About

Subject Area	Waves & Optics
Level	Beyond the First Year
Available Implementation	Python
Learning Objectives	Students who complete this set of exercises will be able to express an equation predicting the profile of a laser oscillating in the TEM00 mode in terms of dimensionless (“scaled”) variables suitable for coding (Exercise 1); produce both line plots and contour plots of the (scaled) irradiance of the beam versus (scaled) position(s) (Exercises 1 and 2); develop a model of, and plot, the knife-edge profile of the laser beam (Exercise 3); and fit the model, i.e., of the irradiance versus knife-edge position, to experimental data (Exercise 4)
Time to Complete	120 min

EXERCISE 3: THE KNIFE-EDGE PROFILE

You can experimentally determine the value of the parameter w0 that describes the width of the beam by measuring the profile of the laser beam using a knife-edge mounted on a linear translation stage together with an optical detector connected to a power meter. The idea is that you allow the laser beam to enter the detector while you translate the knife-edge across the beam and monitor the power meter reading. Initially, when the beam is not blocked, the reading gives the total power of the beam; finally, the beam is completely blocked from entering the detector by the knife-edge and the reading would be zero (in the absence of background light). A schematic is shown below; we assume the beam is centered on the origin.

Imagine that the knife-edge travels in the +x-direction, and that the position of the knife-edge is x. Then the power received by the detector is

where P0 is the total power of the laser beam. Show that this expression is equivalent to

where erf(u)=∫+∞uexp(−t2)dt is the error function. Calculate P(x)/P0 and plot this quantity versus x, the position of the knife edge, when w0=0.5 mm and for −3w0≤x≤3w0.

#

# Beam_Profile_Exercise_3.py

#

# This file will generate a plot of

# the predicted knife-edge beam profile

# for the TEM00 laser mode

#

# Written by:

#

# Ernest R. Behringer

# Department of Physics and Astronomy

# Eastern Michigan University

# Ypsilanti, MI 48197

# (734) 487-8799

# This email address is being protected from spambots. You need JavaScript enabled to view it.

#

# 20160614 by ERB

#

# import the commands needed to make the plot and fit the data

from pylab import xlim,xlabel,ylim,ylabel,grid,show,plot,title

from numpy import linspace,sqrt

from scipy.special import erf

# inputs

npts = 200 # number of intervals in x

w0 = 0.5 # beam width [mm]

# calculated quantity

x_max = 3.0*w0

# set up the array of knife-edge positions

x = linspace(-x_max,x_max,npts+1)

# calculate the scaled power

scaled_P = 0.5*(1.0 - erf(sqrt(2.0)*x/w0))

# Define the limits of the horizontal axis

xlim(-x_max,x_max)

# Label the horizontal axis, with units

xlabel("Knife-edge position \(x\) [mm]", size = 16)

# Define the limits of the vertical axis

ylim(-0.1,1.1)

# Label the vertical axis, with units

ylabel("Scaled transmitted power \(P(x)/P_0\)", size = 16)

# Make a grid on the plot

grid(True)

# Make the title

title('Normalized knife-edge profile for \(w_0 = \)%s mm'%w0)

# Generate the plot. The line color is magenta (m).

plot(x,scaled_P,"m")

show()

 

Translations

Code	Language		Translator	Run

Credits

Fremont Teng; Loo Kang Wee; based on codes by E. Behringer

Sample Learning Goals

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For Teachers

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Research

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Video

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 Version:

1. https://www.compadre.org/PICUP/exercises/exercise.cfm?I=134&A=laser_beam_profile
2. http://weelookang.blogspot.com/2018/06/laser-beam-profile-exercise-3-knife.html 

Other Resources

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