Fourier domain rotational anisotropy-second harmonic generation.

Baozhu Lu,Darius H Torchinsky

doi:10.1364/oe.26.033192

Abstract

We describe a novel scheme of detecting rotational anisotropy-second harmonic generation (RA-SHG) signals using a lock-in amplifier referenced to a fast scanning RASHG apparatus. The method directly measures the nth harmonics of the scanning frequency corresponding to SHG signal components of Cn symmetry that appear in a Fourier series expansion of a general RA-SHG signal. GaAs was used as a test sample allowing comparison of point-by-point averaging with the lock-in based method. When divided by the C∞ signal component, the lock-in detected data allowed for both self-referenced determination of ratios of Cn components of up to 1 part in 104 and significantly more sensitive measurement of the relative amount of different Cn components when compared with conventional methods.

Highlights

Rotational-Anisotropy Second Harmonic Generation (RA-SHG) has emerged as an effective tool for the study of crystallographic point group symmetry and the electronic symmetry breaking states of the surface and bulk[1,2,3,4]
We have shown that a RA-SHG signal may be exactly represented as a finite Fourier series in factors of the rotational angle φ of Cn symmetry and have described a method of interfacing a fast RA-SHG spectrometer with a lock-in amplifier to directly measure these Fourier coefficients
An example of our technique applied to single crystal GaAs indicates that our lock-in based method performs better than competing RA-SHG measurement techniques for a wide range of signal to noise ratio (SNR) values, at higher SNR, i.e., 1000 photons/shot on average

Summary

INTRODUCTION

Rotational-Anisotropy Second Harmonic Generation (RA-SHG) has emerged as an effective tool for the study of crystallographic point group symmetry and the electronic symmetry breaking states of the surface and bulk[1,2,3,4]. In this paper we describe a novel method to detect RASHG signals and, in the spirit of diffraction probes, leverage their inherent periodicity as universally sinusoids as a function of rotational angle φ This method, built upon a fast-scanning RA-SHG spectrometer, is based on a Fourier decomposition of a signal by a lock-in amplifier’s demodulators to select a single frequency component and phase of a periodic time-domain signal. When several concurrent frequencies are detected, one may be divided by the other to permit referencing of the various signal components to remove correlated noise This scheme provides direct access to combinations of second order susceptibility tensor components and can result in up to a 102 improvement in the signal-to-noise ratio of measurements of relative degrees of Cn symmetry breaking, making the measurement more robust to signal imperfections, alignment defects and low signal-to-noise ratios as compared with currently used techniques

BACKGROUND

EXPERIMENTAL SETUP

RESULTS AND DISCUSSION

CONCLUSIONS