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Nonlinear Frequency Conversion

Definition: the conversion of input light to light of other frequencies, using optical nonlinearities

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

German: nichtlineare Frequenzkonversion

Category: nonlinear optics

Author: Dr. Rüdiger Paschotta

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URL: https://www.rp-photonics.com/nonlinear_frequency_conversion.html

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 in order to avoid problems. Numerical simulations may be essential for optimizing the performance.

Suppliers

The RP Photonics Buyer's Guide contains 30 suppliers for nonlinear frequency conversion equipment. Among them:

Stuttgart Instruments

The Stuttgart Instruments Alpha is an ultrafast and fully wavelength-tunable frequency conversion system in an ultra-compact and completely passively stable system based on revolutionary parametric oscillator design which guarantees outstanding stability, reproducibility and shot-noise limited performance.

The revolutionary design of Stuttgart Instruments Alpha, characterized by outstanding low noise and passive long-term stability, is based on the fiber-feedback optical parametric oscillator (FFOPO) technology and results in outstanding performance and high flexibility at the same time.

The Alpha covers a gap-free rapid tunable spectral range from 700 nm to 20 µm wavelengths, while maintaining high output power up to the Watt-level with femto- or picosecond pulses at several MHz pulse repetition rates. It provides multiple simultaneously tunable outputs with a selectable bandwidth from a few to 100 cm⁻¹. Shot-noise limited performance above 300 kHz, passive spectral stability (< 0.02 % rms) and wavelength-independent stable beam pointing (< 30 µrad) enable excellent sensitivity. In addition, each Alpha is equipped with a user-friendly ethernet and Wi-Fi interface and a matching graphical user interface (GUI) as well as easy to access API interfaces for e.g. LabView, Phyton, C++.

Typically, the Alpha is pumped by an ultra-low-noise Primus pump laser, which provides more than 8 W average output power at 1040 nm wavelength and 450 fs pulse duration at 42 MHz repetition rate. In addition, the Alpha can be operated with other pump lasers around 1 µm wavelength and enough power.

Due to our modular platform, the Alpha can be adapted and optimized for various applications and is particularly suited for spectroscopic applications requiring a robust and reliable tunable radiation with low noise.

Kapteyn-Murnane Laboratories

XUUS upconverts ultrafast laser pulses into the Extreme UV (EUV or XUV) or soft X-ray regions of the spectrum. Employing high harmonic generation processes, the output beam inherits the coherent properties of a driving laser such as the KMLabs RAEA with wavelengths that can be tuned from 10 nm to 47 nm. Moreover, customized systems can generate coherent beams with wavelengths as short as 6.5 nm. XUUS employs KMLabs' patented hollow waveguide for the high harmonic upconversion process.

The XUUS hollow-core fiber, or waveguide, architecture enables harmonics generated by the system to be distinguished from other HHG methods, guaranteeing your harmonics originate from the same point in space every time, minimizing any pointing drift. This optimizes repeatability for your experiments. Additionally, the use of a fiber rather than typical gas jet or semi-infinite gas cell target geometries provides superior pressure tunability for phase-matched HHG.

Bibliography

[1]	G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams”, J. Appl. Phys. 39 (8), 3597 (1968), DOI: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/

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!

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