(1) and (2) may vanish.Finally, based on the assumption of unity refractive indices for different frequencies and regions and the theory of surface SHG, we derive the relations that express the expansion coefficients in terms of the susceptibility tensor components for noncentrosymmetric matrials for different experimental geometries. In the case of single-beam SHG, there are three nonvanishing expension coefficents: f_p, g_p andh_s; whereas for the case of two-beam SHG, the number of nonvainshing expension coefficients are four, for example, f_p, g_p, h_s and k_s.â…¡: Uuniqueness of expansion coefficients and determination of susceptibility tensor components. (1) p-poliarzed SH signal in a single-beam geometryWe experimentally showed that the fitted values of expansion coefficients from experimental measurements are not unique for an achiral sample when both initial and second-harmonic light beams are p-polarized. When different initial fit values for the expansion coefficients are used, two equally satisfying fits in Fig. 1, which are fitted well with the measured experimental data and completely overlapped each other, are obtained and the values differ by more than one order of magnitude. This means that the tensor components can not be uniquely determined.Figure.1 p-polarized detection of SHG signal for using p-polarized initial light. The circles are the original experimental data, the solid and dashed lines are the fitting curves with different initial fitting values (a) g₁=0.1, g₂=0 and (b) g₁=2, g₂=0. 1, but the same fitting function.We theoretically investigated the cases for different polarizations of the initial ]beam, such as s- and (p±s)-polarized light. When the initial beam is s-polarized, the expansion coefficients are not unique in theory (Fig. 2). But the (p±s)-polarized initial beam can lead to unique theoretical solutions of expension coefficients, and the experimental results are in a good agreement with the theoretical prediction. By comparing those fitted expansion coefficients for different polarizations of initial beam, we found that combining the different choices of the initial polarization that allow the expansion coefficients to be uniquely determined.Figure .2 p-polarized detection of SHG signal for using s-polarized initial light. The circles are the original experimental data, the solid and dashed lines are the fitting curves with different initial fitting values (a) g₁=50, g₂=-3 and (b) g₁=0.1, g₂=0.1, but the same fitting function.(2) (p±s)-polarized SH signal in a single-beam geometryWe demonstrate theoretically that all the expansion coefficients can be uniquely determined as was done in the earlier literature when the experimental setup is chiral, i.e., a combination of p and s polarization components of second-harmonic signal from the sample is detected, which is equal to be the case for detecting p and s polarization component of second-harmonic signal generated by a chiral molecule. However, the fitted expansion coefficients from practical measurements are shown not to be unique in Fig. 3, especially the real parts of relative expansion coefficient g_p differ by more than one order of magnitude. The experimental results are not in a good agreement with the theoretical prediction. Figure .3 (p+s)-polarized detection of SHG signal for using p-polarized initial light. The circles are the original experimental data, the solid and dashed lines are the fitting curves with different initial fitting values (a) g₁=0.1, g₂=0.1 and (b) g₁=2, g₂=0.1, but the same fitting function.We therefore simulate a SHG signal for the case where the experimental setup is chiral and addressed the discrepancy between practice and theory. Then we also investigated different choices of the initial polarization. For s- and (p±s)-polarized intinial beam, the experimental results support the theoretical prediction that the expansion coefficients can be determined uniquely.The discussion mentioned above showed that the choice of the p-polarized initial beam in a single-beam geometry is the worst possible at least for the present samplewith C_∞ν, symmetry.(3) Uniqueness of expansion coefficiens in a two-beam geometryDue to the practical problems of the chiral experimental setup, which is based on p-polarized initial light and detecting the combination of p and s polarization of second-harmonic signal, in obtaining unique values for the expansion coefficients f,g and h, we developed a new techinique based on a noncollinear two-beam SHG. To fully character the second-order nonlinear response of achiral thin films, it is better to get all the four expansion coefficients:f_p, g_p, h_s and k_s. We have theoreticallyshowed that the expansion coefficients based on two-beam SHG are uniquely determined without the limitation of the polarization of initial beam, and theoretical prediction and the results from practical experiments are in a good agreement.For two-beam SHG, since it is accessible to determine all the susceptibility tensor components of achiral materials by only combining three expansion coefficients f_p,g_p and h_s, we can check the quality of the tensor components according the combination of the forth independent coefficient k_s and the other two expansion coefficients f_p and g_p. This means that two-beam technique have an advantages indetermining the tensor components compared to single-beam geometry.(4) Determination of tensor componentsOnce all the expansion coefficients are uniquely determined in the experiments, the tensor components can also be uniquely extracted relying on proper theoretical model. We took two-beam SHG as an example and discuss how to extract the susceptibility tensor components of the sample. We first derived the main expressions on fundamental fields, nonlinear polarization source, and generated second-harmonic field by using a simple mode which neglects the linear optics properties of the used sample. Based on the Green function formulae of Sipe, we give their detailed expressions inside the sample when the linear optical properties of the media are incorporated. The calculated theoretical expressions for two-beam SHG are also applicable to the case of one-beam SHG. We compared the relative values of tensor components of achiral sample (TSe organic molecule) calculated according to one- and two-beam SHG theories. Although the tensor components are quite close to each other in values, two-beam SHG technique allows precise determination of their relative values.â…¢: The separation of different multipolar reponses.(1) The theoretical description of multipolar responsesWhen multipolar (magnetic dipole and electric quadruple effects) responses were taken into account, we showed that SHG can occur even in the bulk of centrosymmetric materials. Starting with the basic Maxwell's equations, we can describe the effective bulk nonlinear polarization of the bulk of an isotropic material by three bulk parameters depending on magnetic dipole and electric quadruple effects.(?) (3)where one of the bulk parametersβvanishes for isotropic and homogeneous media, another term y behaves like surface response and will be included in the effective surface susceptibility tensor components by redefining them as:χ_zxx+γandχ_zzz+γlast oneδ' is the term only separable from surface response and will be nonzero only when two input beams are incident in a geometry.(2) The suppression of the SH signal in the bulkIn the case of the thickness of the used sample which is more than the overlap region of two fundamental beams, we have showed that SH signal generated by non-phasematched interactions were strongly suppressed when the interaction volume is finite and localized deep inside the bulk of a homogeneous and isotropic material, as opposed to the case where the interaction volume centered at the boundary of the material. Fig.4 showed the experimental data of SH signal obtained by translating the overlap (L≈3mm) of two input beams across a 5.5mm thick nonlinear crystal (KTP). From Fig.4, by placing the overlap region centered at the surface of the sample, we can get the strongest detectable SH signal only if the thickness of the sample is larger than the length of overlap volume of two input beams.Figure .4 Second-harmonic signal obtained by translating the overlap of the input beams across a 5.5 mm thick nonlinear crystal (KTP). The strongest SH signal is obtained near the crystal surfaces whereas SH signal is strongly suppressed in the bulk of the crystal.(3) The separation of surface and bulk contributionsBy analyzing the experimental data based on two-beam SHG, we achieved the separation of the effective dipolar surface nonlinearity and the separable multipolar bulk nonlinearity for optical glass and fused silica. If we assume that the tensor components of two centrosymmetric samples satisfies the approximation ofKleinman symmetry, i.e. X_xxz-=X_zxx ,we found the surface-like contribution isγ= -0.5 and the separable bulk parameter isδ'= 1 . The equationγ=-0.5δ'suggested that the bulk nonlinearity of optical glass and fused silica are both dominated by magnetic, rather than quadrupole, effects. (4) A direct evidence of the bulk contribution to the deteted SH signalBased on theorectical model of two-beam SHG, we demonstrated that the polarization dependence of s-polarized effective surface SH signal can be completely specified by the incident agnles of two input beams. For the seperable bulk contribution, its s-polarized SH signal on the polarization dependence of fundamental beams does not depend on the experimental geometry.From Fig.4, we found that the transmitted s-polarized SH signal for fused silica can not be fitted well with surface-only model based on the external (outside the sample)and internal (inside the sample) input fields, but there is a perfect fit curve based on the model mixing the surface and bulk contributions. This gives a direct evidence of the separable bulk contribution to SHG. Actually, this opens a door to investigate the new nonlinear optical materials with strong mulitipolar responses and without the limation of noncentrosymmetry.Figure. 5 Second-harmonic signal on a transmitted (p, +45°, s) measurement of fused silica. The circles are the original experimental data, blue, red dashed lines and black solid line are the fit curves based on surface-only model based external and internal fields and mixing model including both surface and bulk contributions.(5) The calibration of the absolute values of nonlinear parameters Based on two-beam SHG technique, we developed a new method to calibrate the absolute values of all the nonlinear parameters against with X_xxx or X_xyz of areference quartz crystal, which is simpler than the method of Maker fringes. This new calibration method could also be applied to characterize dipole-allowed bulk SHG responses of noncentrosymmetric crystals and multipolar bulk SHG of centrosymmetric crystals.As we discussed above, there are of several great significances in the thesis:1, By manipulating the structural operation symmeties, we determine the nonvanishing independent susceptibility tensor components for achiral thin film. Based on the assumption of unity refractive indicies in theorectical model, we derive the relastions which express the nonvanishing expansion coefficients in the forms of tensor components for single- and two-beam SHG.2. When the initial beam is p-polarized light, we found that expansion coefficients in traditional single-beam SHG geometry can not be uniquely determined for achiral materials. Although different polarization combinations of initial beam allow us to rule out erroneous values of the fitted expansion coefficients, this requires a lot of experimental mesurements. We therefore developed a new technique based on two-beam SHG. The expansion coefficients based on two-beam SHG are uniquely determined without the limitation of the polarization of initial beam, and different combinations of expansion coefficients can chekck the quality of the calculated tensor components. Thus, two-beam SHG technique is more precise in determining the relative values of tensor components for achiral materials compared to single-beam SHG techinique.3. By using two-beam SHG technique, we achieved the separation of the surface and bulk contributions and give a direct evidentce of the separable bulk contribution to the detected SHG signal.4. Relying on two-beam SHG technique, we developed a new method which is simpler than Maker fringe method to calibrate the absolute values of nonlinear parameters against with a reference crystal. This new calibration method is applicable to all the nonlinear crystals.