Destructive interference for distance-specific illumination?

[timelessmidgen]

From a practical standpoint, can we combine two (or more) lasers tuned to almost-but-not-quite identical frequencies to create distance-specific illumination? For instance, say we have a 1 micron laser and a 0.9999 micron laser which we combine through some beam-combiner optics. In theory I think this should create alternating constructive and destructive interference with a wavelength of (1 micron/(1 micron-0.9999 micron)) x 1 micron=1 cm. Therefore if we took a projection screen and moved it progressively further away from the laser aperture it should fluctuate between bright and completely dark images on a length scale of 1cm. I imagine that by adding more lasers (adding more sine waves) you could make the regions of brightness arbitrarily small and come up with very distance-specific illumination. But is this actually practical or are the material requirements too difficult? Perhaps at maser wavelengths?

 

[Charles Link]

The closest thing I have seen to what you are describing is the two arms of a FTIR (Fourier transform infrared radiometer that uses a Michelson interferometer geometry), where one or both arms/mirrors of the Michelson interferometer are moving, which results in Doppler shifting of one or both signals (in the case of both, Doppler shifts occur in opposite directions in each arm). The result is beat frequencies are observed in the audio range at the detector=the human eye would see it as a steady light, but it is actually getting modulated at an audio frequency). The detector, or fixed screen receiver, as you are describing, would not see a maximum or a minimum when you have two separate frequencies or wavelengths, but rather a signal modulated at the difference frequency. Heterodyneing is a similar process. $\\$ Alternatively, with a Michelson interferometer, with fixed mirrors, and thereby the same wavelength for both arms the large scale maxima and minima can be observed, bit the distance the mirror needs to travel to go from a maximum to a minimum is 1/4 of a wavelength.

 

[sophiecentaur]

to create distance-specific illumination?

If they are not the same frequency, the illumination will vary with distance and with time. If the frequency difference is small enough then there will be a visible interference pattern, moving across the 'screen'.

 

[Charles Link]

If they are not the same frequency, the illumination will vary with distance and with time. If the frequency difference is small enough then there will be a visible interference pattern, moving across the 'screen'.

@sophiecentaur An interesting input and idea. Essentially this result could be achieved by the interference from two pinholes or slits and a beamsplitter along with Doppler shifting the signal into one of the pinholes, but keeping both pinholes or slits stationary. $\\$ Instead of trying to move mirrors, the easiest way to Doppler-shift a beam is to use a moving corner cube. That way alignment constraints are greatly alleviated. To have two separate sources in close proximity, one suggestion would be to use two fiber optic type sources.

 

[sophiecentaur]

@sophiecentaur An interesting input and idea. Essentially this result could be achieved by the interference from two pinholes or slits and a beamsplitter along with Doppler shifting the signal into one of the pinholes, but keeping both pinholes or slits stationary.

I can't see that being a very easy thing to achieve. What I can suggest is to do the interference experiment with two good, stable RF sources (say a few GHz frequency), with a couple of Hz difference. You can get a perfect interference pattern (detectable with an RF probe, which will vary across a wide ange and, with the probe stationary, the level at any point will vary in time.
I don't actually know the limits of frequency (and frequency offset) accuracy that can be achieved in practice [Edit: with lasers] but I do know that the trick is very feasible at Radio Frequencies. Imo, the actual frequency or setup that can show the frequency and position dependence of an interference pattern is a general principle.

The effect at even lower Radio Frequencies is an every day occurrence in unsynchronised LF sound radio networks where there is a 'mush area' where two transmitter service areas overlap. The 'mush area' here has interference peaks and troughs of signal strength, which march over the countryside at a rate of a few tens of metres per second.