sum and difference frequency generation (original) (raw)

Acronyms: SFG, DFG

Definition: nonlinear processes generating beams with the sum or difference of the frequencies of the input beams

Category: article belongs to category nonlinear optics nonlinear optics

Related: frequency doublingfrequency triplingparametric amplificationparametric nonlinearitiesphase matchingmid-infrared laser sources

Page views in 12 months: 5716

DOI: 10.61835/5i3 Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

Content quality and neutrality are maintained according to our editorial policy.

📦 For purchasing sum and difference frequency generators, use the RP Photonics Buyer's Guide — an expert-curated directory for finding all relevant suppliers, which also offers advanced purchasing assistance.

Contents

What are Sum and Difference Frequency Generation?

Crystal materials lacking inversion symmetry can exhibit a so-called ($\chi^{(2)}$) nonlinearity. In such nonlinear crystal materials, sum frequency generation ({SFG=sum frequency generation}) or difference frequency generation ({DFG=difference frequency generation}) can occur, where two pump beams generate another beam with the sum or difference of the optical frequencies of the pump beams.

A sum frequency mixer is sometimes called a FASOR (Frequency Addition Source of Optical Radiation).

A special case is sum frequency generation with an original pump wave and a frequency-doubled part of it, effectively leading to frequency tripling. Such a cascaded process can be much more efficient than direct frequency tripling on the basis of a ($\chi^{(3)}$) nonlinearity.

Sum or difference frequency generation processes require phase matching to be efficient. Usually there is no simultaneous phase matching for both processes, so that only one of them can take place.

Typical Applications

Some typical applications of sum frequency generation are:

Difference frequency mixing with pump waves of similar frequency can lead to a mixing product with a long wavelength. Some examples are:

Such mid-infrared wavelengths are required, e.g., for the laser spectroscopy of gases.

Difference frequency generation can also be used for generating terahertz waves. For efficient terahertz wave generation, there are special semiconductor-based photomixers, where the terahertz beat note of two similar optical frequencies generates an oscillation of the carrier density in the semiconductor, which is translated into an oscillating current and then into terahertz radiation. That physical mechanism is substantially different from the common one based on a ($\chi^{(2)}$) nonlinearity.

Insight from a Photon Picture

Sum Frequency Generation

In a sum frequency mixer, both pump waves experience pump depletion when the signal becomes intense. For efficient conversion, the photon fluxes of both input pump waves should be similar. If one input wave has a lower photon flux, and its power is totally depleted somewhere in the crystal, there can be backconversion during subsequent propagation.

Difference Frequency Generation

In a difference frequency mixer, the lower-frequency wave is amplified rather than depleted. This is because photons of the beam with highest photon energy (shortest wavelength) are effectively split into two lower-frequency photons, thus adding optical power to both lower-frequency waves. The term parametric amplification emphasizes the aspect of amplification, and the difference frequency mixing product is then called the idler wave.

carrier–envelope Offset Frequencies

For operation with trains of ultrashort pulses, the carrier–envelope offset frequency (CEO frequency) of the output of a sum or difference frequency mixer is essentially the sum or difference, respectively, of those frequencies for the input. (The result may have to be corrected by subtracting the line spacing, which is identical to the pulse repetition rate, to get back to the interval from zero to the line spacing.)

It is interesting to consider what happens if difference frequency generation is applied to the low- and high-frequency components of a broadband frequency comb, which can be generated e.g. with a femtosecond laser, possibly followed by an optical fiber for supercontinuum generation. The CEO frequency of the output is then the difference between two identical frequencies, i.e., zero. This implies that the carrier–envelope offset phase is temporally constant. (In practice, it may still exhibit some drift, but only with a quite limited range.) This principle is realized in some devices for obtaining a more or less constant CEO phase without employing active stabilization methods.

Suppliers

Sponsored content: The RP Photonics Buyer's Guide contains 12 suppliers for sum and difference frequency generators. Among them:

HC Photonics

âš™ hardware

sum and difference frequency generators

HCP provides both commercial off-the-shelf (COTS) and custom-designed sum and difference frequency generators based on PPMgO:LN or PPMgO:LT crystals. These solutions support output wavelengths from 355 to 5000 nm, and are available as bare crystals or plug-and-play fiber-coupled mixers — for example, 633 nm output from 1064 nm + 1560 nm pumps.

Covesion

âš™ hardware

sum and difference frequency generators

Covesion’s MgO:PPLN free space and fiber coupled up- and down-conversion solutions offer exceptional conversion efficiency for generating visible and mid-IR wavelengths through sum and difference frequency generation.

We can offer a range of custom free space and fiber coupled solutions suitable for one-off orders to large-volume manufacture with customizable options including:

APE

âš™ hardware

sum and difference frequency generators

The APE HarmoniXX DFG is designed to extend APE’s product line of wavelength converters into the mid-IR range. It mixes signal and idler output beams of synchronously pumped OPOs and is available for various pump sources. The DFG output wavelength can be changed easily by tuning the OPO signal. It covers a wide wavelength range from 4 μm to >15 μm.

Bibliography

[1] M. Bass et al., “Optical mixing”, Phys. Rev. Lett. 8 (1), 18 (1962); doi:10.1103/PhysRevLett.8.18
[2] S. Guha and J. Falk, “The effects of focusing in the three-frequency parametric upconverter”, J. Appl. Phys. 51 (1), 50 (1980); doi:10.1063/1.327353
[3] X. Chen et al., “5.32 W ultraviolet laser generation at 266 nm using sum-frequency method with CsB3O5 crystal”, Opt. Express 31 (2), 802 (2023); doi:10.1364/OE.474095

(Suggest additional literature!)

Questions and Comments from Users

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.