Introduction to Laser Theory

Prof. Dr. Salah I. Hassab ElnabyNILES

LASER PHYSICS I

Prof. Dr. Salah Ibrahim Hassab Elnaby

12 lectures 4 homeworks 20 Report

10 Midterm exam 20 Final exam

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GradesA 85B 75C 65

ReferencesPrinciples of Laser Physics O. SviltoLaser Physics P.W. Milloni & J.H. Eberly

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 Population Inversion is achieved

(i) Three level lasers(ii) Four level lasers

Based on state of active medium used

(i) Gas Laser(ii) Solid state Laser(iii) Semiconductor Laser(iv) Tunable dye Laser

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The Electromagnetic Spectrum

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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.

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Incandescent vs. Laser Light

1. Many wavelengths

2. Multidirectional

3. Incoherent

1. Monochromatic

2. Directional

3. Coherent

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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.

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Laser Components

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).

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Lasing Action

1. 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.

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Lasing Action DiagramEn

erg

y

Intr

od

ucti

on

Ground State

Excited State

Metastable State

Spontaneous Energy Emission

Stimulated Emission of Radiation

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WAVELENGTHS OF MOST COMMON LASERS

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)

0.1930.2220.2480.3080.3510.3250.3370.4410.4760.4880.5100.5140.5280.532

0.5430.5680.570

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)

0.5940.6100.6270.6330.647

0.570-0.6500.6940.8401.0641.15  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)

Wavelength (mm)Laser Type

                                              

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Laser OutputContinuous Output (CW) Pulsed Output (P)

                       

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.

En

erg

y (W

atts

)

TimeE

ner

gy

(Jo

ule

s)Time

Photon Energy

The energy of a green–yellow photon, roughly in the middle of the optical spectrum, has an energy of about 2.5 eV (electron volts). This is the same as about 4x10-19 J ( joules)= 4x10-12 erg. From the infrared to the X-ray region photon energies vary from about 0.01 eV to about 100 eV. For contrast, at room temperature the thermal unit of energy is kT ~ 1/40 eV =0:025 eV. This is two orders of magnitude smaller than the typical optical photon energy just mentioned, and as a consequence thermal excitation plays only a very small role in the physics of nearly all lasers.

Directionality

The output of a laser can consist of nearly ideal plane wavefronts. Only diffraction imposes a lower limit on on the angular spread of a laser beam the beam’s solid angle (ΔΩ) and vertex angle (Δθ) of divergence

ΔΩ = λ2/A =(Δθ)2

This represents a very small angular spread indeed if λ is in the optical range, say500 nm, and A is macroscopic, say (5 mm)2. In this example we compute ΔΩ = (500)210-18 m2/(5x10-6 m2) = 10-8 sr, Δθ = 1/10 mrad.

Coherence Time

The existence of a finite bandwidth Δν means that the different frequencies present in a laser beam can eventually get out of phase with each other. The time required for two oscillations differing in frequency by Δν to get out of phase by a full cycle is obviously 1/ Δν. After this amount of time the different frequency components 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 has the coherence time Δt ~ 1 ms. This is enormously longer than most “typical” atomic fluorescence lifetimes, which are measured in nanoseconds (10-9 s).

Thus even lasers that are not close to the limit of spectral purity 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, so short that unfiltered sunlight cannot be consideredtemporally coherent at all.

Coherence Length

The speed of light is so great that a light beam can travel a very great distance within even a short coherence time. For example, 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 separated by less than Δz are capable ofinterfering constructively with each other.

Spectral Brightness

A light beam from a finite source can be characterized by its beam divergence ΔΩ, source size (usually surface area A), bandwidth Δν, and spectral power density Pν

(watts per hertz of bandwidth). From these parameters it is useful to determine the spectral brightness βν of the source, which is defined to be the power flow per unit area, unit bandwidth, and steradian, namely βν= Pν/A ΔΩΔν.

Notice that Pν/A Δν is the spectral intensity, so βν can also be thought of as the spectral intensity per steradian.For an ordinary nonlaser optical source, brightness can be estimated directly from the blackbody formula for ρ(ν), the spectral 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 can take 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 power level of 1 mWis normal,with a bandwidth of around 104 Hz. That the product of beamcross-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 104 MW. The bandwidth of such a laser is limited by thepulse duration, say tp 30 ps (3010212 s). The bandwidth is greater than 1/tp 3.3x1010 s-1. We convert from radians per second 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 =10-12 m2. The result of combining these, Βν= 2x 1012 W/m2-sr-Hz (Nd : glass laser):