Kurdistan Iraqi Region Ministry of Higher Education University of Sulaimani College of Science Physics Department Numerical Simulation of Laser Pulse Generation Prepared by Rebar F. Karem Gashaw O. Abdullah Zhilan B. Husain Supervised by Dr. Omed Ghareb Abdullah 2009 - 2010
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Kurdistan Iraqi Region Ministry of Higher Education University of Sulaimani College of Science Physics Department
Numerical Simulation of Laser Pulse
Generation
Prepared by
Rebar F. Karem Gashaw O. Abdullah
Zhilan B. Husain
Supervised by
Dr. Omed Ghareb Abdullah
2009 - 2010
ii
Acknowledgments
Praise be to Allah for providing us the willingness and strength
to accomplish this work, we would to express our deepest gratitude
to our supervisor Dr. Omed for his helps and guidance throughout
this work.
True appreciation for Department of Physics in the College of
Science at the University of Sulaimani for giving us an opportunity
to carry out this work.
We wish to extend our sincere thanks to all lecturers who taught
us along our study many other thanks should go to our colleagues
for their encouraging. Lastly thanks and love to our family for their
patience and support during our study.
Rebar, Zhilan, & Gashaw
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Contents
Chapter One: Basic Concepts
1.1 Introduction.
1.2 Construction of a laser
1.3 Absorption and Emissions
1.4 Population Inversion
1.5 Three-level lasers
1.6 Four-level lasers
1.7 The Gain in Laser
1.8 The Loss in Laser
1.9 The ruby laser
Chapter Two: Q-Switching Techniques
2.1 Introduction.
2.2 Principle of Q-switching
2.3 Active Q-switching
2.3.1 Mechanical Q-Switches
3.2.2 Electro-Optical Q-Switches
3.2.3 Acousto-Optic Q-Switches
2.4 Passive Q-switching
2.5 Passive Q-Switch Processes
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Chapter Three: Passive Q-Switching
3.1 Introduction.
3.2 Rate Equations
3.3 Runge-kutta Fehlberg
Chapter Four: Results and Discussion
4.1 Introduction.
4.2 Solution of Rate Equations
4.3 Effect of concentration of the saturable absorber
4.4 Conclusion
References
Appendix
v
Abstract
Q-switching, sometimes known as giant pulse formation, is a technique
by which a laser can be made to produce a pulsed output beam. The
technique allows the production of light pulses with extremely high (Giga
Watt) peak power, much higher than would be produced by the same laser
if it were operating in a continuous wave (constant output) mode.
In this study the passive Q-switched performance of the ruby laser with
[3] McIntyre D.L., "A Laser Spark Plug Ignition System for a Stationary Lean-Burn Natural Gas Reciprocating Engine", PhD Dissertation, West Virginia University, (2007).
[4] Munajat N.F.B., "Study of saturable absorber materials for Q-switching DYE
laser", MSc thesis, University Technology Malaysia, (2005). [5] Kuo Y.K., H.M. Chen, and C.C. Lin, "A Theoretical Study of the
Cr:BeAl2O4
Laser Passively Q-switched with Cr:YSO Solid State Saturable Absorber", Chinese Journal of Physics, Vol. 38, No. 3-I, pp. 443-460, (2000).
[6] Spiekermann S., "Compact diode-pumped solid-state laser", PhD thesis, Royal Institute of Technology, Stockholm, Sweden, (2004).
[7] Longbotham N.W., "Experimental Characterization of Cr4+
:YAG Passively Q-switched Cr:Nd:GSGG Lasers and Comparison with a Simple Rate Equation Model", PhD thesis, University of New Mexico, (2008).
[8] Kuo Y.K., W. Chen, R.D. Stultz, and M. Birnbaum, "Dy2+:CaF2
saturable-absorber Q switch for the ruby laser", Applied Optics, Vol. 33, No. 27, pp. 6348-6351, (1994).
[9] Kuo Y.K., and M. Birnbaum, "Passive Q switching of the alexandrite laser with a Cr4+:Y2SiO5
solid-state saturable absorber", Appl. Phys. Lett. Vol. 67, No. 2, pp. 173-175, (1995).
[10] Kuo Y.K., H.M. Chen, and J.Y. Chang, "Numerical study of the Cr:YSO Q-switched ruby", Opt. Eng., Vol. 40, No. 9, pp. 2031-2035, (2001).
Matlab program to solve the rate equation of passive Q-switching %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%% Numerical Solution of %%%%%%%%%% %%%%%%%%%% Rate Equation of Passive Q-Switch %%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%% Sulaimani University %%%%%%%%%% %%%%%%%%%% College of Science - Physics Department %%%%%%%%%% %%%%%%%%%% (c) Omed Ghareb Abdullah 2009 %%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % ka: Coupling coefficient for active medium (1/sec) % kg: Coupling coefficient for saturable absorber material (1/sec) % ga: Decay rate of the first exited level of the saturable absorber material % gc: Cavity decay rate % gg: Decay rate of the upper laser level % rt: Relaxation time of the first excited level of the saturable absorber material % rp: Pumpin rate % b: Ratio of the absorption x-secs of the first excited to the G.S. of % the saturable absorber levels % lambda: LASER wavelength (nm) % clight: light speed (cm/sec) % gama: Population reduction factor, is 1 for a four-level laser, % and 2 for a thre-level laser. % imax: Position of maximum number of photons % no: initial photon numbers % ph: Maximum photons numbers % calstep: Number of calculated steps % nstep: number of steps % tio: initial time (nsec) % tfo: final time (nsec) % tt: times from tio to tfo (nsec) % dt: time interval (nsec) % pr: The period of the Q-Switched pulse % tt(lleft): Position of left % tt(lmax): Position of center % tt(right): Position of right % rise: Rising time (nsec) % fall: Falling time (nsec) % e: The energy of Q-Switched pulse (J) % power: The power of Q-Switched pulse (Watt) % imax=position of the maximum number of photons % nao: Initial number of suturable absorber molecules in G.S % R: Output coupler reflectivity % np: Initial number of photons % nth: Threshold population inversion % ph: Photons number as a function of time % ng: Population inversion as a function of time % na: Number of saturable absorber material % loss: Photon losses % loabs: Rate absorption of G.S. % upabs: Rate absorption of first E.S. % totabs: Total Rate absorption
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% pr: Period life time (nsec) % rise: Pulse Rising time (nsec) % fall: Pulse Falling time (nsec) % phmax: Maximum number of photons % hphmax: Wave half mean % This program need approximatelly 95 minutes to RUN clc clear all tfo=600000; % number of steps (nsec) tio=0; % initial time (nsec) dt=5; % time interval (nsec) nstep=(tfo-tio)/dt; kg=7.22e-10; ka=3.46e-8; ga=6667; gc=3.42e8; gg=333; b=0.75; rp=1.7e21; % 1/sec lambda=694.3; % nm lambda=lambda*1e-9; % m nao=5.18e15; gama=2; clight=3e8; % m/sec kg=kg*1e-9; % 1/nsec ka=ka*1e-9; % 1/nsec ga=ga*1e-9; % 1/nsec gc=gc*1e-9; % 1/nsec gg=gg*1e-9; % 1/nsec rp=rp*1e-9; % 1/nsec rt=1/ga; tc=1/gc; nth=(b*ka*nao+gc)/kg; ngo=(ka*nao+gc)/kg; npeak=1/gama*(ngo-nth-nth*log(ngo/nth)); R=0.78; ph(1)=3e6; % initial Photon number ---> zero ng(1)=0; % initial Population inversion=zero na(1)=nao; loss(1)=(ka*na(1)+b*ka*(nao-na(1))+gc)/kg; loabs(1)=ka*na(1); upabs(1)=b*ka*(nao-na(1)); totabs(1)=loabs(1)+upabs(1); tt(1)=tio; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Solveing the Rate equation for three-level model % Using Runge-Kutta Fehlberg method %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for j=1:nstep yph=ph(j); yng=ng(j); yna=na(j); tt(j+1)=tt(j)+dt;
ng4(j+1)=ng(j)+dt*(37/378*kng(1)+250/621*kng(3)+125/594*kng(4)+512/1771*kng(6)); na4(j+1)=na(j)+dt*(37/378*kna(1)+250/621*kna(3)+125/594*kna(4)+512/1771*kna(6)); ph5(j+1)=ph(j)+dt*(2825/27648*kph(1)+18575/48384*kph(3)+13525/55296*kph(4)+277/14336*kph(5)+1/4*kph(6)); ng5(j+1)=ng(j)+dt*(2825/27648*kng(1)+18575/48384*kng(3)+13525/55296*kng(4)+277/14336*kng(5)+1/4*kng(6)); na5(j+1)=na(j)+dt*(2825/27648*kna(1)+18575/48384*kna(3)+13525/55296*kna(4)+277/14336*kna(5)+1/4*kna(6)); ph(j+1)=2*ph5(j+1)-ph4(j+1); ng(j+1)=2*ng5(j+1)-ng4(j+1); na(j+1)=2*na5(j+1)-na4(j+1); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if ph(j+1)<ph(1) ph(j+1)=ph(1); end loss(j+1)=(ka*na(j+1)+b*ka*(nao-na(j))+gc)/kg; loabs(j+1)=ka*na(j+1); upabs(j+1)=b*ka*(nao-na(j)); totabs(j+1)=loabs(j+1)+upabs(j+1); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%% whitebg %figure(1) plot(tt,ng,'r-'); hold on; plot(tt,loss,'b--'); title(' '); xlabel('Time (nsec)'); ylabel('Ng configuration & Loos'); legend('Ng ', 'Loss '); xtext=tt(1)+max([tt])/15; ytext=max([ng loss]); ytext=max([ytext]); text(xtext,0.9*ytext,['Wave length = ',num2str(lambda),' nm']); text(xtext,0.8*ytext,['Nao = ',num2str(nao),' ']); text(xtext,0.7*ytext,['B = ',num2str(b),' ']); hold off pause %colordef black %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %figure(2) plot(tt,ph,'r.-'); hold on; title(' '); xlabel('Time (nsec)'); ylabel('n configuration'); xtext=tt(1)+max([tt])/15; xtext=max([xtext]); ytext=max([ph]);
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ytext=max([ytext]); text(xtext,0.9*ytext,['Wave length = ',num2str(lambda),' nm']); text(xtext,0.8*ytext,['Nao = ',num2str(nao),' ']); text(xtext,0.7*ytext,['B = ',num2str(b),' ']); pause hold off %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %figure(3) plot(tt,loss,'r-'); hold on [AX,H1,H2] = plotyy(tt,ng,tt,ph,'plot'); set(get(AX(1),'Ylabel'),'String','Ng configuration & Loos') set(get(AX(2),'Ylabel'),'String','n configuration') set(H1,'LineStyle','--') set(H2,'LineStyle',':') title(' '); xlabel('Time (nsec)'); title(' '); xtext=tt(1)+max([tt])/15; ytext=max([ng loss ph]); ytext=max([ytext]); text(xtext,0.9*ytext,['Wave length = ',num2str(lambda),' nm']); text(xtext,0.8*ytext,['Nao = ',num2str(nao),' ']); text(xtext,0.7*ytext,['B = ',num2str(b),' ']); pause hold off %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Estimating the principal parameters of first pulse %% by Analytical method, and some approximation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% k=1; tol=1e3; nf(k)=1000; ff=ngo-nf(k)-nth*log(ngo/nf(k)); fd=-1+nth/nf(k); nf(k+1)=nf(k)-ff/fd; while abs(nf(k+1)-nf(k))>tol; k=k+1; ff=ngo-nf(k)-nth*log(ngo/nf(k)); fd=-1+nth/nf(k); nf(k+1)=nf(k)-ff/fd; end nff=nf(k+1); disp(['****** Analytical Estimate ****** ']); disp(['Initial population inversion = ',num2str(ngo),' ']); disp(['Threshold population inversion = ',num2str(nth),' ']); disp(['Final population inversion = ',num2str(nff),' ']); disp(['Number of iteration = ',num2str(k+1),' ']); disp(['Maximum photons number = ',num2str(npeak),' ']); hv=6.625e-34*clight/(lambda); eout=(ngo-nff)/gama*hv*(1-R); tpulse=tc*(ngo-nff)/(ngo-nth-nth*log(ngo/nth)); power=eout/(tpulse*1e-9); disp(['Period life time (FWHM) = ',num2str(tpulse),' nsec']); disp(['The energy of Q-Switched pulse = ',num2str(eout*1e3),' mJ']);
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disp(['The power of Q-Switched pulse = ',num2str(power),' Watt']); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Estimating the principal parameters of first pulse %% by Numerical method (Runge-Kutta Fehlberg method) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% disp(['****** Firest Pulse ****** ']); no1=92500; no2=93000; tt1=tt([no1:no2]); ng1=ng([no1:no2]); ph1=ph([no1:no2]); loss1=loss([no1:no2]); na1=na([no1:no2]); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %figure(4) plot(tt1,loss1,'r-'); hold on [AX,H1,H2] = plotyy(tt1,ng1,tt1,ph1,'plot'); set(get(AX(1),'Ylabel'),'String','Ng configuration & Loos') set(get(AX(2),'Ylabel'),'String','n configuration') set(H1,'LineStyle','--') set(H2,'LineStyle',':') title('Firest Pulse'); xlabel('Time (nsec)'); title('Firest Pulse'); xtext=tt1(1)+max([tt1])/15; ytext=max([ng1 loss1 ph1]); ytext=max([ytext]); text(xtext,0.9*ytext,['Wave length = ',num2str(lambda),' nm']); text(xtext,0.8*ytext,['Nao = ',num2str(nao),' ']); text(xtext,0.7*ytext,['B = ',num2str(b),' ']); hold off pause %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% phmax=max([ph1]); nstep1=no2-no1; for i=1:nstep1 if ph1(i)==phmax; imax=i; end end hphmax=(phmax-ph1(1))/2; tmax=tt1(imax); for i=1:imax if ph1(i)<=hphmax; ileft=i+1; end end for i=imax:nstep1 if ph1(i)>=hphmax iright=i+1; end end
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tl=((hphmax-ph1(ileft-1))/(ph1(ileft)-ph1(ileft-1)))*(tt1(ileft)-tt1(ileft-1))+tt1(ileft-1); tr=((hphmax-ph1(iright))/(ph1(iright-1)-ph1(iright)))*(tt1(iright-1)-tt1(iright))+tt1(iright); pr=tr-tl; rise=tt1(imax)-tl; fall=tr-tt1(imax); disp(['Position of left = ',num2str(tt1(ileft)),' ']); disp(['Position of center = ',num2str(tt1(imax)),' ']); disp(['Position of right = ',num2str(tt1(iright)),' ']); disp(['Position of maximum number of photons = ',num2str(imax),' ']); disp(['Maximum photons number = ',num2str(ph1(imax)),' ']); disp(['Period life time (FWHM) = ',num2str(pr),' nsec']); disp(['Pulse Rising time = ',num2str(rise),' nsec']); disp(['Pulse Falling time = ',num2str(fall),' nsec']); for m=2:nstep1 if ph1(m)>(ph1(1)); li=m; end end disp(['Final population inversion = ',num2str(ng1(li)),' ']); disp(['Final number of absorber molecules in the G.S. = ',num2str(na1(li)),' ']); disp(['Final number of absorber molecules in the first excited state = ',num2str(nao-na1(li)),' ']); hv=6.625e-34* clight/(lambda); eout=(ngo-ng1(li))/gama*hv*(1-R); power=eout/(pr*1e-9); disp(['The energy of Q-Switched pulse = ',num2str(eout*1e3),' mJ']); disp(['The power of Q-Switched pulse = ',num2str(power),' Watt']); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Estimating the principal parameters of first pulse %% by Numerical method (Runge-Kutta Fehlberg method) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% disp(['****** Second Pulse ****** ']); no1=100000; no2=101200; tt1=tt([no1:no2]); ng1=ng([no1:no2]); ph1=ph([no1:no2]); loss1=loss([no1:no2]); na1=na([no1:no2]); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %figure(5) plot(tt1,loss1,'r-'); hold on [AX,H1,H2] = plotyy(tt1,ng1,tt1,ph1,'plot'); set(get(AX(1),'Ylabel'),'String','Ng configuration & Loos') set(get(AX(2),'Ylabel'),'String','n configuration') set(H1,'LineStyle','--')
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set(H2,'LineStyle',':') title(' '); xlabel('Time (nsec)'); title('Second Pulse'); xtext=tt1(1)+max([tt1])/15; ytext=max([ng1 loss1 ph1]); ytext=max([ytext]); text(xtext,0.9*ytext,['Wave length = ',num2str(lambda),' nm']); text(xtext,0.8*ytext,['Nao = ',num2str(nao),' ']); text(xtext,0.7*ytext,['B = ',num2str(b),' ']); hold off pause %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% phmax=max([ph1]); nstep1=no2-no1; for i=1:nstep1 if ph1(i)==phmax; imax=i; end end hphmax=(phmax-ph1(1))/2; tmax=tt1(imax); for i=1:imax if ph1(i)<=hphmax; ileft=i+1; end end for i=imax:nstep1 if ph1(i)>=hphmax iright=i+1; end end tl=((hphmax-ph1(ileft-1))/(ph1(ileft)-ph1(ileft-1)))*(tt1(ileft)-tt1(ileft-1))+tt1(ileft-1); tr=((hphmax-ph1(iright))/(ph1(iright-1)-ph1(iright)))*(tt1(iright-1)-tt1(iright))+tt1(iright); pr=tr-tl; rise=tt1(imax)-tl; fall=tr-tt1(imax); disp(['Position of left = ',num2str(tt1(ileft)),' ']); disp(['Position of center = ',num2str(tt1(imax)),' ']); disp(['Position of right = ',num2str(tt1(iright)),' ']); disp(['Position of maximum number of photons = ',num2str(imax),' ']); disp(['Maximum photons number = ',num2str(ph1(imax)),' ']); disp(['Period life time (FWHM) = ',num2str(pr),' nsec']); disp(['Pulse Rising time = ',num2str(rise),' nsec']); disp(['Pulse Falling time = ',num2str(fall),' nsec']); for m=2:nstep1 if ph1(m)>(ph1(1)); li=m; end end
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disp(['Final population inversion = ',num2str(ng1(li)),' ']); disp(['Final number of absorber molecules in the G.S. = ',num2str(na1(li)),' ']); disp(['Final number of absorber molecules in the first excited state = ',num2str(nao-na1(li)),' ']); hv=6.625e-34*clight/(lambda); eout=(ng1(1)-ng1(li))/gama*hv*(1-R); power=eout/(pr*1e-9); disp(['The energy of Q-Switched pulse = ',num2str(eout*1e3),' mJ']); disp(['The power of Q-Switched pulse = ',num2str(power),' Watt']); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Estimating the principal parameters of last pulse %% by Numerical method (Runge-Kutta Fehlberg method) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% disp(['****** Third Pulse ****** ']); no1=102800; no2=104000; tt1=tt([no1:no2]); ng1=ng([no1:no2]); ph1=ph([no1:no2]); loss1=loss([no1:no2]); na1=na([no1:no2]); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %figure(6) plot(tt1,loss1,'r-'); hold on [AX,H1,H2] = plotyy(tt1,ng1,tt1,ph1,'plot'); set(get(AX(1),'Ylabel'),'String','Ng configuration & Loos') set(get(AX(2),'Ylabel'),'String','n configuration') set(H1,'LineStyle','--') set(H2,'LineStyle',':') title(' '); xlabel('Time (nsec)'); title('Third Pulse'); xtext=tt1(1)+max([tt1])/15; ytext=max([ng1 loss1 ph1]); ytext=max([ytext]); text(xtext,0.9*ytext,['Wave length = ',num2str(lambda),' nm']); text(xtext,0.8*ytext,['Nao = ',num2str(nao),' ']); text(xtext,0.7*ytext,['B = ',num2str(b),' ']); hold off pause %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% phmax=max([ph1]); nstep1=no2-no1; for i=1:nstep1 if ph1(i)==phmax; imax=i; end end hphmax=(phmax-ph1(1))/2; tmax=tt1(imax);
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for i=1:imax if ph1(i)<=hphmax; ileft=i+1; end end for i=imax:nstep1 if ph1(i)>=hphmax iright=i+1; end end tl=((hphmax-ph1(ileft-1))/(ph1(ileft)-ph1(ileft-1)))*(tt1(ileft)-tt1(ileft-1))+tt1(ileft-1); tr=((hphmax-ph1(iright))/(ph1(iright-1)-ph1(iright)))*(tt1(iright-1)-tt1(iright))+tt1(iright); pr=tr-tl; rise=tt1(imax)-tl; fall=tr-tt1(imax); disp(['Position of left = ',num2str(tt1(ileft)),' ']); disp(['Position of center = ',num2str(tt1(imax)),' ']); disp(['Position of right = ',num2str(tt1(iright)),' ']); disp(['Position of maximum number of photons = ',num2str(imax),' ']); disp(['Maximum photons number = ',num2str(ph1(imax)),' ']); disp(['Period life time (FWHM) = ',num2str(pr),' nsec']); disp(['Pulse Rising time = ',num2str(rise),' nsec']); disp(['Pulse Falling time = ',num2str(fall),' nsec']); for m=2:nstep1 if ph1(m)>(ph1(1)); li=m; end end disp(['Final population inversion = ',num2str(ng1(li)),' ']); disp(['Final number of absorber molecules in the G.S. = ',num2str(na1(li)),' ']); disp(['Final number of absorber molecules in the first excited state = ',num2str(nao-na1(li)),' ']); hv=6.625e-34*clight/(lambda); eout=(ng1(1)-ng1(li))/gama*hv*(1-R); power=eout/(pr*1e-9); disp(['The energy of Q-Switched pulse = ',num2str(eout*1e3),' mJ']); disp(['The power of Q-Switched pulse = ',num2str(power),' Watt']); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Estimating the principal parameters of last pulse %% by Numerical method (Runge-Kutta Fehlberg method) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% disp(['****** Fourth Pulse ****** ']); no1=105500; no2=106600; tt1=tt([no1:no2]);
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ng1=ng([no1:no2]); ph1=ph([no1:no2]); loss1=loss([no1:no2]); na1=na([no1:no2]); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %figure(7) plot(tt1,loss1,'r-'); hold on [AX,H1,H2] = plotyy(tt1,ng1,tt1,ph1,'plot'); set(get(AX(1),'Ylabel'),'String','Ng configuration & Loos') set(get(AX(2),'Ylabel'),'String','n configuration') set(H1,'LineStyle','--') set(H2,'LineStyle',':') title(' '); xlabel('Time (nsec)'); title('Fourth Pulse'); xtext=tt1(1)+max([tt1])/15; ytext=max([ng1 loss1 ph1]); ytext=max([ytext]); text(xtext,0.9*ytext,['Wave length = ',num2str(lambda),' nm']); text(xtext,0.8*ytext,['Nao = ',num2str(nao),' ']); text(xtext,0.7*ytext,['B = ',num2str(b),' ']); hold off pause %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% phmax=max([ph1]); nstep1=no2-no1; for i=1:nstep1 if ph1(i)==phmax; imax=i; end end hphmax=(phmax-ph1(1))/2; tmax=tt1(imax); for i=1:imax if ph1(i)<=hphmax; ileft=i+1; end end for i=imax:nstep1 if ph1(i)>=hphmax iright=i+1; end end tl=((hphmax-ph1(ileft-1))/(ph1(ileft)-ph1(ileft-1)))*(tt1(ileft)-tt1(ileft-1))+tt1(ileft-1); tr=((hphmax-ph1(iright))/(ph1(iright-1)-ph1(iright)))*(tt1(iright-1)-tt1(iright))+tt1(iright); pr=tr-tl; rise=tt1(imax)-tl; fall=tr-tt1(imax); disp(['Position of left = ',num2str(tt1(ileft)),' ']); disp(['Position of center = ',num2str(tt1(imax)),' ']); disp(['Position of right = ',num2str(tt1(iright)),' ']); disp(['Position of maximum number of photons = ',num2str(imax),' ']);
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disp(['Maximum photons number = ',num2str(ph1(imax)),' ']); disp(['Period life time (FWHM) = ',num2str(pr),' nsec']); disp(['Pulse Rising time = ',num2str(rise),' nsec']); disp(['Pulse Falling time = ',num2str(fall),' nsec']); for m=2:nstep1 if ph1(m)>(ph1(1)); li=m; end end disp(['Final population inversion = ',num2str(ng1(li)),' ']); disp(['Final number of absorber molecules in the G.S. = ',num2str(na1(li)),' ']); disp(['Final number of absorber molecules in the first excited state = ',num2str(nao-na1(li)),' ']); hv=6.625e-34*clight/(lambda); eout=(ng1(1)-ng1(li))/gama*hv*(1-R); power=eout/(pr*1e-9); disp(['The energy of Q-Switched pulse = ',num2str(eout*1e3),' mJ']); disp(['The power of Q-Switched pulse = ',num2str(power),' Watt']); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%