Is the range of a laser beam limited by the width of its wave packet?

[Anton Alice]

I think I am in a misconception concerning laser beams:
Even the best lasers have a small line width. The spectral line is gauss-shaped. therefore the wave in position-pace is also a gauss-shaped wave packet, that travels with a certain group velocity. But this gauss shaped wave packet has a finite width. Doesnt that mean, that the laser beam has a finite range, which is equal to the width of the wave packet?

 

[blue_leaf77]

The spectral line is gauss-shaped.

In fact, it is difficult to realize a laser with such a line shape.

therefore the wave in position-pace is also a gauss-shaped wave packet,

The conjugate space for frequency is time, not position. You probably intended to mean the longitudinal position coordinate, the wave envelope in longitudinal direction will also be Gaussian if the wave is of plane wave.

Doesnt that mean, that the laser beam has a finite range, which is equal to the width of the wave packet?

Taken a snapshot of a pulsed laser, yes it has finite range in space but this pulse is actually travelling.

 

[Anton Alice]

I don't understand what you mean. How does the wave emitted by a continuous laser source with a certain line-width look like?

The conjugate space for frequency is time, not position. You probably intended to mean the longitudinal position coordinate, the wave envelope in longitudinal direction will also be Gaussian if the wave is of plane wave.

If the Shape of the Beam in Time domain(at some fixed position) is gaussshaped , then it should be also gauss-shaped in position domain, not? this is why I directly concluded that. But I don't quite understand yet. What is the difference between what I concluded for the shape of the wave packet, and what you said about the longitudinal coordinate?

Taken a snapshot of a pulsed laser, yes it has finite range in space but this pulse is actually travelling.

How about continuous lasers? I can not imagine them to emit gauss shaped wave forms.

Why does a laser have only a finite coherence length? because of the line width, right? and the coherence length itself would be then correlated to the spatial length of the wave packet.

 

[Andy Resnick]

I think I am in a misconception concerning laser beams:
Even the best lasers have a small line width. The spectral line is gauss-shaped. therefore the wave in position-pace is also a gauss-shaped wave packet, that travels with a certain group velocity. But this gauss shaped wave packet has a finite width. Doesnt that mean, that the laser beam has a finite range, which is equal to the width of the wave packet?

In the limit, spectral lineshapes for homogeneously broadened lasers are typically Lorentzian, while spectral lineshapes for inhomogeneously broadened lasers are Gaussian. In between, the lineshape is called a 'Voight profile". Longitudinal mode profiles can become complicated for pulsed sources, but you are on the right track that the temporal profile of a pulse is related to the spectral lineshape.

This does not have anything to do with the transverse field mode, which can be approximately Gaussian/Hermite/Laguerre, depending on the cavity cross-section shape.

 

[blue_leaf77]

If the Shape of the Beam in Time domain(at some fixed position) is gaussshaped , then it should be also gauss-shaped in position domain, not?

Consider a Gaussian beam, in such a beam the amplitude is modulated by $\frac{A_0}{\sqrt{1+(z/z_R)^2}}$. At least the presence of this term will make the beam envelope along the propagation axis not exactly Gaussian when you take a snapshot of the beam. Only for the case of perfect plane wave does the longitudinal envelope is similar to that in time domain.

How does the wave emitted by a continuous laser source with a certain line-width look like?

It depends on the lineshape, but in practice there are always sources of noise which modifies the intensity profile so that it exhibits randomly jagged structures.