Laser and inverse square law

[psi20]

Does the inverse square law apply to a laser beam? I couldn't tell when I did it. It didn't look like it did. As I got farther from 1 meter, the diameter of the beam got bigger. After about 5 meters away, the beam didn't expand anymore. But I didn't measure the diameter accurately enough to tell what happened.

[timo]

Care to explain what you mean by "inverse square law"? The rest of your post also seems a bit messed up. What are you talking about?

[psi20]

Sorry, I was talking about irradiance. The farther away you go from a light source, the greater the area the light spreads over. The power intensity decreases over a unit area. It's supposed to decrease by the square of the distance from the light source. The problem was to find if it applies to lasers.

[swansont]

The inverse-square law applies to a point source which a laser is decidedly not.

 

Whether a laser follows the inverse-square law (e.g. measuring to the 1/e point of beam intensity) depends on how its optics are arranged. It will behave that way from the beam waist - a reasonable approximation of a point - which could be inside or outside the laser.

[timo]

Well, the inverse square law follows from the assumption that (1) no light is absorbed, (2) the area A(d) covered by light increases with d² as a function of the distance d from the light source and (3) the area A(d) is uniformly illuminated.

Because of (1) the total light shining on A(d) must be the same for all distances. because of (2) the area A(d) goes with d² so because of (3) the ammount of light shining on any unit area at distance d must go with 1/d² (that´s because this value times A(d) must be the same like said in the previous sentence).

 

So your inverse square law is made up of three assumption which -as I will show in the following- are usually not completely true:

 

- No light absorbtion:

That is of course only a simplification. Light will be absorbed by air, scattered, converted to other wavelenght, whatever. A 1st order approximation of the absorbtion would be adding a factor exp(-X*d) with X being a material constant that describes the absorbtion. But for your 1 meter or 5 meters distance from a laser the light absorbtion from air is probably neglectible.

 

- Area uniformly illuminated:

Afaik that´s not true for lasers. Laser intensities rather have a gaussian shape.

 

- Area covered increasing with d²:

Well, you can just measure the area covered. If you neglect absorbtion the total ammount of light shining on any area A(d) must be the same. So by dividing by A(d) you´d get an average intensity (average, because lasers do not light the area uniformly as allready said).

An alternative to measuring all A(d) would be to make the assumption that the laser beam is conical with a small but finite area at the opening of your laser. If you measure A(d) for two different distances and create a formula for A(d) out of these measurements and above assumption you´ll end up with a formula of A(d) ~ (d-d0)². That´s close to A(d)~d² for sufficiently large distances but not exactly the same.

 

 

An short: The inverse square law is almost allways a (very usefull) simplification.

Hope that helped

 

EDIT: Before someone jumps in to start nitpicking I´ll add the following myself:

- (2) is formulated a bit fuzzy but it should be obvious what I mean

- (3) is not nessecary for an invere square law but it greatly simplifies any discussion.

- a (4) "light rays propagate in a straight line" seemed obvious so I ommited it for the sake of readability.

[psi20]

There is a calibration curve due to the absorption? Light is absorbed by air, scattered, converted to other wavelengths, etc. So the diameter reaches a certain maximum before decreasing again. Is that right?

[swansont]

There is a calibration curve due to the absorption? Light is absorbed by air, scattered, converted to other wavelengths, etc. So the diameter reaches a certain maximum before decreasing again. Is that right?

 

The beam won't get smaller unless it's focused that way. As Atheist said, the beam has a gaussian intensity profile, so just by visual inspection you might not be making a consistent measurement. As I had said, you need to pick a point, like the 1/e intensity, and measure that diameter. Your eye isn't a linear device, so you can be fooled in trying to determine the diameter.

[YT2095]

actualy, I`ve experienced a similar thing with 1 or 2 of my lasers, without a lens they seem to scatter like a high brightness LED (I didn`t think a laser needed a lens?).

 

Anyway, with a lens correctly placed the beam doesn`t spread over any realistic/usable distance, but can be made to with a different lens distance, these are Semi-con lasers btw.

 

but why should a laser need a lens at all? I thought that only applied to ordinary omni directional light sources.

[swansont]

actualy' date=' I`ve experienced a similar thing with 1 or 2 of my lasers, without a lens they seem to scatter like a high brightness LED (I didn`t think a laser needed a lens?).

 

Anyway, with a lens correctly placed the beam doesn`t spread over any realistic/usable distance, but can be made to with a different lens distance, these are Semi-con lasers btw.

 

but why should a laser need a lens at all? I thought that only applied to ordinary omni directional light sources.[/quote']

 

Diode lasers have large divergence angle that are not the same in the vertical and horizontal directions, so you get an elliptical beam shape. This is due to the small lasing region that is wider than it is tall, so you get diffraction. Plus, the focal point is different for the two directions. Getting a reasonably well-collimated beam from a laser diode isn't trivial, and this makes some tasks, like coupling the light into single-mode fibers, harder than for some other kinds of lasers.

 

Often you use anamorphic prism pairs to reshape the beam. These expand one dimension of the beam, so if properly aligned the beam is much rounder.

[rajama]

Isn't the 'beam' just the light that's left over after being reflected back and forth many many times in the laser cavity, a bit like a regular light source travelling a long way through a series of small, aligned holes?