File:KellerDoyaT.png

Comparison of the transfer functions for realistic laser amplifiers at the continuous–wave operation (the Doya function) and for the short pulses (the Keller function).

This picture is used as Fig.5.10 at page 55 of book «Superfunctions» ^[1][2].

C++ Generator of cureves

// Files doya.cin and ado.cin should be loaded in order to compile the C++ code below:

 #include <math.h> 
 #include <stdio.h>
 #include <stdlib.h>
 #define DB double
 #define DO(x,y) for(x=0;x<y;x++)
 using namespace std;
 #include <complex>
 typedef complex<double> z_type;
 #define Re(x) x.real()
 #define Im(x) x.imag()
 #define I z_type(0.,1.)

 #include"ado.cin"
 #include"doya.cin"

 z_type Shoka(z_type  z)  { return z + log(exp(-z)+(M_E-1.)); }
 z_type ArcShoka(z_type z){ return z + log((1.-exp(-z))/(M_E-1.)) ;}  

 #define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
 #define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);
 main(){ int j,k,m,n; DB x,y, a;
 FILE *o;o=fopen("KellerDoya.eps","w");ado(o,308,410);
 fprintf(o,"4 4 translate\n 100 100 scale 2 setlinecap 1 setlinejoin\n");
 for(m=0;m<4;m++){ M(m,0)L(m,4)}
 for(n=0;n<5;n++){ M(0,n)L(3,n)}
 // M(0,0)L(3,3) 
 fprintf(o,".004 W 0 0 0 RGB S\n");
 DO(n,154){x=.005+.02*n;y=Re(Shoka(1.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .6 RGB S\n");
 DO(n,154){x=.005+.02*n;y=Re(Tania(1.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .6 0 0 RGB S\n");
 fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
     system("epstopdf KellerDoya.eps");
     system(    "open KellerDoya.pdf"); //these 2 commands may be specific for macintosh
 getchar(); system("killall Preview");// if run at another operational sysetm, may need to modify
 }
//

Latex generator of labels

% File KellerDoya.pdf should be generated with the code above in order to compile the Latex document below.

\documentclass[12pt]{article} %<br>
\usepackage{geometry} %<br>
\usepackage{graphicx} %<br>
\usepackage{rotating} %<br>
\paperwidth 318pt %<br>
\paperheight 424pt %<br>
\topmargin -104pt %<br>
\oddsidemargin -83pt %<br>
\textwidth 1200pt %<br>
\textheight 600pt %<br>
\pagestyle {empty} %<br>
\newcommand \sx {\scalebox} %<br>
\newcommand \rot {\begin{rotate}} %<br>
\newcommand \ero {\end{rotate}} %<br>
\newcommand \ing {\includegraphics} %<br>
\begin{document} %<br>
\sx{1}{ \begin{picture}(310,410) %<br>
\put(1,9){\ing{KellerDoya}} % <br>
\put(-12,400){\sx{2.8}{$y$}} % <br>
\put(-12,303){\sx{2.8}{$3$}} % <br>
\put(-12,203){\sx{2.8}{$2$}} % <br>
\put(-12,103){\sx{2.8}{$1$}} % <br>
\put(0,-8){\sx{2.5}{$0$}} % <br>
\put(100,-8){\sx{2.5}{$1$}} % <br>
\put(200,-8){\sx{2.5}{$2$}} % <br>
%\put(300,-9){\sx{2.5}{$3$}} % <br>
\put(292,-7){\sx{2.6}{$x$}} % <br>
%\put(560,214){\rot{37}\sx{4}{$y=\mathrm{Tania}(x)$}\ero} % <br>
%\put( 88,354){\rot{53}\sx{2.8}{$t\!=\!3$}\ero} %<br>
%\put(160,354){\rot{50}\sx{2.8}{$t\!=\!2$}\ero} %<br>
\put(158,264){\rot{48}\sx{2.8}{$y\!=\!\mathrm{Keller}(x)$}\ero} %<br>
\put(190,231){\rot{47}\sx{2.8}{$y\!=\!\mathrm{Doya}(x)$}\ero} %<br>
\end{picture} %<br>
}  %<br>
\end{document}$<br>
% Copyleft 2011 by Dmitrii Kouznetsov %<br>
%

References

Keywords

«[[]]», «Doya function», «Keller function», «Superfunctions», «Transfer function», «Transferfunction», «[[]]»,