How does spatial coherence affect focusability of laser?

[worwhite]

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.

 

[johnbbahm]

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.

 

[JeffKoch]

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).

 

[Andy Resnick]

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.

 

[jambaugh]

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.

 

[worwhite]

Ah I think that gives me a much better picture. Thanks!