Inverted Wavelength Schemes in Photonics

• Inverted wavelength schemes are advanced photonic architectures that use inverse design and engineered nonlinear processes to achieve precise wavelength control and compact device footprints.
• They employ techniques such as adjoint optimization, self-biasing, and PT symmetry to enable efficient demultiplexing, multiplexing, and wavelength conversion with low insertion losses.
• Recent research shows these methods support robust, high-density integration across telecom, terahertz, and mid-infrared bands, paving the way for scalable, next-generation photonic systems.

Inverted wavelength schemes refer to advanced photonic device architectures and mechanisms whereby functionalities are defined or achieved by manipulating wavelength channels in a manner that extends beyond traditional spatial, geometric, or sequential approaches. Typically, such schemes harness inverse design methods, spatial singularity, wavenumber selectivity, or engineered nonlinear optical processes to realize wavelength multiplexers/demultiplexers, wavelength converters, reconfigurable meta-optics, and parity-time (PT) symmetric systems, often with dramatically increased compactness, selectivity, integration density, and robustness to fabrication imperfections. This paradigm encompasses techniques for both precise wavelength separation and accurate nonlinear conversion, as well as “inverted” device roles realized by port role interchange under reciprocal system conditions. The subsequent sections delineate key methodologies, device structures, performance metrics, operational principles, implications for integrated photonics, and future research directions as supported by primary arXiv references.

1. Inverse Design Frameworks for Wavelength Schemes

Inverse design provides the foundational methodology underpinning most modern inverted wavelength schemes. In contrast to brute-force geometric parameter searches, inverse design methods specify electromagnetic field or device performance objectives (such as coupling efficiency, extinction ratio, or insertion loss), and employ mathematical optimization (typically gradient-based or adjoint methods with solvers such as FDFD, FDTD, or FEM) to obtain an optimal dielectric or material profile. Key formulations involve solving Maxwell’s equations (e.g., $$\nabla \times (\mu_0^{-1} \nabla \times \mathbf{E}_i) - \omega^2 \epsilon \mathbf{E}_i = -i \omega_i \mathbf{J}_i$$) under user-defined constraints encoded via mode overlap integrals:

$$\alpha_{ij} \leq |\iint_{S_{ij}} \mathcal{A}_{dj} \cdot \mathbf{E}_i\, dS| \leq \beta_{ij}.$$

Designs typically proceed through continuous material parameter optimization, followed by binarization or application of thresholding functions, yielding fabrication-ready geometries. Devices such as multi-channel grating couplers (Piggott et al., 2014), compact WDM splitters (Su et al., 2017), and $1 \times N$ demultiplexers (Yilmaz et al., 2019) have been realized with compact footprints (e.g., $\sim$24.75 $\mu$m$^2$), sub-3 dB insertion losses, and channel spacings as small as 40 nm, far surpassing conventional limitations.

2. Advanced Wavelength Demultiplexers and Multiplexers

Recent advances in inverse-designed demultiplexers encompass the integration of narrowband, multi-channel, and multimode separation functionalities on-chip. Devices leverage multi-stage optimization strategies, employing continuous pixelwise optimization followed by level-set binarization and fabrication-aware biasing to achieve manufacturable, binary structures. Notably, biasing techniques (“self-biasing” and “neighbor biasing”) drive feature evolution and improve device robustness (Su et al., 2017).

The principle of reciprocity (under Maxwell’s equations) enables the “inverted” use of such devices: demultiplexers may function as multiplexers when input/output port roles are exchanged, maintaining performance such as $<$–15 dB crosstalk and high transmission. For example, the $1\times N$ T-junction demultiplexer can be reconfigured as a multiplexer (Yilmaz et al., 2019). The scaling of channel number and device density is facilitated by the flexibility of the inverse design algorithm and its adaptability to various optical bands.

3. Wavelength Conversion and Nonlinear Schemes

A distinct class of inverted wavelength schemes targets highly efficient wavelength conversion via nonlinear processes, including two-peak Stark-chirped rapid adiabatic passage (SCRAP) in domain-inverted crystals (Zhang et al., 2021). Here, cascaded three-wave mixing is controlled through spatially engineered quasi-phase-matching gratings, enabling both intuitive and counterintuitive coupling orders. The suppression of intermediate state occupation ($\sim$0.27% of input intensity) and complete energy transfer is achieved by judicious separation of coupling peaks (modulation parameter $s_1$).

Theoretical models employ effective Hamiltonians for three-level systems (with spatial coordinate $z$ mapped to the temporal coordinate $t$), denoting Rabi frequencies by spatially varying coupling coefficients. Compared to stimulated Raman adiabatic passage (STIRAP), two-peak SCRAP designs offer greater convertible wavelength bandwidth ($>$95% efficiency over >30 nm range), reduced phase-matching requirements, and flexible device engineering for mid-infrared laser source generation.

4. Wavenumber Selectivity and Photonic Crystal Resonators

Recent work introduces photonic crystal-mediated wavenumber selectivity to achieve wavelength-accurate nonlinear conversion independent of dispersion engineering (Stone et al., 2022). Modulation of microring resonator sidewalls ($RW' = RW + A_{mod} \cos(N\theta)$) coherently couples counter-propagating modes ($m = N/2$), inducing a photonic bandgap that isolates specific wavenumbers for nonlinear gain. This strategy is validated in third harmonic generation, four-wave mixing Bragg scattering, and Kerr microcomb dispersive wave enhancement.

The induced frequency splitting ($2J$) permits precise balancing of inherent frequency mismatches ($\Delta\nu_{CW}$), ensuring output wavelength control within $<$0.3% error and up to 300 GHz of continuous tuning. This approach eliminates reliance on higher-order dispersion compensation and substantially increases robustness against fabrication tolerances, marking a paradigm shift in microresonator design.

5. PT Symmetry and Spatial Singularities in Wavelength Schemes

An alternative mechanism for wavelength-based inversion is the mapping of parity-time (PT) symmetry into wavelength space rather than conventional dual-resonator geometric symmetry (Li et al., 2019). In this design, gain and loss modes are encoded in distinct optical wavelengths sharing a single spatial resonator loop. Chromatic dispersion and polarization management enable fine control over round-trip delay and power contrast, setting the conditions for PT symmetry ($\gamma^{(1)} = -\gamma^{(2)} = Y_m$, $\omega_{1,2} = \omega_m \pm \sqrt{K^2 - Y_m^2}$).

Experimentally, this system generates high-quality 10-GHz microwave signals with ultra-low phase noise ($-$129.3 dBc/Hz at 10 kHz offset) and high SMSR (66.22 dB), demonstrating over 1000-fold increased resilience to environmental disturbances and further simplifying the configuration. This “spatial singularity” approach paves the way for structurally simple, dense, and stable integrated photonic networks.

6. Multimode and Terahertz Integrated Demultiplexers

Developments in multimode and terahertz integrated photonics extend inverted wavelength schemes to larger modal and spectral domains. Hybrid inverse design approaches combine genetic algorithms (GA) for global structure search with adjoint-driven topology optimization for local performance refinement (Chong et al., 1 Sep 2025). Devices exploit modal overlap merit functions and multi-channel $p$-norm figures-of-merit to simultaneously optimize for multiple orthogonal TE modes (e.g., TE$_{10}$, TE$_{20}$, TE$_{30}$) across differing wavelengths (690 $\mu$m, 700 $\mu$m, 710 $\mu$m).

Experimental outcomes indicate insertion losses below 3 dB per channel and inter-channel crosstalk of –22 dB, with device footprints $<$22 mm$^2$, suitable for high-density on-chip interconnects, signal processing, and multi-dimensional optical communications in the THz regime. This suggests new pathways for tightly integrated photonic infrastructure.

7. Future Directions and Technological Implications

The scope of inverted wavelength schemes, as delineated by the ensemble of referenced works, incorporates future extensions including fully three-dimensional inverse design, robust tolerance-aware optimization, integration of active and reconfigurable elements, generalized parameter-space symmetry, and further reduction of device design cycles. Theoretical and experimental progress in multi-photon, multi-mode, and multiwavelength control using advanced computational and physical principles (e.g., axisymmetric fullwave Maxwell solvers (Christiansen et al., 2020), bandgap engineering, domain-inverted crystals) will underpin next-generation photonic components for quantum information, communications, and precision metrology.

A plausible implication is that these developments will facilitate the creation of scalable, tunable, and highly efficient integrated devices across telecom, microwave, and infrared bands, overcoming limitations imposed by traditional geometries, dispersion management, and fabrication variability, thus reshaping the landscape of photonic system integration and function.