How Does Frequency Affect Laser Diffraction Through a Phase Grating?

In summary, a laser passing through a body of water and hitting a screen is observed to produce different diffraction patterns at different frequencies due to the presence of a piezoelectric quartz crystal in the water. The crystal acts as a diffraction grating, causing the light to diverge and form a pattern on the screen. The speed of sound in water and the frequencies can be used to calculate the wavelengths of the diffraction grating, which are responsible for the observed patterns.
  • #1
franky_boy
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Homework Statement


A laser passes through a body of water and later hits a screen, as shown:

http://img80.imageshack.us/img80/7417/20478103.jpg

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

At 9.5MHz:

http://img207.imageshack.us/img207/5941/9x5.jpg

And, finally, at 12MHz:

http://img14.imageshack.us/img14/178/12x0.jpg

The question is: what is happening?

Homework Equations


No equations are supplied.

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

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.

Many thanks in advance!
 
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  • #2
franky_boy said:

The Attempt at a Solution


A little research shows that one type of diffraction grating is called a phase grating...
That is they key to what is going on; the water waves act as a diffraction grating. You can use the speed-of-sound and frequencies to calculate wavelengths, which are the period of the diffraction grating "rulings". (The 67 and 31 micron values you gave are not the correct water wavelengths, by the way.)
 

Related to How Does Frequency Affect Laser Diffraction Through a Phase Grating?

1. How does a laser pass through a phase grating?

A laser passes through a phase grating by diffracting the beam into multiple beams with different phases. The diffraction occurs due to the periodic pattern of the grating, which alters the phase of the incident light waves.

2. What is the purpose of using a phase grating with a laser?

The purpose of using a phase grating with a laser is to manipulate the laser beam and create a specific diffraction pattern. This can be used for applications such as creating holograms or splitting the beam into multiple directions.

3. How does the spacing of the grating affect the diffraction pattern?

The spacing of the grating affects the diffraction pattern by determining the angle at which the diffracted beams will be emitted. A smaller spacing will result in a wider diffraction angle, while a larger spacing will result in a narrower angle.

4. Can a laser pass through a phase grating multiple times?

Yes, a laser can pass through a phase grating multiple times. Each time, the grating will alter the phase of the beam, resulting in a more complex diffraction pattern. This can be used for advanced applications such as creating 3D images.

5. Are there different types of phase gratings that can be used with a laser?

Yes, there are different types of phase gratings that can be used with a laser. Some common types include binary phase gratings, blazed gratings, and echelle gratings. Each type has its own unique properties and is used for different applications.

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