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Waist of single-mode laser radiation – determining the depth of focus.

Assignment:

We need to focus a single-mode beam with a given waist length Lw.

A single-mode beam is Gaussian, for which there is an expression:

Waist of single-mode laser radiation - determining the depth of focus.

 

where: ω(z) is the beam radius (field strength level 1/е2), ω0 is the same but in the waist (at z=0), λ is the radiation wavelength.

If we switch to transverse dimensions not by field strength but by intensity and use the diamter instead of the radius, then:

Waist of single-mode laser radiation - determining the depth of focus.

 

where: d is the diameter (by 1/е2 intensity level).

By the waist length, we usually understand the length of a segment near the waist where the beam diameter does not exceed twice the diameter in the waist d0. Then for the waist length Lw we have:

Waist of single-mode laser radiation - determining the depth of focus.

 

Using it, we get the beam diameter in the waist length d0 :

Waist of single-mode laser radiation - determining the depth of focus.

At Lw = 10-15 mm, d0 = (44-54) µm.

Usually, the beam exiting the fiber should be collimated first before focusing. In this case the focused beam diameter equals :

Waist of single-mode laser radiation - determining the depth of focus.

where: dc is the central fiber core, Fc and Ff are focus lengths of the collimating and focusing lenses.

Since the numerical aperture of single-mode fibers is usually small, and the numerical aperture of focused radiation is even smaller, ordinary spherical lenses will do for collimating and focusing. The lens diameter must be equal to or more than a certain value:

Waist of single-mode laser radiation - determining the depth of focus.

Waist of single-mode laser radiation - determining the depth of focus.

where: Dc and Df are diameters of the collimating and the focusing lenses, correspondingly,

NA is a numering aperture of the fiber.

 

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