Simple Explanation of Second Harmonic Generation

I realize that SHG is just frequency doubling, but how?

Specifically, I've been told by my professor that when two beams meet at a pinhole in our optics setup and are in phase, that we will be able to see blue light? Is this due to wavelength?

Points for keeping the explanation simple.

Not too sure, but I have a feeling that this would be due to harmonic excitation of the material, rather then the properties of light. I know superposition of waves increases amplitude (intensity), but I do not understand how that could cause a shift in wavelength, other then for the reason I just mentioned. In any case the effect would be shifting the wavelength to the shorter wavelengths (assuming your information is correct) and thus pushing it into the blue section of the spectrum. Like wise if the waves were perfectly out of phase, it would do the opposite and shift to the red side of the spectrum (again assuming your information is correct).

Hopefully some one can fill in the blanks.... -Adrian

A point of clarity. Our laser will be at around 800nm wavelength. This beam will be split into a main beam and a probing beam, that will then converge at this pinhole. This will result in blue light... somehow?

To explain the full SHG process is not a simple affair, but the following link explains things about as simply as possible:

Encyclopedia of Laser Physics and Technology - frequency doubling, frequency-doubled laser, second-harmonic generation, SHG, design, physical mechanism, pulses

But basically two photons with lower energy are combined to form one photon with twice as much energy, and thus twice the frequency.. but the process is quite a bit more complex in reality and has little to do with the photons themselves, instead it has to do with incoming waves and their frequencies.

ok... I'm obviously wrong.... ohh well gave it a shot

I doubt there is any sort of simple explanation.

First, you should look at how light travels through a medium: Something with a refractive index higher than vacuum interacts with light, which "causes" it to travel slower through such a medium. This interaction is between the incoming photon and the electrons in the material, and normally only results in the light travelling slower in the medium than it would trough free space.

In some materials, it is possible for 2 photons (of equal energy and phase) to interact with an electron at the same time, resulting in absorption of the photon and re-emission of a photon at double energy.

With other materials the reverse is also possible, but that would probably be to far to get into, and i'm not sure how much practical application it has.

... and this is as simple as i can put it, the actual physics involved are far from easy to understand

Simply responding to your question about 2 beams at a pinhole: No, two 800nm beams meeting at a pinhole will not give you 400nm light.

Second harmonic generation happens inside a nonlinear crystal, and it is the crystal's interaction with the light that generates the second harmonic.

Indeed, as far as i know free space doesnt allow frequency doubling using slits, pinpoints and such.

In air, this might be different because that does break down at a certain field gradient, usually resulting in a sprak rather than any doubling effect.

BTW it's worth noting that you can't increase the amplitude of a photon without increasing the frequency. That's why it works, instead of just giving you a more powerful 800nm photon.

I'd rather say 'energy' than 'amplitude' there... if its about light, amplitude would probably refer to intensity, or the number of photons (per unit of time).

Benm said:

I'd rather say 'energy' than 'amplitude' there... if its about light, amplitude would probably refer to intensity, or the number of photons (per unit of time).

Click to expand...

That's a good point, when talking about light people usually use amplitude and intensity to refer to the same thing, because very rarely would you need to discuss the amplitude of a photon did you know that the first speedometers worked by shooting a helium laser at a very precise frequency at a moving car, and the energy of the impact with the car changed the reflected frequency enough to measure speed? Now they use interferometry, but I thought that was cool.

I suppose you mean they used doppler lidar to calculate the speed? Guess that would work fine as long as you can measure the reflected wavelength very precisely, since the shift would be that great... a speeding car is pretty slow compared to light speed