6.4 Frequency converters: PPLN SHG, SFG, DFG

L1 Phenomenon

A periodically poled crystal flips its polarization every few microns so that light at one color keeps feeding light at twice the frequency instead of cancelling it. In a thin-film waveguide the light is squeezed into a cross-section about a micron wide; one such waveguide converted more than 80% of a 20 mW pump in a single pass reported.

SHG in a TFLN PPLN waveguide, phase matched, losslessnormalized η in %/W/cm²

ηL² 416.0 %/WP_2ω 1.576 mWconversion 7.9 %Λ (bulk) 18.99 µm

η_norm 2600 %/W/cm²

Length L 4.0 mm

Pump P_ω 20.0 mW

Pump λ1550 nm

Default η_norm 2,600 %/W/cm² reported; highest normalized TFLN waveguide value in the papers cited here 9,600 %/W/cm² reported (its 85% absolute conversion has no stated pump power; not plotted). Marker: > 80% at 20 mW reported. Laws derived; Λ = λ/(2(n_2ω − n_ω)) with bulk Zelmon n_e, 21 C P-db (waveguide periods are shorter). Above a few tens of mW the slope-2 line bends over: the pump is used up.

Conversion 7.9 %

Second-harmonic power: 1.576 mW
ηL²: 416.0 %/W
Poling period (bulk): 18.99 µm

Pump power 20.0 mW

Length 4.0 mm

Normalized efficiency 2600 %/W/cm²

Pump wavelength1550 nm

Above a few tens of mW the slope-2 line bends over: the pump is used up. Laws: undepleted P_2ω = ηL²P_ω², depleted P_ω tanh²(√(ηP_ω) L) derived. Domain stripes are drawn at the computed bulk period from Zelmon n_e, 21 C P-db (waveguide periods are shorter). Default efficiency 2,600 %/W/cm² reported; highest normalized TFLN waveguide value in the papers cited here 9,600 %/W/cm² reported (its 85% absolute conversion has no stated pump power; not plotted). Marker: > 80% at 20 mW reported.

L2 Conversion laws and devices

Undepleted: P_2w = η_norm L² P_w². Depleted (perfect phase matching, lossless): P_2w = P_w tanh²(√(η_norm P_w) L) derived.
QPM period for SHG: Λ = λ_w / (2 (n_2w - n_w)) with effective indices of the waveguide modes; bulk values from Sellmeier (chapter 02).
Consistency check derived: an overall efficiency near 10⁴ %/W (η L² = 100 W⁻¹) gives tanh²(√(100 × 0.020)) = 79% at 20 mW, matching "over 80% at 20 mW" reported.

Device	Value	Conditions	Source
PPLN nanowaveguide	2,600 %/W/cm²	1.5 µm pump, 4 µm period	reported
Adapted poling	near 10⁴ %/W overall, single pass; > 80% conversion at 20 mW	TFLN waveguide	reported
Double-layer, polarization-reversed	9,600 %/W/cm² measured; 85% absolute at high power	highest normalized TFLN waveguide value in the papers cited here (to 2026-10-24)	reported
Blue SHG	33,000 %/W/cm²	blue output	reported
Mid-IR DFG, LN on sapphire	200 %/W/cm², out to 3.66 µm		reported
z-cut PPLN microring	250,000 %/W; 15% absolute at 115 µW		reported
PPLN microring	5,000,000 %/W	d₃₃ via QPM	reported

Normalized waveguide efficiency (%/W/cm²) and resonant efficiency (%/W) are different quantities and are plotted on separate axes.

L3 What sets the efficiency

η_norm depends on the mode overlap, d_eff = (2/π) d₃₃ for 50% duty first-order QPM, and the absolute d₃₃ scale (Shoji et al. 1997 vs older values).
Thin-film thickness variation shifts the phase-matching wavelength along the device; adapted poling compensates measured local phase-matching variation reported.
Output power of TFLN SHG is commonly limited to tens of mW by optical damage (Kuznetsov, Li, Kippenberg, arXiv 2512.07968) reported.

Sources

9 cited in 6.4

Ref	Title	Link
Chen et al. 2023	Adapted poling to break the nonlinear efficiency limit in nanophotonic lithium niobate waveguides	doi:10.1038/s41565-023-01525-w
Kuznetsov et al. 2025	Watt-level second harmonic generation in periodically poled thin-film lithium tantalate	arxiv.org/abs/2512.07968
Li et al. 2024	Highly efficient second-harmonic generation in a double-layer thin-film lithium niobate waveguide	doi:10.1117/1.APN.3.6.066009
Lu et al. 2019	Periodically poled thin-film lithium niobate microring resonators with a second-harmonic generation efficiency of 250,000%/W	doi:10.1364/OPTICA.6.001455
Lu et al. 2020	Toward 1% single-photon anharmonicity with periodically poled lithium niobate microring resonators	doi:10.1364/OPTICA.403931
Mishra et al. 2021	Mid-infrared nonlinear optics in thin-film lithium niobate on sapphire	doi:10.1364/OPTICA.427428
Park et al. 2022	High-efficiency second harmonic generation of blue light on thin-film lithium niobate	doi:10.1364/OL.455046
Wang et al. 2018	Ultrahigh-efficiency wavelength conversion in nanophotonic periodically poled lithium niobate waveguides	doi:10.1364/OPTICA.5.001438
Zelmon et al. 1997	Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol% magnesium oxide –doped lithium niobate	doi:10.1364/JOSAB.14.003319