Fourier transform second harmonic generation for high-resolution nonlinear spectroscopy
Introduction
During the last decades second-order nonlinear optical (NLO) processes have become essential tools within studies of semiconductor materials [1], [2], [3]. Second-order NLO processes have different selection rules from linear optics. This has led to a wealth of applications, where valuable information on inhomogeneous structures, surfaces, interfaces, and metamaterials has been obtained. Furthermore, the NLO techniques benefit from being contact-free, applicable for layers buried in transparent media, and generally non-destructive.
Fourier transform (FT) spectroscopy is a well-established technique applied in many different fields of science such as nuclear magnetic resonance (NMR) spectrometry, optical spectroscopy, and terahertz spectroscopy. [4], [5]
One of the inherent advantages of optical FT spectroscopy is the multiplex nature, i.e. all of the spectral components are measured simultaneously, known as Fellget’s advantage [6], which increases the signal-to-noise ratio. This advantage cannot be exploited in the case of weak NLO signals, since detectors working in the UV range are dominated by shot noise, which equals the gain in signal-to-noise ratio. However, the single-shot feature of the technique using broadband femtosecond pulses is still beneficial in terms of scan duration. Connes’ (the spectral accuracy) advantage [6] may be less well known. Nonetheless, it is very significant to the FT technique. The spectral sampling intervals are inversely proportional to the optical sampling intervals, wherefore the respective errors are directly coupled. The change in optical path difference can be tracked very precisely using the interference pattern of monochromatic light of a HeNe laser. By this approach the accuracy of the optical sampling intervals is entirely determined by the precision of the HeNe laser wavelength itself. Thus, FT spectroscopy measurements have a built-in calibration of the spectral axis giving the technique a very high spectral reproducibility. Finally, the FT approach has the advantage of practically unlimited spectral resolution. This is due to the fact that the resolution does not rely on the input pulse characteristics but is entirely determined by the maximum optical path difference of the interferometer. However, the FT method has primarily gained ground within infrared (IR) and terahertz spectroscopy. [5], [6], [7] Nevertheless, it has been demonstrated that ultrafast laser spectroscopy can take advantage of the benefits of the FT technique. This was accomplished by Bellini et al. by the demonstration of Ramsey spectroscopy with femtosecond laser pulses [8] and most recently McGuire et al. demonstrated IR–visible FT sum-frequency generation (FT-SFG) with femtosecond laser pulses, where the IR beam is modulated by an interferometer [9].
During recent years, more and more research groups have replaced their old nanosecond, picosecond, or 100 fs laser systems with modern ultrafast laser systems. The light pulses of the modern lasers are typically sub-40 fs and thus spectrally broader, which limits the achievable spectral resolution for conventional nonlinear spectroscopy.
In this communication, we present a new NLO technique combining second harmonic generation (SHG) and FT spectroscopy to circumvent this limit and give access to high spectral resolution with ultrafast laser pulses. Broadband femtosecond laser pulses are used to induce a polarization in a sample, whereupon the recorded interferogram of the response is Fourier transformed to acquire the spectral content.
An exhaustive theoretical and experimental study of the exciton resonances of the wide band gap hexagonal semiconductor ZnO in the range of 3.2–3.5 eV photon energy has previously been carried out by Lafrentz et al. [10]. Strong crystallographic SHG signals were reported for parallel p-polarized fundamental and SHG light in transmission at a sample temperature of 1.6 K using a nanosecond-pulse-width laser with narrow spectral bandwidth. Several sharp lines were found in the exciton spectral range from 3.37–3.44 eV. The broadening of the excitons at temperatures exceeding 20 K was found to be almost homogeneous and linearly increasing with temperature. The peak intensity and the full width at half maximum (FWHM) of the -line and the exciton change slower with temperature compared to the states [10]. Regarding our work, the -line at 3.407 eV is pertinent for benchmarking the FT-SHG technique due to its strong and narrow characteristics.
We find that the exciton peak can be resolved if the FT technique is applied. Furthermore, the width of the exciton peak is found to be three times smaller using the FT technique in comparison to regular SHG experiments using 100-fs laser pulses.
Section snippets
Experimental methods and materials
The FT-SHG setup is illustrated in Fig. 1. A beam of laser pulses (725 nm center wavelength, 10 nm FWHM , 100 fs pulse width, 600 mW average power, and 80 MHz repetition rate) generated by a Ti:sapphire Tsunami femtosecond laser from Spectra-Physics, was sent through a home-built Michelson interferometer. A specially designed dielectric 50/50 beam splitter from Femto Optics obviates the need of an additional compensation plate, since each surface has a coated and uncoated section. The optical
Results and discussion
Fig. 2 shows the SHG interferogram of the ZnO crystal wedge. The interferogram was recorded by scanning the optical delay by roughly 3.33 ps in 1.67 fs increments integrating for 500 ms. The magnified tail of the interferogram shown in the inset of Fig. 2 reveals a long-lasting oscillation, which indicates narrow spectral features in the signal.
Prior to the Fourier transform the recorded interferograms were baseline corrected and multiplied by an apodization function. Various apodization
Conclusion
We have shown that the spectral resolution in SHG spectroscopy using femtosecond laser pulses can be efficiently improved by the FT technique to achieve high spectral resolution independent of the input pulse characteristics. This was demonstrated by resolving the strong exciton -line at 3.407 eV in ZnO, which is much narrower than the spectral bandwidth of femtosecond laser pulses used for excitation of the resonance. Furthermore, compared to conventional methods, our FT-SHG technique benefit
CRediT authorship contribution statement
Mathias Hedegaard Kristensen: Methodology (lead), Software, Validation, Investigation, Data curation (lead), Writing - original draft, Visualization, Writing - review & editing (equal). Peter Kjær Kristensen: Methodology, Writing - review & editing (equal). Kjeld Pedersen: Methodology, Resources (equal), Writing - review & editing (equal). Esben Skovsen: Conceptualization, Methodology, Resources (equal), Data curation, Writing - review & editing (equal).
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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