curso de métodos experimentales en la física pcf unam cuernavaca, agosto 2008 cuarta semana

Curso de Métodos experimentalesEn la Física PCF UNAM

Cuernavaca, Agosto 2008

cuarta semana Dr. Antonio M. Juárez Reyes, ICF UNAM

Física Atómica, Molecular y óptica.


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 básicos2.1 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


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


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 Q-Switch, láseres de diodo de cavidad extendida, laseres de tintes

-Otras fuentes de luz: sincrotrónesy Free electron Lasers,


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 reachedThe 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.

http://www.rp-photonics.com/lasers.html

http://www.rp-photonics.com/small_signal_gain.html

http://www.rp-photonics.com/laser_resonators.html

http://www.rp-photonics.com/threshold_pump_power.html

http://www.rp-photonics.com/laser_noise.html




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 small-signal 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.


http://www.rp-photonics.com/laser_threshold.html

http://www.rp-photonics.com/small_signal_gain.html


http://www.rp-photonics.com/raman_lasers.html

http://www.rp-photonics.com/optical_parametric_oscillators.html




Lasing occures whenever the laser threshold is reached




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.

http://www.rp-photonics.com/laser_physics.html

http://www.rp-photonics.com/laser_beams.html



http://www.rp-photonics.com/amplifiers.html

http://www.rp-photonics.com/gain.html




Types of Laser Gain MediaThere 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)

http://www.rp-photonics.com/quantum_wells.html




Types of Laser Gain Media

…Certain laser crystals and glasses such as Nd:YAG (neodymium-doped yttrium aluminum garnet → YAG lasers), Yb:YAG (ytterbium-doped 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.

http://www.rp-photonics.com/laser_crystals.html

http://www.rp-photonics.com/laser_crystals_versus_glasses.html

http://www.rp-photonics.com/neodymium_doped_gain_media.html

http://www.rp-photonics.com/yag_lasers.html

http://www.rp-photonics.com/ytterbium_doped_gain_media.html

http://www.rp-photonics.com/erbium_doped_gain_media.html

http://www.rp-photonics.com/titanium_sapphire_lasers.html

http://www.rp-photonics.com/bulk_lasers.html

http://www.rp-photonics.com/fibers.html

http://www.rp-photonics.com/fiber_lasers.html

http://www.rp-photonics.com/fiber_amplifiers.html

http://www.rp-photonics.com/rare_earth_doped_gain_media.html

http://www.rp-photonics.com/transition_metal_doped_gain_media.html

http://www.rp-photonics.com/doped_insulator_lasers.html





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).

http://www.rp-photonics.com/ceramic_gain_media.html

http://www.rp-photonics.com/dye_lasers.html

http://www.rp-photonics.com/gas_lasers.html

http://www.rp-photonics.com/co2_lasers.html



http://www.rp-photonics.com/excimer_lasers.html

http://www.rp-photonics.com/free_electron_lasers.html




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.

http://www.rp-photonics.com/stimulated_emission.html

http://www.rp-photonics.com/photons.html

http://www.rp-photonics.com/four_level_and_three_level_gain_media.html





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.


http://www.rp-photonics.com/population_inversion.html


http://www.rp-photonics.com/threshold_pump_power.html





An example of a three-level laser medium is ruby (Cr3+:Al2O3)






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.







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.


http://www.rp-photonics.com/yag_lasers.html






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.





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.




Relevant Physical Properties of Laser Gain MediaA 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 region2.- a high transparency of the host medium in this wavelength regiona 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 requireda 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 transfers4.- ideally, four-level behavior, because quasi-three-level behavior introduces various additional constraints 5.- robustness and a long lifetime, chemical stability

http://www.rp-photonics.com/optical_pumping.html

http://www.rp-photonics.com/upper_state_lifetime.html

http://www.rp-photonics.com/q_switching.html

http://www.rp-photonics.com/quantum_efficiency.html

http://www.rp-photonics.com/quenching.html

http://www.rp-photonics.com/excited_state_absorption.html

http://www.rp-photonics.com/multi_phonon_transitions.html

http://www.rp-photonics.com/energy_transfer.html





Bibliography

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)

References

http://prola.aps.org/abstract/PRL/v5/i12/p557_1

http://www.opticsinfobase.org/abstract.cfm?URI=josab-5-7-1412



-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.

http://www.rp-photonics.com/glossary.html

http://www.rp-photonics.com/rate_equation_modeling.html

http://www.rp-photonics.com/rabi_oscillations.html



-General layout-1 Active media-2 External pump source (optical pumping)-3 and 4 optical resonator-5 Laser lightAs an example, consider the dynamics of an erbium-doped gain medium, such as used in, e.g., erbium-doped fiber amplifiers.

Ip Intensidad de bombeoIs Intensidad de luz estimulada

http://www.rp-photonics.com/erbium_doped_gain_media.html

http://www.rp-photonics.com/erbium_doped_fiber_amplifiers.html


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.

http://www.rp-photonics.com/lamp_pumped_lasers.html

http://www.rp-photonics.com/laser_diodes.html

http://www.rp-photonics.com/diode_pumped_lasers.html

http://www.rp-photonics.com/titanium_sapphire_lasers.html

http://www.rp-photonics.com/frequency_doubling.html

http://www.rp-photonics.com/solid_state_lasers.html

http://www.rp-photonics.com/dye_lasers.html

http://www.rp-photonics.com/gas_lasers.html


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 four-level 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 non-isotropic 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.

http://www.rp-photonics.com/photons.html


http://www.rp-photonics.com/lamp_pumped_lasers.html

http://www.rp-photonics.com/saturation_power.html

http://www.rp-photonics.com/beam_quality.html

http://www.rp-photonics.com/end_pumping.html

http://www.rp-photonics.com/vanadate_lasers.html

http://www.rp-photonics.com/vanadate_lasers.html

http://www.rp-photonics.com/intensity_noise.html




[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)

http://www.opticsinfobase.org/abstract.cfm?URI=ol-15-15-842

http://www.opticsinfobase.org/abstract.cfm?URI=josab-14-5-1213



-General layout-1 Active media-2 External pump source (optical pumping)-3 and 4 optical resonator (optical cavity)-5 Laser light



-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.

http://www.rp-photonics.com/cavities.html

http://www.rp-photonics.com/laser_beams.html

http://en.wikipedia.org/wiki/Standing_wave

http://en.wikipedia.org/wiki/Cavity_resonator

http://en.wikipedia.org/wiki/Light_wave


.

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.

http://www.rp-photonics.com/waveguides.html


http://www.rp-photonics.com/bulk_lasers.html

http://www.rp-photonics.com/thermal_lensing.html

http://www.rp-photonics.com/fibers.html


http://www.rp-photonics.com/integrated_optics.html

http://www.rp-photonics.com/modes.html




.

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).

http://www.rp-photonics.com/interference.html


.

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).

http://www.rp-photonics.com/nonlinearities.html

http://www.rp-photonics.com/gain_guiding.html

http://www.rp-photonics.com/saturable_absorbers.html

http://www.rp-photonics.com/output_couplers.html


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… 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.




http://www.rp-photonics.com/resonant_frequency_doubling.html

http://www.rp-photonics.com/stability_zones.html


.



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.




http://www.rp-photonics.com/q_factor.html

http://www.rp-photonics.com/q_factor.html

http://www.rp-photonics.com/dielectric_mirrors.html


Examples of optical cavities

Depending upon its geometry, optical resonators present different stability properties….

What is stability?


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.



http://www.rp-photonics.com/focal_length.html

http://www.rp-photonics.com/ring_lasers.html


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:



http://www.rp-photonics.com/focal_length.html

http://www.rp-photonics.com/ring_lasers.html

http://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis


Values which satisfy the inequality correspond to stable resonators.

The stability can be shown graphically by defining a stability parameter, g for each mirror:

Stability criterion


Interms of g, the stability zones look like:


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

http://www.rp-photonics.com/modes.html

http://www.rp-photonics.com/optical_resonators.html

http://www.rp-photonics.com/cavities.html


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.

http://en.wikipedia.org/wiki/Longitudinal_mode

http://en.wikipedia.org/wiki/Transverse_mode

http://en.wikipedia.org/wiki/Intensity

http://en.wikipedia.org/wiki/Gaussian_beam


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.

http://www.rp-photonics.com/hermite_gaussian_modes.html

http://www.rp-photonics.com/gaussian_beams.html

http://www.rp-photonics.com/laser_crystals.html


The simplest mode is the Gaussian mode, which has a complex amplitude described by the cylindrical equation:

With solution in terms of intensity:


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.


Hermite Gaussian modes.

Example: HG02 mode

The mathematical equation for its complex amplitude is


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


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):


Other cool modes: Laguerre-Gaussian Modes

How complex can They get?


-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

http://www.rp-photonics.com/coherence.html


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

http://www.rp-photonics.com/coherence.html


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)

http://www.rp-photonics.com/coherence_length.html

http://www.rp-photonics.com/velocity_of_light.html


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)

http://www.rp-photonics.com/single_frequency_operation.html


http://www.rp-photonics.com/phase_noise.html

http://www.rp-photonics.com/spontaneous_emission.html

http://www.rp-photonics.com/gain_media.html


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

http://www.rp-photonics.com/linewidth.html

http://www.rp-photonics.com/spotlight_2007_10_11.html


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.)

http://www.rp-photonics.com/phase_noise.html



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.

http://www.rp-photonics.com/quantum_noise.html

http://www.rp-photonics.com/schawlow_townes_linewidth.html

http://prola.aps.org/abstract/PR/v112/i6/p1940_1

http://www.rp-photonics.com/bandwidth.html

http://www.rp-photonics.com/schawlow_townes_linewidth.html


Measurement of Laser LinewidthA 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.

http://www.rp-photonics.com/resonator_modes.html


http://www.rp-photonics.com/interferometers.html

http://www.rp-photonics.com/reference_cavities.html

http://www.rp-photonics.com/single_frequency_lasers.html

http://www.rp-photonics.com/self_heterodyne_linewidth_measurement.html

http://www.rp-photonics.com/beat_note.html

http://www.rp-photonics.com/recirculating_fiber_loops.html

http://www.rp-photonics.com/fiber_amplifiers.html


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 compareTo the natural linewidth of, say Rubidium ( isotope 85) and to the doppler broadening

http://www.rp-photonics.com/beat_note.html

http://www.rp-photonics.com/frequency_combs.html




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.


http://www.rp-photonics.com/single_frequency_lasers.html

http://www.rp-photonics.com/spotlight_2007_10_11.html

http://www.rp-photonics.com/power_spectral_density.html

http://www.rp-photonics.com/wavenumber.html




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





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





Note the units in The scale!!



To keep the power spectral density of a laser narrowAnd stable, one needs to stabilize a laser ( they tendto be very sensitive to changes in temperature ( cavitiesChange length, media change properties.. Etc)

To keep a laser stable, one needs to do tricks


Stabilization of Lasers

Active Laser StabilizationActive 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.



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.

http://www.rp-photonics.com/photodiodes.html

http://www.rp-photonics.com/spiking.html

http://www.rp-photonics.com/intensity_noise.html



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.


http://www.rp-photonics.com/mode_locked_lasers.html

http://www.rp-photonics.com/cross_phase_modulation.html

http://www.rp-photonics.com/kerr_effect.html



Other schemes



( in spanish, please!)




Other schemes.



( in spanish, please!)



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.


Next week:


-Cavidades, ganancia y finesa

-Etalones de Fabri Perot,elementos ópticos, Componentes ópticas especiales ( moduladores optoacústicos, placas de media y cuarto de onda, diodos faraday





-Cavidades, ganancia y finesa







-Cavidades, tipos de resonadores, ganancia y finesa





curso de métodos experimentales en la física pcf unam cuernavaca, agosto 2008 cuarta semana

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