Optical third-harmonic surface microscopy using ultra-short pulsed lasers

We have developed a new approach to studying surfaces and interfaces with third-harmonic generation (THG) that uses the time dependence of third-harmonic generation [5]. It is shown that third-harmonic generation is more sensitive to interfaces than previously reported [1,2]. This has advantages for studying transparent dielectric interfaces, which are many in nature and could be: biological materials, thin films, and in particular interfaces with nano-structure. This is because the efficiency of third-harmonic generation is proportional to  χ³, which is generally dissimilar for materials with similar linear indices of refraction. We show, in our approach, THG measurements must model the full time dependence of harmonic generation. Doing so explains recent contradictory results regarding z-scan THG at interfaces [1,6,7]. The group velocity mismatch (GVM) of the fundamental and harmonic fields determines a walk-off distance, which sets the limit of resolution in THG microscopy. We show how this effect is included, and how third-harmonic generation can be used to achieve sub-Rayleigh length spatial resolution of interfaces.
We model the time dependent phase matching factor with:
where ξ is the position of the laser focus relative to the entrance surface of the nonlinear material [3,4]. Time,  τ(z), accounts for the group velocity mismatch of the fundamental and harmonic pulses. We have performed measurements of transparent, large band-gap semiconductors to test the model, shown in the figure below.
When the data is frequency-resolved, we observe a periodic modulation of the power spectrum, depicted in the figure below.spectrum. Using the time dependence our our model, we show the origin of this effect is not a phase matching effect, which depends on the value e^Δkz, but is instead caused by the interference of the harmonic pulses generated at the interfaces of the dielectric media.

Since many experiments in biology and in materials science work from transparent substrates, these become an inherent source of a reference pulse which can interfere with the signal generated from the sample surface, as in the first figure. Such an experiment has an analog in second-harmonic generation, already found to be useful for surface studies [8]. We believe the introduction of our time-dependent approach to THG at interfaces will benefit a wide audience who work in this area.

References
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