Light [Vol 2 - Laser Light Dynamics]

354 Pages·1985·15.71 MB·English

by  H Haken

LIGHT

Volume 2
LASER LIGHT DYNAMICS

1. HAKEN

vesttut fur Theoreritelie Pleyik, Stuttgart

\oRTE-HOLLAND PHYSICS PUBLISHING
Pretace to the Preface

Dear Reader,

Retine you reat Uris boos, and even its preface, Me Following remarcs
might be useful fo yor. Since this heak is "Wohume 2” yon mey be Irclined.
to believe that yon mnst know all che contents of “Volume 1” kefare you
‘can scart reading and, of conse, tnderstanding) "Volume 2", Ent cis is
hot the case. ‘Ihe present “Volume 2" aga scarts a: a rather elementary
level, and then proceeds step by step to more dificult matters. Only ac these
Taler slages sane more atvanced theure: ical backgrourx! #6 require sshich
ther can he taken thorn "Volune 1”. I have chosen this way of presentation
a make the theary of laser light accessible uo a bmg audience rang ng
Tram students at the Deginaing oF unvie graduate studies te pre essers aad
scivolists interested! in revert develoomenls. For details om the relations
Debween the ehap.crs of these books consul (ae list al lke ead ef the
introduction,

LU, Taken
Preface

This bouk is 4 text which applies to sludemts aud professors al pliysivs
Becanse it offers a hroadl view om laser physics and presents most recent
results on the dynamis of laser Hight, sush as sell-pulsing sad chaos iL will
be of imerest alsa un seiemists and engineers engaged in laser resemieh oF
development, ‘This text scares at a rather elementary level and will smaeehly
Jexd thy reader into the wore difficult problems of luser physics iucluding
the basic features of the eaherence and noise properties of laser light.

In the introductory chapters, typical experimental set ups and laser
muaterials will be dissssod. but ths min part of this book will be devoted
lo x theoretical treament of a gncal vericly vf hase: processes. The liser, or
the optical maser, as it was originally called, is one of the most important
inventions of this century and has cound a great nomber of important
applications in physics, chemistry, medicine, engincecing, telecoramunics
tions, and other fields, 1€ bears great promises for further applications, 2,
in computers. But also from the pout of view of basic research. a smdy of
the physical processes. which produce the unique propecties of laser light
are equelly fascinating. Whe laser 15 2 beamtitial example of a syscem far
fiom thermal equilib-ium which can achieve a miacroscopically ordered
sate thrangh "self organization". i was the fist example for a nonecquii
hsinm phage cansition, and its study eventually gave birth to synergetics,
a new inlarisciplinary Held oF resecnch,

Tegot involved in laser physics a¢ a rather early stage and nner mose
forcinate circumstances. In 1960 L was working £5 visiting setentst at the
Bell "Telephone Laboratories, Murray ILiIL ‘There | soon learned thar these
laboraunvies were seceching law a revolutionary new Fight source, Two years
earlier. In 195%, this sontes had heen proposed by Schawlone and ‘Townes.
who derived in particular the laser condicion and thas demonstrated che
feasibility ov this new device. At Bell Telephone Laboratories | seam gor
involved ima theoretical suudy of the laser processes and continued it at
Swugan Lniversity, T developed a Taser theary whose basic Healures. 7
published in 1962 and whicl 1 lion epplied to various concrete problems,
i Pratace

Jointly with my coworkers, Ac about the same time, in 196, Willis Lamb
published fis cheory, which he and his coworkers applied ta mmerous
problems, It as by now well know that these two theories, which are called
semiclassical and which were developed independently, are equivalent. Ihe
next step consisted in the development of che laser quaneim theory which
allows one to predict the cohe-enee and noise properties of laser light (and
{ut of Hight Grom Iunps). This theory which 1 published in 1964 showed
fr the first time that the statistical properties of lascr light change dramati
cally at kiser Uuesbold, In the following yeurs my group in Stuttgart carried
this work further. eg, to predict the photon statisties close co laser threshold

From 1965 on, Scully smd Larub sticted publishing their resulls on Ux:
quantum theory of tbe Huser, using a dillsremt approach, and Lux aud
Louisell preseuled ler Uncory. Agiin, all of these theories eventually turned
ut tn Be more oF less equivalenL. In those years experimental laser physics
dovelaped (and is sUil descloping) alan enormous price, bul because F shall
rmasiuly Jou with liser #eorp in this book, J buve to cult out a zepreseutalion
fof the history af UnaL Tel

From my above personal cominisconces it may iuaspire that Laser theory
sad, porhups sil] more, laser physics in gensral bury boon highly competitive
ficlds of research. But, what counts mach more. laser physics bas been for
us all a fascinating field of :esearch, When one looks around nowadays,
cone can safely siy Maat is Ls lost molbing of ts original Liscination, Again
‘nid again ness Taser materials are und, new experimental set-ups invomisd
acl nes effects precliclad aul discovered. Lindoubiedlly, live many sears 0
come, lage physies will remain a highly aftractive awd importa Held gr
research, in shich Tundamental problems are intimately imlerwoven with
applications of great practical importance, | hope thal this book will Tel
anspire Une lascination of is el,

‘Over the past. nearly 25 years | greatly profived from the cooperation or
discussion with numerous Scientists and I use this opppetunity to think all
of them, There is Wollgang Kaiser, seho was the first at BTL with whom 1
ad discussions on the Jascr probkim, Then there are the anetubers of wy
group xt Stutlyart who iu the sixties, worked ou Lier tbvory aud who yave
itaportunt coulsibutious. 1 sish to aucution in particular R. Grabant, H.
Geffers, Il. Risken, I. Sanermann, Chr. Sehmid, 1LD. Vollmer, and W
Woidlich, Vos! af them now have their nwa chairs af various universities,
Among nig envvorkers who, in later years, contributed fe laser theary ancl
its applicatious aren particular J, Goll, A, Schenck, H, Ohne, A. Wunderlin
and J, Zorell, Over the yours 1 enjoyed anuny Irieadly and stimulating,
discussions with LI. Aveoshi, WR. Bennett, Jn... loembergen,
R. Romfacio. JH. Eberly, CCE. Garret, KJ. Glauber, K Haake. Yu.
reetoce is

Klimoatovich, WW, Lanib, M. Lax, Wy Lanisell, 1, Lugiat. 1. Mandel,
L, Nardusei, IR, Pike, M, Sargent, M, Scully, 8, Shimoda, $. Sleaholm,
7.€, Wang, 1, Wal, J, Thang, 4nd many niher scientists.

I reish to thanle my cowrarker, Dr. TL. Ohno, for his cantimous and
wuluable assistance inthe preparation of the manuscript. Tn particular. he
carelully checked th: form las amd exercises, cou.sizuled semoin addition,
aud dew the Bgurs, My purtic.lir dawks go le icy secwtary, Mrs, Le
Trunks, sho in spite of Fer hoass administrative work assisied me in many
‘wuss iu writing the mae seript and typed various versiuus uf it butb .apidly
aud porfvclly. Hor indefatigable zeal constanlly sparred gue o:2 la brig il
to a Tins:

The wrikug of this book was gcoatly helped by « progean: of Laz Deutsche
Farschungsgemeinschall, This program vas iniliated by Prof, Dr. Maicr-
Leibniz, sehom Lsvish e thank ceria ly tar hs support tar Tis projeet

H. Haken
Contents

Preface to the prefuce ¥
Preface

Contents xi
oF symbols x

1. Introduction !
11, ‘The muser und faser prncaple 1
412, The problows of laser theory 3
13, The structure of laser theory and les representanen in this

hook w
2 Basic propertis and types of lasers 4
2.1. ‘The laser condition la
22. Typical propertios uf laser light 19
29. examples of lazer sysuems (Iypes of lasers and laser

prucesses} 2
3. Lasor resonators “
3. Survey a
3.2. Modes in w onnfocal resonatas 43
3.3. Modes in a FalvyPeroc resonator 58
4. The intensity of laver Tigh. Rate equations 59
41, Iniraduetion 59
42. The pholon model of a siugle node laser 33
43. Rolacalinn oselations a
Ad. Q-switehi "0
si Content

4s,

46,
4a,

As,

49,

42

The bisic rate equations of as mulGiude laser
Hole burning. Qualitaive discussion

Quantitative treatment of bole burning. Single mode laser
uetivd of an inhomogoucously Luoudened line

Spatial hole burning, Qualitative discussion

The multimode laser, Mode competition aul Darwin's
survival of the Giles

The coexistence OF mies clue 10 spatial hole Burd
(Quantitative treatment

‘The basic equations of the semiclassical laser theory

In-ndustion
Derivation of the wave equation For une electric Hele
strength

The matter equacians

‘The scrmichissicul Inscr equatious for Ure macroscopic
quaulities clecbig ald st-engih, polarization, anc ineorsion
density

The laser equations in a resonator

‘Two important approximtious: The rotating 20
approximation and the slowly earying wnpliude
approximation

The semiclassical Inger equations Ine uhe macroscopic
quantities elecrie Held strength, polarization, and inyersina
density in the rotating wave and! slowly varying amplivuds
Epproximarions,

Dimensionless quantities Har the light lield and introduction
af a sampling constant,

The basic laser equations

Applications of semiclassical theory

‘The single mode laser. Investigation of stability
Single mode laser action, Amplitude and frequency of laser
light im tbs: stetiouary state

The single mode lnser: Teausiems

Mnitamade action af colid state lasers. Darivarion of
reduced equations for the code amplitudes alone

Simple examples of the multimode cave

Froqucuey locking of three modes

The laser gy#o
8S,

40.1

m2,

103.

The gus Iuser, Single mee operation
Dberivac an of she rate ecnations from the semiclassical
Inger eytstioas

Ultrashort pulses,

Scme basic mechantisus, Active and passive mode locking
The busie eyuatioas of self yulsing livers

A gereral metharl lor caleulating evolving patterns close ut
insishilily soins

Onset af ultzashort leser pulses: Linear seability: analysis,
Onset of ulteashoet leser pu.ses: nonlinear analysis
Suluiian of che order pavamele” exuatin

Models of lasers sth saturable absorbers

Instability hierarchies of laser light. Chaos, and routes to
eho

Survey

‘The bsie equatinns

‘The sing @ mace laser equations and thew equivalence with
the Lawenz model of turbulence

Criteria Tor the presence af ehgos

Rowies 19 chads,

awe ta produce Inser light chans. Same theaverical mavlels
Single mede laser with injected signal. Chaos, brestaing,
spiking

Optical bistability

Survey

A specific model

Steady stare azhavior cf the madel wf section 92
The general ease of an arbitrary susceptibility
Coneluding remarks on chapter 9

(Quantum theory af the laser 1
A tise approach via gqanaim mechanical Langevin
equations. Cahe-ence, noise and photon statist

Why qusmtum ibeory of the Lsser?
The laser Haniltonian
Quantum mechanical Langevin equatcons,

234
235
240
iy Coatents

104. Coherence and noise
15, ‘The behavior of the laser at its threshold. Photon statistics

Quanuuun dheory of the lise
A second approach via the clonsity: malrix axyation and
quantum classical correspondence

{LL. ‘The density matire equation of the isser

A short course in gaanaim classical correspondence. ‘he
example of 3 damped field mode (harmonic oscillate}

2. Generalized FokberPleuch. eeuation of the lusee

4. Reduction of the yeuerulized Poldser-Plunck equation

S. Concluding remitks

12, A dheoretival apprusch to the twephoton laser

Introduction

12.2. fective Hamiltonian, quanaim mechanical Langevin

12.3. Isfimingtion al ausmie. ¥a

eqnetions ind semiclassical equations
ables

12.4. Single mode operation, homogeneously hroadened line

and conning Weve

13, “The laser trailblazer af symergeries

12.1, What is synergetios about’
12.2, Self organization and the slaving pvinciple
13.5, Nemaquilibrmm phase transitions

Refereucey and further ceading

ubjeet Index

2a
26

280

30

402
302

303
305

306

309

309
310
34

318
332