Nonlinear Frequency Conversion

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.

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
• The Photonics Spotlight 2007-09-21