Spectroscopy: What Do I See When I Combine Red & Green Beams?

[MaWM]

I have two monochromatic beams, one green, one red. I combine the beams together and get a single yellow beam. I pass the yellow beam through a spectroscope and determine its spectrum. What do I see?

A red band and a green band? A yellow band?

I suspect that what I'd see is: A green band, a red band, a yellow band, a very low frequency band that is a carrier for the yellow, and other weaker bands that represent higher harmonics of the red+green combination. Can anyone confirm this?

By the way, the low frequency carrier that I am suspecting will appear comes from the sum-to-product trig identity. http://en.wikipedia.org/wiki/List_of_trigonometric_identities" The sum of the green and red cause a product of a yellow and a low frequency envelope.

 

[AlephZero]

If your spectroscope is a linear system (which it should be!) then you will just get two lines, red and green.

The only way you can get anything else is if something in the system has a nonlinear response. For a nonlinear system, an input (A sin w1 t + B sin w2 t) can produce output including terms like (C sin w1 t + D sin w2 t)^2.

That squared term contains a term like E sin w1t sin w2t which (using your trig identity) is equivalent to two waves at new frequencies, F sin (w1+w2)t + G sin (w1-w2)t

Your eyes and brain are a nonlinear system for analysing light waves. That's why you see "red+green" as yellow, and you also see monochromatic yellow light as yellow.

A good spectroscope should be almost perfectly linear, so the constants C D E F and G will be very small compared with A and B and you will get just two lines in the spectrum, red and green.

 

[Claude Bile]

Alephzero is correct, you need a medium with a nonlinear response to generate new frequencies.

http://www.rp-photonics.com/sum__and_difference_frequency_generation.html

Claude.

 

[MaWM]

So, a good spectroscope essentially performs a Fourier Transform on the incoming signal. And, because of the uniqueness of the Fourier Transform, a linear combination of red and green will never give anything besides red and green?

But its our eye that somehow aliases the signal..

 

[AlephZero]

My biology knowledge is pretty basic but AFAIK human eyes have three color sensor systems (for red green and blue) which have a fairly broad bandwith. If monochromatic yellow light excites both the red and green sensors, or monochromatic red+green causes the same output, the brain doesn't know the difference and they both "look the same".

Correct, a good spectroscope essentially does an FFT.