Tunable Second Harmonic Generation

Updated 19 November 2025

Tunable SHG is a nonlinear optical process controlled by external parameters like electric fields, strain, and temperature to dynamically double optical frequencies.
It leverages material symmetry breaking, resonant mode engineering, and quasi-phase-matching to significantly enhance conversion efficiency and spectral tunability.
Applications include integrated photonic devices, quantum frequency converters, and nonlinear sensors, enabling active optical switching and signal modulation.

Tunable second harmonic generation (SHG) activity refers to the ability to control, modulate, or dynamically enhance the frequency-doubling nonlinear optical response of a physical system via external parameters such as electric fields, chemical potential, mechanical strain, geometrical design, temperature, or photonic environment. Tunability applies to the amplitude, spectral position, efficiency, directionality, and polarization properties of the SHG process. SHG is governed by the second-order nonlinear susceptibility tensor, χ², and is constrained by the symmetry and electronic properties of the underlying material or structure. The realization of tunable SHG is central to active nonlinear nanophotonics, integrated photonic devices, ultrafast optical switching, frequency metrology, and emerging directions in topological and quantum nonlinear optics.

1. Fundamental Mechanisms and Theoretical Background

In its general form, the nonlinear polarization responsible for second harmonic generation is

$P_i(2\omega) = \varepsilon_0 \sum_{jk} \chi_{ijk}^{(2)}(2\omega; \omega, \omega)\, E_j(\omega)\, E_k(\omega)$

where χ² is the material’s or heterostructure’s second-order nonlinear susceptibility tensor. SHG is symmetry-forbidden in centrosymmetric media (χ²=0) but can arise due to intrinsic crystal symmetry breaking, surface or interface effects, or external inversion-symmetry breaking fields.

Tunable SHG exploits the following key mechanisms:

Electro-optic (Field-Induced) Tuning: Application of a static electric field, which breaks inversion symmetry, leading to electric-field-induced SHG (EFISH) with χ²_eff ∝ χ³·E_DC, applicable to materials as diverse as centrosymmetric bulk semiconductors, van der Waals layered systems, and polymers (Fan et al., 12 Jul 2025, Grillo et al., 10 Oct 2024).
Carrier Doping/Exciton Charging: Electrostatic gating or chemical doping in low-dimensional semiconductors modulates the oscillator strength and transition energies, significantly altering χ² near resonances. In monolayer WSe₂, tuning between exciton and trion transitions enables ∼10× SHG modulation at low temperature (Seyler et al., 2015).
Resonance and Mode Engineering: Structural engineering, including slab thickness, grating spacing, nanoparticle radius, and photonic crystal perturbation, enables alignment of fundamental and SH frequencies to high-Q optical or plasmonic resonances. Modal overlap and dual-resonant geometries provide orders-of-magnitude SHG enhancement and flexible wavelength tunability (You et al., 2020, Ma et al., 2020, Qiu et al., 13 Apr 2025, Marino et al., 2015).
Thermo-Optic Control: Tuning the refractive index via temperature or the exploitation of large material thermo-optic coefficients (e.g. in lithium niobate waveguides) results in continuous, reversible phase-matching control and spectral shifts of SHG peaks (Luo et al., 2018, Chen et al., 2020, Yu et al., 6 May 2025).
Mechanical Strain or Stretching: Application of uniaxial strain—or variable nanowire array spacing—modifies the photonic bandstructure or geometric resonance, shifting SHG spectral response and quantum geometric contributions to χ² (Lou et al., 28 Jan 2025, Saerens et al., 2022).
Phase-Change and Material State: Switching of material state (e.g. amorphous-crystalline phase in GST) underneath a nonlinear nanoantenna modulates the local refractive index environment and resonance frequency, enabling nonvolatile, multi-level SHG switching (Liu et al., 2021).
Optically Written χ² via Photogalvanic Gratings: In Si₃N₄ microresonators, the photogalvanic effect enables spatially periodic internal DC fields and thus a self-organized effective χ² grating, allowing for all-optical quasi-phase-matching and wavelength agility (Yuan et al., 24 Apr 2025).

2. Electrical, Electrostatic, and Field-Induced Tunability

Gate-controlled SHG in atomically thin 2D materials has established electrical field or chemical potential as a powerful tuning handle for nonlinear response. In monolayer WSe₂, the SHG at the A-exciton resonance is tunable by a factor of >10 (cryogenic) to ~4 (room-T) via electrostatic FET gating, by shifting oscillator strength between neutral exciton and charged trion transitions—modelled using gate-dependent oscillator fractions in χ² (Seyler et al., 2015). In atomically thin ReS₂, ReS₂ FETs enable the induction of SHG in otherwise centrosymmetric odd-layer structures, with electrical on/off contrast ≥10×, and continuous enhancement in noncentrosymmetric even layers (Wang et al., 2022).

In the EFISH paradigm, the external DC field E_DC yields an effective χ² via the dominant cubic nonlinearity χ³ operating as χ²_eff = 3 χ³ E_DC. Large electrical modulation depths and reversibility have been realized in bulk semiconductors, nanowires, ferroelectric thin films, and van der Waals heterostructures (Fan et al., 12 Jul 2025), with modulation depths up to 30,000% V⁻¹ (monolayer MoTe₂) and enhancement factors of 40–60× (WS₂, MoS₂ bilayers) (Grillo et al., 10 Oct 2024). In black phosphorene, gate fields E_dc≥10⁷ V/m induce |χ²|≈10³ pm/V along the armchair axis, surpassing bulk reference crystals, with a systematic blue-shift of the SHG peak and the capacity for semiconductor–semimetal transition in bilayers (Meng et al., 9 Oct 2025).

3. Resonant and Geometric Engineering for Broadband Tunability

Metasurface and photonic crystal designs offer highly versatile platforms to modulate and enhance SHG through engineering of resonant conditions and mode overlap:

Graphene–Insulator–Graphene (GIG) Metasurface: Dual-resonant field enhancement at both ω₀ and 2ω₀ is established by independent Fermi-level gating of two graphene nanoribbon gratings, yielding SHG enhancements up to ~10⁶× and ~20 THz spectral tuning range. On-the-fly switching between SHG and THG is achieved by modulating the Fermi energy on the top grating (You et al., 2020).
All-dielectric Photonic Crystals: By opening topological valley gaps at ω₀ and 2ω₀ in honeycomb photonic crystals and engineering the interface to support dual kink modes, bi-directional, phase-matched, and directionally flexible SHG is realized. The directionality and magnitude are controlled by geometric and symmetry parameters, with observed SHG directional dichroism (SHG-DD) up to 0.97 (Lan et al., 2020).
Bound-State-in-Continuum (BIC) Metasurfaces: In lithium niobate metasurfaces, Brillouin-zone-folding induced quasi-BICs yield Q-factors >10⁴, and the narrow linewidth enables electrical switching of SHG output with >99% modulation depth under modest driving voltages (ΔV_pp~12 V). Tuning is mediated by the Pockels effect shifting the resonance by ~1 nm per 10 V (Qiu et al., 13 Apr 2025).
Phase-Change Integrated Antennas: GST under AlGaAs nanoantennas provides large, reversible refractive-index modulation, shifting local Mie-type resonances by ~20 nm and enabling >500% modulation in SHG conversion efficiency. Multi-level, non-volatile SHG tuning is available by partial crystallinity control (Liu et al., 2021).

4. Phase-Matching, Dispersion, and Thermal Tuning

Integrated nonlinear photonic devices leverage temperature, geometry, and periodic poling to dynamically phase-match the fundamental and second-harmonic fields:

Lithium Niobate and Tantalate Nanowaveguides: Z-cut LNOI and TFLT waveguides with precise dispersion engineering achieve type-I or type-0 quasi-phase-matching with normalized conversion efficiencies up to 1900%/W/cm² (LNOI) and 229%/W/cm² (TFLT), tunable by thermal control (–1.71 nm/K LNOI, –0.44 nm/°C TFLT) over 50–60 nm wavelength ranges (Luo et al., 2018, Chen et al., 2020, Yu et al., 6 May 2025).
All-Optical QPM in Si₃N₄ Microresonators: The photogalvanic effect enables optical writing of χ² gratings, yielding reconfigurable quasi-phase-matching and continuous spectral tuning within a ~2.6 nm range in the green, with conversion efficiencies up to 250%/W, limited by the dynamic formation and erasure of space-charge gratings (Yuan et al., 24 Apr 2025).
Mie-Resonant and Periodic Nanostructures: In metasurface and nanoparticle systems, the spectral position of SHG is tuned by geometric control of resonator size, spacing, and lattice constant, as in size-focused LiTaO₃ nanoparticles (200–500 nm, SHG at 400–500 nm) (Ali et al., 10 Sep 2024).

5. Strain, Mechanical, and Quantum-Geometric Tunability

Uniaxial strain and elastomeric stretching modulate both electronic and photonic degrees of freedom to tune SHG:

2D Quantum Geometry: In Bi₂O₂X (X=S, Se, Te), first-principles theory shows that strain controls inversion symmetry and bandgap, while SHG is dominated by gauge-invariant quantum metric and shift-vector contributions. Tensile strain up to 6% enhances |χ²| to ~1 nm/V and induces semiconductor–half metal–polar metal transitions, yielding correlated SHG and topological state control (Lou et al., 28 Jan 2025).
Stretchable Nanowire Arrays: GaAs nanowire arrays in PDMS, under uniaxial stretch (up to 30%), display a factor of two intensity tuning in experiment—and up to three orders predicted—arising from shifting high-Q lattice–Mie resonances. The SHG intensity is primarily tuned by geometry-induced photonic band modifications, not bulk χ² shifts (Saerens et al., 2022).

Unlike classical phase-matched bulk crystals, nanostructured and metamaterial platforms often achieve SHG tunability via modal engineering and overlap:

Hyperbolic Plasmonic Metamaterials: Broadband enhancement (up to 100×) of SHG, relative to smooth gold films, is realized via double-resonant modal overlap in anisotropic nanorod matrices. Tuning is achieved by adjusting nanorod aspect ratio, filling fraction, grating period, or incidence angle, which collectively modulate hyperbolic–elliptic transitions and field enhancement at ω and 2ω (Marino et al., 2015).
Surface Phonon Polaritons: Critically coupled surface phonon polaritons at the SiC–air interface, adjusted via prism–gap distance, yield strong field enhancement and tunable SHG in the mid-IR (8.3–11.4 µm), with spectral Q up to ~100 and full control over bandwidth and out-coupling (Passler et al., 2017).

7. Outlook and Applications

Tunable SHG activity enables multifunctional and reconfigurable devices across spectral regimes:

Integrated Frequency Doublers and Quantum Sources: On-chip devices span telecom, visible, and THz, supporting applications such as quantum frequency conversion, ultrastable clocks, and quantum light generation (Chen et al., 2020, Yuan et al., 24 Apr 2025, Luo et al., 2018).
Programmable and Nonlinear Pixel Arrays: Electrically contacted 2D flakes or metasurfaces allow spatial ‘on/off’ SHG logic, frequency-converting pixels, and active beam shaping (Wang et al., 2022, Qiu et al., 13 Apr 2025).
Sensitive Probing and Nonlinear Sensing: Electric-field-induced SHG serves as a direct probe of symmetry breaking, ultrafast dynamics, and carrier transport, with femtosecond temporal and nanoscale spatial resolution (Fan et al., 12 Jul 2025).
Topological and Directional Nonlinear Optics: Valley-Hall kink-mode SHG offers defect-immune frequency conversion and giant, electrically switchable directional dichroism for applications in chiral sensing (Lan et al., 2020).
Material and Mechanism Diversity: The field now spans continuous chemical, thermal, electric, mechanical, and optical tuning mechanisms in both naturally nonlinear and induced-nonlinear (EFISH) hosts, with extension to emerging polar metals, polaritonics, and phase-change platforms.

The full exploitation of tunable SHG requires precise control over symmetry, resonance, field overlap, and phase-matching—divided between active (electrical, optical, or mechanical control) and passive (geometry, material state) strategies. Cross-platform approaches, including hybrid integration, high-Q resonator engineering, and quantum-geometric design, are actively pursued for next-generation nonlinear photonic systems (Yu et al., 6 May 2025, Grillo et al., 10 Oct 2024, Lou et al., 28 Jan 2025).