In nonlinear wavelength conversion processes, maintaining phase matching is crucial to ensuring the conservation of photon momentum. Consequently, the requirement for phase matching limits the effectiveness of all parametric nonlinear optical processes. Techniques such as quasi-phase-matching, birefringent phase matching, and higher-order-mode phase matching have been developed to address this limitation. However, these methods necessitate specific beam arrangements and precise dispersion engineering, and are typically narrowband. In this study, we demonstrate that a submillimeter metal-clad waveguide can bypass the phase-matching requirement for on-chip nonlinear wavelength conversion by exciting an ultrahigh-order standing-wave field at nonspecial matching incident angles. Additionally, efficient second harmonic generation is observed within the submillimeter waveguide across a broad range of pump wavelengths (from visible to infrared). The results indicate that the ultrahigh-order standing-wave field mitigates traditional phase-matching constraints, facilitating nonlinear interactions and the miniaturization of nonlinear devices.

Nonlinear frequency conversion is of significant importance in the field of optics, with a broad range of applications including all-optical signal processing, quantum communications, biomedicine, data storage, environmental monitoring and more.

To obtain efficient nonlinear optical processes, the phase-matching condition has to be strictly satisfied when the light is generated by a parametric nonlinear interaction. such as second harmonic generation (SHG), sum frequency generation (SFG) and difference frequency generation (DFG) which are dictated by the properties of the input beams. Conventionally, the nonlinear phase matching is achieved using either birefringent or periodically poled nonlinear crystals by careful dispersion engineering. Actually, it is a normal condition that the phase-matching condition is difficult to strictly satisfied, and the amount of the phase mismatchis quantified to present the difference in the momentum of the constituent beams. Therefore, the quasi-phase matching (QPM) based on the periodically poled nonlinear crystals, and the amount of the phase mismatchhas been compensated by the inverse lattice vectors from periodical structure. However, the QPM suffers from the inconvenience of only being phase matched for a single, specific arrangement of beams, typically copropagating, and only for a narrow range of wavelength. These constraints pose severe hindering potential application in nonlinear frequency conversion.

There has been significant interest in using phase-matching free to realize wavelength conversion such resonant structures with (sub-) wavelength-scale mode volumes and metamaterials with a negative refractive index. Therein, the conversion efficiency relies on modal overlap between fundamental modes and higher harmonic in resonant structures. For example, the doubly resonant photonic cavities have been proposed to obtain wavelength conversion due to high quality factors, and the plasmonic nanoantennas where the simultaneous field enhancement at both the fundamental and harmonic wavelengths and spatial overlap between the modes allow for higher conversion efficiencies. Besides, the second harmonic generation of a signal wave propagating against the pump wave through the backward phase matching from the metamaterials. For example, the zero-index medium where the light does not contribute any momentum to phase-matching considerations and propagation direction becomes inconsequential to the phase mismatch, support the existence of direction-independent phase matching.

Here, we theoretically propose and experimentally demonstrate a submillimeter metal-cladding waveguide (SMCW) which supports a higher quality factor and the effective refractive index N_eff ~ 0 to enhance light-matter interactions within a large volume of nonlinear media and the simultaneous generation of both forward- and backward-propagating light support the existence of direction-independent phase matching. SMCW possesses several remarkable properties, with one of the most notable being the presence of ultrahigh order standing waves (UOSs), which can extend to more than 10^4 on the waveguide layer of SMCW. Therefore, the SMCW are able to circumvent the phase-matching requirement in on-chip nonlinear wavelength conversion due to excite an ultrahigh order standing wave field under the non-special matching incident angle. Meanwhile, efficient second harmonic generation in the submillimeter waveguide is not sensitive to variation of pump frequency due to metal properties. Resulting we observe over a wide range of pump wavelength (visible to infrared) by SMCW.

Figure. a) Schematic of SHG in an SMCW. b) the experimental setup and detected SH signal. c) The threshold value. d) The intensity changes with different incident angle.

The research was published in“Qiheng Wei, Hongrui Shan, Hailang Dai , and Xianfeng Chen, Phase-matching-free second-harmonic generation in an ultrahigh-order standing-wave field, Phys. Rev. Applied 22, L051001, (2024)”.

Link: https://doi.org/10.1103/PhysRevApplied.22.L051001