Файл: Weber H., Herziger G., Poprawe R. (eds.) Laser Fundamentals. Part 1 (Springer 2005)(263s) PEo .pdf

Скачать файл
Заказать решение

ВУЗ: Не указан

Категория: Не указан

Дисциплина: Не указана

Добавлен: 28.06.2024

Просмотров: 881

Скачиваний: 0

ВНИМАНИЕ! Если данный файл нарушает Ваши авторские права, то обязательно сообщите нам.

Ref. p. 40]

 

 

 

 

 

1.1 Fundamentals of the semiclassical laser theory

37

 

 

 

 

 

 

 

 

Jpeak =

ω

 

g0

 

2

 

 

 

 

(peak intensity) ,

(1.1.117)

2σ0T2

 

α

Tπ = 2 τ = 2 T2

α

 

(pulse duration) .

(1.1.118)

 

 

g0

 

The pulse propagates approximately with c, depletes at each position the upper level, and converts this energy via the broadband losses α into heat. The saturated gain just compensates the losses. The pulse is only stable for α > 0 and g0 > 0.

So far solutions of the steady-state SVE-equation were presented, assuming resonance and a homogeneously broadened two-level system. O -resonance interaction and inhomogeneously broadened systems are much more complicated and are discussed in detail in the literature [74Sar, 69Ics, 72Cou]. Moreover, the stability of the pulses with respect to small perturbations was not yet mentioned. It is controlled by the area theorem [67McC, 74Sar].

1.1.7.3.2 Superradiance

The spontaneous emission was neglected in the coherent interaction. An initial state, R = (0, 0, µ ∆ n), complete inversion, without external field F would be stable according to the interaction equations (1.1.103). But due to spontaneous emission and amplified spontaneous emission, the R-vector will be pushed a bit out of equilibrium and decay into the stable position R = (0, 0, −µ ∆ n). This phenomenon is called superradiance and discussed in detail in Chap. 6.2.

1.1.8 Notations

Symbol

Unit

Meaning

A21

s−1

Einstein coe cient of spontaneous emission

B

Vs/m2

magnetic induction

B12, B21

m3/VAs3

Einstein coe cient of induced emission

C

As/m2

component of the Feynman vector R

c0

m/s

vacuum velocity of a plane wave

c

m/s

phase velocity of light in a medium

c1,2

–

coe cients of the eigenvector

D

As/m2

electric displacement

E

V/m

electric field

E0

V/m

electric-field amplitude

E1,2

VAs

energy eigenstates of the two-level system

Ein

VAs

amplifier input energy

Eout

VAs

amplifier output energy

ES

VAs/m2

amplifier saturation energy density

f (ω, ωA)

–

line shape factor

G

–

gain factor

G0

–

small-signal gain factor

g

m−1

gain coe cient

g0

m−1

small-signal gain coe cient

g1,2

–

degeneracies of lower/upper laser level

Landolt-B¨ornstein

New Series VIII/1A1

38

1.1.8 Notations

[Ref. p. 40

 

 

 

gh

ginh

H

H0

H0

Hint

h(ω, ωA) j

J

J

J +, J −

Js, Js4

k k k0

n nr n0

n1,2

PA,real

PA

PA0

PH

R

R

R1,2

r S

T1

T2

T2

T2

Tsp

Tπ , T2 π V

v Z Z0

α

χA χe χH χm

δ

∆n

∆tr

∆ωA

∆ωC

m−1

gain coe cient of a homogeneously broadened

m−1

transition

gain coe cient of an inhomogeneously broadened

 

transition

A/m

magnetic field

A/m

magnetic-field amplitude

VAs

Hamilton operator of the undisturbed transition

VAs

Hamilton operator of interaction

s

line shape factor

A/m2

current density

Vs/m2

magnetic polarization

VA/m2

intensity

VA/m2

intensity inside the resonator

VA/m2

saturation intensity of 2-, 3- and 4-level system

m−1

wave number

m−1

wave vector inside the medium

m−1

wave vector in vacuum

m

geometrical length of the active medium

–

complex refractive index

–

real refractive index

m−3

density of active atoms

m−3

density of lower/upper population

As/m2

real polarization of the active atoms

As/m2

complex polarization of the active atoms

As/m2

amplitude of the complex polarization

As/m2

complex polarization of the host material

As/m2

Feynman vector

–

= √

 

, average mirror reflectivity

R1 R2

–

reflectivity of mirror 1, 2

m

position vector

VA/m2

Poynting vector

s

upper-laser-level life time

s

dephasing time due to homogeneous broadening

s

dephasing time due to inhomogeneous broadening

s

resulting dephasing time

s

spontaneous decay time

s

pulse duration of π-, 2 π-pulses

–

resonator loss factor per transit

m/s

pulse peak velocity

V/A

impedance

V/A

vacuum impedance

m−1

absorption coe cient

–

susceptibility of the active atoms

–

electric susceptibility

–

susceptibility of the host material

–

magnetic susceptibility

s−1

detuning

m−3

inversion density

m−2

transverse delta-operator

s−1

line width of homogeneous broadening

s−1

line width of collision broadening

Landolt-B¨ornstein

New Series VIII/1A1

Ref. p. 40]

1.1 Fundamentals of the semiclassical laser theory

39

 

 

 

∆ωR

∆ωS

∆ωL,inh, ∆ ωL,h

ε

ε0

|ϕ |ϕ1,2

κ

λ0

Λ

µ

µ0

µ12, µ21

µA

θ

ρω σ(ω) σe σ0

τ

ω

ωA

ωR

s−1 s−1 s−1

–

8.8542 × 10−12 As/Vm

–

–

1.38 × 10−23 VAs2/K

m s−1

–

4 π × 10−7 Vs/Am Asm

Asm

–

VAs2/m3 m2

A/Vm m2

s s−1 s−1

s−1

line width of inhomogeneous broadening line width of saturation broadening

lasing bandwidth of inhomogeneous/homogeneous transitions

permittivity electric constant

state vector of the two-level system eigenfunctions of the two-level system Boltzmann’s constant

vacuum wavelength Rabi frequency permeability magnetic constant

= µA, dipole moment of the two-level transition dipole moment of the two-level transition

beam divergence, slope of the Feynman vector spectral energy density (per dω)

cross section of the two-level system electric conductivity

cross section of the two-level system in resonance pulse width

frequency of the radiation field

resonance frequency of the homogeneously broadened transition

resonance frequency of the inhomogeneously broadened transition

Landolt-B¨ornstein

New Series VIII/1A1

40

References for 1.1

 

 

References for 1.1

17Ein

Einstein, A.: Phys. Z. 18 (1917) 121.

19Mei

Meissner, A.: Patentschrift Reichspatentamt, Deutsches Reich, No. 291604, 1919.

46Blo

Bloch, F.: Phys. Rev. 70 (1946) 460.

47Lam

Lamb, W.E., Retherford, R.C.: Phys. Rev. 72 (1947) 241.

54Bas

Basov, N.G., Prokhorov, A.M.: Zh. Eksp. Teor. Fiz. 28 (1954) 249.

54Max

Maxwell, J.C.: Treatise on electricity and magnetism, New York: Dover Publications

 

Inc., 1954 (reprint of the 3. edition 1891).

57Fey

Feynman, R.P., Vernon, F.L., Helwarth, R.W.: J.Appl. Phys. 28 (1957) 49.

58Sch

Schawlow, A.L., Townes, C.H.: Phys. Rev. 112 (1958) 1940.

60Mai

Maiman, T.H.: Nature (London) 187 (1960) 493.

60Vuy

Vuylsteke, A.A.: Elements of maser theory, N.Y.: v. Nostrand Comp., 1960.

61Mes

Messiah A.: Quantum mechanics, Vol. I–II, Amsterdam: North Holland Publ. Comp.,

 

1961–1962.

61Mor

Morse, P.M.: Thermal physics, New York: W.A. Benjamin Inc, 1961.

63Fra

Frantz, L.M., Nodvik, I.S.: J. Appl. Phys. 34 (1963) 2346.

63Tan

Tang, C.L., Statz, H., de Mars, G.: Phys. Rev. 34 (1963) 2289.

64Lam

Lamb, W.E.: Phys. Rev. A 134 (1964) 1429.

64Sta

Statz, H., Tang, C.L.: Appl. Phys. 35 (1964) 1377.

66Men

Menne, T.J.: IEEE J. Quantum Electron. 2 (1966) 47.

66War

Ward, J.F.: Phys. Rev. 143 (1966) 569.

67McC

McCall, S.L., Hahn, E.L.: Phys. Rev. Lett. 18 (1967) 908.

68Sch

Schi , L.I.: Quantum mechanics, New York.: McGraw Hill, 1968.

69Are

Arecchi, F.T., Masserini, G.L., Schwendimann, P.: Riv. Nuovo Cimento Soc. Ital. Fis. 1

 

(1969) 181.

69Ics

Icsevgi, A., Lamb, W.E.: Propagation of light pulses in a Laser amplifier; Phys. Rev.

 

185 (1969) 517.

69McC

McCall, L., Hahn, E.L.: Phys. Rev. 183 (1969) 457.

70Hak

Haken, H.: Laser theory, Handbuch der Physik, Vol.XXV/2c, Fl¨ugge, S. (ed.), Berlin:

 

Springer-Verlag, 1970.

71Lam

Lamb, G.L.: Rev. Mod. Phys. 43 (1971) 99.

72Cou

Courtens, E.: Nonlinear coherent resonant phenomena, in: Laser handbook Vol. 2,

 

Arecchi, F.T., Schulz-Dubois, E.O. (eds.), Amsterdam, New York, Oxford: North Hol-

 

land Publ. Comp, 1972, p. 1259.

Landolt-B¨ornstein

New Series VIII/1A1

Смотрите также файлы