This document discusses laser linewidth measurement. It begins by explaining that lasers are not truly monochromatic and have a defined line shape rather than a single frequency. It then covers the different types of broadening mechanisms that contribute to a laser's linewidth, including homogeneous broadening from effects like collisions, and inhomogeneous broadening from Doppler shifts. Measurement techniques are also presented, such as using interferometers to convert frequency fluctuations to intensity fluctuations or using self-heterodyne detection to record beat notes between a laser and its frequency-shifted output. Specific examples of using a Michelson interferometer and self-mixing interferometry for linewidth measurements are also described.

1. Laser Linewidth Measurement

3. 1- Introduction
►It was always thought that Laser is
monochromatic or it is a single frequency
amplified beam of light. The idea of a
monochromatic Laser is not quite true.
The fact is that the Laser beam spectrum
has a defined line shape and not just a
single point on the spectrum.

4. ►This phenomenon is called Laser
broadening and the measure of it is
the Linewidth. In our project we
will discuss the causes of the
broadening of the Laser line shape
and practical methods of measuring
the linewidth in some Lasers.

5. 2- Types of Broadening
Broadening
Homogeneous Inhomogeneous
Doppler Local FieldNatural or Intrinsic Collision

6. 2.1- Homogeneous Broadening
►By Homogeneous Broadening we mean that
the line of each atom broadens in the same
way. In this case the lineshape of the
single-atom cross section and that of the
overall absorption cross section are
identical.

7. 2.1.1Collision Broadening
► In a gas or a liquid it is due to the collision of an atom
with other atoms, ions, free electrons, etc., or with the
walls of the container
► In a solid it is due to the interaction of the atom with the
lattice phonons
]),(41[
1
2),( 222
υυτπ
τυυ
oc
cog
+
=
► The lineshape function resulting from this type of broadening is a
Lorentzian function taking the form:
► And the Full Width Half Maximum of the line (FWHM) is given
by:
c
o
πτ
υ
1
=∆

8. 2.1.2 Natural or Intrinsic Broadening:
►It originates from spontaneous emission.
Since this emission is a feature of any
transition, the corresponding broadening is
called natural or intrinsic. The quantum
electrodynamics theory of spontaneous
emission shows that the spectrum is again
described by a Lorentzian line

9. Lorentzian lineshape function for homogeneous broadening

10. 2.2 Inhomogeneous Broadening:
►A line-broadening mechanism is said to be
inhomogeneous when it distributes the
atomic resonance frequencies over some
spectral range. Such a mechanism thus
broadens the line of the overall system
without broadening the lines of individual
atoms.

11. 2.2.1 Doppler Broadening
► Gas molecules in a laser tube are often hot and travel at high
speeds. When a gas molecule is seen emitting radiation. If the
molecule moves toward the observer when emitting radiation, the
frequency of the radiation appears to increase. Similarly, the
frequency decreases if the molecule speeds away from the
observer when emitting a photon of light. This will yield two values
for the frequency of the laser, one minimum and one maximum,
which will define the range of outputs of the laser.
► Although atoms in a solid-state laser crystal will not move as gas
molecules do, the lattice of a solid-state laser crystal will vibrate
more with increasing temperature. This vibration will affect the
system by making the energy band broader, and hence increase
the spectral linewidth.

12. ► And the Width Half Maximum of the line (FWHM) is
given by:
KTMv
2
1
2
1 2
=
c
vυ
υ
2
=∆
2
2ln2
Mc
KT
oυυ =∆
► Lineshape is a Gaussian function in the form of:
2ln]
)(2
[ 2
2ln2
),( υ
υυ
πυ
υυ ∆
−
−
∆
=
o
eg o

13. 2.2.2 Local Field
► This Mechanism of broadening occurs for ions in ionic crystals or
glasses. Such ions experience a local electric field produced by
surrounding atoms of the material. Due to material
inhomogeneities that are more obvious in a glass medium, these
fields differ from ion to ion. Local field variations then produce
local variation of energy levels and thus of the ions' transition
frequencies. For random local field variations, the corresponding
distribution of transition frequencies turns out to be given by a
Gaussian function.
The Gaussian distribution

14. Comparison of normalized Gaussian and Lorentzian lineshapes

15. Generally, in Solids the broadening is mostly inhomogeneous due to
inhomogeneities in the material. In liquids it is due to collisions and
inhomogeneities. While gases posses more mechanism of broadening due to
Doppler, natural and collisions but that due to Doppler effects tends to dominate
other mechanisms

16. 3- Linewidth measurement:
► A laser linewidth can be measured with a variety of techniques:
► For large linewidths (traditional techniques of optical spectrum
analysis, e.g. based on diffraction gratings, are suitable.
► Another technique is to convert frequency fluctuations to intensity
fluctuations, using a frequency discriminator, which can e.g. be an
unbalanced interferometer.
► For single-frequency lasers, the self-heterodyne technique is often
used, which involves recording a beat note between the laser output
and a frequency-shifted and delayed version of it.
► Very high resolution can also be obtained by recording a beat note
between two independent lasers, where either the reference laser
has significantly lower noise than the device under test, or both
lasers have similar performance.

17. 3.1 Interferometer
► An interferometer is an optical device which
utilizes the effect of interference.
► It starts with some input beam, splits it into
two separate beams with some kind of beam
splitter (a partially transmissive mirror),
possibly exposes some of these beams to some
external influences (e.g. some length changes
or refractive index changes in a transparent
medium), and recombines the beams on
another beam splitter

18. 3.2 Michelson Interferometer

19. ► A Michelson interferometer uses a single beam splitter for
separating and recombining the beams. If the two mirrors
are aligned for exact perpendicular incidence, only one
output is accessible, and the light of the other output goes
back to the light source. If that optical feedback is
unwanted and/or access to the second output is required,
the recombination of beams can occur at a somewhat
different location on the beam splitter. One possibility is to
use retro reflectors, as shown in the lower figure; this also
has the advantage that the interferometer is quite
insensitive to slight misalignment of the retro reflectors.
► If the path length difference is non-zero, as shown in both
figures, constructive or destructive interference e.g. for the
downward-directed output can be achieved.

20. 3.3 Self-heterodyne linewidth measurement
One portion of the laser beam is sent through a long optical fiber
which provides some time delay, while another portion is sent
through an acousto-optic modulator (AOM), which shifts all the
optical frequency components by some tens of megahertz. Both
beams are finally superimposed on a beam splitter, and the
resulting beat note (centered at the AOM frequency) is recorded
with a photodetector

21. 4-Linewidth experimental measurement:
4.1 Experiment 1: Linewidth Measurement
using Michelson Interferometer:

23. 4.2 Experiment 2: Linewidth Measurement by
Means of Self-Mixing Interferometry

25. Thank You