Physical Optics. Lecture 8: Laser Michael Kempe.

Transcription

1 Physical Optics Lecture 8: Laser Michael Kempe

2 Physical Optics: Content 2 No Date Subject Ref Detailed Content Wave optics G Complex fields, wave equation, k-vectors, interference, light propagation, interferometry Diffraction G Slit, grating, diffraction integral, diffraction in optical systems, point spread function, aberrations Fourier optics G Plane wave expansion, resolution, image formation, transfer function, phase imaging Quality criteria and Rayleigh and Marechal criteria, Strehl ratio, coherence effects, two-point G resolution resolution, criteria, contrast, axial resolution, CTF Photon optics K Energy, momentum, time-energy uncertainty, photon statistics, fluorescence, Jablonski diagram, lifetime, quantum yield, FRET Coherence K Temporal and spatial coherence, Young setup, propagation of coherence, speckle, OCT-principle Polarization G Introduction, Jones formalism, Fresnel formulas, birefringence, components Laser K Atomic transitions, principle, resonators, modes, laser types, Q-switch, pulses, power Nonlinear optics K Basics of nonlinear optics, optical susceptibility, 2nd and 3rd order effects, CARS microscopy, 2 photon imaging PSF engineering G Apodization, superresolution, extended depth of focus, particle trapping, confocal PSF Scattering G Introduction, surface scattering in systems, volume scattering models, calculation schemes, tissue models, Mie Scattering Gaussian beams G Basic description, propagation through optical systems, aberrations Generalized beams G Laguerre-Gaussian beams, phase singularities, Bessel beams, Airy beams, applications in superresolution microscopy Miscellaneous G Coatings, diffractive optics, fibers K = Kempe G = Gross

3 3 Laser Sources Laser = Light Amplification by Stimulated Emission of Radiation Typically spectrally narrow beam of light Spatially coherent First demonstrated in microwave regime Maser (Townes, 1954) Laser in VIS shown in Ruby at 694 nm (Maiman, 1960) Requirements: 1. Gain medium (inversion), G 2. Feedback by resonator, G L (losses in resonator) G L G R=100% R<100%

4 4 Photon-Matter Interactions absorption spontaneous emission stimulated emission Probability densities: energy conservation: P abs = n c V σ(ν) P sp = c σ ν V P st = n c V σ(ν) absorbing one photon from a mode with n photons n c V emitting one photon into a mode σ(ν): transition cross section = φ(ν) for monochromatic wave emitting one photon in a mode with n photons atomic energy level differences typically lie in the optical region

5 5 Photon Flux Changes absorption spontaneous emission stimulated emission Change of flux density φ = P st N 2 P abs N 1 z P N = 1 s 1 m 3 φ = φσn 2 φσn 1 z φ = φσ N 2 N 1 z φ(z) = φ 0 e σ N 2 N 1 z N 2 < N 1 loss of photons I(z) = I 0 e σ N 2 N 1 z N 2 > N 1 gain of photons

6 6 Population of Energy Levels for N 2 = N 1

7 4-level system 3-level system 7 Population inversion Ref. M. Kaschke

8 8 Stationary Laser Oscillator Setup Z = 0 Laser Material Z = L L Laser beam mirror (R = 100%) Pump source coupling mirror (R < 100%) HV Intensity inside the resonator ( z) ( z) Ref.: M. Kaschke

9 9 Resonator Modes q=1 q=2 Standing wave (stationary): Intensity is reproduced after roundtrip Knots at the mirror surface L = q λ 2 λ = 2L q = c ν q = 1,2 n ν = q c 2L

10 10 Laser Resonator Types Ref: B. Böhme

11 Stable Gaussian Resonators Principle: - feedback of the radiation field - reproduction of the wave for one round trip - loss compensated by gain - eigenmode solutions of the field w 1 R1 w 0 R2 w 2 Description: - length L - radii of curvature R 1, R 2 L Definition of stability parameter g 1, g 2 Internal ABCD matrix for one round trip M o A C o o g 1 L 1, g2 1 R B D o o 1 2 L 2g 2 1 L R 2 2Lg 2g1g2 g1 g2 4g1g2 2g 2 1 2

12 Stability of a Gaussian Resonator

13 13 Laser Emission Laser condition: gain = losses 2 ln( Ti R) 2 NthL 0 γ = σ ν N T i internal transmission R reflectivity of the mirrors R = R 1 R 2 N th threshold inversion L length of the gain medium The initial small-signal gain γ 0 is reduced due to saturation γ ν = γ 0 ν 1 + φ φ s = N th σ(ν) and fixed ( clamped ) at a value γ = α r The emitted flux is therefore φ = φ s γ 0 (ν) α r 1 Source: Saleh/Teich For 3- and 4-level systems γ 0 = N 0 σ(ν) P in P in : pump power

14 14 Laser Output Power Laser intensity inside the resonator I, N I N th N P th pump power P in If the laser reaches the threshold, the inversion is constant The additional power above threshold increases the intensity in the resonator The output intensity grows linear with the slope efficiency h slope I = η slope (P in P th ) for P in > P th Ref.: M. Kaschke

15 15 Laser Output Power Optimization laser power P CW Optimization of the reflectivity according to gain/loss Rigrod diagram Curve of optimal reflectivities for different pump powers different pump power levels optimal outcoupling case ,5 0,6 0,7 0,8 0,9 1,0 Ref.: M. Kaschke

16 16 Laser Emission: Homogenous Broadening In a homogenously broadened medium all modes interact with the same transition The gain clamping leads to an emission of a single mode, if the modes don t occupy different spatial regions of the gain medium Source: Saleh/Teich

17 17 Laser Emission: Inhomogenous Broadening In an inhomogenously broadened medium the gain comes from different transitions The gain clamping leads to spectral hole burning all modes within the spectrum for which γ 0 > α r can oscillate Source: Saleh/Teich

18 18 Types of Lasers Continuous wave (cw) Dt = s power Pulsed (pw) Dt = 10-6 s = 1 ms power area corresponds to pulse energy time Q-switched pulse Dt = 10-9 s = 1 ns Mode locked pulses Dt = s = 1 fs power Dt time Quasi cw, pulsed with high frequency (khz-mhz) average power Ref.: M. Kaschke time

19 19 Q-Switch Time dependencies for cw and pulsed pumping pump intensity a) continuous wave b) pulsed mode loss inversion laser pulse Ref.: M. Kaschke

20 20 Mode Coupling Axial mode frequencies given by round trip time in resonator of length L All modes inside the gain profile are coupled/synchronized: mode locking Fabry-Perot resonator: Dn q, q1 c 2 L gain typical Dn = 100 Mhz...2 GHz laser lines axial modes resonator gain profile threshold Ref.: M. Kaschke n 0 Dn frequency n

21 21 Laser with Mode Coupling Fixed phase relation between modes Full interference of amplitudes q1 q field E 1st wave E q 2nd wave E q+1 3rd wave E q+2 4th wave E q+3 power P coherent superposition average power P Ref.: M. Kaschke

22 LD Solid State laser Gas laser Laser Source Data Laser type Typical power / energy Operation mode Pulse length Excimer, ArF 193 nm 30 W / 1 J pulse 20 ns Nitrogen-gas laser Argon-ion laser HeNe-gas laser HF-chemical Laser 337 nm nm nm mm 0.5 W / 10 mj pulse 10 ns Beam diameter in mm 6x20 20x30 2x3-6x30 Divergence 2 in mrad efficiency h in % x W cw mw CO 2 gas laser 10.6 mm 1 kw / 1kJ cw or pulse Ruby solid state laser Nd:YAG-solid state laser, flash bulb Nd:YAG-solid state laser, diode-pumped Semiconductor laser cw kw / 4 kj cw or pulse 20 ns ns nm 10 J pulse 0.5 ms mm 1 kw pulse ns mm 2 W cw mm W cw or pulse ms x

23 Gas Laser with Brewster Window Gas laser with flow tube Brewster windows suppress reflected light Outcoupled radiation linear polarized r 0 r 0.4 Brewster angle no reflected light p p no reflected light Brewster angle linear polarised

24 24 Flashlamp Pumped Solid State Laser Typical setup of a flash lamp pumped solid state Nd:YAG laser resonator Laser beam water cooling Laser rod Flow tube outcoupling HR mirror mirror pump chamber flash lamp flash lamp Ref.: M. Kaschke

25 25 Diode Pumped Solid State Lasers Longitudinal pumping geometry Usually good mode quality due to coaxial gain distribution pump diode laser pump optical system resonator mirror Nd:YAG rod 809 nm 1064 nm laser beam Ref.: M. Kaschke

26 26 Diode Pumped Solid State Lasers good mode quality due to coaxial gain distribution enables efficient intra-cavity frequency conversion Second harmonic generation (SHG) in nonlinear crystals with phase matching pump diode laser pump optical system resonator mirror Nd:YAG rod SHG 809 nm 1064 nm/ 532nm laser beam 1064 nm

27 27 Disc Laser Extrem aspect ratio of the laser rod: - very thin disc (< 1mm) - large diameter Advantage: - no thermal lensing high power laser e.g. for material - effective cooling from front side processing applications Complicated pump geometry, skew incident beams Ref.: M. Kaschke

28 28 Fiber Laser outer cladding inner cladding Double clad structure for efficient pumping core Ref: B. Böhme

29 Semiconductor Laser Typical structure of edge-emitting semiconductor laser Astigmatic beam radiation: 1. fast axis perpendicular to junction 2. slow axis parallel to junction y x y metal contact insulator p-region heterojunction n-region substrate metal contact y x light perpendicular x Q z Model of beam profiles: - Gaussian in fast axis E ( y) E yo e y w 2 i y 2 oy R oy parallel - Gaussian with Lorentzian envelope in slow axis E ( x) E xo w w 2 0x 2 0x x 2 e i x 2 R ox

30 Semiconductor Laser Materials Material Color Wavelength in nm Spectral Fwhm in nm Luminence in cd/m 2 InGaAsP NIR GaAs:Si NIR 940 GaAs:Zn NIR GaAlAs NIR GaP:Zn,N dark red 700 GaP red GaAlAs red 660 GaAs 6 P 4 red GaAs 0.35 P 0.65 :N orange 630 InGaAlP orange GaAsP 0.4 amber 610 SiC yellow GaP green InGaAlN green GaN blue 490 InGaN blue InGaN blue SiC deep blue 470

31 Semiconductor Laser Typical laser with housing Continuous transition from incoherent LED below threshold to coherent laser above threshold Laser beam P(W) 1 LED Regime Window Heat sink monitoring PIN photodiode Case Laser chip Laser Regime 0 I threshold V = 2-3 Volt I(A) Ref: M. Kaschke

32 VCSEL-Laser Usual semiconductor lasers: edge emitter, small elliptical emitter surface astigmatic beam form VCSEL-Laser: Emission perpendicular to pn-junction area typical D < 10 mm Good beam quality, monomode Power scaling by area size possible VCSEL LED semiconductor laser edge emitter n-layer p-layer

33 33 Optically pumped VCSEL-Laser Optically pumped semiconductor laser (OPSL) combine high beam quality with wavelength flexibility at low to high cw power Wavelengths: nm and nm with intracavity frequency doubling Optional: SHG Source: Coherent Inc.

34 34 Tunable Semiconductor Lasers Semiconductor laser with external cavity (Littrow configuration: grating with MEMS scanner; semiconductor optical amplifier - SOA) Wavelengths: several bands with nm, nm and nm most common) Tuning speed: 1 khz-150 khz Source: Exalos AG

35 35 Laser Safety Due to its spatial coherence, even a low-power laser can achieve high intensities at the retina For comparison: sun at earth surface: 1000 W/m², focused at retina ~ 0.1 Mio W/m² (2mm pupil) Different wavelength penetrate differently deep in the eye potential damage occurs at different parts of the eye For the retina VIS-NIR light is particularly dangerous

36 Maximum allowed cw power [mw ] 36 Laser Safety Considerations Appoximate values since limits are usually given in J/cm² or W/cm²! Class 3B Class 3R Class 2 Class 1 Wavelength [nm] Class Eye Safety Skin Safety 1 Safe under normal conditions 2 Safe if exposure is less than 0.25s Safe 3R Direct exposure dangerous, indirect exposure safe Safe 3B Indirect exposure safe in distance > 13 cm Skin damage possible