Grating element of an acoustic grating

[Saptarshi Sarkar]

I was reading a pdf on acoustic grating for my practicals when I saw that the grating element of an acoustic grating is equal to the wavelength of the sound wave. I also checked a few other sources and got the same.

I do not understand why. I know that for an acoustic wave, the standing wave causes the density to change at different locations, making it lower at the antinodes and higher at the nodes. So, the antinodes act as slits.

But, from what I know, the distance between two antinodes is half the wavelength of the wave, so the grating element should also be half the wavelength. Can someone please help me understand this.

 

[sophiecentaur]

I’d imagine that the mutual interactions between elements could be more significant unless the spacing is chosen right.

 

[Saptarshi Sarkar]

I’d imagine that the mutual interactions between elements could be more significant unless the spacing is chosen right.

I get that. But I don't understand why the element is equal to the wavelength and not half the wavelength. From the diagram of a standing wave, the distance between two antinodes is equal to half the wavelength.

 

[sophiecentaur]

But the phases at half wave separation are 180 degrees. They have to be In Phase.
Dadaaah!

 

But the phases at half wave separation are 180 degrees. They have to be In Phase.
Dadaaah!

Ah, that's it! I thought I was going crazy for a moment 😜

 

[sophiecentaur]

Radio arrays often have half wave spacing but mutual impedance may be lower than for sound. If the elements were driven in anti phase perhaps they could be closer, which is the arrangement for log periodic tv aerials.

Edit - I have had second thoughts about LP arrays. They are fed from a transmission line and the half wave delay along the line is compensated for by flipping alternate elements.

 

[DaveE]

I always thought that the refractive index had a maximum at one anti-node and a minimum at the other one. Was I wrong?

 

[sophiecentaur]

I always thought that the refractive index had a maximum at one anti-node and a minimum at the other one. Was I wrong?

The refractive index is a property of the material that the wave is traveling through and does not change. The Energy in a stationary wave is a maximum at the antinodes but the phase of the oscillations in an antinode is opposite to the phase in the two adjacent antinodes.

 

[DaveE]

The refractive index is a property of the material that the wave is traveling through and does not change.

That's not what everyone else on the web says. As I understand it, it is the index variation due to stress in a transparent material that generates the interference (grating) effects.
This link is a good place to start: https://en.wikipedia.org/wiki/Acousto-optics

I'm also having a hard time finding references to using standing waves. Most places don't discuss it at all, but some say the wave is launched at one end and effectively absorbed at the other. I think this would be important for tunable gratings.

I'm certainly no expert, but I imagine that the A-O effect is general enough that devices could be built to function in several different ways.

edit: Aargh! I can't type today. I've edited this short bit 4 times for grammar and spelling!

 

[DaveE]

I know that one thing the people I used to work with didn't like about A-O modulators was that they were slow. You have to wait for the wave to propagate across the beam diameter. Then if you focus the beam too tightly you risk optical damage to the modulator (this was in high power laser applications). I imagine that if you have to wait for the standing wave to be established that would be even slower since the crystal is so long compared to the bit you care about.

I was asked a couple of times to design a very-fast HV driver to make E-O modulators because of these speed concerns. However, we never did it. You can buy that stuff for lab work, and the regulatory requirements for inclusion in real products was a huge burden.

 

[sophiecentaur]

That's not what everyone else on the web says.

That make sense, of course. I was thinking of the mechanical property of the medium and not the optical refractive index - not relevant here. I was also thinking of surface acoustic waves, rather than pressure waves inside the medium. Both forms of grating are used, I believe. The propagation would be significantly slower so perhaps not so quick to modulate the light beam.

 

[DaveE]

...I was also thinking of surface acoustic waves, rather than pressure waves inside the medium. ... The propagation would be significantly slower so perhaps not so quick to modulate the light beam.

I also wonder if the P-waves have an advantage because of the index modulation in the "vertical" dimension. The index change is small in any case, so limiting it to the surface might make an inefficient device. I suppose you could also do S-waves throughout the bulk of the material, that was common in the "olden days" of crystal radios (ok, today too, in your computer).

I think this is really interesting, but way above my "pay grade" and, frankly, I'm probably too lazy to actually investigate.

 

[sophiecentaur]

so limiting it to the surface

Surface waves are neither P or S (bulk) waves but like water waves. They are a lot slower and a surface wave grating would operate by reflection rather than refraction. I have read that the slowness restricts the bandwidth of the modulation achievable but i'd imagine the deflection is potentially higher. But optical comms should have the advantage of wide bandwidth so that could be why they're not used.

that was common in the "olden days" of crystal radios

What is this about? Crystal radios used rectification at a crude junction. I am trying to work out what you are referring to.

 

[DaveE]

What is this about? Crystal radios used rectification at a crude junction.

It's about sloppy writing. I meant crystals used in radios, you know, the good radios

 

[sophiecentaur]

It's about sloppy writing. I meant crystals used in radios, you know, the good radios

Do you mean Quartz crystals for oscillators and filters? They mostly use (afaik) flexing of a bar shaped crystal - (like a glockenspiel that kids use) and are of a similar length to the wavelength of the wave along them (or a multiple wavelengths for overtone modes).

 

[DaveE]

There are lots of ways to vibrate a simple crystal. Yes, the "flexure mode" is most common at low frequencies. Frankly, I'm not sure I understand the difference between higher order flexure modes and the shear wave modes. They also have "longitudinal modes", which I think are what we've called P-waves, and torsional modes.

 

[sophiecentaur]

the difference between higher order flexure modes and the shear wave modes

I would have thought that the bulk shear mode would involve a big ('infinite enough') volume of material where the flexure mode would be a much lower mechanical impedance mode. A narrow bar requires much less force to excite a lateral displacement than a very fat bar. Whilst the individual molecules would obey the same rules, the overall effect is significantly different.

 

[tech99]

But the phases at half wave separation are 180 degrees. They have to be In Phase.
Dadaaah!

I know the gratings work, and they were used for a large screen TV display in about 1939 in the form of the Jeffree Cell. However, it never occurred to me before that the grating effect must be pulsing on and off at acoustic frequency.
With the Jeffree Cell I believe the cell used an acoustic traveling wave and the light beam was made to scan along the cell using a rotating mirror so it remained fixed relative to the grating.