Are there any limits to the frequencies for which laser frequency doubling (or multiplying) can be applied? For example, is it possible to convert a far infrared or microwave laser/maser to ultraviolet or x-ray by using multiple frequency doublers/multipliers in series?
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You don’t need multiple doublers. There’s a process called High Harmonic Generation that converts infrared to x-ray (coherently!). You may be interested in this answer https://physics.stackexchange.com/questions/432137/what-is-chirped-pulse-amplification-and-why-is-it-important-enough-to-warrant-a/432138#432138 – Superfast Jellyfish Jun 10 '20 at 12:39
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Frequency doubling is a pretty slow way to do that -- particularly when high-harmonic generation allows you to produce harmonics of order >100 and even >1000 (example) in a single step. – Emilio Pisanty Jun 10 '20 at 12:40
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In principle, no, there are no limits.
In particular, this type of daisy-chaining of frequency upconversion steps was extremely common for frequency metrology. This is because the key task of precision metrology is to provide an accurate measurement of the frequency at which some atomic transition emits, and this needs to be referenced to the definition of the SI second, which is in the MHz range of the microwave regime. For a long time, the only way this could be done was by a stage-by-stage translation of a microwave frequency standard up to whatever optical wavelength you wanted to use, and this is indeed possible, but it is, as they say, somewhat laborious.
Sample frequency upconversion chain, taken from
The measurement of optical frequencies. L Hollberg et al. Metrologia 42, S105 (2005); NIST eprint
which is probably a good starting reference if you really want to dig into the subject.
As I understand it, however, this process was made completely obsolete by the invention of the frequency comb, and is no longer in use.
That said, in the real world, there are always limits. One is that optical frequency upconversion is a nonlinear process and as such requires a lot of power at each stage for each stage to work, so you have an uphill battle to ensure that the (weak) output of each stage is strong enough (or suitably amplified) to reach the (high) power levels necessary for the next stage.
And more fundamentally, nonlinear optics is a hard thing to observe (let alone use productively) as you go into the higher ranges of the UV region, and there is a hard limit to the wavelengths at which nonlinear processes have been observed.
Emilio Pisanty
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