Laser Optics-II. ME 677: Laser Material Processing Instructor: Ramesh Singh 1

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1 Laser Optics-II 1

2 Outline Absorption Modes Irradiance

3 Reflectivity/Absorption Absorption coefficient will vary with the same effects as the reflectivity For opaque materials: reflectivity = 1 - absorptivity For transparent materials: reflectivity =1- (transmissivity + absorptivity) 3

4 Reflectivity In metals the radiation is predominantly absorbed by free electrons in an electron gas Free electrons are free to oscillate and reradiate without disturbing the solid atomic structure The reflectivity increases from visible to high wavelength As a wavefront arrives at a surface all the free electrons in the surface vibrate in phase generating an electric field 18 out of phase with the incoming beam The sum of this field will be a beam whose angle of reflection equals the angle of incidence 4

5 Effect of Wavelength Reflectivity is a function of the refractive index, n, and the extinction coefficient, k At shorter wavelengths, the more energetic photons can be absorbed by a greater number of bound electrons Reflectivity decreases and absorptivity increases 5

6 Reflectivity of Metals 6

7 Reflectivity of Non-metals 7

8 Effect of Temperature Temperature increase results in increase in phonon population and phonon-electron energy exchanges Reflectivity decreases Absorption increases 8

9 Surface Roughness Surface Roughness has a large effect on absorption due to: The multiple reflections in the undulations Also some "stimulated absorption" due to beam interference with sideways reflected If roughness is less than the beam wavelength, the light will perceive the surface as flat 9

10 Case Study-145 steel 1

11 Angle of Incidence At certain angles the surface electrons may be constrained from vibrating since to do so would involve leaving the surface. This they would be unable to do without absorbing the photon The electric vector is in the plane of incidence, the vibration of the electron is inclined to interfere with the surface and absorption is thus high 11

12 Refraction On transmission the ray undergoes refraction described by Snell s law: 1

13 Refraction Scattered intensity is a function of 1 /l 4 Rayleigh Scattering Law. The normal form of a dispersion curve (refractive index vs wavelength) is known as a Cauchy Equation: 13

14 Beam Mode Two spatial modes describe the beam Longitudinal Transverse Essentially independent of each other Transverse dimension in a resonator is normally considerably smaller than the longitudinal The standing wave condition will be amplified, i.e., there can be only integer number of half wavelengths in the cavity, d= q. λ/ or qλ=d q is a large integer referring to the number of nodes in the longitudinal standing, d is the cavity length (mirror separation), and λ is the wavelength. The longitudinal mode number is large in industrial lasers and is normally ignored on beam characteristics and performance. The transverse electromagnetic mode (TEM) is more important. 14

15 Longitudinal Mode Longitudinal Mode (integral multiples of l/) D l=d, l=d 15

16 Transverse Mode TEM describes the variation in beam intensity with position in a plane perpendicular to the direction of beam propagation It characteries the intensity maxima in the beam The TEM is determined by: The geometry of the cavity Alignment and spacing of internal cavity optics Gain distribution and propagation properties of the active medium Presence of apertures in the resonator 16

17 TEM Both r and f can have modes; TEMpl Radial, p Angular, l 17

18 Intensity Plots a.tem; b. TEM 1; c. TEM1* 18

19 Propagation Generic equation for cylindrical symmetry Equations for Hermite Gaussian beam in (x-y coordinates) x y E( x, y) = E H p H l e w w where E = Electric _ field _ amplitude E = No min al _ amplitude x = x _ dis tan ce _ from _ axis y = y _ dis tan ce _ from _ axis w = No min al _ beam _ radius x y w 19

20 Propagation Hn(x) is a Hermite polynomial = = = = = ) ( ) ( ) ( ) (, _. ), ( 1 ) ( 1 w r w r w y x x n n x n n e I r I r E r I e E r E coordinates Circular e E y x E x H e dx d e x H

21 Gaussian Beam Gaussian function goes out to infinity Low powered lasers mimic the TEM TEM beams can be focused to smallest spot as compared to any other distribution 1

22 Beam Properties The point where irradiance drops to 1/e of the peak The radius containing 1-1/e power A two dimensional plot, the x value of which 95% of the plot area is contained between x and x.

23 Gaussian Distribution For different gaussian beams: I() r = I e r w P I = w Other beam, I() r = I e I 9P = w 9r w 3

24 Equations 4

25 Examples I(x, y ) = P A I(x, y ) = P A y x [1 b ][1 ] (1) a y [1 ][1 b I(x, y ) = P A (1) I(x, y ) = P x x a 1 y A y x [1 ][1 b ] () b y [1 ][1 b a 1 y b ] () a ] 5

26 Propagation of laser beam For a monochromatic beam propagating in the complex electric field amplitude w r kr E( r, ) = E Exp Exp i k tan 1 w w R R where E is the peak amplitude; w is beam waste radius; k = π/l ; Z R is the Rayleigh length; R is the radius of curvature of the wave front 6

27 The variation of beam radius in propagation w R = w 1 R w = l 7

28 Propagation of Laser Beams A laser beam propagating in space (lower case for TEM and upper case for real beams) Beam waist or minimum diameter, d /D Beam waist diameter, d /D at a location from the waist Beam waist or minimum radius, w /W Beam waist radius, w /W at a location from the waist q/q = Full-angle beam divergence l = Wavelength of light Q BEAM WAIST RADIUS, W Z Q 8

29 Propagation of Ideal Beam For a TEM beam, the diameter d for any distance form the waist is: Hyperboloid _ TEM Divergence d d d d d d = = = = q l q q l

30 Real Beam Real beams can be defined in terms of TEM It can be postulated a fictitious embedded Gaussian beam having a smaller dia d exists in the real beam; D=M.d, where M>1 q l l l l l M D M D D D M D D D M D D D M M D M D d d d = Q = Q = = = = = 3

31 Focused Beam Calculations For ideal beam, 1 = f ( ) 1 ( f ) f 1 f 1 = f D1 ( 1 f) Q Q1 d 4l d1 = 1 d d1 f f 4l 4. l. M For real beam with Q=,. D ( f ) f = 1 D D f f 31

32 Final Calculation Once D is calculated, Q could be found 4. l. M Q=. D Depth of focus where focal spot sie changes by ±5%. Approximate solution for focused beam diameter if lens is placed at from the beam waist If unfocused beam diameter at, is D. D = D Q D 4. f. l. M = D. 3

33 Laser Optics Setup at IITB Indian Patent Application No 44/MUM/11 Filed on 17 February 11 Method and device for generating laser beam of variable intensity distribution and variable spot sie

34 Aberrations Spherical Aberration Thermal Distortion Astigmatism Damage 34

35 Spherical Aberration There are two reasons why a lens will not focus to a theoretical point Diffraction limited problem Spherical lens is not a perfect shape. Most lenses are made with a spherical shape since this can be accurately manufactured economically The alignment of the beam is not so critical as with a perfect aspheric shape 35

36 Thermal Distortion High power laser beams are absorbed by lenses/optics Selection of right optics ZnSe with CO The power distribution in TEM causes more severe gradients than Donut Shape change of lens Varies the refractive index, specially in ZnSe 36

37 Astigmatism and Damage Due to optical misalignment Damage Due to dirt accumulation and burning on lens surface 37

38 Summary Absorption Beam Modes Propagation Focusing Aberrations 38

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