Curso de Métodos experimentales En la Física PCF UNAM Cuernavaca, Agosto 2008 cuarta semana

1. 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.

2. 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

3. Cuernavaca, Agosto 2008 • I.3.- Conceptos generales de láseres y fuentes de luz: • - Cavidades, ganancia y finesa • Etalones de FabriPerot, • Quarter wave plates, half wave plates, Stokes parameters • Optoacusticmodulators • Dicroicmirrors • Láseres pulsados de nitróngeno, Nd:YAG, pulsadores del tipo Q-Switch, láseres de diodo de cavidad extendida, • -Otras fuentes de luz: sincrotrónesy Free electronLasers, • 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

4. Cuernavaca, Agosto 2008 • Interferómetro de Fabri-Perot ( etalon) A Fabry–Pérot interferometer (also called Fabry–Pérot resonator) is a linear optical resonator (or cavity) which consists of two highly reflecting mirrors (with some small transmittivity) and is often used as a high-resolution optical spectrometer. One exploits the fact that the transmission through such a resonator exhibits sharp resonances and is very small between those.

5. Cuernavaca, Agosto 2008 • Interferómetro de Fabri-Perot ( etalon) For optical spectrum analysis, the Fabry–Pérot interferometer is often made short enough to achieve a sufficiently large free spectral range; the bandwidth of the resonances is then the free spectral range divided by the finesse Figure 2: Frequency-dependent transmission of a linear Fabry–Pérot cavity with mirror reflectivities of 90%.

6. Cuernavaca, Agosto 2008 • Interferómetro de Fabri-Perot ( etalon) free spectral range; The free spectral range of an optical resonator (cavity) is the frequency spacing of its axial (Gaussian-shaped) resonator modes. It is therefore also called axial mode spacing. For an empty standing-wave resonator of length L, it can be calculated as Bandwidth the width of the frequency range which can be transmitted by some element, e.g. an optical fiber FinesseThe finesse of an optical resonator (cavity) is defined as its free spectral range divided by the (full width at half-maximum) bandwidth of its resonances. Figure 2: Frequency-dependent transmission of a linear Fabry–Pérot cavity with mirror reflectivities of 90%.

7. Cuernavaca, Agosto 2008 • Interferómetro de Fabri-Perot ( etalon) FinesseThe finesse of an optical resonator (cavity) is defined as its free spectral range divided by the (full width at half-maximum) bandwidth of its resonances. If a fraction ρ of the circulating power is left after one round-trip (i.e., a fraction 1 − ρ of the power is lost), assuming that there is no incident field from outside the resonator, it can be shown that the finesse, F can be given by: Figure 2: Frequency-dependent transmission of a linear Fabry–Pérot cavity with mirror reflectivities of 90%.

8. Cuernavaca, Agosto 2008 • Interferómetro de Fabri-Perot ( etalon) FinesseThe finesse of an optical resonator (cavity) is defined as its free spectral range divided by the (full width at half-maximum) bandwidth of its resonances. If a fraction ρ of the circulating power is left after one round-trip (i.e., a fraction 1 − ρ of the power is lost), assuming that there is no incident field from outside the resonator, it can be shown that the finesse, F can be given by: A high finesse can be useful for optical spectrum analysis, because it allows the combination of a large free spectral range with a small resonator bandwidth. Therefore, a high spectral resolution in a wide spectral range is possible.

9. Cuernavaca, Agosto 2008 • Interferómetro de Fabri-Perot ( etalon)

10. Cuernavaca, Agosto 2008

11. Cuernavaca, Agosto 2008 • I.3.- Conceptos generales de láseres y fuentes de luz: • - Cavidades, ganancia y finesa • Etalones de FabriPerot, • Quarter wave plates, half wave plates, Stokes parameters • Spacialfilters • Opticalmodulators • Dicroicmirrors • Láseres pulsados de nitróngeno, Nd:YAG, pulsadores del tipo Q-Switch, láseres de diodo de cavidad extendida, • -Otras fuentes de luz: sincrotrónesy Free electronLasers,

12. Cuernavaca, Agosto 2008 • Quarter wave plates, half wave plates, Stokes parameters Optical waveplates (also called wave plates or retarder plates) are transparent plates with a carefully adjusted birefringence, which are mostly used for manipulating the polarization state of light beams. A waveplate has a slow axis and a fast axis, both being perpendicular to the surface and the beam direction, and also to each other. The phase velocity of light is slightly higher for polarization along the fast axis. This induces a Phase shift between orthogonal components Of light

13. Cuernavaca, Agosto 2008 • Quarter wave plates, half wave plates, Stokes parameters A waveplate has a slow axis and a fast axis, both being perpendicular to the surface and the beam direction, and also to each other. The phase velocity of light is slightly higher for polarization along the fast axis. This induces a Phase shift between orthogonal components Of light The wave plate is characterized by the amount of relative phase Γ; that it imparts on the two components, which is related to the birefringence Δn and the thickness L of the crystal by the formula

14. Cuernavaca, Agosto 2008 Exercise: Proof that, considering Is the phase shift induced by A biorrefringent material with A given ∆n Then: Phase velocity Refractive index The most common types of waveplates are quarter-wave plates (λ/4 plates) and half-wave plates (λ/2 plates), where the difference of phase delays between the two linear polarization directions is π/2 or π, respectively

15. Cuernavaca, Agosto 2008 Ok, this is interesting, but, how does one use waveplates? • When the plate is a half-wave plate(π -shift), then the polarization stays linear, • but the polarization direction is rotated. For example, for an angle of 45° • to the axes, the polarization direction is rotated by 90°. • When the incident polarization is at an angle of 45° to the axes, a • quarter-wave (π /2 shift)plate generates a state of circular polarization. • (Other input polarizations lead to elliptical polarization states.) • Conversely, ccircularly polarized light is converted into linearly polarized • light. • See mathematica ...

16. Cuernavaca, Agosto 2008 Ok, this is interesting, but, how does one use waveplates? Waveplates are in a few words, the tools one uses to Manipulate the state of light. Remember that a general polarization state is expressed In terms of the Stokes Parameters. See Stokes parameter .PDF …

17. Cuernavaca, Agosto 2008 • Optical modulators

18. Cuernavaca, Agosto 2008 An optical modulator is a device which can be used for manipulating a property of light – often of an optical beam, e.g. a laser beam. Depending on which property of light is controlled, modulators are called intensity modulators, phase modulators, polarization modulators, spatial light modulators, etc. A wide range of optical modulators are used in very different application areas, such as in optical fiber communications, displays, for active Q switching or mode locking of lasers, and in optical metrology.

19. Cuernavaca, Agosto 2008 Types of Optical Modulators There are very different kinds of optical modulators: Acousto-optic modulators are based on the acousto-optic effect. They are used for switching or continuously adjusting the amplitude of a laser beam, for shifting its optical frequency, or its spatial direction. Electro-optic modulators exploit the electro-optic effect in a Pockels cell. They can be used for modifying the polarization, phase or power of a beam, or for pulse picking in the context of ultrashort pulseamplifiers. Electroabsorption modulators are intensity modulators, used e.g. for data transmitters in optical fiber communications. Interferometric modulators, e.g. Mach–Zehnder modulators, are often realized in photonic integrated circuits for optical data transmission.

20. Cuernavaca, Agosto 2008 Acousto-optic Modulators An acousto-optic modulator (AOM) is a device which can be used for controlling the power, frequency or spatial direction of a laser beam with an electrical drive signal. It is based on the acousto-optic effect, i.e. the modification of the refractive index by the oscillating mechanical pressure of a sound wave.

21. Cuernavaca, Agosto 2008 Acousto-optic Modulators The key element of an AOM is a transparent crystal (or piece of glass) through which the light propagates. A piezoelectric transducer attached to the crystal is used to excite a sound wave with a frequency of the order of 100 MHz. Light can then experience Bragg diffraction at the periodic refractive index grating generated by the sound wave; therefore, AOMs are sometimes called Bragg cells

22. Cuernavaca, Agosto 2008 Acousto-optic Modulators The scattered beam has a slightly modified optical frequency (increased or decreased by the frequency of the sound wave) and a slightly different direction. The frequency and direction of the scattered beam can be controlled via the frequency of the sound wave

23. Cuernavaca, Agosto 2008 Electro-optic modulators

24. Cuernavaca, Agosto 2008 Electro-optic modulators An electro-optic modulator (EOM) (or electrooptic modulator) is a device which can be used for controlling the power, phase or polarization of a laser beam with an electrical control signal. typically contains one or two Pockels cells, and possibly additional optical elements such as polarizers. The principle of operation is based on the linear electro-optic effect (also called the Pockels effect), i.e., the modification of the refractive index of a nonlinear crystal by an electric field in proportion to the field strength.

25. Cuernavaca, Agosto 2008 Electro-optic modulators An electro-optic modulator (EOM) (or electrooptic modulator) is a device which can be used for controlling the power, phase or polarization of a laser beam with an electrical control signal. typically contains one or two Pockels cells, and possibly additional optical elements such as polarizers. The principle of operation is based on the linear electro-optic effect (also called the Pockels effect), i.e., the modification of the refractive index of a nonlinear crystal by an electric field in proportion to the field strength.

26. Cuernavaca, Agosto 2008 Electro-optic modulators A Pockels cell is a device consisting of an electro-optic crystal (with some electrodes attached to it) through which a light beam can propagate. The phase delay in the crystal (→ Pockels effect) can be modulated by applying a variable electric voltage. Only non-centrosymmetric materials (mostly crystals) exhibit the linear electro-optic effect, also called the Pockels effect, where the refractive index change is proportional to the electric field strength

27. Cuernavaca, Agosto 2008 Electro-optic modulators The Pockels effect (first described in 1906 by the German physicist Friedrich Pockels) is the linear electro-optic effect, where the refractive index of a medium is modified in proportion to the applied electric field strength. This effect can occur only in non-centrosymmetric materials. The most important materials of this type are crystal materials such as lithium niobate (LiNbO3), lithium tantalate (LiTaO3), potassium di-deuterium phosphate (KD*P), β-barium borate (BBO), potassium titanium oxide phosphate (KTP), and compound semiconductors such as gallium arsenide (GaAs) and indium phosphide (InP).

28. Cuernavaca, Agosto 2008 Other optical modulators An electroabsorption modulator (or electro-absorption modulator) is a semiconductor device which can be used for controlling (modulating) the intensity of a laser beam via an electric voltage Its principle of operation is based on the Franz–Keldysh effect [1, 2], i.e., a change in the absorption spectrum caused by an applied electric field, which changes the bandgap energy [1]L. V. Keldysh, “Behaviour of non-metallic crystals in strong electric fields”, J. Exp. Theor. Phys. (USSR) 33, 994 (1957); translation: Sov. Phys. JETP 6, 763 (1958)

29. Cuernavaca, Agosto 2008 Electro-optic modulators The Pockels effect (first described in 1906 by the German physicist Friedrich Pockels) is the linear electro-optic effect, where the refractive index of a medium is modified in proportion to the applied electric field strength. This effect can occur only in non-centrosymmetric materials. The most important materials of this type are crystal materials such as lithium niobate (LiNbO3), lithium tantalate (LiTaO3), potassium di-deuterium phosphate (KD*P), β-barium borate (BBO), potassium titanium oxide phosphate (KTP), and compound semiconductors such as gallium arsenide (GaAs) and indium phosphide (InP).

30. Cuernavaca, Agosto 2008 Electro-optic modulators Mathematically, the Pockels effect is best described via the induced deformation of the index ellipsoid, which is defined by in a Cartesian coordinate system. An electric field can now change the coefficients according to

31. Cuernavaca, Agosto 2008 Electro-optic modulators Figure 1: Pockels cells of various types.

32. Cuernavaca, Agosto 2008 • Dicroic mirrors

33. Cuernavaca, Agosto 2008 • Dicroic mirrors Definition: mirrors with significantly different reflection or transmission properties at two different wavelengths

34. Cuernavaca, Agosto 2008 • Dicroic mirrors Definition: mirrors with significantly different reflection or transmission properties at two different wavelengths Figure 1: Reflectivity spectrum of a dichroic mirror coating, designed for high transmission (low reflectivity) around 808 nm and high reflectivity at 1064 nm.

35. Cuernavaca, Agosto 2008 • Dicroic mirrors A dielectric mirror consists of multiple thin layers of (usually two) different transparent optical materials (→ dielectric coatings, thin-film coatings, interference coatings). Dielectric coatings, also called thin-film coatings or interference coatings, consist of thin (typically sub-micron) layers of transparent dielectric materials, which are deposited on a substrate. Their function is essentially to modify the reflective properties of the surface by exploiting the interference of reflections from multiple optical interfaces.

36. Cuernavaca, Agosto 2008 • Dicroic mirrors Even if the Fresnel reflection coefficient from a single interface between two materials is small (due to a small difference in refractive indices), the reflections from many interfaces can (in a certain wavelength range) constructively interfere to result in a very high overall reflectivity of the device. he simplest and most common design is that of a Bragg mirror, where all optical layer thickness values are just one-quarter of the design wavelength.

37. Cuernavaca, Agosto 2008 • Dicroic mirrors A Bragg mirror (also called distributed Bragg reflector) is a structure which consists of an alternating sequence of layers of two different optical materials. The most frequently used design is that of a quarter-wave mirror, where each optical layer thickness corresponding to one quarter of the wavelength for which the mirror is designed.

38. Cuernavaca, Agosto 2008 • Dicroic mirrors The principle of operation can be understood as follows. Each interface between the two materials contributes a Fresnel reflection. For the design wavelength, the optical path length difference between reflections from subsequent interfaces is half the wavelength; in addition, the reflection coefficients for the interfaces have alternating signs.

39. Cuernavaca, Agosto 2008 • Dicroic mirrors Figure 1: Field penetration into a Bragg mirror. The intensity distribution inside the dielectric mirror can be rather complex!

40. Cuernavaca, Agosto 2008 More complex separations cangive rise to mirrors which Reflect over a wide band of frequencies Figure 3: Field penetration into the Bragg mirror as a function of wavelength. The colors indicate the optical intensity inside the mirror.

41. Cuernavaca, Agosto 2008 • Zone Plates

42. Cuernavaca, Agosto 2008 • Zone Plates A zone plate is a device which focuses light using diffraction instead of refraction. They were devised by by Augustin-Jean Fresnel and are also called Fresnel zone plates For this reason A zone plate consists of a set of radially symmetric rings, known as Fresnel zones, which alternate between opaque and transparent. Light hitting the zone plate will diffract around the opaque zones. The zones can be spaced so that the diffracted light constructively interferes at the desired focus,

43. Cuernavaca, Agosto 2008 • Zone Plates A zone plate consists of a set of radially symmetric rings, known as Fresnel zones, which alternate between opaque and transparent. Light hitting the zone plate will diffract around the opaque zones. The zones can be spaced so that the diffracted light constructively interferes at the desired focus,

44. Fuentes de luz UV. 1.- Introducción 2.- Principios básicos de radiación sincrotrónica. 2.1 Un poco de historia. 2.2 Propiedades de la radiación sincrotrónica 2.3 Aplicaciones y usos. 3.- Fotoionización de hidrógeno molecular, H2. 3.1 Ortho y para-hydrógeno: O, de como la estadística Fermi-Dirac nos brinda dos tipos de moléculas de H2. 3.2 Como obtener para-H2 a partir de H2 normal. 3.3. Medición de niveles rotacionales en para-H2 usando radiación sincrotrónica.

45. 1. Introducción * La investigación basica inicia como un ejercicio de curiosidad… e inevitablemente se traduce en aplicaciones en campos diversos y distintos del original. El desarrollo de fuentes de luz , como el laser y la radiacion sincrotrónica (de la que hablaremos en esta plática) son ejemplos de lo anterior.

46. 1. Introducción. Que cosa es, antes que nada, la radiacion sincrotrónica ? Brevemente, se puede definir como la radiación electromagnética emitida por un electrón que se acelera mientras viaja a velocidades cercanas a la velocidad de la luz, C . Esta radiación va de el infrarrojo a los rayos X (pasando por el ultravioleta) , es continua en frecuencia y muy intensa.

47. 2.- Principios básicos de radiación sincrotrónica. 2.1 Un poco de historia... El fenomeno de difracción de Bragg….. ...Así como el descubrimiento de la doble hélice de ADN.

48. 2.- Principios básicos de radiación sincrotrónica. 2.1 Un poco de historia... A pesar de esa importancia, las fuentes de luz en el utravioleta y los rayos X estuvieron limitadas por más de medio siglo a fuentes relativamente débiles, y que emitían luz en unas cuantas frecuencias... Aparato de rayos X (esquema)

49. 2.- Principios básicos de radiación sincrotrónica. 2.1 Un poco de historia... El interés en colisiones a altas energías en la década de los 50´s llevo a los físicos a desarrollar aceleradores que permitieran realizar colisiones frontales entre partículas a velocidades enormes ( y observar los productos resultantes) Las partículas se hacen girar en órbitas circulares opuestas, y se hacen colisionar en lugares específicos del tunel. Tunel en CERN

50. 2.- Principios básicos de radiación sincrotrónica. 2.1 Un poco de historia... En 1947 (mientras se pretendia hacer otra cosa), técnicos y cientificos de la General electrics descrubrieron la radiación sincrotrón. Esto fue un tanto accidental puesto que la cámara de vacío del acelerador era de vidrio. A la radiación descubierta se le llamo inicialmente Radiación de Schwinger Luz emanando del famoso acelerador en laboratorios de la General Electrics.