Question

a Gaussian beam passes through a lens with focal length $f$, and then is incident upon a sample. The waist of the Gaussian beam (before passing through the lens) is at $z = 0$. The lens is located at $z =$ $l$. Assume that the input beam has $z_0 << l$. $2w_0$ $L$ $z = 0$ $z = l$ $Z$ $\text{focal length } f$ Calculate the lens focal length $f$ needed to ensure that Gaussian beam has a waist at the front surface of the sample. Show that for a given $l$ and $L$, two solutions for $f$ exist. Sketch the beam behaviour for each of these solutions

          a Gaussian beam passes through a lens with focal length $f$, and then is incident upon a sample. The
waist of the Gaussian beam (before passing through the lens) is at $z = 0$. The lens is located at $z =$
$l$. Assume that the input beam has $z_0 << l$.
$2w_0$
$L$
$z = 0$
$z = l$
$Z$
$\text{focal length } f$
Calculate the lens focal length $f$ needed to ensure that Gaussian beam has a waist at the front surface
of the sample. Show that for a given $l$ and $L$, two solutions for $f$ exist.
Sketch the beam behaviour for each of these solutions

a Gaussian beam passes through a lens with focal length f, and then is incident upon a sample. The
waist of the Gaussian beam (before passing through the lens) is at z = 0. The lens is located at z =
l. Assume that the input beam has z0 << l.
2w0
L
z = 0
z = l
Z
focal length f
Calculate the lens focal length f needed to ensure that Gaussian beam has a waist at the front surface
of the sample. Show that for a given l and L, two solutions for f exist.
Sketch the beam behaviour for each of these solutions

Added by Kelly P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

06/06/2023

Step 1

Step 1: The complex beam parameter q is defined as: q = z + i * Zr where z is the distance from the waist to the current position, Zr is the Rayleigh range, and i is the imaginary unit. Show more…

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a Gaussian beam passes through a lens with focal length f, and then is incident upon a sample. The waist of the Gaussian beam (before passing through the lens) is at z=0. The lens is located at z= l. Assume that the input beam has flLfz_(0)<. Calculate the lens focal length f needed to ensure that Gaussian beam has a waist at the front surface of the sample. Show that for a given l and L, two solutions for f exist. Sketch the beam behaviour for each of these solutions (Please solve using Complex beam parameter q) a Gaussian beam passes through a lens with focal length f,and then is incident upon a sample. The waist of the Gaussian beam (before passing through the lens) is at z = 0. The lens is located at z = l. Assume that the input beam has zo << l. L 2Wo z=0 Z focal length f Calculate the lens focal length f needed to ensure that Gaussian beam has a waist at the front surface of the sample. Show that for a given l and L, two solutions for f exist. Sketch the beam behaviour for each of these solutions