Second harmonic generation
; also called frequency doubling
) is a nonlinear optical
process, in which photons
interacting with a nonlinear material are effectively "combined" to form new photons with twice the energy, and therefore twice the frequency
and half the wavelength
of the initial photons.
Second harmonic generation was first demonstrated by P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich at the University of Michigan, Ann Arbor, in 1961. The demonstration was made possible by the invention of the laser, which created the required high intensity monochromatic light. They focused a ruby laser with a wavelength of 694 nm into a quartz sample. They sent the output light through a spectrometer, recording the spectrum on photographic paper, which indicated the production of light at 347 nm. Famously, when published in the journal Physical Review Letters (citation below), the copy-editor mistook the dim spot (at 347 nm) on the photographic paper as a speck of dirt and removed it from the publication.
In recent years, SHG has been extended to biological applications. Researchers Leslie Loew and Paul Campagnola at the University of Connecticut have applied SHG to imaging of molecules that are intrinsically second-harmonic-active in live cells, such as collagen, while Joshua Salafsky is pioneering the technique's use for studying biological molecules by labeling them with second-harmonic-active tags, in particular as a means to detect conformational change at any site and in real time. SH-active unnatural amino acids can also be used as probes.
Derivation of Second Harmonic Generation
The simplest case for analysis of second harmonic generation is a plane wave of amplitude
traveling in a nonlinear medium in the direction of its
vector. A polarization is generated at the second harmonic frequency
where .The wave equation at (assuming negligible loss and asserting the slowly varying envelope approximation) is
At low conversion efficiency (