Second Harmonic Light Generation

September 30, 2011

Since I once worked with laser materials, it was only natural that I would be seduced by the peripheral materials that abound in laser systems.[1] One such class of materials is nonlinear optical crystals that are used to generate higher frequency (lower wavelength) harmonics of a laser line. Nonlinear optical effects occur when these crystals are excited by the intense electric field component of pulsed, high power laser light, about 10⁸ V/m.

Neodymium-YAG (Nd:YAG) is a common solid state laser, but its emission line at 1.064 μm is too far in the infrared for some applications. Directing light from this laser through a nonlinear optical crystal will generate the second harmonic of 1.064 μm, which is 532 nm, or green light.

A 5 mm diameter Nd:YAG laser rod. Laser rods such as this are core drilled from large diameter crystal boules. Neodymium-doped YAG crystal boules are routinely grown at three inches in diameter and up to a foot in length. (Via Wikimedia Commons).

Materials with exceptionally high nonlinear coefficients are lithium niobate (LiNbO₃), lithium tantalate (LiTaO₃), potassium titanyl phosphate (KTP, KTiOPO₄), lithium triborate (LBO, LiB₃O₅) and β-barium borate (BBO, β-BaB₂O₄).

There are quite stringent requirements on the crystalline quality of the nonlinear material. After all, you're blasting these directly with a high-power laser. Defects in the crystal, such as bubbles and inclusions, will cause areas of localized thermal stress that are sometimes large enough to shatter the crystal. It's good that laser jocks wear protective eye wear.

Instead of having a laser pulse produce a sufficiently high electric field for nonlinear effects, you can apply an electric field directly to the material. Very soon after second harmonic generation was demonstrated in laser systems, it was found that application of an electric field to calcite results in frequency doubling of light.[2] This effect is called electric-field-induced second harmonic generation (EFISH).

Gallium nitride is an EFISH material. When this semiconductor is made into a diode, the depletion region in the reverse-biased state is very narrow. This leads to high electric field strengths, of the order of 10⁸ V/m, and large second harmonic generation. [3]

A conceptually simple way to increase field strength is through the use of nanotechnology to shrink the gap between electrodes to a very small dimension. Ten volts applied across a 100 nanometer gap yields an electric field strength in the gap of 10⁸ V/m. This is the tactic used by a group of materials scientists from Stanford University to produce a device that allows modulation of second harmonic generation.[4-5] The group is led by Mark L Brongersma, Associate Professor of Materials Science and Engineering.

The device, as shown in the figure, uses a plasmonic effect to enhance the second harmonic generation. Plasmons are quasiparticles formed by the free electrons in a metal. The grating on the electrodes acts as an antenna that directs plasmonic waves toward the slit. The slit contains a nonlinear optical material, in this case, Poly(methyl methacrylate) (PMMA). This plasmonic grating amplifies the second harmonic generation by a factor of eighty.[4]

A nanoscale plasmomic electric-field-induced second harmonic generator. Two gold electrodes carry the modulating voltage to a second harmonic generator in a thin slit. (Stanford University image by Mark Brongersma).

In their experiments, the Stanford team demonstrated voltage-dependent second harmonic generation with a normalized magnitude of about 7% per volt for light from a 1.56 micrometer wavelength femtosecond fiber laser.[5]

Acknowledgement:

Thanks to Wenshan Cai of Stanford University for providing information for this article.

References:

1. D.M. Gualtieri, B.H.T. Chai and M.H. Randles, Growth of Beta-Barium Borate from NaCl-Na₂O Solutions, J. Crystal Growth 97, 613-616 (1989).
2. R. W. Terhune, P. D. Maker, C. M. Savage, "Optical Harmonic Generation in Calcite," Phys. Rev. Lett., vol. 8, no. 10 (May 15, 1962), pp. 404-406.
3. Kristen A. Peterson and Daniel J. Kane, "Electric-field-induced second-harmonic generation in GaN devices," Optics Letters, vol. 26, no. 7 (April 1, 2001), pp. 438-440.
4. Andrew Myers, "Plasmonics Intensifies a Novel Nanoscale Light Source," Stanford School Of Engineering Press Release, September 22, 2011.
5. Wenshan Cai, Alok P. Vasudev and Mark L. Brongersma, "Electrically Controlled Nonlinear Generation of Light with Plasmonics," Science, vol. 333, no. 6050 (September 23, 2011), pp. 1720-1723.
6. Mark Brongersma's Laboratory at Stanford University.