Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 Propagation parameters of semiconductor laser Haider Y. Hammod *,Adnan H. Ali **, aa K.Ibrahim * * Ministry of science and technology, Dept. of physics ** Technical college,baghdad Abstract A typical shape of the spot laser diameter have been surveyed and measured it`s dimensions and compare the results ith the theoretical calculation. As ell the intensity distributed along this spot as measure by using (Si) detector. elative poer also have been calculated versus the beam radius for different values of distance from the aperture of diode laser source to the target. it is clear from the empirical results that the increasing of laser poer at small values of distance faster than that at large distances, and the spot diameter for different values of distance have smallest value near the source ( distance 0mm ) but it expanded progressively for far distances from the source. الخالصة : ف هزا انبحث ح ج يؼا ت شكم بقؼت انه ضس, وي ثى ق اط ابؼادها ويقاس ت رنك بانحساباث ان ظش ت. وكزنك حى ق اط حىص غ شذة بضت انه ضس ان قابهت ػهى طىل انبقؼت انه ضس ت بأسخخذاو كاشف سه كى. باألضافت انى رنك حى حساب انقذسة ان سب ت كذانت ن صف قطش حضيت انه ضس ن سافاث يخخهفت ػ فخحت انخشج انه ضسي. ي ان خائج انخجش ب ت ك ا الحظ ص ادة قذسة انه ضس نه سافاث انصغ شة اسشع ي ص ادحها نه سافاث انكب شة. وا قطش انبقؼت انه ضس ت نه سافاث ان خخهفت ح هك اقم ق ت نها بانقشب ي ان صذس ( ن سافت حصم انى يهى ) نك ها حخسغ حذس ج ا نه سافاث األبؼذ ػ ان صذس. هز ان خائج حقىد ا انى اخخ اس افضم يىقغ ن صذس انضخ ف ي ظىياث انه ضس راث انضخ انجا ب. - Introduction The investigation of measuring the propagation parameters hich help to select the suitable system of side pumping processes. The source of side pumping is the semiconductor laser hich have divergence bigger than any solid or dye lasers, so it's important for effectively pumping study and measure the spot diameter and the relative intensity distribution and relative poer distribution, theoretically and empirically []. In the next section e put the mathematical processes of Gaussian beam distribution of laser spot, and the free propagation hich depend on the beam radius and the curvature of output beam laser. Then,e built up the experimental system to measure the spot diameter and the poer distribution. - Gaussian Beam As an approximation the light ave in the resonator is considered as a scalar ave field. The diffraction due to the finite transversal dimension e.g. of the laser crystal, is taken into account only in a first order approximation. The amplitude (A) of the electric field then fulfills the time independent ave equation in its sloly varying envelope (SVE) - approximation. With the formulation for the electric field []. E= A m (x, y, z) exp (-ikz), () The SVE ave equation reads: 66
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 A m / x + A m / y ik A m / z = 0 () Where: is the Wave number. The simplest solution for rotational symmetry is the Gaussian beam or fundamental mode TEM 00 ith an amplitude distribution A(r, z) given as: ( r, z) To exp{ r (/ ik / ) i( kz )} 0 o c m m (3) o Where: Ф : arc tan ( z/z ) longitudinal phase. c = c (z) adius of curvature of the ave front. Z = лω To / λ: the ayleigh length. ω To : the beam radius at the aist. The beam radius (ω o ) and the curvature ( c ) are given by ( z) [ ( z / z ) ] (4) o c To Z Z ( z) Z ( ) (5) Z Z providing that the origin of the (z) coordinate is in the aist of the beam. The Gaussian beam is fixed by to parameters the beam aist ω To and the ayleigh length Z. A beam has a aist ith radius ω To hen the radius of curvature is infinite i.e. for c =. - ABCD La The description of the ray propagation for the TEM 00 mode and higher modes are normally carried out by means of the matrix formalism. Let us consider no the notion of the matrix arises. A pair of linear equation U= A x +B y V= C x +D y Where A,B,C and D are knon constants, and( x, y) are variables. These equations enable us to calculate U and V if x and y are knon [3]. Usually U and V represent the distance and angle respectively, the optical matrix is used to calculate the characteristics of transferred rays from point to point. - Geometric Optics A beam can be characterized in every position (Z) by its angle (α ) and its distance () relative to a given axis. this holds for small angles only, the so-called paraxial approximation. 67
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 If the beam starts at the origin one can assign the curvature at the position Z [4] (6) After a distance (L) the ne parameters α, W are ( ) ( L ) ( 0 ) ( ) L (7) 0 or more generally ( A ) ( B ) ( C ) ( D) A B (8) C D The propagation in homogeneous isotropic material is described by the optical matrix M: M A C B D The equations are used to transform the beam parameters are [4] AC ( AD BC)/ BD{/ ( A B ) ( B / ) 68 / (9) Where : is the radius of curvature. )}
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 [ A B / ) ( B / ) ] (0) Where i is the beam radius. [( C D)/ ) ( D / ) ] () Where Θ i : is the divergence. Therefore from here on ard no distinction ill be made beteen fundamental mode and higher order modes unless it is necessary for better understanding. Fig () shos the transformation of the optical beam parameters. W W W T W T Θ Θ Fig () Transformation of optical beam parameters -- Free Propagation in Z Direction The matrix for free propagation is [,3] M Z 0 This matrix yields the dependence of the beam radius and the curvature through the folloing equations [5] : ( z) ( Z / ) Z () / Z[/ /( ( z) ( Z / ) ( Z / ) (3) 69 ) ]
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 ( / ) (4) Equations () to (4) can be applied to any mode order. if the origin is a aist ( = T, = ) then it follos that: ( z) [ ( Z / ) ] (5) T Z z) Z ( Z / Z Z / Z ) (6) ( T Z 3- Theoretical Calculations Three final equations ere used to calculate the intensity and the poer distribution at different values of distance from the aperture of the diode laser source [6] ) (7) d I I ) ( / ) exp( r / ) (8) O P exp( r / ) 3) P (9) O Where: ω =.5 mm θ = m rad r = ( 0 mm) d = (0, 5, 50 00 50, 00, 50, 300, 350, 400, 450 500) mm. We assume that, T O because the laser resonator of source is very small and the aist of beam is approximately in the same position of ω. These calculation are very important for constructing the diode laser side pumped systems,here one ant to obtain the homogeneous pumping. Figure () and (3) sho the Intensity and poer distribution respectively []. 63
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 Fig () Gaussian intensity distribution (z=0) Fig (3) Gaussian poer distribution (z=0) 636
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 4 - Experimental measurements The setup for this experiment, hich as used to measure the spot diameter, is illustrated in figure (4). 4. Diode laser. CCD camera 3. Attenuator 4. Target 3 Fig (4 ) The setup used to measure the spot diameter Figure (5) illustrates the other setup as used to measure the poer distribution, these figures also illustrate the main components ere employed in these experiments. In the first step and hen the laser diode turns on the spot incident on the target, the CCD camera has been used transport the picture of this spot to the TV- screen. Atypical shape of the spot hose diameter has been measured by a ruler. 4 3.Diode laser.ccd camera 3.Attenuator 4.Detector 5.Avometer 5 Fig (5) The setup used to measure the poer distribution 63
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 In the second one,e employed the (Si) detector to scan poer distributed on spot of the source beam. This detector as placed on a movable holder hich is moving by steps of 50μm. The beam from the source ill pass through an attenuator and cross the pinhole before it is incident on the detector. An avometer as used to measure the detector current hich represents values equivalent to the distribution poer along the spot diameter. Then the influence of distance of the source pump to the detector upon poer distribution. The beam diameter of spot ere finally studied and concluded. 5 - Theoretical esults Using the main equations concerned ith these parameters, the values of intensity and poer relative the values of them at zero position (r=0,d=0) can be calculated Where r : the radius of spot d : the distance from the source of beam to the target When e plotted the relationship beteen the ratio I/I 0 (I 0 : the intensity in the zero position ) and the values of (r ), e can see this ratio has different values at different positions,figure (6 a,and b) shos that. from this figure the ratio I/I 0 decreases at points close to peak of Gaussian shape and increases at points close to tail of shapes especially hen the distance has a large. This variation is due to the increasing the spot size hich causes the rearrangement the photons distribution on the spot area. Fig (6- a ) relative intensity versus the beam radius for different values of distance ( d= 5 50 ) 633
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 : d = 00mm : d = 50mm Δ: d = 300mm X: d = 350mm Ж:d = 400mm Ο: d = 450mm +: d =500mm Fig (6 b ) relative intensity versus the beam radius for different values of distance ( d= 00 500 ) In parallel e have calculated also the relative poer distribution P/P 0, using the folloing equation : P o ToIo (0) ith radius of spot for different values of distance from the source to the target that is shon in figure (7 a,and b) it is clear that the increase of poer at small values of distance faster than the increase at large distances at specific values of distance the poer distribution may be reached approximately fixed increasing (sloest increasing) along the radius of the beam. these results lead to select the suitable positions of pumping sources hen e ant to side pumped laser systems. prior to the study of these distribution e have calculated the spot diameter for different values of distance, figure (8) shos this relation. Fig ( 7 a ) relative poer distribution versus radius of beam for variable values 634 of distance ( d= 0-00 )
r (mm) Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 Fig ( 7 b ) relative poer versus beam radius for variable values of distance ( d= 50 500 ) 5 0 5 0 5 0 0 00 00 300 400 500 600 d(mm) Fig(8) the relation of spot diameter and the distance from the source 6 - Empirical results When the system as set as illustrated in figure (5) e measured the poer distribution along the laser spot, figures (9,0,) sho hat e predicted from the theoretical calculation i.e. (expended the peak of Gaussian profile ith distance). also e can see that the distribution of poer or intensity along the laser spot has been varied by varying the distance from the laser source until reached approximately the same manner of that in the positions close to the center of the spot i.e. the number of photons distributed in equal values along the spot diameter. 635
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 Fig (9) detector current versus the position in spot of source beam ( d= 0 cm ) Fig (0) detector current versus the position in beam of source ( d = 0 cm ) 636
Journal of Kerbala University, Vol. 8 No.4 Scientific. 00 Fig () detector current versus the position in beam of source ( d = 40 cm ) 7- Conclusion From the empirical study e can concluded that, hen increase the distance from the laser source there is decreasing in intensity because the increasing in spot size. and then the decreasing in number of photon per unit area. eferences [].Ifflander Solid State Laser for Materials Processing Springier Verlag, Berlin Heidelberg, (00). [] W.F.Krupke,M.D.Shinn,J.E.Marion,J.ACarid,and S.E.Stokoski, J.Opt.Soc.Amer.,Vol.3,p.0,(986). [3] A. Gerrard, and J.M.Burch, Introduction to Matrix Method In Optics (975). [4] D.Sands,department of physics, " Diode Lasers ", university of Hall,UK.IOP Publishing Ltd 005. [5] Toshiaki Suhara,"Semiconductor Laser Fundamental", Osaka University, Osaka, Japan, Marcel Dekker, Inc.004. [6] Kjell J. Gasvik, " Optical Metrology ",Spectra vision AS, Trondheim, Noray, JOHN WILEY & SONS, LTD, 00. 637