Nonlinear Frequency Conversion
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: the conversion of input light to light of other frequencies, using optical nonlinearities
More general term: nonlinear effects
More specific terms: frequency doubling, frequency tripling, frequency quadrupling, sum and difference frequency generation, optical rectification, supercontinuum generation, optical parametric oscillation and generation, stimulated Raman scattering, high harmonic generation
DOI: 10.61835/bbc Cite the article: BibTex plain textHTML Link to this page LinkedIn
Nonlinear frequency conversion means that an optical nonlinearity is utilized for converting part of the optical power of some input light to output light in a different wavelength region. This is often quasi-monochromatic light with a fixed wavelength or sometimes a tunable wavelength; in some cases, broadband light is generated. In almost all cases, the input light is provided in the form of a laser beam with a substantial optical intensity; only under such conditions, nonlinear frequency conversion processes can be highly efficient. The output is then also usually obtained in the form of a laser-like beam, i.e., with high spatial coherence.
Not all wavelength regions of interest are directly accessible with lasers. Therefore, it is common e.g. to generate visible or ultraviolet light by nonlinear conversion of near-infrared light from one or several lasers. Also, mid-infrared laser sources are often realized based on a near-infrared laser combined with some nonlinear frequency conversion apparatus.
Examples of nonlinear conversion processes are:
- frequency doubling and sum and difference frequency generation in crystals with a <$\chi^{(2)}$> nonlinearity
- parametric oscillation and amplification (also in nonlinear crystal materials)
- optical rectification for generating terahertz pulses from optical picosecond or femtosecond pulses
- Raman conversion in bulk crystals or in optical fibers, exploiting the delayed <$\chi^{(3)}$> nonlinear response (→ Raman lasers, Raman amplifiers)
- supercontinuum generation, e.g. in photonic crystal fibers, where a combination of different optical nonlinearities simultaneously contributes to the generation of a wide range of new frequency components
- high harmonic generation in gases, occurring at extremely high optical intensities of the order of 1014 W/cm2 or higher
Many but not all of these processes can be efficient only with phase matching and with polarized light. Laser radiation is usually linearly polarized, but some devices (e.g. certain high-power fiber lasers and amplifiers) are not well suited for nonlinear frequency conversion because they do not emit with a stable linear polarization state, or because they have insufficient spatial or temporal coherence.
Efficient Conversion at High Optical Intensities
As nonlinear frequency conversion can be efficient only at sufficiently high optical intensities, the intensities often have to be increased with one or several of the following methods:
- A pulsed (e.g. mode-locked or Q-switched) laser can have a peak power which is much higher than the average power. Still, the optical bandwidth may will be small enough for efficient phase matching.
- For single-frequency lasers and for mode-locked lasers, a resonant enhancement cavity can be used (→ resonant frequency doubling). This typically requires looking the laser frequency to the resonator with some kind of automatic feedback system.
- Nonlinear conversion can also be done inside a laser resonator (→ intracavity frequency doubling), exploiting the higher intracavity power.
- Another possibility is to increase the interaction length by using a waveguide (e.g. made of LiNbO3) or a fiber (the latter usually for <$\chi^{(3)}$> processes only). Particularly waveguides with small effective mode area can lead to high conversion efficiencies even with low optical powers.
Applicable intensities are often limited by the damage threshold of the nonlinear materials. There are situations where that limitation prevents highly efficient frequency conversion. An example is frequency doubling of ultrashort pulses into the ultraviolet spectral region, where the large group velocity mismatch limits the interaction length while the damage threshold is relatively low.
Design Issues

The design of nonlinear frequency conversion devices can involve subtle issues. For devices based on parametric nonlinearities, there can be beam quality effects due to spatial walk-off, gain guiding, pump depletion and backconversion. Such effects can be investigated with numerical computer models, which can simulate the evolution of the spatial (and possibly temporal) profiles of the interacting beams. Particularly for the conversion of ultrashort pulses, there is a wide range of phenomena which should be properly understood to avoid problems. Numerical simulations may be essential for optimizing the performance.
More to Learn
Encyclopedia articles:
- frequency doubling
- frequency tripling
- frequency quadrupling
- sum and difference frequency generation
- optical rectification
Blog articles:
- The Photonics Spotlight 2007-03-05: “More Efficient Frequency Doubling with Shorter Pulses?”
- The Photonics Spotlight 2007-09-21: “Optimum Crystal Length for Frequency Doubling”
Bibliography
[1] | G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams”, J. Appl. Phys. 39 (8), 3597 (1968); https://doi.org/10.1063/1.1656831 (a seminal work with a comprehensive quantitative discussion) |
[2] | R. L. Sutherland, Handbook of Nonlinear Optics, 2nd edn., Marcel Dekker, New York (2003) |
[3] | A. V. Smith, SNLO software for simulating nonlinear frequency conversion in crystals, free download, http://www.as-photonics.com/snlo, from AS-Photonics |
[4] | A. V. Smith, Crystal nonlinear optics with SNLO examples, ISBN 978-0-692-40044-9, https://as-photonics.com/products/crystal-nlo-book/ |
(Suggest additional literature!)

This encyclopedia is authored by Dr. Rüdiger Paschotta, the founder and executive of RP Photonics AG. How about a tailored training course from this distinguished expert at your location? Contact RP Photonics to find out how his technical consulting services (e.g. product designs, problem solving, independent evaluations, training) and software could become very valuable for your business!
Suppliers
The RP Photonics Buyer's Guide contains 31 suppliers for nonlinear frequency conversion equipment. Among them:
Shalom EO

Shalom EO offers a vast selection of nonlinear crystals, including BBO, KDP and KD*P, LBO, KTP, HGTR KTP, KTA, BIBO, LiIO3, LiNbO3, MgO:LiNbO3, RTP, ultra-thin BBO, LBO crystals and infrared nonlinear crystals ZnGeP2 (ZGP).
Our nonlinear crystals are excellent for applications ranging from frequency conversion to short-pulse generation. The NLO crystals offer reliable performance for harmonic generation (SHG, THG, 4HG, 5HG), sum and difference frequency generation (SFG, DFG), for optical parametric oscillators (OPOs) and optical parametric amplifiers (OPAs). Off-the-shelf and customized crystals are optional to our customers. Miscellaneous coating options including uncoated, AR, HR, HT, PR coatings, and custom coatings can be tailored. All the crystals will undergo rigorous inspection before dispatch.
GLOphotonics

Hollow-core fiber technology has enabled gas–light interactions with an unprecedented efficiency. Our frequency conversion and laser products take direct advantage of this feature, offering ‘multiple lasers in a single device’ in the form of CombLas – a highly versatile and stable Raman laser source which spans the UV-VIS spectral range. Combined with the device’s compact footprint, we obtain a highly-potent light source which perfectly suits the fields of gas spectroscopy and bio-imaging.
Femto Easy

The Nano4th is an ultra-compact device that converts your femtosecond low-energy IR laser pulses (nJ-range) into 2nd and 4th harmonics with best-in-class conversion efficiency. Its industrial-grade design makes it a robust and reliable solution that will extend the capabilities of your laser. The design is easily adaptable to higher pulse energies, up to the microjoule or millijoule level.
EKSMA OPTICS

EKSMA Optics offers a complete portfolio of nonlinear optical crystals: BBO, LBO, KTP, KDP, DKDP, LiIO3, LiNbO3, MgO:LiNbO3, AGS, AGSe, ZGP, GaSe, CdSe from stock or manufactured according to customers specifications or for specific applications.
NLIR

Our U2050 2–5 µm fiber to fiber wavelength conversion module converts mid-infrared 2–5 µm light to 695–877 nm light enabling the mid-infrared light to be measured with low noise near-visible detector technology.
APE

APE offers well engineered devices for nonlinear frequency conversion of picosecond and femtosecond pulses, including:
Also, we offer optical parametric oscillators and amplifiers. The accessible wavelength range spans from 190 nm up to 15 µm, with femtosecond or picosecond pulse durations.
RP Photonics
We offer advice on all aspects of nonlinear frequency conversion, e.g. the design of frequency conversion devices, choice of nonlinear materials, simulation of nonlinear conversion. Also: specialized in-house training courses, tailored to your needs.
TOPTICA Photonics

TOPTICA provides tunable continuous-wave laser systems including nonlinear frequency conversion for accessing the wavelength range from 190 nm to 4000 nm. The conversion processes are second-harmonic generation and optical parametric generation.
Covesion

MgO:PPLN provides a highly efficient and reliable solution of generating wavelengths and power levels not commercially available from standard laser diodes. Covesion poling technology and high-quality packaging designs provide a versatile basis for the design and manufacture of unique PPLN solutions with a range of customizable options including:
- free space or fiber coupled solutions
- multiple grating, chirped or fan-out designs
- tailored AR coatings
- custom grating apertures
- 2×1, 2×0, 1×1 or 1×0 fiber input/output configurations
- resistive or Peltier temperature control
- integrated or external temperature control
- broad coverage from 390 nm to 6000 nm
- power monitoring, control and output filtering
- compatibility with both CW and pulsed lasers
Radiantis

Radiantis offers second harmonic generators for MHz repetition-rate femtosecond and picosecond Ti:sapphire oscillators with conversion of efficiencies of 50%. The company also provides femtosecond SHG devices to double the 990 – 1550 nm range into the 495 – 775 nm range. Products are fully automated. Customised frequency doublers for other spectral ranges can also be developed.
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