“Comparisons are odorous,” Shakespeare once lampooned a medieval saying, which meant that comparing things can lead to difficulties or even troubles. However, in nonlinear optics, particularly in surface second-harmonic generation (SSHG) studies, comparisons may be necessary: One can perform absolute measurements of the nonlinear optical coefficients of materials by comparing the nonlinear optical signal of the sample under study against that of some known standard reference. The most common type of referencing is a simple comparison of the sample and reference signal amplitudes. A less common type permits measurement of both sample signal amplitude and phase relative to that of the reference material. Knowledge of the phase is important since it provides access to information not available through the relative-amplitude measurements. For instance, it may yield the molecular orientation at an interface between two media, which is important to the understanding of basic interactions at interfaces but is impossible to obtain using conventional linear-optical techniques.

In the typical experimental configuration of the relative-amplitude method, one either splits the beam into two parts to generate two separate second-harmonic (SH) signals from the sample and reference materials, or takes individual measurements for each of the two materials using the same beam. In the phase-sensitive method, the fundamental beam generates SH signals from both sample and reference materials inline, i.e., along its path, and the two signals interfere to yield a single composite signal at the detector. We consider only the latter type in the following discussions. In this method, the total SH intensity — associated with the combined sample and reference SH electric fields that are parallel to each other — is proportional to three intensity terms corresponding to the sample, reference, and a cross-term that describes the phase shift between the two original fields (assuming a coherent phase relationship exists between these fields). Hence there are three relevant elements to this inline-reference method: sample, reference, and phase shifter. In previous inline-reference SSHG studies, a typical setup involved a reflected SSHG signal, e.g., from molecules adsorbed at a surface; a reference source that has a flat optical response within the spectral region of interest, e.g., a quartz crystal; and a phase shifting mechanism, e.g., dispersion of air. Another scheme to modify the relative phase of the two sources is to insert and vary the thickness of a strongly dispersive material between them, e.g., by translating a piece of wedge relative to a second wedge or by rotating a piece of plate. One may also introduce and adjust an amount of gas molecules within a sealed container along the optical path between the sources. Other workers have demonstrated that by incorporating frequency domain techniques, inline referencing can also be used in extracting the SH spectrum and phase within a large SHG bandwidth generated by a broadband, ultrashort pulse.

In this paper by the Heiz group, the authors demonstrate an elegant twist to this referencing technique by combining the three elements described above, sample, reference and phase shifter, into a single substrate comprised of a centrosymmetric medium. Within the dipole approximation, the SH signal is generated by a medium where inversion symmetry is broken, thus SHG is possible only from the front and back surfaces of the substrate. To demonstrate this new method, the authors deposited molecules on one side of a very thin substrate. The transmitted SH beams generated by the laser, arising from the molecule-adsorbed and back surfaces of the substrate, travel to the detector and interfere as the substrate is rotated about an axis perpendicular to the incident plane. Their relative phase arises from the difference in the group velocities of the fundamental and SH beams within the substrate. By carrying out a series of experiments at various input wavelengths with and without the test molecules, the authors were able to isolate and extract the nonlinear optical spectrum of the adsorbed molecules over a large wavelength range. Brewster’s incidence angle was used to eliminate multiple reflections of the fundamental. Part of the extraction of the spectrum includes subtraction of the spectrometer function, which depends on various factors including the optical geometry of the system, wavelength-dependent laser power, and detector efficiency. Comparison of the SSHG spectrum with linear UV-Vis absorption measurements from thick molecular layers shows excellent agreement of the location of the electronic resonances although small but important differences are present due to molecule-substrate interactions. It is important to emphasize that SSHG probes the molecules at the interfacial region, whose thickness is of the order of the size of the molecule (Å to nm), whereas linear-optical absorption measurements probe macroscopically thick molecular layers. Together with this novel inline-reference method, SSHG becomes a powerful and indispensable spectroscopic tool for supported molecules over a wavelength range that may begin to rival that of the complementary technique, UV-Vis spectroscopy.

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