College of Engineering and Science Gaussian TEM00 He-Ne Laser Mode and its
Parameters
Report from a laboratory experiment conducted on 22 March 2012
as part of ELEN 533 001 Optoelectronics
Yanhong Yang
102-13-631
9th April 2012
Abstract:
Gaussian beam is very important model in laser optics. “Many lasers emit beams that approximate a Gaussian profile, in which case the laser is said to be operating on the fundamental transverse mode, or "TEM00 mode" of the laser's optical resonator.”From Wikipedia,/wiki/Gaussian_beam.
In this report, author calculates beam waist and diversity angle in TEM00 mode He-Ne laser. In Gaussian beam, the w should be same in Horizontal and Vertical data, however it is different. The author gives some reasons to explain. Because of the equipment limited, the experiment could not give the exactly position of the waist beam. However, it can be calculated.
Table of Contents
Abstract: (i)
Table of Contents (ii)
1.Introduction (1)
2.Theory (1)
3.Experimental Setup (2)
4.Equipment Used (2)
5.Procedure (2)
6.Data (3)
7.Analysis of Data (4)
8.Discussion of Results (4)
9.Conclusions (5)
10.References (5)
1. Introduction
Usually the cross-section of amplitude of electrical field distribution in laser resonator complies with the Gaussian function. It is known as the Gaussian beam. Generally, the laser resonator don ’t shoot exactly Gaussian distribution beam. However, the TEM 00 mode is purely Gaussian beam. In that way, this experiment we observe the intensity distribution of the He-Ne laser. It is very simular to Gaussian function. And also we use the Gaussian beam knowledge calculate the beam waist and divergence angle in TEM 00 mode of the He-Ne laser.
In the rest of the report we discuss the reason of difference in Horizontal and Vertical calculation. Also, we analyse and calculate the actual position of the beam waist of He-Ne laser.
2. Theory
In Gaussian beam the amplitude is complex amplitude.
U (x ,y ,z )=A 0w 0w (z )exp -r 2w 2(z )éëêùûúexp -jkz -jk r 2
2R z ()+j z z ()éëêêùû
úú (1)
In equation (1) r =x 2+y 2 Where
()[]
201)(z z z z R += (2)
()[]
2
02
02/1)(z z w z w += (3)
λ
π2
0w n z =
(4)
From equation (1) we can separately calculate the intensity of x direction and y direction.
I (x ,0)=U (x ,0,0)2
=I 0exp -2x 2w 2(z )éëêù
û
ú (5)
I (0,y )=U (0,y ,0)2
=I 0exp -2y 2w 2(z )éëêù
û
ú (6)
In case we can find two different distances z as z 1 and z 2. Also at the w distance in x direction we have the intensity fall
en to 1/e 2(13.5%). That’s our w 1 and w 2. From equation (3) we can easily find that
z 1=
p l
w 0w 12+w 0
2
(7) z 2=
p w 0w 22+w 0
2
(8)
