Generation of optical harmonics

Raphael Bouskila

Overview

First experimental observation of optical SHG

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Background

Laser (“optical maser”) invented by Maiman Active region: ruby crystal Pumping: 550 nm optical Output: 694.3 nm pulse

Maiman, T.H. “Stimulated Optical Radiation in Ruby,” Nature, 187 4736, 493-494 (1960).

Nonlinear nature of dielectric media known since Pockels (1890s)

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http://www.llnl.gov/nif/library/aboutlasers/how.html

Theory Nonlinear (“harmonic”) polarization

is induced along vector of E-field (perpendicular to direction of propagation)

Magnitude depends on propagation direction relative to crystal symmetry axes

For quartz crystal (rhombohedral class 32): Along x-axis: zero Along y-axis: Pr

2 = α2Ex4

Along z-axis: Pr2 = α2Er

4

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Trapezohedral (rhombohedral #32) crystal http://www.johnbetts-fineminerals.com/jhbnyc/diamdiag.htm

Quartz crystal http://en.wikipedia.org/wiki/Image:Kwarc_z_kalcytem.jpg

Experiment

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Source: Ruby laser ω1 = 694.3 nm (visible red light)

Nonlinear medium: crystalline quartz Non-centrosymmetric crystal nonzero Pockels

coefficient r = 5 x 10-13 m/V

Output ω2 = 347.2 nm (visible blue light)

Experiment

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Results

Really small, but there?

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Harmonic Fundamental

(Scale in hundreds of angstroms)

Results

Amount of SHG: ~1011 photons Output pulse energy: 5.7 x 1011 J Input pulse energy: 3 J Conversion efficiency: 1.9 x 10-6 %

Modern SHG conversion efficiency: up to 82% R. Paschotta et al., "82% efficient continuous-wave frequency

doubling of 1.06 μm with a monolithic MgO:LiNbO3 resonator", Opt. Lett. 19 (17), 1325 (1994)

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Limitations

Amount of SHG intensity: v: “volume of coherence”; ~ 10-11 cm3

“Second harmonic intensities as high as a fraction of a percent could be achieved”

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Limitations

Note that the experiment is only quasi-phase matched Degree of mismatch:

Δn = (5 x 10-13 m/V) (107 V/m)=5 x 10-6

Wave mixing coherence length: LC = = 6.943 cm

Negligible in comparison with laser coherence length (~ 1 mm)

Not to be confused with wave mixing coherence length!

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n∆20λ

Limitations

Concept of phase matching as yet unknown The quartz crystal used happens to be quasi-

phase matched at the frequencies used Phase matching theory predicted soon after

J. A. Giordmane, “Mixing of light beams in crystals,” Phys. Rev. Lett. 8 1, 19-21 (1962).

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Limitations

Coherence length of ruby laser (~1 mm) Primary limitation on this experiment Effect of low laser coherence length: fundamental

and harmonic fall out of phase very quickly Similar to phase mismatch but due to source

instead of medium

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Limitations

The authors predict:

Coherence length of ruby laser: ~ 1 mm Coherence length of gas laser: ~ 20 cm

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Limitations

Subsequent work on gas lasers: N.I. Adams, P.B. Schoefer, “Continuous optical harmonic

generation,” Appl. Phys. Lett. 3, 19-21 (1963) S.L. McCall, L.W. Davis, “Observation of continuous-wave

optical harmonics,” J. Appl. Phys. 34, 2921 (1963) A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical

second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).

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Conclusion

Very influential paper! Some limitations Somewhat archaic terminology and focus

“optical maser” rather than “laser” Focus on coherence rather than phase matching

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Conclusion

Really small, but not there!

Copy editor at PRL thought the SHG mark was a speck of dirt and erased it!

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HarmonicFundamental

(Scale in hundreds of angstroms)