Prof. Dr. Salah Ibrahim Hassab ElnabyIntroduction to Laser Theory Prof. Dr. Salah I. Hassab Elnaby NILES
12 lectures 4 homeworks 20 Grades Report 10 A 85 B 75 Midterm exam 20 C 65 Final exam 50
Contents Introduction Energy Levels Absorption & Emission of Radiation Electro-Magnetic field Rate Equations Laser Cavity MID TERM EXAM CW and Pulsed operations Gas Lasers Solid State Lasers Semi-Conductor Lasers Other Types of Lasers (Free Electron & Liquid Chemical) SIMINAR OF REPORTS
Types of LaserBased on the mode of operation (i) Pulsed Laser systems (ii) High power Q-switched systems (iii) Continuous wave Laser systemsBased on the mechanism in which PopulationInversion is achieved (i) Three level lasers (ii) Four level lasersBased on state of active medium used (i) Gas Laser (ii) Solid state Laser (iii) Semiconductor Laser (iv) Tunable dye Laser
Laser Fundamentals The light emitted from a laser is monochromatic, that is, it is of one color/wavelength. In contrast, ordinary white light is a combination of many colors (or wavelengths) of light. Lasers emit light that is highly directional, that is, laser light is emitted as a relatively narrow beam in a specific direction. Ordinary light, such as from a light bulb, is emitted in many directions away from the source. The light from a laser is said to be coherent, which means that the wavelengths of the laser light are in phase in space and time. Ordinary light can be a mixture of many wavelengths. These three properties of laser light are what can make it more hazardous than ordinary light. Laser light can deposit a lot of energy within a small area. 9
Incandescent vs. Laser Light1. Many wavelengths 1. Monochromatic2. Multidirectional 2. Directional3. Incoherent 3. Coherent 10
Common Components of all Lasers1. 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.2. Excitation Mechanism Excitation mechanisms pump energy into the active medium by one or more of three basic methods; optical, electrical or chemical.3. High Reflectance Mirror A mirror which reflects essentially 100% of the laser light.4. Partially Transmissive Mirror A mirror which reflects less than 100% of the laser light and transmits the remainder. 11
Laser ComponentsGas lasers consist of a gas filled tube placed in the laser cavity. Avoltage (the external pump source) is applied to the tube to excite theatoms in the gas to a population inversion. The light emitted from thistype of laser is normally continuous wave (CW). 12
Lasing Action1. Energy is applied to a medium raising electrons to an unstable energy level.2. These atoms spontaneously decay to a relatively long-lived, lower energy, metastable state.3. A population inversion is achieved when the majority of atoms have reached this metastable state.4. Lasing action occurs when an electron spontaneously returns to its ground state and produces a photon.5. If the energy from this photon is of the precise wavelength, it will stimulate the production of another photon of the same wavelength and resulting in a cascading effect.6. The highly reflective mirror and partially reflective mirror continue the reaction by directing photons back through the medium along the long axis of the laser.7. The partially reflective mirror allows the transmission of a small amount of coherent radiation that we observe as the “beam”.8. Laser radiation will continue as long as energy is applied to the lasing medium. 13
Lasing Action Diagram Excited State Spontaneous Energy Emission Metastable StateIntroduction Stimulated Emission of RadiationEnergy Ground State 14
Laser Output Continuous Output (CW) Pulsed Output (P) Energy (Joules)Energy (Watts) 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. 17
Photon EnergyThe energy of a green–yellow photon, roughly inthe middle of the optical spectrum, has an energyof about 2.5 eV (electron volts). This is the same asabout 4x10-19 J ( joules)= 4x10-12 erg. From the infrared to the X-ray region photonenergies vary from about 0.01 eV to about 100 eV.For contrast, at room temperature the thermal unitof energy is kT ~ 1/40 eV =0:025 eV. This is twoorders of magnitude smaller than the typicaloptical photon energy just mentioned, and as aconsequence thermal excitation plays only a verysmall role in the physics of nearly all lasers.
DirectionalityThe output of a laser can consist of nearly ideal planewavefronts. Only diffraction imposes a lower limit onon the angular spread of a laser beam the beam’s solidangle (ΔΩ) and vertex angle (Δθ) of divergenceΔΩ = λ2/A =(Δθ)2This represents a very small angular spread indeed ifλ is in the optical range, say500 nm, and A is macroscopic, say (5 mm)2.In this example we computeΔΩ = (500)210-18 m2/(5x10-6 m2) = 10-8 sr, Δθ = 1/10 mrad.
Coherence TimeThe existence of a finite bandwidth Δν means that thedifferent frequencies present in a laser beam can eventuallyget out of phase with each other.The time required for two oscillations differing in frequencyby Δν to get out of phase by a full cycle is obviously 1/ Δν.After this amount of time the different frequencycomponents in the beam can begin to interfere destructively,and the beam loses “coherence.”Thus,Δt = 1/ Δν is called the beam’s coherence time.
For example, even a “broadband” laser with Δν ~ 1 MHz hasthe coherence time Δt ~ 1 ms. This is enormously longer thanmost “typical” atomic fluorescence lifetimes, which aremeasured in nanoseconds (10-9 s).Thus even lasers that are not close to the limit of spectralpurity are nevertheless effectively 100% pure on the relevantspectroscopic time scale.By way of contrast, sunlight has a bandwidth Δν almost asgreat as its central frequency (yellow light, ν= 5x1014 Hz).Thus, for sunlight the coherence time is Δt~ 2x10-15 s, soshort that unfiltered sunlight cannot be consideredtemporally coherent at all.
Coherence LengthThe speed of light is so great that a light beam can travel avery great distance within even a short coherence time. Forexample, within Δt 1 ms light travels Δz ~300 m.The distance Δz= c Δt is called the beam’s coherencelength. Only portions of the same beam that are separatedby less than Δz are capable ofinterfering constructively with each other.
Spectral BrightnessA light beam from a finite source can be characterized by itsbeam divergence ΔΩ, source size (usually surface area A),bandwidth Δν, and spectral power density Pν(watts per hertz of bandwidth). From these parameters it isuseful to determine the spectral brightness βν of the source,which is defined to be the power flow per unit area, unitbandwidth, and steradian, namely βν= Pν/A ΔΩΔν.
Notice that Pν/A Δν is the spectral intensity, so βν can also bethought of as the spectral intensity per steradian.For an ordinary nonlaser optical source, brightness can beestimated directly from the blackbody formula for ρ(ν), thespectral energy density (J/m3-Hz): The spectral intensity (W/m2-Hz) is thus cρr, and c ρ /Δν is the desired spectral intensity per steradian. Taking Δν= 4p for a blackbody, we have
The temperature of the sun is about T=5800K 20(300K).Since the main solaremission is in the yellow portion of the spectrum, we cantake hν= 2.5 eV. βν= 1.5 x10-8 W/m2-sr-Hz for the sunSeveral different estimates can be made for laser radiation,depending on the type of laserconsidered. Consider first a low-power He–Ne laser. A powerlevel of 1 mWis normal,with a bandwidth of around 104 Hz. That the product ofbeamcross-sectional area and solid angle is just λ2, which for He–Ne light λ2(6328 x10-10 m)2. Combining these, we find βν =2:5 105W=m2-sr-Hz (He–Ne laser):
Another common laser is the mode-locked neodymium–glass laser, which can easily reach power levels around 104MW. The bandwidth of such a laser is limited by thepulse duration, say tp 30 ps (3010212 s). The bandwidth isgreater than 1/tp 3.3x1010 s-1. We convert from radians persecond to cycles per second by dividingby 2π and get Δν = 5x109 Hz.The wavelength of a Nd : glass laser is 1.06 μm, so λ2 =10-12m2.The result of combining these,Βν= 2x 1012 W/m2-sr-Hz (Nd : glass laser):