Packing Game: Multi-Wavelength Beam Optimization

• Packing Game is the efficient management of multi-wavelength beams using spectral diversity and precise phase control.
• It employs techniques like PB geometric phase engineering, multi-plane light conversion, and neural-network-based diffractive design to enhance performance.
• Applications range from high-power optical communications and metrology to quantum sensors, underscored by rigorous performance metrics and optimization trade-offs.

A multi-wavelength beam approach describes any methodology or device that manipulates, generates, routes, or utilizes optical beams comprising multiple, distinct wavelengths, either simultaneously or with agile spectral reconfigurability. This paradigm underpins a broad class of technologies across photonic information processing, metrology, manufacturing, sensing, communications, and quantum optics. Multi-wavelength beam systems leverage wavelength diversity to achieve enhanced functionality, robustness, and spectral-multiplexed processing that is unattainable with single-wavelength strategies.

1. Underlying Physical Principles and Device Architectures

Multi-wavelength beam approaches rely on exploiting fundamental wavelength dependencies in light–matter interaction, device transfer functions, and modal behavior. The core mechanisms include:

• Pancharatnam–Berry (PB) geometric phase engineering—Angle-controlled phase shifts in metasurfaces yield wavelength-proportional phase gradients for precise beam shaping and splitting across broad bands, with meta-atom dimensions sub-wavelength to suppress unwanted orders (Hemayat et al., 2023).
• Dispersion in phase and propagation—Devices such as multi-plane light conversion (MPLC) sort or combine beams by harnessing the wavelength-dependent phase accrued through diffractive masks and free-space propagation (Zhang et al., 2020).
• Photonic bandgap formation in periodic structures—Hollow-core photonic crystal fibers (PBGFs) are architected with dual-apex 2-uniform tiling to create strongly wavelength-separated transmission windows, supporting fundamental and harmonic propagation in a common core (Montz et al., 2019).
• Wavelength-selective interference—Triple-slit metallic structures with asymmetrically filled slits use intra- and inter-slit dual-wave resonances to route different wavelengths to spatially distinct channels, with analytical design rules for on/off switching at λ and 2λ (Huang et al., 2012).
• Optically and electronically tunable phase retarders—Liquid-crystal Q-modules, with voltage-dependent birefringence, offer real-time, multi-wavelength control over beam polarization, phase, and orbital angular momentum (Piłka et al., 2023).
• Synthetic wavelength generation—Electro-optic modulation enables dynamic synthesis of difference frequencies far from accessible laser lines, facilitating multi-scale interferometric measurements with fast (<30 ms) wavelength switching (Vossgrag et al., 4 Feb 2025).
• Semiconductor multi-wavelength lasers—Monolithic InP multi-mode lasers support all-optical wavelength conversion, broadcasting, and agile selection among >1 THz-separated bands via feedback phase control (Marin-Palomo et al., 9 Sep 2025).

2. Optimization and Design Methodologies

Dedicated optimization frameworks are essential to realize uniformity, efficiency, and broadband operation in multi-wavelength systems:

• Modified Particle Swarm Optimization (PSO) for metasurfaces maximizes both diffraction efficiency η and uniformity U over all target wavelengths and output orders. The cost function penalizes order imbalance and leverages periodic noise injection and cluster-centroid reflection to prevent premature convergence in high-dimensional spaces (Hemayat et al., 2023).
• Inverse design and multi-objective regression are central to holographic volumetric additive manufacturing, simultaneously co-optimizing phase masks, beam amplitudes, and multiple wavelengths through nonlinear light–matter coupling models and automatic differentiation (Li et al., 28 Jan 2024).
• Wavefront matching for MPLC iteratively propagates and backpropagates target fields across phase planes, converging to phase-mask sets that enable unitary wavelength–mode sorting with low insertion and mode-dependent losses (Zhang et al., 2020).
• Neural-network-based diffractive design in multi-layer DOEs enables joint training for multiple wavelengths and beam profiles using physics-informed loss functions and backpropagation for millimeter-scale devices (Jacob et al., 17 Sep 2025).

3. Performance Metrics, Trade-offs, and Parameter Dependencies

The efficacy of multi-wavelength beam approaches is benchmarked by specific, quantitative metrics:

Metric	Representative Value / Result	System
Diffraction efficiency (η)	>90% across 1525–1575 nm (splitter/combiner)	PB metasurface (Hemayat et al., 2023)
Uniformity (U)	>97% across 50 nm band (diffraction order balance)	PB metasurface (Hemayat et al., 2023)
Insertion/mode-dependent loss	IL = 1.27 dB, MDL = 2.45 dB (4λ×3mode MPLC)	MPLC sorter (Zhang et al., 2020)
Stability/repeatability	<1% drift over 104 switching cycles	DOE neural network (Jacob et al., 17 Sep 2025)
OAM conversion efficiency	>90% for Q-modules at half-wave voltage	Liquid crystal Q-plate (Piłka et al., 2023)
Fade-probability reduction	From 0.25 to 0.0012 (single to triple-λ, 15 m, underwater)	UWOC, 3λ (Tayebnaimi et al., 2 Dec 2025)

Key trade-offs governed by physical constraints, spectral bandwidth, and device principles include:

• Bandwidth vs. phase accuracy: Intrinsically achromatic PB phase elements require near-π phase difference between transmission coefficients, which is challenging to maintain over broad spans. Large Δϕ variation reduces conversion efficiency.
• Efficiency vs. uniformity: Varying cost-function weights balances peak performance and operational bandwidth.
• Resolution vs. unambiguous range: In interferometry, synthetic-wavelength approaches increase the range at the expense of axial resolution, restored hierarchically using multi-Λ cascades (Vossgrag et al., 4 Feb 2025).

Material and design parameter scaling—lateral meta-atom dimensions, cell gap in retarders, unit-cell period in PBGFs—strongly tune wavelength coverage, spatial resolving power, and passive or reconfigurable device architectures.

4. Applications Across Photonics and Quantum Technologies

Multi-wavelength beam approaches address multiple optical engineering grand challenges:

• High-power beam combining and WDM/SDM transceivers: MPLC-based devices enable low-loss, low-crosstalk spatial and spectral sorting/combining for fiber and free-space optical networks (Zhang et al., 2020).
• Volumetric additive manufacturing (VAM): Joint phase optimization with multi-wavelength and multi-beam coupling leverages nonlinear photoresponse (e.g., two-photon absorption) to sculpt microstructures with sharp edge definition and speckle suppression (Li et al., 28 Jan 2024).
• Interferometry and metrology: Dynamically reconfigurable synthetic wavelength ladders deliver on-demand range and resolution, with <30 ms reconfiguration times for surface profiling and non-laboratory inspection (Vossgrag et al., 4 Feb 2025).
• Atomic cooling and clocking: Integrated metasurface arrays generate fully three-dimensional, dual-wavelength, polarization- and divergence-controlled beam sets for Sr MOTs, eliminating the need for bulk optics and facilitating the miniaturization of quantum sensors (Jammi et al., 14 Feb 2024).
• OAM beam generation and manipulation: Modular Q-plates with voltage-tuned birefringence controllably set OAM charge and working wavelength, enabling arithmetic stacking for multi-wavelength structured light (Piłka et al., 2023); stable vortex beams at dual wavelengths with GHz–THz spacing are generated using broadband Yb:CALGO solid-state lasers and π/2 mode converters (Shen et al., 2018).
• Underwater communications and imaging: Multi-wavelength beams drastically suppress the effects of turbulence-induced scintillation (σ_I^2), lowering fade probabilities and increasing link reliability, as demonstrated for three-wavelength Gaussian beams (Tayebnaimi et al., 30 Nov 2025, Tayebnaimi et al., 2 Dec 2025).

5. Security Implications and Vulnerabilities

Multi-wavelength beam properties can also expose vulnerabilities in photonic systems. In quantum key distribution (QKD) architectures using fused-biconical-taper (FBT) beam splitters, the wavelength dependence of the transmission/reflection ratio creates a fatal side channel. An attacker equipped with a dual-wavelength source can deterministically force a passive QKD receiver into the "correct" basis with near-100% success, recovering the full key while introducing only ~0.1% excess QBER, far below alarm thresholds. Rigorous spectral filtering, component selection, or migration to active-basis designs are required to exclude this vulnerability (Li et al., 2011).

6. Generalization, Scalability, and Future Directions

Scaling multi-wavelength beam strategies to broader spectra or higher mode-counts requires:

• Robust device scaling: For metasurfaces, lateral and vertical geometric scaling with λ/n_eff preserves sub-wavelength operation. In PBGFs, multi-bandgap tilings and dual-apex architectures provide simultaneous multi-band guidance.
• Inverse-design expansion: Optimization methodologies naturally generalize to multi-objective landscapes, supporting simultaneous optimization for arbitrarily many wavelengths, spatial modes, or functional outputs, constrained by computational tractability.
• Integration of reconfigurability: Emerging platforms, such as monolithic InP lasers with integrated feedback, liquid crystal Q-module arrays, or neural-network–designed DOEs, support real-time agility—electronic or otherwise—over multi-wavelength parameter spaces.
• Limitations: Increased system complexity, potential fabrication-induced disorder, increased optimization demand with the number of channels, and the need for calibration and drifts compensation must be addressed.

In summary, the multi-wavelength beam approach constitutes a unifying and enabling strategy across modern photonics, expanding device capabilities through spectral diversity, advanced optimization, and flexible device architectures (Hemayat et al., 2023, Li et al., 28 Jan 2024, Zhang et al., 2020, Marin-Palomo et al., 9 Sep 2025, Piłka et al., 2023, Tayebnaimi et al., 30 Nov 2025, Tayebnaimi et al., 2 Dec 2025, Vossgrag et al., 4 Feb 2025, Jammi et al., 14 Feb 2024, Shen et al., 2018, Li et al., 2011, Huang et al., 2012, Montz et al., 2019).