# Laser through a phase grating

1. Dec 1, 2009

### franky_boy

1. The problem statement, all variables and given/known data
A laser passes through a body of water and later hits a screen, as shown:

http://img80.imageshack.us/img80/7417/20478103.jpg [Broken]

However, suspended in the water is a piezoelectric quartz crystal which can produce waves within the water. When set at 5.5MHz, the following is observed on the screen:

http://img207.imageshack.us/img207/3624/5x5p.jpg [Broken]

At 9.5MHz:

http://img207.imageshack.us/img207/5941/9x5.jpg [Broken]

And, finally, at 12MHz:

http://img14.imageshack.us/img14/178/12x0.jpg [Broken]

The question is: what is happening?

2. Relevant equations
No equations are supplied.

3. The attempt at a solution
A little research shows that one type of diffraction grating is called a phase grating, which I assume works in roughly the following way:

http://img513.imageshack.us/img513/5749/85592676.png [Broken]

Where the grey patches represent parts of the water which are in a state of compression (resulting in an altered refractive index). Given that the speed of sound in water is about 1466m/s, these bands are about 67 microns thick when at 5.5MHz, and about 31 microns when at 12MHz.

I'm unclear as to whether the resulting vibration in the water results in a standing wave, or something which propagates. And why doesn't a diffraction grating which constantly changes its properties result in a smeared image on the screen?

It makes good sense to me that 'ordinary' light would produce a diffraction pattern after passing through a phase grating, but presumably a laser is different. What is causing the light to diverge so much? Can Huygens's principle help in this case?

Any pointers in the right direction would be highly appreciated.