Quasi-phase matched second harmonic generation in high-Q spherical micro-resonators

Abstract

Some spherical or other kinds of circular micro-resonators exhibit high Q factors which result in very sharp resonances for the light that propagates in the so-called whispering gallery modes. In active devices one may take advantage of such high Q factors to enhance laser light generation or nonlinear interactions. In recent years, there has been some work with the goal to achieve efficient second or third harmonic generation [1 ,2]. In such circular configuration phase matching amounts to angular momentum conservation, which may be achieved using different radial whispering gallery modes for the fundamental and harmonic fields. In that case, however, the overall overlap of the two or three interacting waves is limited. Quasi-phase matching is an alternative route that offers, in principle, more flexibility [3]. Here we will present the design and fabrication of a nonlinear spherical resonator to experimentally measure quasi-phase matched second harmonic generation (SHG) from a low number of molecules per unit area. For such process is advantageous that molecules are placed on the surface of the micro-sphere where the inversion symmetry is broken as required for a second order nonlinear interaction in the dipole approximation. In addition, for the lowest order whispering gallery radial mode, the field is confined by the sphere surface around one equatorial plane. On such molecular monolayer, we wrote a periodical pattern on roughly one quarter of the sphere around the equator perpendicular to the stem that holds it. The pattern consists of alternated periods of nonlinear molecules 8.8 mum in width at the equator and periods of the same width but with no nonlinear molecules. The width of each domain must be exactly one coherence length of the corresponding nonlinear interaction. Using a tunable laser as a pumping source, we saw that SHG, strongly peaks at exactly 403 nm very close to the 403.5 nm predicted from the theory in [3]. This agreement is remarkable and the 0.5 nm displacement could be attributed to a small error in measuring the diameter of the sphere. To conclude, we have demonstrated SHG in a new configuration that could have interesting applications in sensing of label-free or unmarked molecules. Sensitivity may be brought to the level of measuring SHG from single molecules since there is no fundamental physics aspect that prevents taking advantage of quality factors of up to 109 found routinely in microspheres.