Inter-Modal Optical Conversion

• Inter-modal optical conversion is a process that enables coherent transfer between distinct optical modes through nonlinear interactions and engineered device architectures.
• Techniques such as four-wave mixing, Brillouin scattering, and Kerr-induced gratings allow high conversion efficiency, addressing phase-matching and mode overlap challenges.
• Applications include high-dimensional multiplexing, quantum interfacing, and all-optical switching, driving innovations in advanced photonics and communications.

Inter-modal optical conversion refers to the physical mechanisms and device architectures that enable coherent transfer, mixing, or redistribution of optical energy between distinct electromagnetic modes—spatial, spectral, polarization, or hybrid—in a guided or free-space system. These processes, realized through nonlinearities, optomechanical effects, engineered refractive index distributions, material modulations, and advanced device designs, are central to modern photonics. They underpin high-dimensional multiplexing, bandwidth scaling, fine-grained mode control, quantum interfacing, and innovative optical information protocols.

1. Theoretical Frameworks and Physical Mechanisms

Inter-modal conversion encompasses a broad range of interactions:

• Scattering Matrix Theory and Reciprocity Linear systems described by a static scalar dielectric function $\epsilon(\mathbf{r})$ have a symmetric scattering matrix $S$ by the reciprocity theorem, implying $t_{12} = t_{21}$ for two-port devices; directional modal conversion alone cannot yield isolation or true nonreciprocity, as reflected signals can traverse the same path in reverse (Yu et al., 2011).
• Four-Wave Mixing (FWM) Both intramodal (same spatial mode) and intermodal (distinct spatial modes) FWM processes are critical for frequency and mode conversion in fibers. The phase-matching condition for intermodal FWM in graded-index (GRIN) fibers is: $$\Delta \beta = \beta_\mu^s + \beta_\eta^{as} - \beta_\nu^{p} - \beta_\kappa^p = 0$$ and the nonlinear coupling coefficient depends on mode overlap integrals. Intermodal FWM allows frequency conversion across ultrabroad spectral ranges when modal indices and dispersion are engineered appropriately (Stefańska et al., 2 May 2024).
• Brillouin and Optomechanical Scattering Stimulated Brillouin interactions, including inter-modal variants, mediate optical mode conversion via acoustic phonons. Phase-matching for Stokes ($q_s = k_1(\omega_p) - k_2(\omega_s)$) and anti-Stokes ($$q_{as} = k_1(\omega_{p} + \Omega_{as}) - k_2(\omega_p)$$) scattering can be separated in engineered waveguides, yielding symmetry breaking and single-sideband amplification or entanglement (Kittlaus et al., 2016, Zoubi, 2022).
• Kerr-Induced Dynamic Gratings Kerr nonlinearity enables transient long-period gratings, allowing efficient, ultrafast mode conversion in integrated waveguides and fibers via the coherent scattering of probe light between transverse modes (Hellwig et al., 2013, Hellwig et al., 2015).
• Electro-Optic and Magneto-Optic Coupling Electro-optic and magneto-optic effects exploit $\chi^{(2)}$ or magnetically controlled refractive index changes to enable inter-modal conversion, with cavity designs enhancing efficiency through mode hybridization under the beam splitter Hamiltonian $$H = \hbar\omega_1 a^\dag a + \hbar\omega_2 b^\dag b + (\hbar g/2)(a b^\dag + a^\dag b)$$ (Lambert et al., 2019).

2. Device Architectures and Modulation Strategies

Device realizations are diverse:

• Coupled Fabry–Pérot Resonators By introducing tunable impedance mismatch (frequency and spatial-sensitive transmission) between coupled resonators, the conversion efficiency between Hermite–Gauss (HG) modes exceeds 75%. The transmission is governed by $$T_{23}^{i \leftrightarrow j}(\omega) = |\alpha_{ij}|^2 T_{23}^j(\omega)$$ where $\alpha_{ij}$ is the mode overlap. Impedance matching ($T_1 = T_{23}^{i \leftrightarrow j}$) synchronizes spatial and spectral conversion (Stone et al., 2020).
• Graded-Index Multimode Fibers and Waveguides Exploiting the nearly equidistant modal dispersion and strong confinement, both transient (Kerr effect-written) and permanent gratings induce highly efficient inter-modal conversion. Dual-color conversion schemes circumvent polarization crosstalk, enabled by flat phase-matching curves ($\Delta$ remains near zero across $\sim$800 nm) (Hellwig et al., 2013, Stefańska et al., 2 May 2024, Zhang et al., 2020).
• Quantum and Atomic Platforms Mode conversion via spatiotemporally modulated atomic susceptibility utilizes auxiliary Stark-shifting beams to sculpt atomic refractive index in space and time, effecting high-fidelity conversion between orbital angular momentum (OAM) states (e.g., $l=3 \rightarrow l=0$) in an optical cavity. The process can saturate near unity internal efficiency via collective cooperativity $N\eta$ and Stark Rabi frequency $\Omega$ (Baum et al., 2022).
• Structured Planar Optics Liquid-crystal geometric-phase superstructures, designed by fractional Fourier transformation, directly modulate spatial modes (HG/LG) and enable reciprocal OAM conversion on the modal sphere; higher-order geometric phases $(|l|+1)\Omega/2$ offer expanded phase resources for quantum applications (Li et al., 2023).
• Hybrid Photonic-Phononic Integrated Waveguides Thin-film lithium niobate (TFLN) with continuous phase-matching (not discrete resonance) supports multi-channel microwave-to-optic conversion via traveling phonon modes, achieving >40 nm bandwidth and simultaneous operation of nine channels, with internal efficiency up to 2.2% (Yang et al., 12 Sep 2025).
• Quasi-Phase-Matched Acousto-Optic Devices Periodic waveguide width modulation supplies additional momentum $K = 2\pi/\Lambda$, enabling forward Brillouin inter-modal scattering (e.g., TE$_{00}$ to TE$_{10}$) at visible wavelengths, attaining complete conversion over $\sim$1.1 mm with only 1 mW acoustic power (Chen et al., 9 Oct 2025).

3. Efficiency, Bandwidth, and Switching Performance

Conversion metrics depend on the physical process and device design:

• Intermodal FWM in GRIN Fibers Achievable parametric gains reach $\sim$400 dB/m at visible ($<$0.65 μm) and mid-IR ($>$3.5 μm) wavelengths, far beyond step-index fiber limits. Modal overlap and phase-matching dictate channel strengths (Stefańska et al., 2 May 2024).
• Optomechanical Devices Impedance-matched cooperativities $C_1 = C_2$ ($C_i = 4G_i^2/\kappa_i \gamma_m$) result in photon conversion efficiency $\eta = \frac{4C_1C_2}{(1+C_1+C_2)^2}$ with near-unity efficiency when $C_i \gg 1$ (Dong et al., 2012). Fiber-based systems can extend operational bandwidth to tens of THz, removing phase-matching and cavity constraints typical of conventional nonlinear methods (Xi et al., 2021).
• Mode-Selective Nonlinear Upconversion Mode selectivity yields extinction ratios up to 60 ($18$–$21$ dB), vital for pattern recognition and multiplexed quantum channels (Kumar et al., 2018).
• Laser-Based All-Optical Wavelength Conversion Intermodal carrier-induced gain modulation in monolithic InP multi-wavelength lasers allows data transfer over 1.3 THz and signal rates up to 10 GBd, with agile feedback causing nanosecond switching or broadcasting. Numerical modeling reveals optimal injection and cross-saturation regimes for minimal BER (Marin-Palomo et al., 9 Sep 2025).
• Traveling-Wave Brillouin Conversion Multi-channel TFLN converters, with $g/2\pi =$ 63 m$^{-1}$W$^{-1/2}$ (experimental), achieve simultaneous operation in up to nine channels and internal efficiency $\eta_{\rm int}$ scaling as $g^2 L^2 P_{\rm pump}$ (Yang et al., 12 Sep 2025).

4. Limitations and Fundamental Constraints

• Reciprocity and Symmetric Scattering Directional modal conversion does not realize total isolation unless system reciprocity is broken (e.g., via time-dependent dielectric modulations, nonlinearity, or magnetic effects). Otherwise, reflected or converted modes can propagate backward, as enforced by a symmetric $S$ (Yu et al., 2011). Modal conversion alone is therefore insufficient for optical isolation.
• Group Delay and Walk-off Differential modal group delay (DMGD) limits conversion bandwidth and interaction length in fiber-based multimode FWM (conversion bandwidth narrows, performance degrades above a few Gbit/s) (Zhang et al., 2020).
• Mode Overlap and Dispersion Management Efficient conversion requires engineered overlap integrals and dispersion profiles; in FWM, both self-phase and cross-phase effects must be considered, and non-ideal coupling can suppress specific channels (Stefańska et al., 2 May 2024).

5. Applications and Emerging Opportunities

Inter-modal conversion strategies are fundamental to:

• Space-Division and Mode-Division Multiplexing Multi-mode fibers and on-chip converters enable high-dimensional communication, increasing throughput and resilience (Hellwig et al., 2013, Kittlaus et al., 2016, Baum et al., 2022, Li et al., 2023).
• Quantum Information and Hybrid Networks Microwave-to-optics and photon–phonon entanglement via intermodal Brillouin scattering facilitate quantum interfacing and distributed computing between superconducting and photonic platforms (Lambert et al., 2019, Zoubi, 2022, Yang et al., 12 Sep 2025).
• All-Optical Switching and Advanced Filtering Ultrafast, low-power switches based on Kerr-induced gratings and integrated waveguide geometries enable on-chip routing with >90% efficiency, minimizing cross-talk and energy cost (Hellwig et al., 2015, Marin-Palomo et al., 9 Sep 2025).
• Sensing, Spectroscopy, and State Preparation Fiber-based optomechanical converters and atomic susceptibility modulation schemes expand the available spectral and spatial operational space for high-sensitivity applications (Xi et al., 2021, Baum et al., 2022).
• Acousto-Optic and Electro-Optic Integrated Devices Forward Brillouin scattering and quasi-phase-matched structures in TFLN or LN devices support compact, low-power, robust conversion and modulation at visible wavelengths—critical for interfaces with atomic quantum systems (Chen et al., 9 Oct 2025).

6. Future Directions

Prospective advances include:

• Expansion to Micro/Nanophotonics Scaling inter-modal conversion strategies to nano-guides, microresonators, and photonic chips can boost bandwidth and density.
• Hybrid and Adaptive Architectures Combining optomechanical, electro-optic, and structured light techniques promises versatile, programmable, and loss-minimized conversion platforms.
• Quantum State Engineering and Modal Entanglement Harnessing entangled photon–phonon states and high-dimensional OAM encoding will enable topological state preparation and robust quantum communications.
• Integration and Inverse Design The use of optimization, inverse filtering, and geometric-phase engineering in both guided and free-space devices may realize tailored mode conversion for specific signal processing tasks in classical and quantum regimes.

Inter-modal optical conversion, as evidenced by recent work, is a multifaceted discipline at the intersection of nonlinear optics, quantum information, advanced photonic design, and high-dimensional communication. Its development continues to redefine the domain of optical control, multiplexing, and interfacing across wavelength, spatial, and hybrid quantum degrees of freedom.