Experimental Observation of Second Harmonic Generation Enabled by Longitudinal Components in Indium Gallium Phosphide Nanowires

Novel integrated photonics platforms are having a large impact on nonlinear optics. The inherent strong confinement and highly nonlinear materials allow for ultra-efficient frequency conversion. Recent reports on second harmonic (SH) generation for example posted record conversion efficiencies in millimetre long waveguides [1,2]. These promising results predict an exciting future for frequency conversion in subwavelengths structures. Yet, the vectorial nature of waves propagating in high index contrast nanowaveguides is often overlooked. Here we demonstrate second harmonic generation enabled by the longitudinal component of both the pump and the second harmonic wave. We use a 680 nm wide, 320 nm thick Indium Gallium Phosphide nanowaveguide [3]. As in other III-V materials, only the χ
²
_xyz
component is nonzero. Previous demonstrations of second harmonic generation used waveguides that are rotated 45° in order to split the main transverse component along two axes [1,4]. Conversely, we use a 1.5 mm long waveguide whose propagation direction is aligned along the z crystallographic axis. The effective nonlinearity is hence proportional to the overlap integral ∫ x
²
_xyz
(E
_x
*
^SH
E
^F
_y
+ E
_y
*
^SH
E
_x
^F
+ E
_z
*
^SH
E
_x
^F
E
^F
_y
) dxdy where E(x,y) is the spatial distribution of the electric field in the transverse plane. Full-vectorial simulations predict phase matching and a nonzero overlap between a fundamental quasi-transverse magnetic (TM) pump mode and a higher order SH TM mode around 1575 nm. Importantly, such conversion would not be permitted without strong longitudinal field components. The effective index of both the pump and SH as well as the different field components are shown in Fig. 1. As can be seen, most field components have nonnegligible amplitudes and hence contribute to the effective nonlinearity. We launch a 3 mW telecom band pump in our waveguide through a lensed fiber and collect the second harmonic by use of a high NA (0.9) objective. Our results are shown in Figure 1. We find a maximum conversion of 0.2 %/W/cm
²
, around 2 orders of magnitude less that the theoretical prediction, indicating that the second harmonic mode likely suffers from strong propagation losses. Our experimental image of the SH mode confirms the excitation of an antisymmetric TM higher order mode. In conclusion we demonstrated second harmonic generation through mixing of transverse and longitudinal field components. Not only does it demonstrate the vector nature of the propagating waves, it also allows to excite higher order modes with different symmetries. Furthermore, full-vectorial simulations show that similar wave-mixing is the most efficient conversion scheme for waveguides fabricated in thick (>200nm) InGaP layers.