Direct Determination of Effective Interfacial Optical Constants by Nonlinear Optical Null Ellipsometry of Chiral Films

Abstract

Nonlinear optical null ellipsometry (NONE) measurements of chiral interfaces allowed direct experimental measurement of the linear interfacial optical constants in surface second harmonic generation (SHG) measurements. Since phase information is retained in NONE measurements, the real and imaginary components of the interfacial refractive index (n and k, respectively) were uniquely obtained from the measured chiral chi((2)) tensor elements of a fluorescein-labeled bovine serum albumin film. The sensitivity of the calculated chi((2)) tensor elements on the assumed values of the interfacial optical constants allowed measurements of n and k to four significant figures with no additional adjustable parameters and independent of molecular symmetry. The optical constants measured by SHG agreed within a relative error of 0.8% with values predicted independently using a simple effective medium approximation, also with no adjustable parameters. Additionally, those same optical constants produced relationships between the achiral chi((2)) tensor elements in excellent agreement with predictions for systems exhibiting weak orientational order. This study suggests that the far-field intensity and polarization state of the nonlinear optical beam may be largely independent of the near-field optical constants within the interfacial layer in the limit of a film thickness much less than the wavelength of light.

Polarization-resolved second-harmonic generation microscopy as a method to visualize protein-crystal domains

“…Owing to its coherent nature, the emerging polarization state of SHG generated from the sample is highly dependent on both the polarization state of the incident light as well as the symmetry and orientation of the crystal (Haupert & Simpson, 2011;Boyd, 2003;Simpson et al, 2005). The polarization-dependent tensor describing SHG has up to 18 unique tensor elements defining its orientation and polarization-dependent response, compared with just three for linear optics (i.e.…”

Microscopic molecular optics theory of surface second harmonic generation and sum-frequency generation spectroscopy based on the discrete dipole lattice model

“…37,42 There are also efforts trying to show that the dielectric constant of the extremely thin monolayer is just the simple arithmetic average of the two bulk dielectric constants. 52,58,67,68 Event though the results from these approaches seemed reasonable, neglecting the anisotropic microscopic local field effect in the molecular monolayer is not likely to be physically sound.…”

“…51 This work is obviously not consistent with the above treatment by Shen et al It was further criticized by Roy on the inconsistency that the SAM film is considered anisotropic for SHG but assumed to be isotropic in terms of its linear optical properties. 57 Roy then outlined a macroscopic phenomenological model that treats linear and nonlinear optics of the anisotropic interface layer in a single framework, which nevertheless requires a minimum of six unknown parameters of the interfacial optical constants even for an uniaxial monolayer in SHG or SFG-VS. 57,58 Thus, Roy concluded that the conventional SHG measurement of phase and intensity may not be enough to determine the orientation of SAM. However, even though the anisotropy is undoubtedly significant on the nonlinear responses, Roy's criticism might have exaggerated the influence of the anisotropy on the linear optical property within the monolayer, which in fact only slightly modifies the reflectivity of the surface as judged from ellipsometry measurement.…”

“…42,52,58,67,68,69,70,71 In SFG-VS, some considered the film anisotropic and its optical constant is determined using the Clausius-Mossotti relationship with the ellipsometry data of the film.…”

“…Researchers in the field also agree that the definition of the dielectric constant of the monolayer or even submonolayer film is unclear and meaningless in the macroscopic optics, because when the film is as thin as one molecular layer the macroscopic reflection and transmission coefficients simply converge to the bare interface limit. 58,59,60 Therefore, even though the treatment provided by Shen and coworkers is generally valid, there are still issues need to be clarified. One problem in the existing model is that the macroscopic and microscopic linear optical properties of the nonlinear molecular layer are not totally compatible.…”