Curso de Métodos experimentales
En la Física PCF UNAM
Cuernavaca, Agosto 2008
cuarta semana
Dr. Antonio M. Juárez Reyes, ICF UNAM
Física Atómica, Molecular y óptica.
Cuernavaca, Agosto 2008
TEMARIO PARTE 1
I.- Instrumentos y conceptos básicos (Toño, 5 semanas)
I.1.- Conceptos básicos de instrumentación
-Conceptos generales de seguridad en el laboratorio (eléctrica, de gases
comprimidos, láseres y químicos.
--El proceso de medida y asignación de incertidumbres.
I.2.- Instrumentos básicos
2.1 sistemas de vacío.
-Conductancia, velocidad de bombeo, viscosidad,
-bombas: Rotatorias, de diafragma, difusoras, turbo, de sublimación,
ionicas. razón de compresión en bombas,
- transductores de presión, pirani, Bayer Alpert, Baratrón, análisis de
gases
residuales.
2.2 Instrumentos básicos de electrónica:
-osciloscopios, generadores de señales,
electrómetros,
2.3 Instrumentos avanzados
-Amplificador Lock In
-Integrador Boxcar
-Monocromadores
Cuernavaca, Agosto 2008
I.3.- Conceptos generales de láseres y fuentes de luz:
- Cavidades, ganancia y finesa
- Etalones de Fabri Perot,elementos ópticos
- Láseres pulsados de nitróngeno, Nd:YAG, pulsadores del tipo Q-Switch,
láseres de diodo de cavidad extendida,
-Otras fuentes de luz: sincrotrónesy Free electron Lasers,
I.4.-Conceptos generales de diseño: herramientas de dibujo, herramientas de
simulación de circuitos, criterios generales de diseño de piezas asociadas a
instrumentación científica.
El taller de electrónica y el taller de mecánica del ICF
1.5 Elección del proyectos semestrales de instrumentación
Cuernavaca, Agosto 2008
I.3.- Conceptos generales de láseres y fuentes de luz:
-Cavidades, tipos de resonadores, ganancia y finesa
-Etalones de Fabri Perot,elementos ópticos,
-Componentes ópticas especiales ( moduladores optoacústicos,
placas de media y cuarto de onda, diodos faraday
-Láseres pulsados de nitróngeno, Nd:YAG, pulsadores del tipo QSwitch, láseres de diodo de cavidad extendida, laseres de tintes
-Otras fuentes de luz: sincrotrónesy Free electron Lasers,
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Lasing occures whenever the laser threshold is reached
The threshold of a laser is the state where the small-signal gain just
equals the resonator losses. This is the case for a certain pump power
(the threshold pump power), or (for electrically pumped lasers) a
certain threshold current. Significant power output, good power
efficiency and stable, low-noise performance requires operation well
above the threshold.
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Lasing occures whenever the laser threshold is reached
The threshold pump power of a laser is the value of the pump power
at which the laser threshold is just reached. At this point, the smallsignal gain equals the losses of the laser resonator. A similar threshold
exists for some other types of light sources, such as Raman lasers and
optical parametric oscillators.
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Lasing occures whenever the laser threshold is reached
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Within the context of laser physics, a laser gain medium is a
medium which can amplify the power of light (typically in
the form of a light beam).
Such a gain medium is required in a laser to compensate for
the resonator losses, and is also called an active laser
medium. It can also be used for application in an optical
amplifier. The term gain refers to the amount of
amplification.
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
There are a variety of very different gain media; the most
common of them are: Certain direct-bandgap
semiconductors such as GaAs, AlGaAs(aluminium Galium
arsenide), or InGaAs(aluminium Galium arsenide), are
typically pumped with electrical currents, these lasers are
often in the form of quantum wells.
A quantum well is a thin layer which can confine (quasi-)particles (typically electrons or holes) in the
dimension perpendicular to the layer surface, whereas the movement in the other dimensions is not
restricted. The confinement is a quantum effect. It has profound effects on the density of states for the
confined particles. For a quantum well with a rectangular profile, the density of states is constant
within certain energy intervals.
[1]T. Makino, “Analytical formulas for the optical gain of quantum wells”, IEEE J. Quantum Electron. 32, 493
(1995) [2]P. S. Zory (ed.), Quantum Well Lasers – Principles and Applications, Academic Press, New York (1993)
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
…Certain laser crystals and glasses such as Nd:YAG (neodymiumdoped yttrium aluminum garnet → YAG lasers), Yb:YAG (ytterbiumdoped YAG), Yb:glass, Er:YAG (erbium-doped YAG), or Ti:sapphire
are used in the form of solid pieces (→ bulk lasers) or optical glass
fibers (→ fiber lasers, fiber amplifiers). These crystals or glasses are
doped with some laser-active ions (in most cases trivalent rare earth
ions, sometimes transition metal ions) and optically pumped. Lasers
based on such media are sometimes called doped insulator lasers.
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
There are ceramic gain media, which are also normally doped with rare
earth ions. Laser dyes are used in dye lasers, typically in the form of
liquid solutions. Gas lasers are based on certain gases or gas mixtures,
typically pumped with electrical discharges (e.g. in CO2 lasers and
excimer lasers). More exotic gain media are chemical gain media
(converting chemical energy to optical energy), nuclear pumped media,
and undulators in free electron lasers (transferring energy from a fast
electron beam to a light beam).
Cuernavaca, Agosto 2008
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
In most cases, the physical origin of the
amplification process is stimulated emission,
where photons of the incoming beam trigger the
emission of additional photons in a process where e.g.
initially excited laser ions enter a state with lower energy.
Here, there is a distinction between
four-level and three-level gain media.
Cuernavaca, Agosto 2008
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
four-level and three-level gain media.
In a three-level system, the laser transition ends on the ground state.
The unpumped gain medium exhibits strong absorption on the laser
transition. Only by pumping more than half of the ions (or atoms)
into the upper laser level do a population inversion and consequently
net laser gain result; the threshold pump power is thus fairly high.
Cuernavaca, Agosto 2008
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
four-level and three-level gain media.
An example of a three-level laser medium is ruby (Cr3+:Al2O3)
Cuernavaca, Agosto 2008
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
four-level and three-level gain media.
A lower threshold pump power can be achieved with a four-level
laser medium, where the lower laser level is well above the ground
state and is quickly depopulated e.g. by multiphonon transitions.
Ideally, no appreciable population density in the lower laser level can
occur even during laser operation. The gain usually rises linearly with
the absorbed pump power.
Cuernavaca, Agosto 2008
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
four-level and three-level gain media.
The most popular four-level solid-state gain medium is Nd:YAG. All
lasers based on neodymium-doped gain media, except those operated
on the ground-state transition around 0.9–0.95 μm, are four-level
lasers.
Cuernavaca, Agosto 2008
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
four-level and three-level gain media.
A quasi-three-level laser medium is the intermediate situation, where
the lower laser level is so close to the ground state that an appreciable
population in that level occurs in thermal equilibrium at the operating
temperature. As a consequence, the unpumped gain medium causes
some loss at the laser wavelength, and lasing is reached only for
some finite pump intensity. For higher pump intensities, there is gain,
as required for laser operation.
Cuernavaca, Agosto 2008
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
Figure 2: Gain and absorption (negative gain) of erbium (Er3+) ions in germano-alumino-silicate
glass for excitation levels from 0 to 100% in steps of 20%. Strong three-level behavior (with
transparency reached only for > 50% excitation) occurs at 1530 nm. At longer wavelengths (e.g.
1580 nm), a lower excitation level is required for obtaining gain, but the maximum gain is
smaller.
Cuernavaca, Agosto 2008
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
Relevant Physical Properties of Laser Gain Media
A great variety of physical properties of a gain medium can be relevant for use in a laser. The
desirable properties include:
1.- a laser transition in the desired wavelength region, preferably with the maximum gain
occurring in this region
2.- a high transparency of the host medium in this wavelength region
a pump wavelength for which a good pump source is available (in case of an optically pumped
laser);
3.- efficient pump absorption a suitable upper-state lifetime: long enough for Q-switching
applications, short enough if fast modulation of the power is required
a high quantum efficiency, obtained via a low prevalence for quenching effects, excited-state
absorption and the like, but also possibly by strong enough beneficial effects such as certain
multi-phonon transitions or energy transfers
4.- ideally, four-level behavior, because quasi-three-level behavior introduces various additional
constraints
5.- robustness and a long lifetime, chemical stability
Bibliography
Cuernavaca, Agosto 2008
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Types of Laser Gain Media
References
P. P. Sorokin and M. J. Stevenson, “Stimulated infrared emission
from trivalent uranium”, Phys. Rev. Lett. 5 (12), 557 (1960) (the
first four-level laser)
W. P. Risk, “Modeling of longitudinally pumped solid-state lasers
exhibiting reabsorption losses”, J. Opt. Soc. Am. B 5 (7), 1412
(1988)
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source (optical pumping)
-3 and 4 optical resonator
-5 Laser light
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source (optical pumping)
-3 and 4 optical resonator
-5 Laser light
Definition: electronically exciting a
medium with light, or specifically
populating certain electronic levels
Optical pumping processes can often be described with
rate equation modeling. However, this disregards some aspects
of the quantum nature of the atom–photon interaction. More
comprehensive physical models exist which can also
describe coherent phenomena such as Rabi oscillations.
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source (optical pumping)
-3 and 4 optical resonator
-5 Laser light
As an example, consider the dynamics of an
erbium-doped gain medium, such as used in, e.g.,
erbium-doped fiber amplifiers.
Ip Intensidad de bombeo
Is Intensidad de luz estimulada
Cuernavaca, Agosto 2008
Common types of optical pump sources are:
discharge lamps (→ lamp-pumped lasers)
laser diodes (→ diode-pumped lasers)
other types of lasers or laser sources:
Examples of the latter case are titanium–sapphire lasers pumped with
frequency-doubled solid-state lasers, and dye lasers pumped with gas
lasers.
Cuernavaca, Agosto 2008
Pump light for optical pumping has to fulfill a number of requirements:
The optical spectrum of the pump light must be suitable. Ideally, all the photons
should have a suitable energy for the wanted electronic transitions. However, certain
laser-active ions (e.g. neodymium ions) can also be pumped with fairly broadband
light e.g. for flash lamps or arc lamps, albeit with a strongly reduced power
conversion efficiency.
The pump intensity must be sufficiently high. Lasers are often pumped with
intensities of the order of the saturation intensity of the laser transition, but fourlevel lasers can also be operated with lower pump intensities.
Depending on the geometry, there can be more or less stringent requirements on the
pump beam quality. This applies mostly to end-pumped lasers.
In some cases, the polarization state of the pump light is also important. Some nonisotropic gain media, such as Nd:YVO4, exhibit very different levels of absorption
for different polarization directions. In spectroscopy, circularly polarized light is
sometimes required for populating certain hyperfine levels.
The intensity noise of the pump source should not be too large, because at least its
low-frequency components can be transferred to the laser output.
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source (optical pumping)
-3 and 4 optical resonator
-5 Laser light
[1]
M. Peroni and M. Tamburrini, “Gain in erbium-doped fiber amplifiers: a simple analytical
solution for the rate equations”, Opt. Lett. 15 (15), 842 (1990)
[2]
C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers”, J. Lightwave Technol.
9 (2), 271 (1991)
[3]
R. Paschotta et al., “Characterization and modeling of thulium:ZBLAN blue upconversion
fiber lasers”, J. Opt. Soc. Am. B 14 (5), 1213 (1997)
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source (optical pumping)
-3 and 4 optical resonator (optical cavity)
-5 Laser light
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source (optical pumping)
-3 and 4 optical resonator (optical cavity)
-5 Laser light
An optical resonator (or resonant optical cavity) is an arrangement
of optical components which allows a beam of light to circulate in
a closed path. Such resonators can be made in very different
forms.
Depending upon the geometry an optical cavity or optical
resonator forms a standing wave cavity resonator for light waves.
Cuernavaca, Agosto 2008
An optical resonator can be made from bulk optical components, as shown
in the next page , or as a waveguide resonator, where the light is guided
rather than sent through free space.
.
Bulk-optical resonators are used e.g. for solid-state bulk lasers. The
transverse mode properties depend on the overall setup (including the
length of air spaces), and mode sizes can vary significantly along the
resonator. In some cases, the mode properties are also significantly
influenced by effects such as thermal lensing.
Waveguide resonators are often made with optical fibers (e.g. for fiber
lasers) or in the form of integrated optics. The transverse mode properties
(see below) are determined by the local properties of the waveguide.
There are also mixed types of resonators, containing both waveguides and
parts with free-space optical propagation. Such resonators are used e.g. in
some fiber lasers, where bulk-optical components need to be inserted into
the laser resonator.
Cuernavaca, Agosto 2008
Linear versus Ring
Linear (or standing-wave) resonators (Figure 1, top) are made such that the
light bounces back and forth between two end mirrors. For continuously
circulating light, there are always counterpropagating waves, which
interfere with each other to form a standing-wave pattern.
In ring resonators (Figure 1, bottom), light can circulate in two different
directions . A ring resonator has no end mirrors.
.
Figure 1: A simple linear optical resonator with
a curved folding mirror (top) and a four-mirror
bow-tie ring resonator (bottom).
Cuernavaca, Agosto 2008
During a resonator round trip, light experiences various physical effects
which change its spatial distribution: diffraction, focusing or defocusing
effects of optical elements (sometimes involving optical nonlinearities), in
special cases also gain guiding, saturable absorption, etc.
Some important differences between linear resonators and ring
resonators are:
.
In a ring resonator, light can circulate in two different directions. If
there is an output coupler mirror, this leads to two different output
beams. A linear resonator with the output coupler at an end does not
exhibit this phenomenon.
An optical component within a resonator is hit by the light once per
round trip in the case of a ring laser, and twice per round trip in a
linear resonator (except for the end mirrors).
Cuernavaca, Agosto 2008
During a resonator round trip, light experiences various physical effects
which change its spatial distribution: diffraction, focusing or defocusing
effects of optical elements (sometimes involving optical nonlinearities), in
special cases also gain guiding, saturable absorption, etc.
Some important differences between linear resonators and ring
resonators are:
.
… When light is injected into a linear resonator via a partially
transparent mirror, reflected light can propagate back to the light
source. This is not the case for a ring resonator. Therefore, ring
resonators are sometimes preferred for resonant frequency doubling
with a laser source which is sensitive against optical feedback.
A linear bulk resonator can have two stability zones (see below), e.g.
for variation of the dioptric power of an internal lens, or of a
resonator arm length. A ring resonator has only one stability zone.
Cuernavaca, Agosto 2008
During a resonator round trip, light experiences various physical effects
which change its spatial distribution: diffraction, focusing or defocusing
effects of optical elements (sometimes involving optical nonlinearities), in
special cases also gain guiding, saturable absorption, etc.
Some important differences between linear resonators and ring
resonators are:
.
The non-normal incidence of light on every resonator mirror of a ring
resonator causes astigmatism if a resonator mirror has a curved
surface. A bow-tie ring resonator geometry is often used to minimize
astigmatism by keeping the incidence angles small.
Monolithic ring resonators with high Q factor can exploit total
internal reflection at all surfaces, and thus may not require any
dielectric mirror.
Cuernavaca, Agosto 2008
Examples of optical cavities
Depending upon its
geometry, optical
resonators present
different stability
properties….
What is stability?
Cuernavaca, Agosto 2008
Definition of stability zones : parameter regions of an
optical resonator where the beam is geometrically stable
When a parameter of a laser resonator (optical cavity) such
as an arm length or the dioptric power (inverse focal
length) of the focusing element in the resonator is varied,
the resonator may go through one (for ring resonators) or
two (for standing-wave resonators) stability zones.
In a purely geometric sense, stability means that a ray injected into the optical
system will stay at a finite distance from the axis even after many round trips.
Cuernavaca, Agosto 2008
Definition of stability zones : parameter regions of an
optical resonator where the beam is geometrically stable
When a parameter of a laser resonator (optical cavity) such
as an arm length or the dioptric power (inverse focal
length) of the focusing element in the resonator is varied,
the resonator may go through one (for ring resonators) or
two (for standing-wave resonators) stability zones.
In a purely geometric sense, stability means that a ray injected into the optical
system will stay at a finite distance from the axis even after many round trips.
Cuernavaca, Agosto 2008
Definition of stability zones : parameter regions of an
optical resonator where the beam is geometrically stable
When a parameter of a laser resonator (optical cavity) such
as an arm length or the dioptric power (inverse focal
length) of the focusing element in the resonator is varied,
the resonator may go through one (for ring resonators) or
two (for standing-wave resonators) stability zones.
Only certain ranges of values for R1, R2, and L produce stable resonators in which
periodic refocussing of the intracavity beam is produced. If the cavity is unstable,
the beam size will grow without limit, eventually growing larger than the size of
the cavity mirrors and being lost. By using methods such as
ray transfer matrix analysis, it is possible to calculate a stability criterion:
Cuernavaca, Agosto 2008
Stability criterion
Values which satisfy the inequality correspond to stable resonators.
The stability can be shown graphically by defining a stability parameter,
g for each mirror:
Cuernavaca, Agosto 2008
Interms of g, the stability zones look like:
Cuernavaca, Agosto 2008
Modes:
In general, radiation patterns which are reproduced on every
round-trip of the light through the resonator are the most stable, and these
are the eigenmodes, known as the modes, of the resonator.
Resonator modes are the modes of an optical resonator (cavity),
i.e. field distributions which reproduce themselves (apart from a
possible loss of power) after one round trip. They can exist whether
or not the resonator is geometrically stable, but the mode properties
of unstable resonators are fairly sophisticated. In the following,
only modes of stable resonators are considered
Cuernavaca, Agosto 2008
Examples of optical cavities
Resonator modes can be divided
into two types: longitudinal modes,
which differ in frequency from
each other; and transverse modes,
which may differ in both frequency
and the intensity pattern of the
light. The basic, or fundamental
transverse mode of a resonator is a
Gaussian beam.
Cuernavaca, Agosto 2008
In the simplest case of a resonator containing only parabolic
mirrors and optically homogeneous media, the resonator
modes (cavity modes) are Hermite–Gaussian modes.
The simplest of those are the Gaussian modes, where the field
distribution is defined by a Gaussian function (→ Gaussian
beams). The evolution of the beam radius and the radius of
curvature of the wavefronts is determined by the details of the
resonator. As an example, Figures 1 and 2 show the Gaussian
resonator modes for two versions of a simple resonator with a
plane mirror, a laser crystal, and a curved end mirror. For a
more strongly curved end mirror (Figure 2), the mode radius
on the left mirror becomes smaller.
Cuernavaca, Agosto 2008
The simplest mode is the Gaussian mode,
which has a complex amplitude described by the cylindrical
equation:
With solution in terms of intensity:
Cuernavaca, Agosto 2008
Hermite Gaussian modes.
The Gaussian mode is a specific case of the more
generalized Hermite-Gaussian (HG) modes.
The HG modes are also referred to as
Transverse Electro-Magnetic, or TEM.
A TEM mode is described as TEMmn,
where m and n are the indices of the mode.
m refers to the number of intensity minima in the
direction of the electric field oscillation, and n refers
to the number of minima in the direction of the
magnetic field oscillation.
Cuernavaca, Agosto 2008
Hermite Gaussian modes.
The Gaussian mode is a specific case of the more
generalized Hermite-Gaussian (HG) modes.
The HG modes are also referred to as
Transverse Electro-Magnetic, or TEM.
A TEM mode is described as TEMmn,
where m and n are the indices of the mode.
m refers to the number of intensity minima in the
direction of the electric field oscillation, and n refers
to the number of minima in the direction of the
magnetic field oscillation.
Cuernavaca, Agosto 2008
Hermite Gaussian modes.
Example: HG02 mode
The mathematical equation for its complex amplitude is
Cuernavaca, Agosto 2008
In addition to the Gaussian modes, a resonator also has
higher-order modes with more complicated intensity
distributions
¿What can you do
With them..
Example of a box
For an atom
Cuernavaca, Agosto 2008
Other cool modes: Laguerre-Gaussian Modes
LG modes, like the Gaussian mode, are circularly symmetric.
However, all LG modes except LG00 are hollow. Their key
feature is the presence of a screw phase dislocation, which
means that is has orbital angular momentum. One cool
application of this is the transfer of this momentum to a
particle, making it spin. This screw phase dislocation is
also the origin of the hollow center of an LG beam, since
that type of phase dislocation appears as a dark spot. An
LG mode is described by the equation (with symbols
defined as they were for HG modes):
Cuernavaca, Agosto 2008
Other cool modes: Laguerre-Gaussian Modes
How complex can
They get?
Cuernavaca, Agosto 2008
Light amplificated by stimulated emission of radiation (LASER)
-General layout
-1 Active media
-2 External pump source
-3 and 4 optical resonator
-5 Laser light
Cuernavaca, Agosto 2008
-5 Laser light ( IMPORTANT DEFINITIONS)
-Coherence length and coherence time
-Linewidth
-Power
Coherence (time):a measure of temporal coherence, expressed as the
time over which the field correlation decays
The coherence time can be used for quantifying the degree of temporal
coherence of light. In coherence theory, it is essentially defined as the
time over which the field correlation function decays. This correlation
(or coherence) function is
where E(t) is the complex electric field at a certain location.
This function is 1 for = 0 and usually decays monotonically
for larger time delays
Cuernavaca, Agosto 2008
Coherence (time):a measure of temporal coherence, expressed as the
time over which the field correlation decays
The coherence time can be used for quantifying the degree of temporal
coherence of light. In coherence theory, it is essentially defined as the
time over which the field correlation function decays. This correlation
(or coherence) function is
For an arbitrary shape of this function, the coherence time can
be defined by
Cuernavaca, Agosto 2008
Instead of the coherence time, it is common to specify
the coherence length, which is simply the coherence
time times the vacuum velocity of light, and thus also
quantifies temporal (rather than spatial) coherence.
[1]B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, John Wiley &
Sons, Inc., New York (1991)
Cuernavaca, Agosto 2008
The reason for often using the term coherence length instead of
coherence time is that the optical time delays involved in some
experiment are often determined by optical path lengths.
Lasers, particularly single-frequency solid-state lasers,
can have very long coherence lengths, e.g. 9.5 km for a
Lorentzian spectrum with a linewidth of 10 kHz.
The coherence length is limited by phase noise which can
result from, e.g., spontaneous emission in the gain medium.
[1]B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, John Wiley &
Sons, Inc., New York (1991)
Cuernavaca, Agosto 2008
The coherence time is intimately linked with the linewidth
of the radiation, i.e., the width of its spectrum.
In the case of an exponential coherence decay
as above, the spectrum has a Lorentzian shape,
and the (full width at half-maximum) linewidth is
Cuernavaca, Agosto 2008
A finite linewidth arises from phase noise if the phase
undergoes unbounded drifts, as is the case for free-running
oscillators.
Drifts of the resonator length (e.g. related to 1 / f noise) can
further contribute to the linewidth and can make it
dependent on the measurement time.
This shows that the linewidth alone, or even the linewidth
complemented with a spectral shape (line shape), does by
far not provide full information on the spectral purity of
laser light. (This is particularly the case for lasers with
dominating low-frequency phase noise.)
Cuernavaca, Agosto 2008
For simple cases, the fundamental limit for the laser
linewidth arising from quantum noise was calculated by
Schawlow and Townes [1] even before the first laser was
experimentally demonstrated. According to the Schawlow–
Townes equation [1]A. L. Schawlow and C. H. Townes, “Infrared and optical masers”, Phys.
Rev. 112 (6), 1940 (1958) (contains the famous Schawlow–Townes equation)
the linewidth (FWHM) is proportional to the square of the
resonator bandwidth divided by the output power
(assuming that there are no parasitic resonator losses).
The article on the Schawlow–Townes linewidth contains a
more practical form of the equation.
Cuernavaca, Agosto 2008
Measurement of Laser Linewidth
A laser linewidth can be measured with a variety of techniques:
For large linewidths (e.g. > 10 GHz, as obtained when multiple modes of the
laser resonator are oscillating), 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 be, e.g., an unbalanced interferometer
or a high-finesse reference cavity.
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.
For sub-kilohertz linewidths, the ordinary self-heterodyne technique usually
becomes impractical, but it can be extended by using a recirculating fiber loop
with an internal fiber amplifier.
Cuernavaca, Agosto 2008
Measurement of Laser Linewidth
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. This method is
conceptually very simple and reliable, but the requirement of a second laser
(operating at a nearby optical frequency) can be inconvenient. If linewidth
measurements are required in a wide spectral range, a frequency comb source
can be very useful.
Exercise: What are the linewidths of the lasers in the lab? How do they compare
To the natural linewidth of, say Rubidium ( isotope 85) and to the doppler broadening
Cuernavaca, Agosto 2008
-5 Laser light ( IMPORTANT DEFINITIONS)
-Coherence length and coherence time
-Linewidth
-Power
The linewidth (or line width) of a laser, typically a
single-frequency laser, is the width (typically the full
width at half-maximum, FWHM) of its optical spectrum.
More precisely, it is the width of the power spectral density
of the emitted electric field in terms of frequency,
wavenumber or wavelength.
Cuernavaca, Agosto 2008
-5 Laser light ( IMPORTANT DEFINITIONS)
-Coherence length and coherence time
-Linewidth
-Power
Or, to be more precise, power spectral density
Definition: optical power or noise power per unit frequency
Interval
In optics, power spectral densities (also sometimes just called power densities) occur
basically in two different forms: optical power spectral densities, defined as the
optical power per optical frequency (or wavelength) interval, e.g. specified in
mW/THz or mW/nm
Cuernavaca, Agosto 2008
Or, to be more precise, power spectral density
Definition: optical power or noise power per unit frequency
Interval
In optics, power spectral densities (also sometimes just called power densities) occur
basically in two different forms: optical power spectral densities, defined as the
optical power per optical frequency (or wavelength) interval, e.g. specified in
mW/THz or mW/nm
Cuernavaca, Agosto 2008
Or, to be more precise, power spectral density
Definition: optical power or noise power per unit frequency
Interval
Note the units in
The scale!!
Cuernavaca, Agosto 2008
To keep the power spectral density of a laser narrow
And stable, one needs to stabilize a laser ( they tend
to be very sensitive to changes in temperature ( cavities
Change length, media change properties.. Etc)
To keep a laser stable, one needs to do tricks
Cuernavaca, Agosto 2008
Stabilization of Lasers
Active Laser Stabilization
Active stabilization schemes usually involve some kind of
electronic feedback system, where fluctuations of some
parameters are converted to an electronic signal, which is
then used to act on the laser in some way.
Cuernavaca, Agosto 2008
Stabilization of Lasers
The output power of a laser may be stabilized with a scheme as
shown in Figure 1. The laser power is monitored with a photodiode
and corrected e.g. via control of the pump power or the losses in or
outside the laser resonator. In this way, both spiking after turn-on and
the intensity noise under steady-state conditions can be reduced.
Cuernavaca, Agosto 2008
Stabilization of Lasers
Passive schemes do not involve electronics and are based
on purely optical effects.
Examples are: The frequency of a laser can be stabilized
via optical feedback from a stable reference cavity.
Synchronization of two mode-locked lasers is possible via
cross-phase modulation in a Kerr medium, in which the
intracavity pulses of both lasers meet.
Cuernavaca, Agosto 2008
Stabilization of Lasers
Other schemes
Examples are: The frequency of a laser can be stabilized
via optical feedback from a stable reference cavity.
Synchronization of two mode-locked lasers is possible via
cross-phase modulation in a Kerr medium, in which the
intracavity pulses of both lasers meet.
( in spanish, please!)
Cuernavaca, Agosto 2008
Stabilization of Lasers
Other schemes.
Examples are: The frequency of a laser can be stabilized
via optical feedback from a stable reference cavity.
Synchronization of two mode-locked lasers is possible via
cross-phase modulation in a Kerr medium, in which the
intracavity pulses of both lasers meet.
( in spanish, please!)
Cuernavaca, Agosto 2008
Stabilization of Lasers
A reference cavity is a passive optical resonator
(resonant cavity) which is used as a kind of fly-wheel
oscillator (short-term frequency reference) in an
optical frequency standard. The optical frequency of a
single-frequency laser (or of a single line of the output
of a mode-locked laser) can be stabilized to the frequency
of a resonance of the reference cavity, effectively transferring
the higher frequency stability of the cavity to the laser.
Such stabilization or frequency locking can be achieved
e.g. with an electronic feedback system based on the
Pound–Drever–Hall method or the Hänsch–Couillaud method.
Cuernavaca, Agosto 2008
Next week:
I.3.- Conceptos generales de láseres y fuentes de luz:
-Cavidades, ganancia y finesa
-Etalones de Fabri Perot,elementos ópticos, Componentes ópticas
especiales ( moduladores optoacústicos, placas de media y cuarto
de onda, diodos faraday
-Láseres pulsados de nitróngeno, Nd:YAG, pulsadores del tipo QSwitch, láseres de diodo de cavidad extendida, laseres de tintes
-Otras fuentes de luz: sincrotrónesy Free electron Lasers,
Cuernavaca, Agosto 2008
I.3.- Conceptos generales de láseres y fuentes de luz:
-Cavidades, ganancia y finesa
-Etalones de Fabri Perot,elementos ópticos,
-Componentes ópticas especiales ( moduladores optoacústicos,
placas de media y cuarto de onda, diodos faraday
-Láseres pulsados de nitróngeno, Nd:YAG, pulsadores del tipo QSwitch, láseres de diodo de cavidad extendida, laseres de tintes
-Otras fuentes de luz: sincrotrónesy Free electron Lasers,
Cuernavaca, Agosto 2008
I.3.- Conceptos generales de láseres y fuentes de luz:
-Cavidades, tipos de resonadores, ganancia y finesa
-Etalones de Fabri Perot,elementos ópticos,
-Componentes ópticas especiales ( moduladores optoacústicos,
placas de media y cuarto de onda, diodos faraday
-Láseres pulsados de nitróngeno, Nd:YAG, pulsadores del tipo QSwitch, láseres de diodo de cavidad extendida, laseres de tintes
-Otras fuentes de luz: sincrotrónesy Free electron Lasers,
Cuernavaca, Agosto 2008
I.3.- Conceptos generales de láseres y fuentes de luz:
-Cavidades, tipos de resonadores, ganancia y finesa
-Etalones de Fabri Perot,elementos ópticos,
-Componentes ópticas especiales ( moduladores optoacústicos,
placas de media y cuarto de onda, diodos faraday
-Láseres pulsados de nitróngeno, Nd:YAG, pulsadores del tipo QSwitch, láseres de diodo de cavidad extendida, laseres de tintes
-Otras fuentes de luz: sincrotrónesy Free electron Lasers,
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5 Laser light

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