# Can a phase array evoke a standing wave at a focal point that has a much higher frequency that the constituent emitted frequencies?

This is a phased array: How can you focus sound?

It can focus many waves of weak radio wave or light into a single focal point that's very strong.

Now imagine that we delay half of the emitters by a constant amount that is equal to 0.5 of the period of the waveform. Now wouldn't we have evoked a standing wave at the focal point that is twice the frequency (but half the amplitude) of the emitted waves?

Now we can repeat it by delegating the emitters into 10 groups, and have them emit in increments of 1/10 the period of the wave. Wouldn't that evoke a standing wave that oscillates at 10x the frequency (but 1/10th the amplitude) of the original?

If scaled to a very extreme level, shouldn't we be able to generate visible light just by combining a whole bunch of radio waves? If not, why not?

• Linear superposition of waves does not change their frequency. The answer is negative. Dec 29, 2014 at 20:31
• Can you explain why? Where is the flaw in my reasoning? In sound it is known that multiple waves of same frequency that are shifted in phase can introduce "phasing artifacts" and we can actually hear higher-frequency harmonics caused by the waves -- is this not the same or similar phenomenon to what I propose with EM waves?
– pete
Dec 29, 2014 at 21:45
• "Phasing" is a property of your ears and the way your brain processes acoustic information (we need to be able to tell phases differences to tell direction of movement of our prey and predators). Superposition of electromagnetic waves in free space is perfectly linear. If you want strong non-linear effects that shape waves into short pulses, you need non-linear effects, like in NLTL (non-linear transmission lines), see e.g. ece.ucsb.edu/Faculty/rodwell/publications_and_presentations/…, but none of this happens in free space. Dec 29, 2014 at 21:50
• If my technique doesn't generate a high frequency at the focal point, then what exactly is going on at the focal point? I'm trying to imagine (using circular ripples as a drawing, the same way they show it in phased arrays diagrams) and cannot figure out why it wouldn't work, and I don't know what you mean by "perfectly linear" and why that means it won't work
– pete
Dec 29, 2014 at 23:34
• You have linear superposition at the focal point and everywhere else. There is nothing to imagine. Look up the formula for the addition of trigonometric functions: en.wikipedia.org/wiki/… and calculate the sum of two functions with the same frequency but different phase. Dec 29, 2014 at 23:54

If half the aperture is delayed by half the carrier period then in the far field you will get a null in the bore-sight of the radiator but you will also end up with a pair "shoulders", a kind of grating lobe. Check out mono-pulse antennas (radar), here is good picture http://en.wikipedia.org/wiki/Monopulse_radar. No second harmonic and no standing wave just redistribution of the energy from bore-sight to off bore-sight. More complicated aperture distribution variation can also be used to achieve direct amplitude modulation of the signal.

• I find this answer somewhat confusing. Can you elaborate a little about my initial proposal and why it would or would not work? In sound it is known that multiple waves of same frequency that are shifted in phase can introduce "phasing artifacts" and we can actually hear higher-frequency harmonics caused by the waves -- is this not the same or similar phenomenon to what I propose with EM waves?
– pete
Dec 29, 2014 at 21:47
• As @CuriousOne has said above ether is a linear medium, so waves can be added without creating any funny effect. Now it is true that air is not a perfectly linear medium because it can break down (sparks) at very high voltages ~2kV/mm. This is a really high intensity field and I do not know how you could manage it; think of controlled lightning at microwave rates. Is this what you are after? There have been experiments with two acoustic arrays operating at different frequencies so that difference frequency is audible, but the frequency mixing is done by the ear not by the medium. Dec 29, 2014 at 22:16
• If my technique doesn't generate a high frequency at the focal point, then what exactly is going on at the focal point? I'm trying to imagine (using circular ripples as a drawing, the same way they show it in phased arrays diagrams) and cannot figure out why it wouldn't work. Why should multiplied frequency at the focal point be a "funny effect"? It seems like the only possible outcome of combining ripples (waves) in that manner.
– pete
Dec 29, 2014 at 23:35