Nonlinear Nanophotonic Chip-space Interfaces: On-chip Generation of Structured, Topological and Spatiotemporal Lights Via Nonlinear Čerenkov Radiation

Abstract

Miniaturized and reconfigurable interfaces between confined optical modes within integrated photonic chips and structured light propagating in free space would serve as a cornerstone for fundamental optical science and modern photonic technology. In this work, we exploit the anisotropic nonlinear susceptibility tensors associated with thin-film lithium niobate to construct nanophotonic chip-space interfaces capable of flexibly generating and multi-dimensionally engineering structured light via injections of photons to on-chip waveguides. By harnessing the nonlinear Čerenkov radiation in integrated nonlinear microring resonators, we successfully tailor the spatial profile, polarization state, emission wavelength, topological charge and temporal wave packet of structured optical vortices, exhibiting reconfigurabilities and tuning ranges far beyond the state-of-the-art. To further showcase the capabilities of our platform, we use a single pump to generate tunable optical skyrmions via the spin-orbit coupling and multi-state integrated vortex microcombs in the visible range via synergistic $χ^{(2)}$ and $χ^{(3)}$ nonlinear optical processes. Our work bridges the research fields of structured light and integrated nonlinear optics, providing unprecedented opportunities for spatiotemporal light generation and on-chip multidimensional nonlinear optics.

Figures (6)

• Figure 1: Working principle of the NCR-based SF process. (a) Generation of out-of-plane SF photons via the second-order nonlinear optical interaction between two counter-propagating photons in the microring governed by the NCR principle. The coherence of the SF photons provides a necessary condition to form a structured wavefront. The inset shows the NCR angle of SF field. (b) Theoretical analysis of the NCR SFG based on the three-wave mixing process, where wavevectors of interacting waves are introduced to analyze the structured SF wavefront. The TC and frequency of the SF field are $l_\text{SF}=m-n+l_\chi$ and $\omega_\text{SF}=\omega_m+\omega_n$, respectively. (c) Generation of structured vortices with independently tunable wavelength and TC, optical skyrmions with controlled skyrmion number and tunable wavelength, and spatiotemporal vortex pulses with engineerable wave packets by tailoring the SF wave in multiple degrees of freedom. The CCW and CW WGMs are excited by the incident fields, labeled as $\lambda_m$ and $\lambda_n$ from the left port and the right port of the coupling straight waveguide, respectively.
• Figure 2: Engineering on-chip structured SF fields in multiple degrees of freedom. (a, e, i, m) Measured near-field patterns of the SHG in the four cases. Homogeneous bright circular intensity patterns are observed in cases 1, 3 and 4 while amplitude modulation with two circular arcs is obtained in case 2. The arrows above the intensity patterns represent the polarization states. (b, f, j, n) Measured far-field patterns of SHG in the four cases with dominant $x$-polarization component in cases 1 and 2 and distinct cylindrical polarization states in cases 3 and 4. (c, g, k, o) Measured near-field patterns of the SFG in the four cases, which are the same as that in SHG but carry modal-difference induced spiral phases with TCs of $l_\text{WGM}=\ \pm4,\pm2,2, \text{and} -1$, respectively. The arrows and colorful rings above the intensity patterns represent the polarization states and phases, respectively. (d, h, l, p) Measured far-field patterns of SFG with $l_\text{WGM}=\ \pm4,\pm2,2, \text{and} -1$ for cases 1 to 4, respectively, showing the scalar vortex in case 1, the scalar superposition state in case 2, and the spin-orbit coupling states in cases 3 and 4.
• Figure 3: Independent and wide-range tunings of the wavelength and TC of the structured optical vortices. (a) The scheme for achieving optical vortices with tunable wavelengths but a fixed TC of $l_\text{SF}=\ m-n$ by simultaneously changing the orders of two fundamental waves along the same direction. (b) The scheme for achieving optical vortices with tunable TCs following the laws of $l_\text{SF}=2\Delta l$ and $l_\text{SF}=2\Delta l+1$ but at a fixed wavelength by simultaneously changing the orders of two fundamental waves along the opposite direction. Temperature control on the microring is employed to fine-tune the resonant wavelength by half of the FSR, compensating for the wavelength difference between SF vortices with odd and even TCs. (c) Experimental demonstrations of optical vortices with tunable wavelengths without changing the TC by keeping $m-n= 4$ in case 1 based on the scheme in (a). The emission wavelength spans from 767.77 nm to 793.62 nm. (d) Experimental demonstrations of optical vortices with tunable TCs without changing the wavelength in case 1 based on the scheme in (b). The TC ranges from -7 to 7 continuously and the wavelength difference between the odd and even TCs is compensated by temperature control. (e) The scalar SF vortex with a TC of $l_\text{SF}=$ 109 by keeping $m-n= 109$ and the on-chip interference pattern for $l_\text{SF}= \pm109$.
• Figure 4: Wavelength-tunable optical skyrmions with skyrmion numbers of -2 and 4. (a, e) Measured Stokes parameters in case 4 with $m-n=1$ and case 3 with $m-n=2$, respectively. (b, f) Recovered polarization distributions based on (a, e) and corresponding spin textures mapped from a unit Poincaré sphere onto a confined plane. Skyrmion numbers of -1.87 and 3.94 are experimentally extracted, respectively. (c, g) The theoretical polarization distributions and vortex textures for optical skyrmions with skyrmion numbers of -2 and 4, respectively. (d, h) The tunable wavelength of the optical skyrmions in (b, f) by simultaneously changing the orders of both fundamental waves along the same direction with $\Delta l= \pm2$.
• Figure 5: Spatiotemporal vortex pulses with engineerable wave packets. (a) A schematic illustrating the principles of $\chi^{(3)}$ and $\chi^{(2)}$ nonlinear interactions that produce telecom-band Kerr solitons and short NIR spatiotemporal SF vortex. The telecom-band Kerr solitons are generated by the CCW pump via four-wave mixing processes while the short NIR spatiotemporal SF vortex is produced from the circulating NP packet formed by the interactions between the CCW soliton and the CW continuous pump at the group velocity of $v_{\text{g}}$ but with a superluminal phase velocity along the azimuthal direction. (b) Spectrum of a Kerr soliton with the repetition rate of 250 GHz (2 nm in wavelength) in the telecom band and spectrum of the corresponding short NIR spatiotemporal SF vortex with the same repetition rate of 250 GHz (0.5 nm in wavelength) in short NIR. A notch filter (gray area denoted as NF) is used to suppress the SH spectrum from the CCW and CW pumps and a bandpass filter (blue area denoted as filtered spectral lines) is employed to spectrally select the spectral lines of interest (with low TCs). The dispersive waves at short (orange area) and long (purple area) wavelengths are marked by DW$_1$ and DW$_2$, respectively. (c) Radiated intensity profiles of spatiotemporal SF vortex. The far-field patterns associated with the vortices with different OAMs selected by the bandpass filter and dispersive waves correspond to the green, blue and orange rings, respectively. (d) The filtered spatiotemporal SF vortex is dispersed by a blazed grating, resulting in different diffraction angles for the spectral lines at different wavelengths. The zoomed-in comb lines at different wavelengths in the spectrum overlay the corresponding diffractive rings (I, II, III, IV) at different angles. (e-h) Amplified single NIR spectral lines of spatiotemporal SF vortex and corresponding vortex far-field patterns (I, II, III, IV) by tuning an extra CCW pump mimicking the targeted soliton comb line to interact with the CW pump. (i, j) The spectra of the dual-soliton state and soliton-crystal state generated in the telecom band. Above them are the zoomed-in spectra of the up-converted spatiotemporal SF vortex in the short NIR range. (k, l) are the diffracted far-field patterns associated with the spatiotemporal SF vortex with different temporal wave packets. The clear intensity modulations respective to (d) reveal the characteristics of a dual-soliton state with a modulated envelope and a soliton-crystal state with doubled mode spacing.