考试时间： 2011.1.4 上课时间和教室

1. 考试时间：2011.1.4上课时间和教室

2. Chapter 7.Lasers (acronym) Light Amplification by Stimulated Emission of Radiation

3. The History • 1916, Einstein predicted the stimulated emission. • 1954, Townes and co-workers developed a Microwave Amplifier by Stimulated Emission of Radiation(maser) using ammonia, NH3. • 1958, Schawlow and Townes showed that the maser principle could be extended into the visible region . • 1960, Maiman built the first laser using ruby as the active medium. • From then on, laser development was nothing short of miraculous, giving optics new impetus and wide publicity.

5. 7.1 Stimulated Emission of Radiation • Boltzmann Distribution • the transitions that occur between different energy states • absorption: the upward transition from a lower energy state to a higher state, E1 E2 • Emission: the downward transition, E2 E1, • population N :the number of atoms, per unit volume, that exist in a given state. given by Boltzmann's equation • E : energy lever of the system • : Boltzmann's constant T : absolute temperature.

6. 7.1 Stimulated Emission of Radiation • Boltzmann's ratio or relative population : the ratio of the populations in the two states, N2 / N1. • Or • plot the energy in the higher state relative to that in the lower state, versus the population in these states(E versus N), the result is an exponential curve known as a Boltzmann distribution. • When the Boltzmann distribution is normal, it means that the system is in thermal equilibrium, having more atoms in the lower state than in the higher state.

7. 7.1 Stimulated Emission of Radiation • 2. Einstein's Prediction • Assume first: an ensemble of atoms is in thermal equilibrium and not subject to an external radiation field. • At higher temperatures, a certain number of atoms is in the excited state; on return to the lower state, these atoms will emit radiation, in the form of quanta h . -- spontaneous emission • rate of the transition: the number of atoms in the higher state that make the transition to the lower state, per second. • lifetime of the transition: the reciprocal of the rate of transition. • rate of the spontaneous transition: • A21: constant of proportionality • N2: number of atoms (per unit volume) in the higher state

8. 7.1 Stimulated Emission of Radiation • Assume next: the system is subject to some external radiation field. one of two processes may occur, depending on: the direction (the phase) of the field with respect to the phase of the oscillator.

9. 7.1 Stimulated Emission of Radiation • the two phases coincide:a quantum of the field may cause the emission of another quantum. -- stimulated emission. • Its rate is • B21 : constant of proportionality • u(): energy density (J m-3), function of frequency . • the two phase is opposite : the impulse transferred counteracts the oscillation, energy is consumed, and the system is raised to a higher state -- absorption. • Its rate is • B12 : constant of proportionality.

10. 7.1 Stimulated Emission of Radiation Transitions between energy states

11. 7.1 Stimulated Emission of Radiation Einstein's coefficients: A21, B21, B12 Einstein's relations B21 = B12 (1) the coefficients for both stimulated emission and absorption are numerically equal (2) the ratio of the coefficients of spontaneous versus stimulated emission is proportional to the third power of the frequency of the transition radiation explains why it is so difficult to achieve laser emission in the X-ray range, where  is rather high

12. 7.1 Stimulated Emission of Radiation • 3. Population Inversion • thermal equilibrium system absorption and spontaneous emission take place side by side N2 < N1, absorption dominates: an incident quantum is more likely to be absorbed than to cause emission. • population inversion condition a majority of atoms in the higher state, N2 > N1 on return to the ground state, the system will probably lase.

13. Incandescent vs. Laser LightLight from bulbs are due to spontaneous emission • Many wavelengths • Multidirectional • Incoherent • Monochromatic • Directional • Coherent

14. Coherence Coherent: If the phase of a light wave is well defined at all times (oscillates in a simple pattern with time and varies in a smooth wave in space at any instant). Example: a laser produces highly coherent light. In a laser, all of the atoms radiate in phase. Incoherent: the phase of a light wave varies randomly from point to point, or from moment to moment. Example: An incandescent or fluorescent light bulb produces incoherent light. All of the atoms in the phosphor of the bulb radiate with random phase.

15. Stimulated vs Spontaneous Emission Stimulated emission requires the presence of a photon. An “incoming” photon stimulates a molecule in an excited state to decay to the ground state by emitting a photon.The stimulated photons travel in the same direction as the incoming photon. Spontaneous emission does not require the presence of a photon. Instead a molecule in the excited state can relax to the ground state by spontaneously emitting a photon.Spontaneously emitted photons are emitted in all directions.

16. Em, Nm Em, Nm En, Nn En, Nn • two-level system(ex. ammonia maser) Even with very a intense pump source, the best one can achieve with a two-level system is excited state population = ground state population

17. three-level system  in equilibrium  normal Boltzmann distribution  absorptive rather than emissive  excited  population inversion

18. 7.2 Practical Realization • 1. General Construction • Pumping:an energy source to supply the energy needed for raising the system to the excited state. • active medium: in which, reaches population inversion and lases when excited. may be a solid, liquid, or gas thousands of materials that have been found to lase • cavity:optional laser amplifiers: no cavity laser oscillators: medium enclosed in a cavity  provides feedback and additional amplification  cavity formed by two mirrors: one full reflectance, the other partially transparent

20. 7.2 Practical Realization Basic components of a laser oscillator  Energy source  Medium  Full reflectance mirrors  Partially transparent mirrors  Radiation

21. Common Components of all Lasers • Active Medium • The active medium may be solid crystals such as ruby or Nd:YAG, liquid dyes, gases like CO2 or Helium/Neon, or semiconductors such as GaAs. Active mediums contain atoms whose electrons may be excited to a metastable energy level by an energy source. • Excitation Mechanism • Excitation mechanisms pump energy into the active medium by one or more of three basic methods; optical, electrical or chemical. • High Reflectance Mirror • A mirror which reflects essentially 100% of the laser light. • Partially Transmissive Mirror • A mirror which reflects less than 100% of the laser light and transmits the remainder.

22. 7.2 Practical Realization • 2. Excitation • optical pumping: ruby laser  a light source  another laser. • electron excitation: argon laser , helium-neon laser • direct conversion of electric energy into radiation: light-emitting diodes(LEDs), semiconductor lasers • thermal excitation : CO2 laser. • chemical pumping: chemical laser H2 + F2  2HF

23. 7.2 Practical Realization • 3. Cavity Configurations • Plane-parallel cavity: very efficient ( good filling), difficult alignment(low stability) • confocal cavity: poor filling, easier to align • concentric cavity (spherical cavity) : poor filling, easier to align • hemispherical cavity: poor filling, much easy to align • long-radius cavity: good compromise between the plane-parallel and the confocal variety, type of cavity used most often in today's commercial lasers.

24. 7.2 Practical Realization Cavity configurations L:distance between mirrors R:radius of curvature

25. 7.2 Practical Realization • 4. Mode Structure Assume: the cavity is limited by two plane-parallel mirrors. • the wavelength possible of the standing-wave pattern inside the cavity is: L : length of the cavity q : number of half-wavelengths, or axial modes • the resonance condition for axial modes: n: index of medium contained in a laser cavity axial modes

26. 7.2 Practical Realization two consecutive modes (which differ by q = 1), are separated by a frequency difference, • different frequencies are closely, and evenly, spaced, lie within the width of a single emission line. • the output of the laser consists of a number of lines separated by c/2S

27. Mode-locking

28. Active mode-locking

29. 7.2 Practical Realization transverse modes • TEM: transverse electromagnetic, modes • few in number, easy to see. • Aim the laser at a distant screen, spread the beam out by a negative lens.: • bright patches, separated from one another by intervals called "nodal lines". • Within each patch, the phase of the light is the same, but between patches the phase is reversed.

30. 7.2 Practical Realization • TEM00 : • lowest possible transverse mode • no phase reversal across the beam, the beam is "uniphase" • highest possible spatial coherence, can be focused to the smallest spot size and reach the highest power density. TEM modes • lowest possible axial mode: • laser oscillates in one frequency • highest possible temporal coherence

32. 7.2 Practical Realization 5. Gain Gain of a laser depends on several factors. Foremost among them is the separation of the energy levels that provide laser transition. The two levels are father apart, the gain is higher because then the laser transition contains a larger fraction of the energy compared to the energy in the pump transition

33. 7.2 Practical Realization • Gain is the opposite of absorption • --definition : initial power in the cavity : power of exit light • absorptivity positive: for thermal equilibrium where N2 < N1. • absorptivity negative: in population inversion, where N2 > N1, laser emission could be considered negative absorption • gain coefficient : the negative of the "absorption coefficient“

34. 7.2 Practical Realization As the wave is reflected back and forth between the mirrors, it will lose some of its energy, mainly because of the limited reflectivity of one of mirrors. If the two mirrors have reflectivities r1 and r2, --each round trip : loss per round trip --For the system  > : system will lase, threshold condition necessary to sustain laser emission.

35. 7.3 Types of Lasers • Solid-state Lasers • ruby laser • Ruby is synthetic aluminum oxide, Al2O3, with 0.03 to 0.05% of chromium oxide, Cr2O3, added to it. The Cr3+ ions are the active ingredient; the aluminum and oxygen atoms are inert. • The ruby crystal is made into a cylindrical rod, several centimeters long and several millimeters in diameter, with the ends polished flat to act as cavity mirrors. • Pumping is by light from a xenon flash tube.

36. 7.3 Types of Lasers E3: fairly wide and has a short lifetime; the excited Cr3+ ions rapidly relax and drop to the next lower state, E2. This transition is nonradiative. E2: metastable and has a lifetime longer than that of E3, and the Cr3+ ions remain that much longer in E2 before they drop to the ground state, E1. Three-level energy diagram typical of ruby The E2 E1 transition is radiative; it produces the spontaneous, incoherent red fluorescence typical of ruby, with a peak near 694 nm. As the pumping energy is increased above a critical threshold, population inversion occurs in E2 with respect to E1 and the system lases, with a sharp peak at 694.3 nm.

37. Stimulated Emission of Radiation Lasing Action Diagram Excited State Spontaneous Energy Emission Energy Introduction Metastable State Ground State

38. fast Metastable state Population inversion slow slow relaxation efficient pumping Fast relaxation Requirements for Laser Action

39. 7.3 Types of Lasers neodymium: YAG laser The active ingredient is trivalent neodymium, Nd3+, added to an yttrium aluminum garnet, YAG, Y3Al5O12. It has four energy levels. The laser transition begins at the metastable state and ends at an additional level somewhat above the ground state.

40. 7.3 Types of Lasers 2. Gas Lasers Gas lasers consist of a gas filled tube placed in the laser cavity. A voltage (the external pump source) is applied to the tube to excite the atoms in the gas to a population inversion. The light emitted from this type of laser is normally continuous wave (CW). helium-neon laser Typically, it consists of a tube about 30 cm long and 2 mm in diameter, with two electrodes on the side and fused silica windows at both ends. The tube contains a mixture of 5 parts helium and 1 part neon, kept at a pressure of 133 Pa.

41. 7.3 Types of Lasers argon laser It generates a strong turquoise-blue line at 488 nm and a green line at 514.5 nm, in either pulsed or c. w. operation. helium-cadmium It emits a brilliant blue at 441.6 nm.

42. 7.3 Types of Lasers • carbon dioxidelaser • high power:the first CO2 lasers had a continuous output of a few milliwatts. Today we have powers of some 200 kW, more than enough to cut through steel plates several centimeters thick in a matter of seconds. • High efficient: the efficiency in converting electrical energy into radiation is better (more than 10%) than that of any other laser.(TEA CO2 laser) • Relatively simple in construction and operation are. • Tunable in a small range • Emission is at 10.6 m.

43. 7.3 Types of Lasers Excimer lasers contain rare-gas halides such as XeCl, KrF, or others. These molecules are unstable in the ground state but bound in the excited state. • exceedingly powerful, with outputs as high as several GW. • emit in the ultraviolet.

44. 7.3 Types of Lasers 3. Semiconductor Lasers LED: light-emitting diode • main application : • waveguides • integrated optics • emit almost anywhere in the spectrum, from the UV to the IR • an efficiency much higher than with optical pumping (around 40% versus 3%). • small ,less than 1 mm in diameter

45. 7.3 Types of Lasers • 4. Tunable Lasers •  dye lasers: first tunable lasers •  parametric oscillator: more compact  less expensive  easier to operate  tuning range much wider Color center lasers: tuned over wide bands in the UV, the visible, and the IR.  free-electron laser:  high powers of the order of megawatts • very efficient  tuned through a wide range of wavelengths. Tunable lasers are most welcome to spectroscopists

46. Argon fluoride (Excimer-UV)Krypton chloride (Excimer-UV)Krypton fluoride (Excimer-UV)Xenon chloride (Excimer-UV)Xenon fluoride (Excimer-UV)Helium cadmium (UV)Nitrogen (UV)Helium cadmium (violet)Krypton (blue)Argon (blue)Copper vapor (green)Argon (green)Krypton (green)Frequency doubled      Nd YAG (green)Helium neon (green)Krypton (yellow)Copper vapor (yellow) 0.1930.2220.2480.3080.3510.3250.3370.4410.4760.4880.5100.5140.5280.5320.5430.5680.570 Helium neon (yellow)Helium neon (orange)Gold vapor (red)Helium neon (red)Krypton (red)Rohodamine 6G dye (tunable)Ruby (CrAlO3) (red)Gallium arsenide (diode-NIR)Nd:YAG (NIR)Helium neon (NIR)Erbium (NIR)Helium neon (NIR)Hydrogen fluoride (NIR)Carbon dioxide (FIR)Carbon dioxide (FIR) 0.5940.6100.6270.6330.6470.570-0.6500.6940.8401.0641.15  1.5043.392.709.6   10.6    Key:      UV   =   ultraviolet (0.200-0.400 µm)              VIS   =   visible (0.400-0.700 µm)              NIR   =   near infrared (0.700-1.400 µm) WAVELENGTHS OF MOST COMMON LASERS Laser Type Wavelength (mm)

47. Continuous Output (CW) Pulsed Output (P) Laser Output Energy (Watts) Energy (Joules) Time Time watt (W) - Unit of power or radiant flux (1 watt = 1 joule per second). Joule (J) - A unit of energy Energy (Q) The capacity for doing work. Energy content is commonly used to characterize the output from pulsed lasers and is generally expressed in Joules (J). Irradiance (E) - Power per unit area, expressed in watts per square centimeter.

48. 7.4 Applications • Compared to radiation from other sources, laser radiation stands out in several ways: • highly coherent, both spatially and temporally • generated in the form of very short pulses, at high powers

49. 7.4 Applications 1. Beam Shape laser operating in the TEM00 mode the energy has a Gaussian distribution at a given distance r from the axis, the irradiance I falls off exponentially parameter w: the distance from the axis at which I has dropped to 1/e2 of I0, the irradiance in the center

50. 7.4 Applications w(z) :beam's radius  : wavelength w0:radius at the waist. For a confocal cavity, this simplifies to L : distance between the mirrors.