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Resonant Light Conversion

December 14, 2011

I wrote about harmonic generation of light in a previous article (Second Harmonic Light Generation, September 30, 2011). Nonlinear optical crystals will generate higher frequency (lower wavelength) harmonics when excited with an intense light source, such as a pulsed, high power laser. Such nonlinear optical effects occur in these crystals because of the large electric field component of the light, about 108 V/m.

Such harmonic generation usually requires rather high intensity laser light, but useful harmonic power can be obtained at the second harmonic, and sometimes at the third harmonic. For example, you can get the 532 nm second harmonic of light from a neodymium-YAG (Nd:YAG) solid state laser emitting at 1.064 μm.

The amount of harmonic generation depends not just on the intensity of the excitation light, but also on the length of the optical path through the crystal, so you wouldn't think that such systems could be miniaturized. However, you would be discounting the ingenuity of optical physicists who have devised methods to circulate the light repeatedly in the same crystal.

One method to do this is analogous to the whispering galleries in architecture. These are elliptical domes built so that there are focus points at opposite sides of a room. Acoustic signals (e.g., "whispers") will be reflected from one focus point to another.

You can imagine a symmetrical dome under the floor of such a structure, so that a signal injected at one focus would circulate around the structure many times. Optical structures like this are easy to build using today's photolithographic techniques, so you can circulate a light wave many times in a structure.

Nature tries to disrupt your elegant device by introducing birefringence in crystals. To make a long story short, your attempts at making an efficient whispering gallery harmonic generator are thwarted by birefringence. Interested readers can research phase matching for the full story.

To counter birefringence, it's possible to "pole" ferroelectric crystals so that they have alternating regions of positive and negative birefringence, so that, on average, the birefringence cancels. By such periodic poling, you can make an optical whispering gallery that allows harmonic generation in a small device.

It's also possible to make your whispering mode structure resonant.[1] Resonance is a useful physical phenomenon, and I've mentioned it in several previous articles.[2-3] By forming a whispering gallery resonator, it's possible to produce harmonics of light using much lower input power than previously required. So low, in fact, that small semiconductor laser sources can be used. This is a huge advance in the state of the art in the generation of short wavelength light.

There have been several recent experimental studies of resonant whispering gallery harmonic generators.[4-7] One Japanese study used a periodically poled lithium niobate (LiNbO3) disk resonator to generate third harmonic light from a 1.55 μm laser source at high efficiency.[4] A multi-national team fabricated a similar lithium niobate whispering gallery resonator to generate the second harmonic of 1.064 μm light from a Nd:YAG laser with an efficiency of 9% at an input power of just 30 μW.[5-7]

A whispering gallery harmonic generator fabricated by a research team at the University of Michigan Department of Electrical Engineering and Computer Science has produced continuous second, third and fourth harmonic light from an inexpensive telecommunications laser light source.[8-10] Through use of variable crystal poling and and a resonator quality factor ("Q") of more than 107 they were able to generate the ultraviolet fourth-harmonic at input laser excitation as low as 200 mW.[OE]

University of Michigan UV resonator

In the University of Michigan experiment, a long wavelength infrared light source is coupled from an optical fiber by a gradient-index (GRIN) lens to a diamond prism to generate near-infrared, visible, and ultraviolet light. (Photo by Mona Jarrahi/University of Michigan).

The resonator disk needed to have a precise shape and extremely smooth surfaces to attain the high Q. The high Q is required, since the efficiency for fourth harmonic generation in harmonic generators is low, so many passes through the material are required.[9] The device was designed also for tunability, as explained by Mona Jarrahi, an assistant professor in the department:
"We optimized the structure to achieve high gain over a broad range of optical wavelengths... This allows us to make low-cost, wavelength-tunable ultraviolet sources using low IR power levels."[10]

The study authors write that the device would be a good ultraviolet light source for information storage, microscopy, and chemical analysis.[8,10] This research was funded by the National Science Foundation and the Air Force Office of Scientific Research.[9]


  1. V. B. Braginsky, M. L. Gorodetsky and V. S. Ilchenko, Phys. Lett. vol. A 137, no. 7-8 (29 May 29, 1989), pp. 393-397.
  2. This Blog, "Screech!" November 17, 2011.
  3. This Blog, "MEMS Resonator Logic Gate," April 4, 2011.
  4. Kiyotaka Sasagawa and Masahiro Tsuchiya, "Highly Efficient Third Harmonic Generation in a Periodically Poled MgO:LiNbO3 Disk Resonator," Appl. Phys. Express, vol. 2 (December 11, 2009), Document No. 122401.
  5. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt and G. Leuchs, "Naturally-phasematched second harmonic generation in a whispering gallery mode resonator," Phys. Rev. Lett. vol. 104, no. 25 (April 16, 2010), Document No. 153901 (4 pages).
  6. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt and G. Leuchs, "Naturally-phasematched second harmonic generation in a whispering gallery mode resonator," arXiv Preprint Server, September 9, 2010.
  7. Tobias J. Kippenberg, "Viewpoint: Second-harmonic generation in microresonators through natural phase matching," Physics (American Physical Society), vol. 3, no. 32 April 12, 2010.
  8. Jeremy Moore, Matthew Tomes, Tal Carmon and Mona Jarrahi, "Continuous-wave ultraviolet emission through fourth-harmonic generation in a whispering-gallery resonator," Opt. Express vol. 19, no. 24 (November 21, 2011) pp. 24139-24146.
  9. Nicole Casal Moore, "A smarter way to make ultraviolet light beams," University of Michigan Press Release, November 29, 2011.
  10. By John Wallace, "Whispering-gallery resonator generates CW fourth-harmonic UV light," Laser Focus World, November 30, 2011.

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Linked Keywords: Nonlinear optics; crystal; frequency; wavelength; harmonic; pulsed, high power laser; nonlinear optical; electric field; Poynting vector; second harmonic; third harmonic; neodymium-YAG; solid state laser; micrometer; μm; intensity; optical path; optical physicist; whispering gallery; elliptical; focus point; acoustic signal; symmetry; symmetrical; photolithographic; Nature; birefringence; phase matching; periodic poling; resonance; resonant; semiconductor laser; Japanese; lithium niobate; energy conversion efficiency; University of Michigan; Department of Electrical Engineering and Computer Science; telecommunications; quality factor; gradient-index; lens; diamond; prism; Mona Jarrahi; assistant professor; information storage; fluorescence microscope; microscopy; analytical chemistry; chemical analysis; National Science Foundation; Air Force Office of Scientific Research.