考试时间： 2011.1.4 上课时间和教室. Chapter 7. Lasers Light Amplification by Stimulated...

考试时间： 2011.1.4上课时间和教室

Chapter 7. Lasers

Light Amplification by Stimulated Emission of Radiation

(acronym)

The History 1916, Einstein predicted the stimulated emission. 1954, Townes and co-workers developed a Microwave A

mplifier 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.

7.1 Stimulated Emission of Radiation 1. 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

TEeN /E : energy lever of the system : Boltzmann's constantT : absolute temperature.

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.

TE

TE

e

e

N

N

/

/

1

2

1

2

TEEeNN /)(12

12

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

21221 ANP

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.

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.

uBNP 21221

uBNP 12112

7.1 Stimulated Emission of Radiation

Transitions between energy states

7.1 Stimulated Emission of Radiation Einstein's coefficients: A21, B21, B12

Einstein's relations

B21 = B123

3

21

21 8

c

h

B

A

(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

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 mo

re 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.

Incandescent vs. Laser Light Light from bulbs are due to spontaneous emission

1. Many wavelengths

2. Multidirectional

3. Incoherent

1. Monochromatic

2. Directional

3. Coherent

CoherenceCoherent: 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.

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.

two-level system(ex. ammonia maser)

En, Nn

Em, Nm

En, Nn

Em, Nm

Even with very a intense pump source, the best one can achieve with a two-level system is

excited state population = ground state population

three-level system

in equilibrium normal Boltzmann distribution absorptive rather than emissive

excited

population inversion

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:optionallaser amplifiers: no cavitylaser oscillators: medium enclosed in a cavity provides feedback and additional amplification cavity formed by two mirrors: one full reflectance, the other partially transparent

7.2 Practical Realization

Energy source Medium Full reflectance mirrors Partially transparent mirrors Radiation

Basic components of a laser oscillator

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.

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



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.

7.2 Practical Realization Cavity configurations

L:distance between mirrors

R:radius of curvature

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 cavityq : number of half-wavelengths, or axial modes

the resonance condition for axial modes:

n: index of medium contained in a laser cavity

Lq

2λ

nL2

cqν


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

two consecutive modes (which differ by q = 1), are separated by a frequency difference ,

S2

cν

Mode-locking

Active mode-locking


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.


lowest possible axial mode:

laser oscillates in one frequency

highest possible temporal coherence

TEM modesTEM00 :

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.

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


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“

xe 0

xe 0

0


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 trip210 rr err 21

: loss per round trip

--For the system xe )(

0

> : system will lase, threshold condition necessary to sustain laser emission.


7.3 Types of Lasers

1. 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.

7.3 Types of Lasers E3: fairly wide and has a short lif

etime; the excited Cr3+ ions rapidly relax and drop to the next lower state, E2. This transition is non

radiative.

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 grou

nd state, E1.The E2 E1 transition is radiative; it produces the spontaneous, incoh

erent 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, wit

h a sharp peak at 694.3 nm.

Three-level energy diagram typical of ruby

Lasing Action DiagramEn

erg

y

Intr

od

ucti

on

Ground State

Excited State

Metastable State

Spontaneous Energy Emission

Stimulated Emission of Radiation

effi

cien

t p

um

pin

g

slo

w r

elax

atio

n

Metastable state

fast

slow Population inversion

Fast relaxation

Requirements for Laser Action

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.

7.3 Types of Lasers

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.

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.

7.3 Types of Lasers carbon dioxide laser

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.

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.

7.3 Types of Lasers

3. Semiconductor Lasers

LED: light-emitting diode

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

main application :

• waveguides

• integrated optics

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

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)

WAVELENGTHS OF MOST COMMON LASERS

Wavelength (m)Laser Type

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

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

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

2)/2(0)( wreIrI

w(z) :beam's radius

: wavelength w0:radius at the waist.

For a confocal cavity, this simplifies to

L : distance between the mirrors.

2

20

0 1)(

w

zwzw

20

Lw

7.4 Applications

far field: farther away from the laser

beam's parameters can be considered linear functions of the distance

far-field half-angle divergence

0w

7.4 Applications

place a converging lens in the path of the light:

• beam to contract to a "focus“• another waist where the beam's wavefronts are plane• diameter radius of beam at the focus 2r:

f: the lens a focal length•radius of beam at the focus r

7.4 Applications

0

42

d

fr

D

fr

22.1

Rayleigh's criterion : D

22.1

7.4 Applications

2. Power and Power Density

A typical laser pulse contains about 10 J of energy. If this energy is delivered within a pulse only 0.5 ms long, the output power is 20 kW.

Q awitching: compressing the energy into a very short period of time.

7.4 Applications

3. Nonlinear Effects

Linear:the refractive index and the absorptivity of a material are independent of the intensity of the light that passes through.

Nonlinear: with very intense light, either the index or the absorptivity or both may become nonlinear functions of the intensity.

•change the refractive index, even of completely transparent material.

•Heat and thermal expansion, as they occur with absorbing materials, are not involved.

7.4 Applications

plasma: a mixture of ions and free electrons rarely found in nature except in the atmosphere of the sun

self-focusing: a beam of light contracts into thin, short lived, powerful threads of light that quickly shatter the material through which they pass.

Optical bistability arises in saturable systems

Phase conjugation(wavefront reversal): a molecular reflection of light. The reflected wavefronts are now distorted opposite to those in the incident beam,

Frequency doubling: generation of second harmonics.

7.4 Applications

4. Industrial Applications

Cutting

Drilling

Welding

Communications

Optical radar

precision measurements

Laser Technique in GIS Data Acquisition

GIS:Globe Information System

Tasks

Acquire Laser mapping equipment for GIS spatial data acquisition:– Utility mapping (power poles, water valve, gas

pipe, water pipe, etc)– Construction (ask for higher accuracy)– Digital geology mapping (geologic features)

Laser Mapping – Why It is Needed

Laser + GPS = fast 3D spatial data acquisition

Mapping the inaccessible area

More efficient and cost effective

Technical Basics

Distance measure + Angle (H & V) measure

Using NIR / Red Laser pulse for distance measure

Using magnetic compass or encoder for angle measurement

Emitter

Receiver

Laser Instrument

Distance

Distance = C x T / 2

C – speed of light

T – time

Technical Assessment Standards

Accuracy Distance Angle (horizontal & verti

cal) Function

Support Reflectorless Motorized Autotrack (high-caliber) Continuous mode Remote control (high-ca

liber)

Ease of use

GPS integration

External interface

Display

Laser Plummet (high-caliber)

Cost

Performance

Measurement Time

Measurement Range

Company Briefs

Laser Atlanta Optics, Inc., Norcross, GA USA, has been designing and manufacturing eye-safe laser-based distance and speed measuring systems since 1989.

Currently manufacture a product line based on a core technology called the Advantage. All of its rangefinder products are based on this proven design.

Measurement Devices Ltd. (MDL) is a leading designer, manufacturer and supplier of laser measurement systems.MDL is committed to preserving a quality system throughout all levels of our business, as well as providing consistent, high standards of customer service.

Advantage V.S. LaserAce/ALS

Laser Atlanta

Advantage

MDL

LaserAce / ALS

Accuracy Distance ±15.3 cm Typically 10 cm Typically 5 cm

Angle ±0.01°(en) both H & V;

H:±1°;V:±0.4° w/o en

H(encoder):0.2°; V: 0.3°;

Better ±1° w/o encoder;

H & V(en):0.02°

Performance Range 2-610m w/o reflector;

2-91800m w/ reflector

300m w/o reflector;

5,000m w/ refelctor

300 (DM)/600(RF) w/o

5km (DM)/10km(RF) w/

Time 0.34 sec 0.3 sec 0.5s(DM)/self-adp(RF)

Function Reflectorless? yes Yes yes

Motorized? no No yes

Cont. Mode yes yes yes

Ease of Use

Ext. Interface RS232 to PC RS232 to PC RS232 to PC

GPS integration Yes(plug & play) No No

Display HUD+ LCD LCD LCD

Cost $4000 -$6000 $4,300 – $5,525 $21,000 - $27,720

Advantage From Laser Atlanta

Physicals

•905 nm class I eye safe laser

•11.5Hx21.5Wx19Lcm

•4.5 lbs(2.1kg)

•Handle batteries

LaserAce From MDL

Physical •GaAs Laser Diode 905nm•Class I eye Safe•175x106x55 mm (LxWxH)•600g•Alignment Telescope: red dot•Compass(option)•Pocket PC (option)

Physical•Semi-conductor 905 nm•Class I eye safe•209 x 243 x 420mm (LxWxH)

•9.7kg /10.3 kg (w/ tribrach)

•Optical encoder

•Laptop/palm/desk top PC

Topcon: Pulse Total Station GPT-2000 series

Using pulse laser technology Support both prism/non-prism mode High accuracy:

Millimeter accuracy in distance measurement (5mm+2ppm xD in non prism mode; 3mm+2ppmxD in prism mode)

1”/ 5” (H & V) angle measurement accuracy Fast data acquisition:

0.3 sec tacking mode 1.2 second fine mode

Long range: Prism: 7,000m Non prism: 150m

All weather operation: water /dust proof Large data storage: 8000 points Laser plummet

Total Station GTS-800/800A seriesfrom Topcon

Motorized & automatic tracking – high speed rotation (up to 50º /sec) and high speed auto-tracking (up to 5º /sec)

Remote control through radio link or optical remote controller – enables one man operation

Flexible data management: Huge data storage – 2Mb memory plus PCMCIA card, space for data and software

User friendly Large graphic display Built-in MS-DOS OS Compact and light weight Water / dust resistant Handheld data collector TDS Survey Pro software allows more

functions: job classification, stake out, etc.

Motorized, automatic target recognition, reflectorless and remote control

Accuracy: Angle measurement: from 1.5” to 5” Distance measurement: 3mm+2ppm w/o reflector; 2m

m+2ppm w/ reflector Range: 200m (w/o reflector) to 7.5 km (w/reflector) Time

1sec w/ reflector 3 sec w/o reflector

Data storage: PCMCIA card or export via RS232 Software supports:

computations of area, height, tie distance etc. stake outs Exchange data between instrument and PC Create code list

Leica TCRA1100 series Total Station

Laser Plummet

GPT2000 series Display

External Interface

The external interface provides a way for the instrument to communicate with a PC, a laptop, a palm or a data logger. All the models here have this ability

7.4 Applications

5. Medical Applications

Coagulation & photocoagulation.

Photodisruption

Treatment of retinal

Laser refractive surgery

Correcting a refractive error by changing the shape of the cornea with surgery.

Diagram of the Eye

diagram of an eye

Normal Focus

Short sightedness(Myopia)

•Distance vision blurry, near usually OK.

Short-sightedfocus

Short-sightedcorrection

Long-sightedness(Hyperopia)

•Difficulty seeing clearly and comfortably up close.Long-sighted focus Long-sighted correction

AstigmatismIrregular curvature of the eye (shaped more like a football than a basketball)Light in different planes focuses at different points

A

B90

180

Shaping the cornea

Flattening the cornea, decreases myopia Steepening the cornea decreases hyperopia Making the cornea more spherical decreases

astigmatism All are possible in most refractive surgeries

Suitability for refractive surgery

Stable refractive error

– must not have changed for at least two years

Healthy eyes

– no underlying corneal abnormalities

Contact lens wear

– needs to be ceased at least three weeks prior to surgery

Refractive surgery does not mean you will never wear glasses

again

Most people over 40-50 years will need glasses for reading– this may not be fixed by laser surgery

Sometimes the corneal shape can gradually change– (although this is minimised)

考试时间： 2011.1.4 上课时间和教室. Chapter 7. Lasers Light Amplification by Stimulated...

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