Counter-propagating mixing second harmonic generation in poled polymer waveguides
Authors: Otomo Akira , Stegeman George I. , Flipse Marinus C. , Diemeer Mart B. J. , Horsthuis Winfried H. G. , Möhlmann Guus R. 
Published: February 2023

Until recently, second harmonic generation (SHG) was used to extend the wavelength capability of high power lasers. In the conventional SHG process the fundamental and the growing second harmonic propagate together (Fig. 1a). The most recent progress has allowed mW of doubled power to be generated with 100’s of mW of input fundamental power. This has been achieved with waveguides from dielectric media such as LiNbO3, KTiOPO4 (KTP), etc.1,2 Organic materials have attracted attention due to their possible large nonlinearity. Although there has been some excellent pioneering work using organic materials, organic waveguide doublers have not yet achieved such efficiencies.3,4 One of the problems has been the disadvantageous trade-offs between λmax, the magnitude of the nonlinearity and the absorption of the doubled light. A different SHG interaction geometry, in which the second harmonic radiates upwards from a waveguide surface by mixing the counter-propagating fundamental guided waves (Fig. 1b), was reported 16 years ago, primarily for using second order interactions for signal manipulation and processing.5,6 The early works concentrated on ion-exchanged LiNbO3 waveguides with quite small conversion efficiencies. More recently AlGaAs multi layer waveguides have been used as a form of quasi-phase matching (QPM) in the transverse direction with much larger nonlinear cross-section coefficients. A number of interesting applications have been demonstrated including convolution, a spectrometer, etc. This interaction has different trade-offs from the usual copropagating case. The signal at the harmonic frequency only traverses the waveguide depth so that the attenuation coefficient can be as large as 104 cm-1 and hence the interaction length is limited primarily by attenuation at the fundamental wavelength. As a result the harmonic wavelength can in principle be near λmax, the peak absorption wavelength, and hence utilize a resonantly enhanced nonlinearity. The fractional power conversion into SHG for the co-propagating and the counter-propagating schemes is proportional to
[deff(2)L]2I and
[deff(2)L]2LHI respectively. I is the intensity and
deff(2) , L and H are the effective second order nonlinearity, the effective interaction length and the waveguide depth respectively. In terms of efficient SHG, the key question is whether the resonant enhancement in
[deff(2)]2 is larger or comparable to L/H. This represents the trade-off between co-propagating and counter-propagating SHG. If indeed the trade-offs are comparable, this counter-propagating approach could be attractive because there are no wavevector matching constraints as there are in co-propagating SHG. Such constraints have made it difficult to obtain phase-matching over a centimeter, require precise wavelength tuning and control of the input laser, and tight temperature control of the waveguide. Thus the large nonlinearity of poled polymers can be effectively utilized for SHG in the counter-propagating geometry. In this study we compared possible conversion efficiency between co-propagating and counter-propagating SHG by defining figures of merit and investigate efficient surface emitting SHG (SE-SHG) in poled polymer waveguides made from 4-dimethylamino-4′-nitrostilbene side-chain polymers (DANS-SCP).