lasers - coas | drexel university

Physics 480

“How Things Work”

LASERSLASERS

LASERSLASERSLight Amplification by Stimulated Emission of Radiation

Aside: More Optics .......

●Lenses●Eyes●Cameras●Fiber Optics

Fiber Optics –

Uses Total Internal Reflection.

f

Converging Lens

Ciliary Muscle

Normal Eyesight

Normal Eyesight

Near Point – closest point at which you can still focus on object – about 25 cm

Farsighted Eyesight


Farsighted Eyesight

Use converging lens.

Nearsighted Eyesight


Nearsighted Eyesight

Use Diverging Lens

P

N

e

Nucleus

Particle Mass Charge

Proton 1.67 X 10-27 kg 1.6 X 10-19 CNeutron 1.67 X 10-27 kg 0.0 CElectron 9.11 X 10-31 kg -1.6 X 10-19 C

+ -

+

--

+

Like charges repel, unlike charges attract.

F 21F 12

F 21

F 21

F 12

F 12

F 21=− F 12

+ +

F 21 F 12r

r21

∣F 21∣=k∣q1∣∣q2∣

r 2r12

k=9 X 109 N m2

C 2

Electric Potential is the potential energy per charge.

V=Uq

Electric Potential is the potential energy per charge.

12 V

+ --

vo=0m / s

U=K

qV=12mv2

v= 2qVm= 2 1.6 X 10−19C 12V

9.11 X 10−31kg=2.05 X 106 m

s

PHOTOELECTRIC EFFECT

V

A

Anode Cathode

Evacuated Quartz Tube

+ --

Electron

F


V

A

Anode Cathode


+ --

Electron

If I give the electron enough energy, it could break away from the positive plate and jump the potential barrier.


V

A

Anode Cathode


+ -Electrons

- -

One way to give the electrons energy is to shine light on the anode.


V

A

Anode Cathode


+ -Electrons

- -

If the “retarding potential” is increased, fewer and fewer electrons make the jump.


V

A

+ -

Energy distribution in the emitted electrons ( called photoelectrons) is independent of the intensity of the light.

More intense (stronger) light beam means more electrons, NOT higher energy electrons.

A strong beam yields more electrons than a weak beam of the same frequency, but the same average kinetic energy.

Photoelectron current is proportional to the light intensity for all retarding voltages. The extinction voltage V

O is the same

for all intensities of light of a given frequency, n.


V

A

-

There is no time lag between the arrival of the light at the metal surface and the emission of the photoelectrons.

+


V

A

-

Consider sodium. A detectable photo electric current will result when 10-6 W/m2 of electromagnetic energy is absorbed by the surface.

Assume 1019 atoms in a layer of sodium 1 atom thick an 1 m2 , each atom will receive energy at 10-25 W. At this rate it would take about 2 weeks to accumulate the 1 eV of energy needed.

+

Plot of maximum kinetic photoelectron energy, Kmax

,

versus frequency show that the maximum kinetic energy is proportional to the frequency.

K max=h −o=h−ho

h=6.626 X 10−34 Js Planck's Constant

PHOTOELECTRIC EFFECT - Summary

VA

+ -

Dependence of Photoelectron kinetic energy on light Intensity:

Classical Prediction: Electrons absorb energy continuously from E-M Waves. A more intense light should transfer into metal faster and produce electrons with higher KE.

Experimental Results: Maximum Kinetic Energy is independent of light intensity.


VA

+ -

Time interval between incidence of light and ejection of photoelectrons:Classical Prediction: For a very weak light, a measurable time interval should pass between the incidence of the light and the ejection of an electron. This is the time required for an electron to absorb the incident radiation before it requires enough energy to escape metal.

Experimental Results: Electrons are emitted from the surface almost instantaneously, even at a very low light intensity.


VA

+ -

Dependence of ejection of electrons on light frequency:

Classical Prediction: Electrons should be ejected at any frequency of the incident light as long the intensity is strong enough.

Experimental Results: No electrons are emitted if the incident light frequency drops below a cut-off frequency, f

O , no matter how intense the

light is.


VA

+ -

Dependence of photoelectron kinetic energy on light frequency:Classical Prediction: KE should not depend on frequency, only intensity.

Experimental Results: Maximum KE increases as frequency increases. Higher intensity means more electrons, not faster electrons.

P= Ae T 4−T s4

0≤e≤1

=5.67 X 10−8 W

m2 K 4

Black Body RadiationBlack Body Radiation

peak T=2.88 X 10−3mK

peakT=2.88 X 10−3mK

Classical Theory

UltraViolet Catastrophe – Classical theory fits well at long wavelengths but does not do well at short wavelengths.

Max Planck: Imagine charged oscillators exist at surface.

●Energy of the oscillator is quantized.

En=nh f

h=6.626 X 10−34 Js


●Energy of the oscillator is quantized. The number n is the quantum number.

En=nh f

h=6.626 X 10−34 Js

●Energy is absorbed or emitted in discrete units.

E=h f


●Energy is absorbed or emitted in discrete units.

E=h

0

h2h3h4h5hE n

543210

Quantum effects become important and measurable only on the submicroscopic level of atoms and molecules.

A 2.0 kg block is attached to a massless spring of force constant of k = 25 N/m. The spring is stretched 0.40 m from its equilibrium position and released.

ETot=12k A2=0.525N /m0.40m2=2.0 J

f = 12 k

m= 1

2 25 N /m2.0 kg

=0.56 Hz



ETot=2.0 Jf =0.56 Hz

En=nh f

n=En

hf= 2.0 J

6.63 X 10−34 Js 0.56Hz=5.4 X 1033



ETot=2.0 Jf =0.56 Hz

En=nh f

n=5.4 X 1033

How must energy must be dissipated away for the oscillator to move to next energy level?

E=h f =6.63 X 10−34 Js0.56 Hz =3.7 X 10−34 J


Using this theory of quantized energy levels, Max Planck was able to fit the experimental data.

PHOTOELECTRIC EFFECT - Photons

VA

+ -

Albert Einstein used Planck's concepts to explain photoelectric effect.

h=K maxho

h=energy content of eachquatumof incident lightK max=maximum photoelectronenergy

ho=minimumenergy needed dislodge anelectron


VA

+ -

Albert Einstein used Planck's concepts to explain photoelectric effect.

h=K max

h=energy content of eachquatumof incident lightK max=maximum photoelectronenergy

=Work Function=min energy needed dislodge anelectron

Quantum Maximum work functionEnergy = electron energy + of surface.


VA

+ - h=K maxQuantum Maximum work functionEnergy = electron energy + of surface.

Element Work Function(eV)Aluminum 4.08Beryllium 5.0Cadmium 4.07Calcium 2.9Carbon 4.81Cesium 2.1Cobalt 5.0Copper 4.7Gold 5.1Iron 4.5Lead 4.14Magnesium 3.68Mercury 4.5Nickel 5.01Niobium 4.3Potassium 2.3Platinum 6.35

PHOTOELECTRIC EFFECT – Photon Model

VA

+ -

Dependence of photoelectron kinetic energy on light intensity.

h=K maxQuantum Maximum work functionEnergy = electron energy + of surface.

Photon Model: Max KE independent on intensity. Max KE depends on frequency of light and work function.

K max=h−Double the intensity, double the number of photoelectrons that leaves the surface.


VA

+ -

Time interval between incidence of light and ejection of photoelectrons.


Photon Model: There is a one to one relationship between photoelectrons ejected and photons. Low intensity light means less photons but still eject electrons, just not as many.


VA

+ -

Dependence of ejection of electrons on light frequency.


Photon Model: Energy of photon depends on frequency of the light. Below the cutoff frequency the photons do not have enough energy to provide to the photoelectrons top overcome the work function and break free from the surface.


VA

+ -

Dependence of photoelectrons kinetic energy on frequency.


Photon Model: Higher frequency of light means higher maximum kinetic energy.

K max=h−

Compton Effect:

-

-

Incident Photon

Target Electron

Scattered Electron v

Scattered Photon

E=h

p=hc

E=moC2

p=0

E=h '

p=h 'c

E=mo2c4 p2c2

p= p

LASERSLASERS

Characteristics:

Coherent – Individual waves of light maintain a fixed phase relationship with one another resulting in no destructive interference.

Monochromatic – Very small range of wavelengths.

Small angle of Divergence – Beam spreads out very little, even over large distances.

Three kinds of transitions involving electromagnetic radiation can occur between two energy levels in an atom.

Ej

Ei

Induced Absorption

h

Spontaneous Emission

h

Induced Emission

h

hh

h=E j−E i


Ej

Ei

Induced Emission

h

hh

h=E j−E i

Alternating Force

If the applied force is in phase with the oscillating pendulum, then the amplitude of the pendulum and the energy of the pendulum increases.


Ej

Ei

Induced Emission

h

hh

h=E j−E i

Alternating Force

If the applied force is 180O out of phase with the oscillating pendulum, then the amplitude of the pendulum and the energy of the pendulum decreases (Induced Emission).

Lasers are used in many applications, Lasers are used in many applications, from CD Players to dental drills to high-from CD Players to dental drills to high-speed metal cutting machines to speed metal cutting machines to measuring systemsmeasuring systems..

The Optical Damage Threshold test station at NASA Langley Research Center has three lasers: a high-energy pulsed ND:Yag laser, a Ti:sapphire laser and an alignment HeNe laser.

●Atoms are constantly in motion. They continuously vibrate, move and rotate.

●Atoms can be in different states of excitation.

●They can have different energies.

●If we apply a lot of energy to an atom, it can leave what is called the ground-state energy level and go to an excited level.

●The level of excitation depends on the amount of energy that is applied to the atom via heat, light, or electricity.

Ej

Ei

Induced Absorption

h

h=E j−E i

Applying some energy (heat, light, etc.) to an atom, expect that some of the electrons in the lower-energy orbitals would transition to higher-energy orbitals farther away from the nucleus.

Ej

Ei

Induced Absorption

h

h=E j−E i

•In a laser, the lasing medium is “pumped” to get the atoms into an excited state. •Typically, very intense flashes of light or electrical discharges pump the lasing medium and create a large collection of excited-state atoms.

Ej

Ei

Induced Absorption

h

h=E j−E i

●It is necessary to have a large collection of atoms in the excited state for the laser to work efficiently. ●In general, the atoms are excited to a level that is two or three levels above the ground state.

Ej

Ei

Induced Absorption

h

h=E j−E i

●Population Inversion - the number of atoms in the excited state versus the number in ground state.●This increases the degree of population inversion.

Ej

Ei

Induced Absorption

h

h=E j−E i

●The excited electrons have energies greater than the more relaxed electrons. ●Just as the electron absorbed some amount of energy to reach this excited level, it can also release this energy. ●The electron can simply relax, and in turn rid itself of some energy.

Ej

Ei

Induced Absorption

h

h=E j−E i

●The emitted energy comes in the form of photons (light energy). ●The photon emitted will have very specific wavelength (color) that depends on the state of the electron's energy when the photon is released. ●Two identical atoms with electrons in identical states will release photons with identical wavelengths.

Ej

Ei

Induced Emission

h

hh

h=E j−E i

●Stimulated Emission●The photon that any atom releases has a certain wavelength that is dependent on the energy difference between the excited state and the ground state.

●If this photon should encounter another atom that has an electron in the same excited state, stimulated emission can occur.

● The first photon can stimulate or induce atomic emission such that the subsequent emitted photon (from the second atom) vibrates with the same frequency and direction as the incoming photon.

Ej

Ei

Induced Emission

h

hh

h=E j−E i

●Pair of mirrors, one at each end of the lasing medium.

●Photons, with a very specific wavelength and phase, reflect off the mirrors to travel back and forth through the lasing medium.

●In the process, they stimulate other electrons to make the downward energy jump and can cause the emission of more photons.

Ej

Ei

Induced Emission

h

hh

h=E j−E i

●A cascade effect occurs, and soon we have propagated many, many photons of the same wavelength and phase.

●The mirror at one end of the laser is "half-silvered"

● reflects some light and lets some light through.

● The light that makes it through is the laser light.

●Solid-state lasers ●Gas lasers ●Excimer lasers ●Dye lasers ●Semiconductor lasers

Types of Lasers:Types of Lasers:

Solid-state lasers

Have lasing material distributed in a solid matrix

(such as the ruby or neodymium:yttrium-aluminum garnet "Yag" lasers).

The neodymium-Yag laser emits infrared light at 1,064 nanometers (nm).

Gas lasers

(helium and helium-neon, HeNe, are the most common gas lasers) have a primary output of visible red light.

CO2 lasers emit energy in the far-infrared, and are used for cutting hard materials.

Excimer lasers

(the name is derived from the terms excited and dimers)

Use reactive gases, such as chlorine and fluorine, mixed with inert gases such as argon, krypton or xenon.

When electrically stimulated, a pseudo molecule (dimer) is produced. When lased, the dimer produces light in the ultraviolet range.

Dye lasers Use complex organic dyes, such as rhodamine 6G, in liquid solution or suspension as lasing media.

They are tunable over a broad range of wavelengths.

Semiconductor lasersSometimes called diode lasers, are not solid-state lasers.

These electronic devices are generally very small and use low power.

They may be built into larger arrays, such as the writing source in some laser printers or CD Players

The first successful laser was made of a Ruby rod ( 1960 ).

RUBY LASERRUBY LASER

Mirror Partially Transparent Mirror

Xenon Flash Lamp

Ruby

First Ruby LaserFirst Ruby Laser

Ground State

2.25 eV

1.79 eV

OpticalPumping

=550nm

Radiationless Transition

Metastable State

LaserTransition

=694.3nm

Ruby – crystal of aluminum oxide, Al2O

3

- some Al3+ ions replaced with

chromium Cr3+

- Responsible for red color

- Cr3+ metastable level with a lifetime of about 0.003 s

- Xenon flash lamp excites Cr3+ to a higher energy

First Ruby LaserFirst Ruby Laser

Ground State

2.25 eV

1.79 eV

OpticalPumping

=550nm


Metastable State

LaserTransition

=694.3nm

Ruby – crystal of aluminum oxide, Al2O

3

- Cr3+ fall to metastable level losing

energy to other ions.

- Photons from spontaneous decay are reflected back and forth between mirrored ends.

- These photons stimulate other excited Cr3+ ions to radiate.

- After a few microseconds, a large pulse of monochromatic, coherent red light.

- Rod length is an integral number of half wavelength, radiation trapped forms optical standing waves. Since induced emissions are stimulated by standing waves, their waves are all in step with it.

Helium-Neon Helium-Neon LaserLaser

Helium-Neon Helium-Neon LaserLaser

Ground State

20.61 eV

Ground State

20.66 eV

18.70 eV


Metastable State

LaserTransition =632.8nmCollision

Metastable State

Helium Atom

Neon Atom

Spontaneous Emission

●Mixture of about 7 parts helium with 1 part neon at low pressure ( approx. 1 mmHg ).●Glass tube has mirrors both ends, one partially transparent.●Spacing between mirrors is equal to integral number of half wavelengths.

●Electrical discharge is produced by electrodes outside the tube, connected to a high-frequency AC source.●Collisions with electrons from the discharge excite He and Nhe atoms to metastable state of 20.61 and 20.66 eV.●Some excited He atoms transfer their energy to ground state Ne atoms in collisions with the 0.05 eV of additional energy provided by KE of of atoms.

●He atoms help achieve population inversion in Ne atom population.●Laser transition is from the metastable state at 20.66 eV to excited state at 18.70 eV, with emission of 632.8 nm photon. ●Another photon is spontaneously emitted in a transition to a lower metastable state, yielding only incoherent light.

●Remaining excitation energy lost to collssions with tube walls.●Because electrons impacts that excite He and Ne atoms occur all the time, unlike pulsed excitation from Xenon lamp, He-Ne laser operates continuously.

lasers - coas | drexel university

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