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Thin Optical Doubler

July 23, 2014

Harmonic generation is an undesirable feature of some electronic systems, such as audio amplifiers, but it's useful in other cases. In the early days of FM radio, frequency control of transmitters at their 100 MHz frequency was difficult. Quartz crystals, at that time the preeminent means of deriving a precise frequency, only had fundamental frequencies up to about 20 MHz. The solution was to force the crystal to resonate at a harmonic of its fundamental frequency.

If you need to operate at 90 MHz, the fifth harmonic of a crystal with a fundamental frequency of 18 MHz will get you there. The situation is somewhat more complicated, since a crystal's harmonics are not exact multiples of the fundamental, so the fundamental frequency is adjusted to compensate. Only odd harmonics can be excited, since only these wavelengths satisfy reflection symmetry at the crystal surface. Today, atomic clocks are substituting for many crystal oscillators.[1]

Synthetic BerliniteSynthetic Berlinite (AlPO4) crystals grown by hydrothermal synthesis.

This material is isostructural with quartz, and it has similar piezoelectric properties.

(Wikimedia Commons photo by the author.)

The harmonics of quartz crystals are generated mechanically by the crystals themselves, but there are ways to generate harmonics electronically through use of nonlinear devices. These nonlinear devices can be diodes or specially biased transistors, and one common use is in frequency doublers. Frequency doublers are useful components in radio frequency systems, allowing you to convert a stable, lower frequency into a stable signal at twice the frequency. A bandpass filter allows selection of the doubled frequency and rejection of the fundamental and other harmonics.

As I wrote in an earlier article (Second Harmonic Light Generation, September 30, 2011), this same frequency doubling trick can be done optically in media having an optical non-linearity. Nonlinear optical crystals will generate higher frequency (lower wavelength) harmonics of an intense light source, typically the output of a high-power laser.

These non-linear optical effects only occur at high light intensities, where the electric field component of the light is correspondingly high. That's why the first demonstration of optical frequency doubling, in 1961, was after the invention of the laser.[2] That was a doubling of the 694 nanometer (nm) emission of a ruby laser to 347 nm by a quartz crystal. A year later, optical frequency doubling was demonstrated in calcite.[3]

Quite a number of efficient optical doubling crystals have been found. These include lithium niobate (LiNbO3), lithium tantalate (LiTaO3), potassium titanyl phosphate (KTP, KTiOPO4), lithium triborate (LBO, LiB3O5) and β-barium borate (BBO, β-BaB2O4). However, these will only work when excited by intense laser light, and a long optical path length is generally required.

Now, a team of electrical engineers and physicists from the University of Texas at Austin (Austin, Texas) and the Technische Universität München (Garching, Germany) have advanced the technology of nonlinear optical materials with the result that even the low intensity light from a laser pointer could be doubled.[4-6]

They used the nonlinear response of intersubband electron transitions in multi-quantum-well semiconductor heterostructures. To do this, they needed to engineer a metamaterial that could use these modes, which are limited to light with electric field polarized normal to the semiconductor layers.[4] They were able to produce a nonlinear mirror of 400 nm thickness with a nonlinear electric susceptibility greater than 5 x 104 picometers per volt to frequency double normally-incident infrared light.[4]

The research team calls their device a "nonlinear mirror." This 400 nm thick mirror is about a million times more efficient as an optical frequency doubler on a thickness basis than conventional crystal doublers.[5-6] The heterostructure is about a hundred alternating nanoscale layers of indium gallium arsenide and aluminum indium arsenide, created using molecular beam epitaxy (see photo). There's a gold electrode at the bottom, and a pattern of gold nanostructures on top. The dimensions of the heterostructure and electrode pattern determine the operating frequency of the device.[5-6] The experimental device converts 8000 nm light to 4000 nm.[6]

Technische Universitaet Muenchen molecular beam epitaxy (MBE) systemOh, shiny!

Technische Universität München molecular beam epitaxy (MBE) system.

From my Tom Swift days, I've enjoyed seeing diagrams and photos of scientific instruments.

(Technische Universitaet Muenchen image.)[5]

Aside from the high conversion efficiency, the nonlinear mirrors are not subject to an important criterion for transmission optical frequency doublers; namely, the need to match the phase velocities of the primary and doubled waves.[5] Although this device is not quite capable of operation at visible light frequencies, it can be designed to work from near-infrared to terahertz frequencies. It will also function as a sum- and difference-frequency generation medium, and also as a means for four-wave mixing.[5]

Among the applications for such a device is the ability to detect terahertz radiation by mixing with an optical local oscillator to put it into the range of a more sensitive detector. The terahertz spectrum is of interest for many sensing and imaging applications, since such radiation is harmless to biological tissue, unlike X-rays.[5] Says study participant, Andrea Alù, an associate professor at the University of Texas at Austin,
"This work opens a new paradigm in nonlinear optics by exploiting the unique combination of exotic wave interaction in metamaterials and of quantum engineering in semiconductors."[6]
The research was funded by the National Science Foundation, the US Air Force Office of Scientific Research, the US Office of Naval Research, and the German Research Foundation.[5-6]

Representation of optical doublingRepresentation of optical doubling from a thin nonlinear mirror.

The pattern for the top electrode is seen in this image.

(University of Texas (Austin) image.)[6]


  1. Ytterbium Atomic Clock, This Blog, March 16, 2012.
  2. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett., vol. 7, no. 4 (August 15, 1961), pp. 118-119.
  3. 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.
  4. Jongwon Lee, Mykhailo Tymchenko, Christos Argyropoulos, Pai-Yen Chen, Feng Lu, Frederic Demmerle, Gerhard Boehm, Markus-Christian Amann, Andrea Alù, and Mikhail A. Belkin , "Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions," Nature, vol. 511, no. 7507 (July 3, 2014), pp. 65-69.
  5. Highly non-linear metamaterials for laser technology, Technische Universitaet Muenchen Press Release, July 2, 2014.
  6. Researchers Invent 'Meta Mirror' to Help Advance Nonlinear Optical Systems, University of Texas at Austin Press Release, July 2, 2014.

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