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MIT 2.71/2.710 Optics 10/20/04 wk7-b-1 Todays summary Multiple beam interferometers: Fabry-Perot resonators – Stokes relationships – Transmission and reflection.

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Presentation on theme: "MIT 2.71/2.710 Optics 10/20/04 wk7-b-1 Todays summary Multiple beam interferometers: Fabry-Perot resonators – Stokes relationships – Transmission and reflection."— Presentation transcript:

1 MIT 2.71/2.710 Optics 10/20/04 wk7-b-1 Todays summary Multiple beam interferometers: Fabry-Perot resonators – Stokes relationships – Transmission and reflection coefficients for a dielectric slab – Optical resonance Principles of lasers Coherence: spatial / temporal

2 MIT 2.71/2.710 Optics 10/20/04 wk7-b-2 Fabry-Perot interferometers

3 MIT 2.71/2.710 Optics 10/20/04 wk7-b-3 Relation between r, rand t, t airglassairglass Stokes relationships Proof: algebraic from the Fresnel coefficients preservation of the or using the property of preservation of the field properties upon time reversal

4 MIT 2.71/2.710 Optics 10/20/04 wk7-b-4 Proof using time reversal airglassairglass

5 MIT 2.71/2.710 Optics 10/20/04 wk7-b-5 Fabry-Perot interferometers reflected incident transmitted Resonance condition: reflected wave = 0 all reflected waves interfere destructively wavelength in free space refractive index

6 MIT 2.71/2.710 Optics 10/20/04 wk7-b-6 Calculation of the reflected wave airglassair incoming reflected transmitted reflected transmitted

7 MIT 2.71/2.710 Optics 10/20/04 wk7-b-7 Calculation of the reflected wave Use Stokes relationships

8 MIT 2.71/2.710 Optics 10/20/04 wk7-b-8 Transmission & reflection coefficients reflection coefficient transmission coefficient

9 MIT 2.71/2.710 Optics 10/20/04 wk7-b-9 Transmission & reflection vs path Reflection Transmission Path delay

10 MIT 2.71/2.710 Optics 10/20/04 wk7-b-10 Fabry-Perot terminology Transmission coefficient free Spectral range band width resonance frequencies Frequency v

11 MIT 2.71/2.710 Optics 10/20/04 wk7-b-11 Transmission coefficient FWHM Bandwidth is inversely proportional to the finesse F (or quality factor) of the cavity Fabry-Perot terminology bandwidth free spectral range finesse

12 MIT 2.71/2.710 Optics 10/20/04 wk7-b-12 Spectroscopy using Fabry-Perot cavity Goal Goal: to measure the specimens absorption as function of frequency ω Experimental measurement principle: Light beam of known spectrum Spectrum of light beam is modified by substance Scanning stage (controls cavity length L ) Transparent windows Container with specimen to be measured Partially-reflecting mirrors (FP cavity) Power meter

13 MIT 2.71/2.710 Optics 10/20/04 wk7-b-13 Spectroscopy using Fabry-Perot cavity Goal Goal: to measure the specimens absorption as function of frequency ω Experimental measurement principle: Light beam of known spectrum Spectrum of light beam is modified by substance Transparent windows Container with specimen to be measured Partially-reflecting mirrors (FP cavity) Power meter Electro-optic (EO) modulator (controls refr. Index n)

14 MIT 2.71/2.710 Optics 10/20/04 wk7-b-14 Spectroscopy using Fabry-Perot cavity Fabry–Perot transmissivity Unknown spectrum Sample measured:

15 MIT 2.71/2.710 Optics 10/20/04 wk7-b-15 Spectroscopy using Fabry-Perot cavity aaaFabry–Perot transmissivity Unknown spectrum Sample measured:

16 MIT 2.71/2.710 Optics 10/20/04 wk7-b-16 Spectroscopy using Fabry-Perot cavity aaaFabry–Perot transmissivity Unknown spectrum Sample measured:

17 MIT 2.71/2.710 Optics 10/20/04 wk7-b-17 Spectroscopy using Fabry-Perot cavity aaaFabry–Perot transmissivity Unknown spectrum Sample measured: unknown spectrum width should not exceed the FSR

18 MIT 2.71/2.710 Optics 10/20/04 wk7-b-18 Spectroscopy using Fabry-Perot cavity aaaFabry–Perot transmissivity Unknown spectrum Sample measured: spectral resolution is determined by the cavity bandwidth

19 MIT 2.71/2.710 Optics 10/20/04 wk7-b-19 Lasers

20 MIT 2.71/2.710 Optics 10/20/04 wk7-b-20 Absorption spectra human vision Atmospheric transmission

21 MIT 2.71/2.710 Optics 10/20/04 wk7-b-21 Semi-classical view of atom excitations Energy Atom in ground state Atom in excited state

22 MIT 2.71/2.710 Optics 10/20/04 wk7-b-22 Light generation Energy excited state equilibrium: most atoms in ground state ground state

23 MIT 2.71/2.710 Optics 10/20/04 wk7-b-23 Light generation Energy excited state ground state A pump mechanism (e.g. thermal excitation or gas discharge) ejects some atoms to the excited state

24 MIT 2.71/2.710 Optics 10/20/04 wk7-b-24 Light generation Energy excited state ground state The excited atoms radiatively decay, emitting one photon each

25 MIT 2.71/2.710 Optics 10/20/04 wk7-b-25 Light amplification: 3-level system Energy excited state Super-excited state ground state equilibrium: most atoms in ground state; note the existence of a third, super-excited state

26 MIT 2.71/2.710 Optics 10/20/04 wk7-b-26 Light amplification: 3-level system Energy excited state Super-excited state ground state Utilizing the super-excited state as a short-lived pivot point, the pump creates a population inversion

27 MIT 2.71/2.710 Optics 10/20/04 wk7-b-27 Light amplification: 3-level system Energy excited state Super-excited state ground state When a photon enters,...

28 MIT 2.71/2.710 Optics 10/20/04 wk7-b-28 Light amplification: 3-level system Energy excited state Super-excited state ground state When a photon enters, it knocks an electron from the inverted population down to the ground state, thus creating a new photon. This amplification process is called stimulated emission

29 MIT 2.71/2.710 Optics 10/20/04 wk7-b-29 Light amplifier Gain medium (e.g. 3-level system w population inversion)

30 MIT 2.71/2.710 Optics 10/20/04 wk7-b-30 Light amplifier w positive feedback Gain medium (e.g. 3-level system w population inversion) When the gain exceeds the roundtrip losses, the system goes into oscillation

31 MIT 2.71/2.710 Optics 10/20/04 wk7-b-31 Laser initial photon Gain medium (e.g. 3-level system w population inversion) Partially reflecting mi rro r Light Amplification through Stimulated Emission of Radiation

32 MIT 2.71/2.710 Optics 10/20/04 wk7-b-32 Laser initial photon Gain medium (e.g. 3-level system w population inversion) Partially reflecting mi rro r Light Amplification through Stimulated Emission of Radiation amplified once

33 MIT 2.71/2.710 Optics 10/20/04 wk7-b-33 Laser initial photon Gain medium (e.g. 3-level system w population inversion) Partially reflecting mi rro r Light Amplification through Stimulated Emission of Radiation amplified once reflected

34 MIT 2.71/2.710 Optics 10/20/04 wk7-b-34 Laser initial photon Gain medium (e.g. 3-level system w population inversion) Partially reflecting mi rro r Light Amplification through Stimulated Emission of Radiation amplified once reflected amplified twice

35 MIT 2.71/2.710 Optics 10/20/04 wk7-b-35 Laser initial photon Gain medium (e.g. 3-level system w population inversion) Partially reflecting mi rro r Light Amplification through Stimulated Emission of Radiation amplified once reflected amplified twice reflected output

36 MIT 2.71/2.710 Optics 10/20/04 wk7-b-36 Laser initial photon Gain medium (e.g. 3-level system w population inversion) Partially reflecting mi rro r Light Amplification through Stimulated Emission of Radiation amplified once reflected amplified twice reflected output amplified again etc.

37 MIT 2.71/2.710 Optics 10/20/04 wk7-b-37 Confocal laser cavities diffraction angle waist w 0 Beam profile: 2D Gaussian function TE 00 mode

38 MIT 2.71/2.710 Optics 10/20/04 wk7-b-38 Other transverse modes (usually undesirable)

39 MIT 2.71/2.710 Optics 10/20/04 wk7-b-39 Types of lasers Continuous wave (cw) Pulsed – Q-switched – mode-locked Gas (Ar-ion, HeNe, CO2) Solid state (Ruby, Nd:YAG, Ti:Sa) Diode (semiconductor) Vertical cavity surface-emitting lasers –VCSEL–(also sc) Excimer(usually ultra-violet)

40 MIT 2.71/2.710 Optics 10/20/04 wk7-b-40 CW (continuous wave lasers) Laser oscillation well approximated by a sinusoid Typical sources: Argon-ion: 488nm (blue) or 514nm (green); power ~1-20W Helium-Neon (HeNe): 633nm (red), also in green and yellow; ~1-100mW doubled Nd:YaG: 532nm (green); ~1-10W Quality of sinusoid maintained over a time duration known as coherence time t c Typical coherence times ~20nsec (HeNe), ~10μsec (doubled Nd:YAG)

41 MIT 2.71/2.710 Optics 10/20/04 wk7-b-41 Two types of incoherence temporalincoherencespatialincoherence point source matched paths Michelson interferometerYoung interferometer poly-chromatic light (=multi-color, broadband) mono-chromatic light (= single color, narrowband)

42 MIT 2.71/2.710 Optics 10/20/04 wk7-b-42 Two types of incoherence temporalincoherencespatialincoherence point source matched paths waves from unequal paths do not interfere waves with equal paths but from different points on the wave front do not interfere

43 MIT 2.71/2.710 Optics 10/20/04 wk7-b-43 Coherent vs incoherent beams amplitude Mutually coherent: superposition field amplitude sum of complex amplitude is described by sum of complex amplitude intensity Mutually incoherent: superposition field intensity sum of intensities is described by sum of intensities (the phases of the individual beams vary randomly with respect to each other; hence, we would need statistical formulation to describe them properly statistical optics)

44 MIT 2.71/2.710 Optics 10/20/04 wk7-b-44 Coherence time and coherence length incoming laser beam Michelson interferometer much shorter than coherence length ct c Intensity much longer than coherence length ct c Sharp interference fringes no interference

45 MIT 2.71/2.710 Optics 10/20/04 wk7-b-45 Coherent vs incoherent beams amplitude Coherent: superposition field amplitude sum of complex amplitudes is described by sum of complex amplitudes intensity Incoherent: superposition field intensity sum of intensities is described by sum of intensities (the phases of the individual beams vary randomly with respect to each other; hence, we would need statistical formulation to describe them properly statistical optics)

46 MIT 2.71/2.710 Optics 10/20/04 wk7-b-46 Mode-locked lasers Typical sources: Ti: Sa lasers (major vendors: Coherent, Spectra Phys.) Typical mean wavelengths: 700nm –1.4μm (near IR) can be doubled to visible wavelengths or split to visible + mid IR wavelengths using OPOs or OPAs (OPO=optical parametric oscillator; OPA=optical parametric amplifier) Typical pulse durations: ~psec to few fsec (just a few optical cycles) Typical pulse repetition rates (rep rates): MHz Typical average power: 1-2W; peak power ~MW-GW

47 MIT 2.71/2.710 Optics 10/20/04 wk7-b-47 Overview of light sources non-LaserLaser Thermal: polychromatic, spatially incoherent (e.g. light bulb) Gas discharge: monochromatic, spatially incoherent (e.g. Na lamp) Light emitting diodes (LEDs): monochromatic, spatially incoherent Continuous wave (or cw): strictly monochromatic, spatially coherent (e.g. HeNe, Ar +, laser diodes) Pulsed: quasi-monochromatic, spatially coherent (e.g. Q-switched, mode-locked) ~nsec~psec to few fsec pulse duration mono/poly-chromatic = single/multi color


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