How does spatial coherence affect focusability of laser?

In summary, lasers are highly focusable because of their high spatial coherence. This coherence is due to the fact that lasers have high temporal coherence as well, as stimulated emission produces identical photons. However, spatial coherence is important too, as it allows the beam to be focused more tightly.
  • #1
worwhite
25
0
Hi,

In studying about lasers, it was mentioned that lasers are highly focusable, and this was because of the high spatial coherence of lasers. Just want to ask:

1. Why and how does spatial coherence affect focusability?

2. How is a laser typically focused (using a lens?)

3. Why do lasers have a high spatial coherence? I know that lasers have high temporal coherence because stimulated emission produces identical photons (thus they all have the same wavelength). But I'm not too sure why that results in spatial coherence.

Thanks in advance.
 
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  • #2
There is something called doppler width, that affects the coherence length of lasers.
the closer the doppler width is to the natural width, the longer the coherent length.
The reference I have says the doppler broadening is due to how thermal light sources emit wave trains.
 
  • #3
johnbbahm said:
There is something called doppler width, that affects the coherence length of lasers.
the closer the doppler width is to the natural width, the longer the coherent length.

This is utter nonsense, and has nothing to do with the question either. Spatial coherence basically relates to the "size" of the source, if the light were coming from a random incoherent disk source and then collimated with a perfect lens. Or you can think of it in terms of angle. Starlight is very spatially coherent because, even though a star is huge, it is very very far away - the lightbulb next to your desk, however, is not very spatially coherent. Spatial coherence is not related to longitudinal coherence (narrowness of the spectrum).
 
  • #4
worwhite said:
Hi,

In studying about lasers, it was mentioned that lasers are highly focusable, and this was because of the high spatial coherence of lasers. Just want to ask:

1. Why and how does spatial coherence affect focusability?

2. How is a laser typically focused (using a lens?)

3. Why do lasers have a high spatial coherence? I know that lasers have high temporal coherence because stimulated emission produces identical photons (thus they all have the same wavelength). But I'm not too sure why that results in spatial coherence.

Thanks in advance.

The spatial coherence of a raw laser beam is typically low but can be increased by using a spatial filter. Spatial coherence has nothing to do with spectral width (temporal coherence).

A highly spatially coherent beam can be focused more tightly than a spatially incoherent beam, but I don't know of a simple quantitative relationship between the degree of coherence and minimum spot size.
 
  • #5
Keeping it simple, spatial coherence is the matching of the phase for the beam as you move across the breadth of the beam.

Imagine say a laser (with circular cross section) where the upper half circle of the beam were 180deg out of phase with the lower half. Treat it as two stacked lasers half a wavelength out of phase. Geometric optics says it focuses to a point (assuming a perfect parabolic lens or mirror) but if you trace the phase for each half they will, when 180deg out of phase destructively interfere at the focus. You'll instead have an interference pattern wider than the focus point.

Do the detailed math for focusing a coherent beam with a given aperture and you won't have a perfect point but an interference pattern which you can calculate. (You basically sum phase components over paths). [Note that in doing this the refraction of a lens or reflection of the mirror is automatically incorporated, in a sense refraction and reflection, and even plane wave motion are all interference phenomena via Huygens' principle.]

The sharpest focus for a parabolic mirror will occur where there is no phase difference across the width of the beam. The focal point will have absolutely the maximum constructive interference from all beam parts. The amount will go down sharply as you move away and less sharply the less spatial coherence you have.

If you have a conventional lens then there is a bit of radial phase shifting due to the longer paths through the refractive medium for photons closer to the lens axis. The sharpest focus occurs with light from a laser with spatial phase shifts which happen to cancel this effect.
 
  • #6
Ah I think that gives me a much better picture. Thanks!
 

Related to How does spatial coherence affect focusability of laser?

1. How does spatial coherence affect the focusability of laser?

Spatial coherence refers to the correlation between the phases of different points on a wavefront. In laser systems, spatial coherence plays a crucial role in determining the quality of the beam and its focusability. When a laser beam has high spatial coherence, it means that all the points on the wavefront have a consistent phase relationship, resulting in a beam with a well-defined direction and focus.

2. What is the relationship between spatial coherence and beam divergence?

Spatial coherence is inversely related to beam divergence. This means that as the spatial coherence of a laser beam increases, its beam divergence decreases, resulting in a more focused and collimated beam. Conversely, a beam with low spatial coherence will have a higher divergence and will be more difficult to focus.

3. How does the spatial coherence of a laser beam affect its ability to deliver energy to a target?

The spatial coherence of a laser beam is directly related to its ability to deliver energy to a target. A laser beam with high spatial coherence will have a well-defined focus, allowing it to deliver a high concentration of energy to a specific point. On the other hand, a beam with low spatial coherence will have a less defined focus and will spread its energy over a larger area, resulting in a lower energy density at the target.

4. Can spatial coherence be controlled in a laser system?

Yes, spatial coherence can be controlled in a laser system through various methods such as using spatial filters, adjusting the geometry of the laser cavity, and using special optical elements. These techniques can improve the spatial coherence of the laser beam, resulting in a more focused and higher quality beam.

5. What are the practical applications of understanding how spatial coherence affects laser focusability?

Understanding the relationship between spatial coherence and laser focusability is crucial in various applications where precise and accurate laser focusing is required. These include laser cutting, welding, medical procedures, and lithography. By controlling the spatial coherence of a laser beam, scientists and engineers can improve the precision and quality of these applications.

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