Laser physics M. A. Bouchene Laboratoire « Collisions, Agrégats, Réactivité », Université Paul Sabatier, Toulouse, France.

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1 Laser physics M. A. Bouchene Laboratoire « Collisions, Agrégats, Réactivité », Université Paul Sabatier, Toulouse, France

2 Outlook 1- Basic introduction 2- Optical cavity 3- Energetic model of the interaction 4- Laser oscillation (CW laser) 5- Laser frequency 6- Pulsed regime (summary)

3 1- Basic introduction

4 Basic Ideas AbsorptionSpontaneous emission Stimulated emission

5 Basic Ideas AbsorptionSpontaneous emission Stimulated emission

6 Basic Ideas AbsorptionSpontaneous emission Stimulated emission

7 Mirror Population inversion

8 Mirror Spontaneous emission

9 Mirror Stimulated emission

10 Mirror Feed-back by the cavity

11 Mirror Stimulated emission

12 Mirror Feed-back by the cavity

13 Mirror Laser beam After several round trips… Photons with: - same energy : Temporal coherence - same direction of propagation : Spatial coherence …..

14 Mirror Laser beam After several round trips… Photons with: - same energy : Temporal coherence - same direction of propagation : Spatial coherence

15 External medium Active medium L ight A mplification by S timulated E mission of R adiation Optical cavity (Resonator)

16 Pumping process External medium Active medium L ight A mplification by S timulated E mission of R adiation Optical cavity (Resonator)

17 Pumping process External medium Active medium - Population inversion - Amplification by stimulated emission L ight A mplification by S timulated E mission of R adiation Optical cavity (Resonator)

18 Pumping process External medium Active medium - Population inversion - Amplification by stimulated emission L ight A mplification by S timulated E mission of R adiation Optical cavity (Resonator) - Feed-back - Spectral and spatial shape

19 Some properties… Laser Spectral lamp CW: 10MHz (standard) 10GHz CW kW/cm 2

20 2- Optical cavity

21 Transfer matrix Optical system Optical axis x

22 Transfer matrix Optical system Optical axis x

23 Transfer matrix Optical system Optical axis x

24 Transfer matrix In the paraxial approximation Optical system Optical axis x

25 Some examples 0 d z z Free propagation mirror ……………….. …. M1M1 M2M2 Mn M = M n......M 2 M 1 z

26 Geometric stability Condition: StableUnstable

27 Geometric stability

28 g1g1 g2g2 Unstable g 1 g 2 = 1 1 1

29 Geometric stability g1g1 g2g2 Unstable g 1 g 2 = 1 1 1 R 1 =R 2 = R 1 =R 2 = L/2 concentric Plan R 1 =R 2 = L confocal

30 Cavity Modes Elementary solution of Maxwell equation in vacuum

31 Cavity Modes Arbitrary (plane-wave) solution of Maxwell equation in vacuum

32 Cavity Modes Arbitrary (plane-wave) solution of Maxwell equation in cavity : Define longitudinal modes

33 Cavity Modes Arbitrary solution of Maxwell equation in cavity : beyond plane-wave approximation : Define longitudinal modes z x y

34 Cavity Modes Arbitrary solution of Maxwell equation in cavity : beyond plane-wave approximation : Define transverse modes : Define longitudinal modes z x y

35 Cavity Modes Arbitrary solution of Maxwell equation in cavity : beyond plane-wave approximation : Define transverse modes : Define longitudinal modes Mode: elementary solution of Maxwell equation inside cavity Complete basis set

36 Transverse modes Monochromatic wave:

37 Transverse modes Monochromatic wave: Solution of propagation equation inside the cavity within the paraxial approximation

38 Transverse modes Monochromatic wave: One possible solution: Gaussian beam Solution of propagation equation inside the cavity within the paraxial approximation

39 Transverse modes Monochromatic wave: One possible solution: Gaussian beam Condition: cavity is stable Solution of propagation equation inside the cavity within the paraxial approximation

40 FUNDAMENTAL MODE: GAUSSIAN BEAM Z AXIS 1/e 2 of I

41 FUNDAMENTAL MODE: GAUSSIAN BEAM Z=0 plane wave Z AXIS 1/e 2 of I 0

42 FUNDAMENTAL MODE: GAUSSIAN BEAM Z AXIS 1/e 2 of I

43 FUNDAMENTAL MODE: GAUSSIAN BEAM Z AXIS 1/e 2 of I

44 FUNDAMENTAL MODE: GAUSSIAN BEAM Z AXIS 1/e 2 of I

45 Z AXIS Everything depends on the waist How to get w 0 and z=0 in a cavity ??

46 In a cavity: The wavefront adapts to the shape of the mirors ( stability)

47 High order modes Solutions : Hermite-gauss beams (a complete basis set)

48 High order modes Solutions : Hermite-gauss beams (a complete basis set) TEM m,n Nodes in x,y x y

49 Longitudinal modes Condition of resonance :

50 Longitudinal modes Condition of resonance : ………

51 Longitudinal modes Condition of resonance : ………

52 Cavity losses

53 transmission

54 Cavity losses Diffusion, Spont.emission

55 Cavity losses absorption

56 Cavity losses diffraction

57 Cavity losses transmission Diffusion, Spont.emission diffraction absorption

58 Cavity losses Consequence: broadenning of the longitudinal modes transmission Diffusion, Spont.emission diffraction absorption

59 3- Energetic model of the Interaction

60 1- Evolution of populations Absorption 1 2 Two-level open system

61 1- Evolution of populations Absorption Stimulated emission 1 2

62 1- Evolution of populations Absorption Relaxation Stimulated emission 1 2

63 1- Evolution of populations Absorption Relaxation Stimulated emission 1 2 Rate equations Pumping

64 1- Evolution of populations Absorption Relaxation Stimulated emission 1 2 Rate equations Pumping

65 Stimulated emissionAbsorption 2- Evolution of Intensity Stimulated emissionAbsorption 1 2

66 2- Evolution of Intensity Stimulated emissionAbsorption 1 2

67 Inversion of population ? In a CLOSED two-level system, an incoherent excitation can never accomplish population inversion Arb. parameter 1 2 N2N2 1/2

68 Solution : More levels 0 3 2 1 FOUR LEVEL SYSTEM

69 Solution : More levels 0 3 2 1 pumping

70 Solution : More levels fast relaxation 0 3 2 1

71 Solution : More levels Inversion of population Laser transition 0 3 2 1

72 Solution : More levels 0 3 2 1 A 21 Spontanous emission

73 Solution : More levels 0 3 2 1 relaxation CONDITION: A 21

74 Solution : More levels 0 2 1 relaxation CONDITION: A 21 Three level system Laser transition

75 Solution : More levels 1 3 2 fast relaxation CONDITION: A 21 Three level system Laser transition

76 4- Laser Oscillation (CW laser)

77 Amplifier in an optical cavity Active medium Gain

78 Amplifier in an optical cavity Active medium Losses<0 (spread) Laser equations

79 : Not sufficient! Gain must overcome the losses

80 : Not sufficient! Gain must overcome the losses Laser works (Stationnary regime): Gain = losses Photons created on a round trip = photons lost on a round trip

81 Laser equations

82 Two regimes :

83 Pumping Stimulated emission Losses

84 Pumping Stimulated emission Losses Increases the gain (Pop. Inv)

85 Pumping Stimulated emission Losses Decreases the gain Increases the gain

86 Pumping Stimulated emission Losses equilibrium Fixes the laser intensity Increases the gain Decreases the gain

87 5- Laser frequency

88 1 2

89 1 2 Frequency Spectral line

90 1 2 Frequency Gain cavity modes Spectral line

91 1 2 Frequency Gain Losses cavity modes

92 1 2 Frequency Gain Losses cavity modes Possible laser frequencies

93 Ring laserLinear laser Homogenous linewidth MonomodeMultimode Inhomogenous linewidth Multimode travelling waveSpatial stationnary wave

94 6- Pulsed regime (summary)

95 Relaxation regime: µs pulses (10 -6 s) Q-switch regime : Nanosecond pulses (10 -9 s) Mode-locking Regime: Picosecond (10 -12 s) and femtosecond pulses (10 -15 s)

96 Bibliography -YARIV: "Quantum Electronics" (Willey interscience 1975) - RABIN&TANG: "Quantum Electronics" (Academic Press 1975) - A.E. SIEGMAN: "Lasers" (University Science Books 1986) - P.W. MILONNI & J.H. EBERLY "Lasers" (John Wiley & Sons 1988) - - M. SARGENT III, M.O. SCULLY, W.E. LAMB,Jr. :"Laser Physics" (Addison-Wesley Publishing Company 1974)

97 Go to www.google.com !!!!!!!