Lecture 6 Proper,es of laser beams *

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1 Lecture 6 Proper,es of laser beams * Min Yan Op,cs and Photonics, KTH 12/04/16 1 * Some figures and texts belong to: O. Svelto, Principles of Lasers, 5th Ed., Springer.

2 Reading Principles of Lasers (5th Ed.): Chapter 11. Skip: , Squeeze: , , Web (with video) Mitsubishi CO 2 laser Mitsubishi fiber laser 12/04/16 2

3 Laser Pump I in I out Mirror 1 Gain medium Mirror 2 Amplitude, frequency, and phase vary w.r.t.,me. Always more than one frequency exist. 12/04/16

4 Contents Content Time 1. Monochromaticity Coherence - Spatial - Temporal Directionality Brightness Laser speckle 10 Total: 80 12/04/16 4

5 Contents Content Time 1. Monochromaticity Coherence - Spatial - Temporal Directionality Brightness Laser speckle 10 Total: 80 12/04/16 5

6 Monochromaticity Pure monochroma,c light just does not exist. Causes for frequency fluctua0on: - Amplitude fluctua,on (change in pump or cavity loss, <1%) - Phase fluctua,on (zero-point fluctua,on limit + vibra,on and thermal effects) Ac0ve stabiliza0on: 10-50kHz 0.1Hz Q-switched or mode-locked laser: Δν L can be 100MHz even 50THz Narrow Δν L (10-100kHz): metrology, coherent applica,ons Broad Δν L (1MHz): other common applica,ons (e.g. DWDM) DWDM: channel spacing 50 GHz (0.4 nm) 12/04/16 6

7 Contents Content Time 1. Monochromaticity Coherence - Spatial - Temporal Directionality Brightness Laser speckle 10 Total: 80 12/04/16 7

8 Coherence Order, harmony, consistency xy z Spa0al coherence: waves at two lateral points (along x/y direc,on) Temporal coherence: waves at two,me instances (same posi,on) 12/04/16 8

9 Quan,fica,on For sta,onary beam r=r 1 xy t t 1 t 2 The 1 st -order correla,on func,on: Complex degree of temporal coherence γ (1) (r 1,r 1,τ): Degree of temporal coherence: γ (1) 12/04/16 9

10 γ (1) (r 1,r 1,τ) Proper0es: 1. γ (1) =1 for τ=0 2. γ (1) (r 1,r 1,-τ) = γ (1)* (r 1,r 1,τ) 3. γ (1) (r 1,r 1,τ) 1 Two extremi0es: Perfect temporal coherence: γ (1) =1 for τ 0 Zero temporal coherence: γ (1) =0 for any τ>0 General case: Coherence,me τ co Coherence length L c =cτ co 12/04/16 10

11 γ (1) (r 1,r 2,0) Complex degree of spa,al coherence Again two extremi,es exist, and in general: γ (1) (r 1,r 2,0) 1 for r 1 -r 2 >0 Coherence area Complex degree of coherence: [Temporal + spa,al] 12/04/16 11

12 Measurem t: Spa,al coherence Method: Young s interferometer Light beam L 1 P Fringe visibility at P: L 1 It can be shown that where If L 1 =L 2 12/04/16 12

13 Measurem t: Temporal coherence Method: Michelson interferometer where V p Hence 12/04/16 L c 13

14 More remarks on coherence Temporal coherence and monochroma,city Single-mode laser: spa,ally coherent, τ co limited by Δυ L Single-transverse-mul0-longitudinal-mode laser: Spa,ally coherent, τ co limited by Δυ 0 (if mode-locked: spa,ally coherent, τ co limited by Δυ L ) Example: If Δυ L =20kHz, τ co =? L c =? Mul0-transverse-mul0-longitudinal mode laser: par,al spa,al coherence, τ co limited by Δυ 0 Thermal light: τ co <1ps, spa,al correla,on as distance 12/04/16 14

15 Coherence length: single-pinhole test Light beam Laser pointer Supercon,nuum source Pinhole diameter: 600μm 12/04/16 15

16 Coherence length of Sun Photo courtesy of Gunnar Björk Photo taken with a Thorlabs 50μm-diameter pinhole mounted about 50 mm from the CMOS-detector of a Sony α300 digital camera mounted on a tripod. Exposure,me ¼ s at ISO /04/16 16

17 Contents Content Time 1. Monochromaticity Coherence - Spatial - Temporal Directionality Brightness Laser speckle 10 Total: 80 12/04/16 17

18 Direc,onality (divergence) spa,al coherence Measurement methods: Measure spot size at a very large distance: θ d =W/z Measure beam spot at a lens focus: θ d =r/f r θ d f 12/04/16 18

19 Perfect spa,al coherence Hard-edge plane-wave beam Laser 12/04/16 19

20 Perfect spa,al coherence Hard-edge plane-wave beam Laser f 12/04/16 20

21 Perfect spa,al coherence Hard-edge plane-wave beam At lens focus Diffrac,on limited beam: Airy beam: D: aperture (lens) diameter Gaussian beam with 50% of hard-edge case 12/04/16 21

22 Par,al spa,al coherence Un-correlated small beams: θ d =βλ/d Correlated small beams: θ d =βλ/d General case: Ac: coherence area θ d =βλ/d c 12/04/16 22

23 M 2 factor Eliminates ambiguity of beam-diameter defini,on Simplified defini0on: Quality of a general beam compared to a Gaussian beam M 2 1, being 1 for TEM 00 Gaussian mode. A mul0mode laser beam propaga,ng along z axis, its beam waist (across x) As Hence 12/04/16 23

24 Contents Content Time 1. Monochromaticity Coherence - Spatial - Temporal Directionality Brightness Laser speckle 10 Total: 80 12/04/16 24

25 Brightness Brightness (power per unit area per solid angle) Irradiance (power per unit area) Propor,onal to the max peak intensity achievable by focusing a beam P: power A: area Ω: Solid angle Cause: Coherence direc,onality brightness Example: o Ar laser (TEM 00, 1W, λ=514nm): B = 4P/ λ 2 = W/cm 2 sr o Lamp (10W output, examined at λ=546nm): B = 95W/cm 2 sr Use: Material processing 12/04/16 25

26 Contents Content Time 1. Monochromaticity Coherence - Spatial - Temporal Directionality Brightness Laser speckle 10 Total: 80 12/04/16 26

27 Laser speckles Cause: high degree of laser light coherence 12/04/16 27

28 Calcula,on and impact Grain size d g D<<L d g = 2λL/D if d g = 2λL /D Scawerer size d s Impact: Limits the image resolu,on of an object illuminated with laser (speckle noise rather than diffrac,on limit ) Use: Sensors (stress, vibra,ons) 12/04/16 28

29 Contents Content Time 1. Monochromaticity Coherence - Spatial - Temporal Directionality Brightness Laser speckle 10 Total: 80 12/04/16 29

30 One more slide Laser v.s. Thermal light 10W W 12/04/16 30

E x Direction of Propagation. y B y

E x Direction of Propagation. y B y x E x Direction of Propagation k z z y B y An electromagnetic wave is a travelling wave which has time varying electric and magnetic fields which are perpendicular to each other and the direction of propagation,