Laser linewidth measurement

Laser Linewidth Measurement

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.

►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.

2- Types of Broadening

Broadening

Homogeneous Inhomogeneous

Doppler Local Field Natural or Intrinsic Collision

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.

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[12),( 222 υυτπ

τυυoc

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:

co πτ

υ 1=∆

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

Lorentzian lineshape function for homogeneous broadening

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.

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.

► And the Width Half Maximum of the line (FWHM) is given by:

KTMv21

21 2 =

cvυυ 2

=∆

2

2ln2Mc

KToυυ =∆

► Lineshape is a Gaussian function in the form of:

2ln])(2

[ 22ln2),( υυυ

πυυυ ∆

−−

∆=

o

eg o

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

Comparison of normalized Gaussian and Lorentzian lineshapes

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

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.

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

3.2 Michelson Interferometer

► 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.

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

4-Linewidth experimental measurement:

4.1 Experiment 1: Linewidth Measurement using Michelson Interferometer:

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

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