# How does spot size of a laser depend on wavelength?

Does the spot size of a laser depend on wavelength? We have a laser source that is fed into a spectrometer to set the wavelength we want. No other optics are used after the spectrometer. I was going to do the "knife-edge" experiment at a bunch of wavelengths (400-1100nm) to see if the spot size changes, but I figured I would ask here first.

• I'm not an expert in this field but if i recall correctly a laser beam is (in ideal case) a Gaussian beam and according to en.wikipedia.org/wiki/Laser_beam_quality the waist, therefore the spot, has a wavelength dependence. Commented Jan 24, 2019 at 14:48

How does spot size of a laser depend on wavelength?

Largely, it doesn't. The spot size of the laser can be set independently on the wavelength.

That said, there is a nontrivial relationship that links the wavelength $$\lambda$$, the focal waist $$w_0$$, and the Rayleigh range $$z_\mathrm{R} = \frac{\pi w_0^2}{\lambda},$$ where the latter is the distance from the focal plane at which the area of the beam is doubled. This relation encodes the diffraction of the beam from the focal spot: at a fixed wavelength, the smaller the spot size, the faster the beam diverges.

In practice, of course, the details of how things change will depend on the details of the configuration. In particular, for the configuration you report,

We have a laser source that is fed into a spectrometer to set the wavelength we want. No other optics are used after the spectrometer.

there isn't enough information to determine the behaviour of the system.

Yes it does, and that is mostly because a coherently illuminated slit/hole (diffraction limited case) has a main lobe whose angular extent is $$\approx k\frac {\lambda}{D}$$ where $$k\approx 1$$ and $$D$$ is the linear dimension of the slit. In the case of a laser source the output diaphragm determines the minimum extent of the beam.

• For laser diodes which have a tiny aperture the diffraction is huge but a collimating lens captures these beams asap (short focal length) and collimates the beam, the spectrometer as well as the knife edge will also diffract thereby increase the spot size. Commented Jan 24, 2019 at 15:36
• @PhysicsDave sure but that just says it depends on where you define the effective coherent output. With your amplifier drive a dipole antenna having a near omni antenna pattern, a receiver thousands of meters away sees the effective "antenna" that is the parabolic dish sitting behind the dipole and then the dish's diameter controls the beamwidth. Commented Jan 24, 2019 at 15:50