Wavelength-adaptive spin-orbit orbital angular momentum management in three-wave mixing

TL;DR

The paper addresses how to control and read structured light across two wavelengths in nonlinear processes. It introduces a voltage-tunable spin–orbit liquid crystal device integrated with a type-0 χ^{(2)} crystal to independently modulate OAM for each colour during difference-frequency generation. Key findings show near-complete conversion for one wavelength ($η_{IR} ≈ 0.98$) with the other largely unchanged ($η_{NIR} ≈ 0.03$) at 4.70 V, and simultaneous, high-efficiency operation ($η_{NIR} ≈ η_{IR} ≈ 0.72$–$0.79$) at other voltages; modal purity reaches up to $|p_2|^2 ≈ 0.92$. This demonstrates a flexible, spectrally adaptive platform for multimode photonics with potential impact on quantum imaging, metrology, and high-density information encoding.

Abstract

Here we propose the use of an adjustable liquid crystal spin-orbit device to shape bi-colour structured light to create bimodal states. We demonstrate the proof-of-principle for two individual wavelengths in a nonlinear optics framework. The spin-orbit device has an inhomogeneous optical axis orientation and birefringence, allowing it to modulate two wavelengths of light with pre-selected transmission functions by simply tuning a voltage. We combine this bi-colour functionality in a nonlinear optical experiment by employing three-wave mixing in a periodically poled crystal to show how the combined effect of linear spin-orbit transformation rules and nonlinear selection rules gives rise to novel approaches for light to modulate light, and light to unravel light. We show that the roles of the nonlinear crystal and spin-orbit device can be switched to either characterise the device with known light, or unravel unknown light with the device. This synergy between spin-orbit and nonlinear optics offers a novel paradigm where light manipulates and reveals its own structure across spectral domains.

Figures (5)

• Figure 1: (a) Side-view sketch of the spin-orbit liquid crystal device made of a nematic slab with uniform orientation at rest $\bm{n_0}$ aligned with the $z$ axis, sandwiched between two glass substrates provided with transparent electrodes delivering a square waveform voltage $U$ at 100 kHz. The device is operated using the combined action of a uniform quasistatic electric field and a structured static magnetic field obtained from a ring magnet (RM) with uniform magnetisation $\bm{M}$. Not to scale. (b) Top-view image of the packaged device. (c) Observation of the topological structure of the nematic liquid crystal slab under an applied voltage of 4.70 V by optical imaging between crossed linear polarisers. Scale bar: 300 $\upmu$m. (d) Spin-to-orbital conversion efficiency efficiency, $\eta_\lambda$, as a function of applied voltage for $\lambda_{\mathrm{NIR}} = 808$ nm and $\lambda_\mathrm{IR} = 1550$ nm. Solid curves are guides for the eyes.
• Figure 2: Schematic of the experimental setup for nonlinear spatial mode detection with a spin-orbit device. A 532 nm (VIS) beam and a 1550 nm (IR) beam are expanded and collimated using a 4$f$-lens system before being modulated by spatial light modulators ($\mathrm{SLM_\mathrm{VIS}}$ and $\mathrm{SLM_\mathrm{IR}}$). Half-wave plates (HWP) adjust the polarisation before the beams are combined in a nonlinear crystal (NLC) via a dichroic mirror (DM). The DFG process in the NLC produces an 808 nm (NIR) beam, whose spatial mode structure is analysed using a single-mode fibre (SMF) and an avalanche photodiode (APD). The inset shows that the spin-orbit device is placed either in the NIR or IR arm. HWPs and quarter-wave plates (QWP) control the ingoing and outgoing polarisation.
• Figure 3: Modal decomposition with the spin-orbit device in the 808 nm arm of the nonlinear system. After the crystal, $l_\mathrm{NIR} = l_\mathrm{VIS} - l_\mathrm{IR}$. When $l_\mathrm{NIR}= 0$ after the device, maximal counts are detected. (a) Without an applied voltage, the spin-orbit coupling leaves the $l_\mathrm{NIR}$ unaltered. When the optimal NIR voltage of 3.75 V is applied, we observe the device adds a topological charge of (b) 2 for incident left circular light and (c) an equal superposition of 2 and -2 for incident linear light. We infer these OAM conversions from the diagonal shifts of maximal detection events in the modal decomposition. The red square outlines indicate when $l_\mathrm{VIS} = l_\mathrm{IR}$. The insets show the schematic set ups for recording this data.
• Figure 4: Characterisation of the spin-orbit device as a function of applied voltage for wavelengths (a) 1550 nm and (b) 808 nm. Modal decomposition is illustrated in the bottom plots, showing the mean detection counts of 11 repeats for different $\mathrm{LG}_{p=0, \ l}$ modes with $l$ ranging from -5 to 5 prepared on SLM VIS. (a) Detection counts are maximised when $l_\mathrm{IR}$ after the device equals $l_\mathrm{VIS}$. We observe that for a left-circularly polarised input beam, a topological charge of 2 is added by the device. (b) Here $l_\mathrm{NIR}=l_\mathrm{VIS}$, and detection counts are maximised when there is no OAM remaining in the NIR beam after the device. Again, we observe that for a left-circularly polarised input beam, a topological charge of 2 is added by the device. The top plots illustrate the modal purity of the $l=2$ component after the spin-orbit device as a function of voltage. Highest modal purities were found to be (a) 0.92 $\pm$ 0.02 at 4.70 V and (b) 0.84 $\pm$ 0.02 at 3.75 V. "Full/zero" conversion for IR/NIR is achieved at $\approx$ 4.70 V. The insets show the schematic setups for recording this data.
• Figure 5: Modal decomposition at "full/zero" conversion voltage in the 1550 nm (a, b, c) and 808 nm (d, e) arm of the nonlinear system. Error bars show the standard deviation of 11 repeats for a 1 s measurement time. Without an applied voltage, the spin-orbit coupling leaves the (a) $l_\mathrm{ IR} = 0$ and (d) $l_\mathrm{NIR} = 0$ OAM values unaltered. When the optimal "full/zero" conversion voltage of 4.70 V is applied, we observe the spin-orbit device converts $l_\mathrm{IR}$ = 0 to (b) $l_\mathrm{IR}$ = 2 for incident left circularly polarised light and (c) an equal superposition of $l_\mathrm{IR} = \{-2, \, 2\}$ for linearly polarised incident light. (e) The NIR beam remains unaffected at a voltage set to $\approx$ 4.7 V, corresponding to the flat region of the curve in Fig. \ref{['fig:voltage_characterisation']} (b). The insets show the schematic setups for recording this data.