The Helium-Neon laser
Theory
The following and the literature from the course.
Theory of modes in resonators
The different modes of the laser correspond to different spatial distributions of the
electromagnetic field in the cavity, Fig. 1. The field is separated into components parallel
to the optical axis (axial or longitudinal modes) and components normal to the optical axis
(transverse modes). A given
transverse mode can be
brought to lase at several axial
modes at the same time, and
vice versa.
A laser mode is usually
TEM 02 TEM 00
Mirrors
described by the transverse
Fig. 1. Principal beam path for the transversal
mode TEMlmn.
The mode parameters l and m TEM 00 and TEM02 modes.
state the number of nodes of the electrical field (i.e.
positions where the field is zero) in a plane normal
to the axis of the laser. The longitudinal parameter n
states the number of nodes along the axis of the
laser, i.e. the number of half-wavelengths between
the mirrors minus one. Since the laser cavity is
much longer than the wavelength of the emitted
light, n will be a very high number, which is usually
not written.
Fig. 2. The gain profile of
The transverse TEM00 mode is symmetric with
a HeNe-laser.
respect to the longitudinal axis in contrast to the
TEM01 mode, which has an asymmetric field
distribution. One way to picture this, is that the
optical beam is diverging from the laser axis. The higher values for l and m, the greater is
the beam divergence from the central axis.
Every mode has a specific resonance frequency. A laser will normally lase at several
different modes with different frequencies at the same time (it is, however, possible to
suppress all but one mode). A gas laser will emit light at frequencies for which the
Doppler broadened gain profile exceeds the losses in the resonator (see Fig. 2).
1
The frequency separation between two consecutive axial modes is given by:
 0 
c
2  ni  L
(1)
Where c = The speed of light in vacuum
ni = The index of refraction
L = The distance between the mirrors
This formula is valid for resonators with both plane and/or spherical mirrors.
The general resonance condition for a laser with spherical mirrors with radii R 1 and R2
and the mirror distance L is given by:

L 
L 
 1   

R1  
R2  


Changing l, m and n results in a frequency difference, :
  0  n 
1


 l  m  1  arccos 1 


1
L 
L 
  0  n   l  m  arccos 1   1   

R1  
R2  



For a confocal resonator R1 = R2 = L, which leads to:
(2)
(3)


1
   0   n    l  m 
(4)


2
Equation (4) shows the degeneration of the confocal resonator. If (1 + m) is increased by 2
and n decreased by 1 is there no change in frequency. A laser operating at a single
transverse configuration TEMlm is often called a single mode laser. It usually radiates
with several frequencies separated by  A laser that only emits one mode and thus only
one frequency is called a single frequency laser.
There are a number of ways to suppress the high order resonator modes and thus reduce
the number of excited modes. One way to get a laser to operate in a single frequency mode
is to reduce the optical pumping of the gain medium until only one axial mode is above the
threshold for lasing. The drawback is that the remaining mode will be weak. A better
method is to suppress all axial modes but one by adding another resonator to the laser,
such a resonator could be a Fabry-Perot etalon or a simple glass plate. Introducing losses
to all but one mode has the same effect as making the gain profile more narrow without
reducing the peak gain.
2
Description of the laser
The laser tube used is from the American Company Melles Griot. A discharge tube is
filled with He and Ne gas. The He-atoms are excited by a discharges in the tube and the
excitation energy is transferred to the Ne-atoms through collisional processes. It is the Ne
gas that is used for the lasing. The tube is sealed with a Brewster window at one end and a
plane mirror at the other end. The tube is mounted on an optical bench and an external
concave mirror can be placed in front of the Brewster window to produce a stable
resonator. The voltage supplier can deliver a few kV without load. The voltage is reduced
to 1.5 kV while the tube is working due to the internal impedance of the voltage supplier.
There are three different concave mirrors for the laser: Two with a 1.0 m radius of
curvature, one has a reflectivity of 99.97 % and the other is 98.3 %. The third has a 0.45 m
radius of curvature and a reflectivity of 98 %. To achieve such high reflectivities all the
mirrors are dielectric mirrors made to reflect wavelengths centred at 632.8 nm. The
mirrors can be adjusted horizontally and vertically using two micrometer screws at each
mirror mount.
Description of frequency selection by laser etalon / glass plate
A laser etalon or glass plate only transmits certain frequencies. The principal physical
mechanism for this can be seen in Fig. 3. The incoming light is reflected many times
inside the component. Every time the light hits a surface a part of it is reflected and a part
of it is transmitted. For some frequencies the optical path between the two reflecting
surfaces corresponds to an integer number of half-wavelengths. The corresponding waves
are in phase and thus constructively interfering and are transmitted. For other frequencies
the waves will be out of phase and interfere destructively. The transmission curve for a
glass plate can be seen in Fig. 4.
Transmission
FSR
Fig. 3. Frequency selective
transmission of a glass plate.
(The angle of the plate is much
smaller in reality)
Frequency
Fig. 4. Transmissions maxima for a glass plate.
The free spectral range of the etalon,  FSR , separates the transmission maxima.  FSR is
calculated in same way as  0 for the laser cavity. An etalon placed inside a cavity will
block the frequencies that get to big losses due to the etalon. By choosing the right etalon
monofrequency lasing can be obtained.
3
Description of the spectrum analyzer
The spectrum of the laser is analysed with a scanning Fabry-Perot interferometer (Spectra
Physics Optical Spectrum Analyzer Model 470). This instrument can show the intensity
distribution within a narrow spectral band on an oscilloscope (Fig. 5).
Fabry-Perot
Mirror 2
Mirror 1
Oscilloscope
Photo diod
Laser
trig
Piezoelectric
Spacer rings
Y
Sawtooth generator
Fig. 5. Scheme for measuring with a scanning Fabry-Perot interferometer.
The analyser is a confocal Fabry-Perot-interferometer mounted in front of a photodiode.
One of the mirrors is mounted on a piezoelectric material, so the distance between the
mirrors can be changed. This is done with a saw tooth voltage pulse, which also is used to
trigger the oscilloscope displaying the signal. The free spectral range of the interferometer
(The frequency difference between two neighbouring transmissions peaks) is   2000
MHz. For a given distance between the mirrors the frequencies Nwill be transmitted
where N is a big integer that corresponds to the optical frequencies. The distance between
the interferometer mirrors is scanned using the saw tooth voltage pulse. This will shift the
transmission maxima of the interferometer. The detector will only detect light if the
incoming light has the same frequency as the transmission maxima of the interferometer.
We get a frequency scale that depends on the total displacement of the plates. If the
frequency scale is larger than  the laser frequency will show up two or more times. The
vertical displacement on the oscilloscope is proportional the laser irradiance at that
frequency, and the peak position is determined by the frequency.
4
Preparation exercises
1.
Calculate the power used by the laser if it the voltage is 1450 V and the current is 6.5
mA.
2.
The quantum efficiency is defined as number of electrons that are generated by one
photon. If the quantum efficiency for a photodiode is 0.5, what current, in mA, will
the photodiode generate if you shine light with a wavelength of 633 nm and a power
of 1.0 mW?
Hint: Power of monochromatic light 1.0 mW = 1.0.10-3J/s Number of photons/s.
3.
What mirror distances are stable for a resonator with a plane mirror and a concave
mirror with a 0.45 m radius of curvature?
4.
Calculate the frequency difference between the TEM00-mode and the TEM02-mode
for
L = 0.4 m, ni = 1, R1  and R21 m.
5.
Fig. 6 shows the oscilloscope picture similar to Fig. 5.
Mark for the laser and FSRfor the Fabry-Perot Interferometer. Figure out which
effects are caused by the Fabry-Perot interferometer and which the laser causes.
Calculate the length of the laser cavity and determine, by using realistic assumptions,
the radius of curvature of the two cavity mirrors.
500 MHz
Fig. 6. Oscilloscope picture of a measurement with a Fabry-Perot interferometer
5
Lab exercises
1.
Remove carefully the lasertube and the loose mirrors. Direct another laser by with two
mirrors (why two?), so the beam is parallel to and centred on the optical bench. Adjust
the lasertube and the loose mirror (R = 0.45 m) with the help of the laser beam. Turn
on the lasertube and adjust the lasertube and mirror to maximum output laser power.
The power can be measured with a photodiode, which delivers an output current to
one milliamperemeter. This type of procedure is called alignment. The sensitivity of
the photo diode is 0.4 mA/mW. Measure the output power of the laser. The voltage
over the operating tube is about 1.45 kV and the current is about 6.5 mA. Calculate
the laser efficiency. Calculate the corresponding quantum efficiency of the detector.
number of photoelect rons
Quantum efficiency 
number of incomming photons
2.
Move the loose mirror and measure the output power for different resonator lengths.
Compare the measurements with the stability diagram and write down how increasing
the resonator length effects the position in diagram. Look especially at treshold for
lasing. Note the output power for at least four different resonator lengths (use at least
two lengths close to lasing).
3.
Use a polariser to study the polarisation of the laserlight. Why is there a Brewster
window in the lasercavity?
The discharge current for this particular laser is adjusted for maximal effect. How do
you think that variation of the current affects the output effect? What happens if the
current is greatly enhanced (hint: Look at figure 10.3 in Svelto)? State 2-3 effects that
will affect the output power. Draw a graph that shows the main characteristics of the
output effect as a function of the discharge current.
4.
Use a lens and a screen to study the laser intensity profile. Place an iris or a haircross
inside the resonator to study the tranversal modes. Draw a picture of some modes you
get in each case and explain the pattern.
5.
Mount a Scanning Fabry-Perot interferometer. The output signal is studied using an
oscilloscope. The free spectral range of the interferrometer is 2 GHz. What is the
distance between the plates?
Study the signal from the interferometer when the laser beam is almost perpendicular
to the mirrors of the interferometer. Adjust the laser so that only one transversal mode
(TEM00) exists. Think about how it should look transversally (on the screen) and
spectrally. Make a drawing of the oscilloscope screen. Measure the frequency
difference between the axial modes and calculate the mirror distance. Compare with
the measured mirror distance.
6. Adjust the laser to get a mixture of two transversal modes, for example the TEM01
and TEM00. Make a drawing of the oscilloscope screen and mark the different modes
on the graph. Determine the frequency difference and compare the result with a
theoretical calculation. At the same time study how the beam looks on a screen. Do
you see both modes?
6
7.
Replace the moveable mirror with the 1 m radius of curvature and 99.97% reflectivity
mirror. First place a glass plate near the lasertube and then align it so a single axial
mode is generated. The laser now operates in single frequency mode. Place a laser
etalon inside the cavity. What has changed compared to the glass plate? Why? Make a
figure that describes how the single frequency lasing is obtained.
8.
Use one of the two mirrors with a 1 m radius of curvature. Obtain maximum power
and measure the output power. Do also measure the output power from the permanent
end mirror (think in terms of systematic errors). This value should be used as a
monitor value for the laser power in the cavity. Do the same with the other 1 m radius
of curvature mirror. How is the laser power inside the cavity affected? Why? What is
the gain, in %, (per optical roundtrip) for both cases? What is the gain of the gain
medium in dB/m?
7