1 function dat=noise_lcgt(parm,bw,prg,sbg);
   2 
   3 %  noise.m
   4 %  calculate LCGT sensitivity
   5 %           June 24, 2001
   6 %           Masaki Ando
   7 
   8 if nargin==0
   9 %    parm=802.249e3; bw=202.9999; prg=10; sbg=10; 
  10    parm=771.7754e3;
  11    bw=236.9261;
  12    prg=10.6285;
  13    sbg=14.6838; 
  14 
  15 %else 
  16 %    prg=1;
  17 end;
  18 
  19 p0=75*(parm/771.775e3)*(bw/236.9261*14.6838/sbg)*(10.6285/prg);
  20 finesse=249.827*100./bw*sbg;
  21 
  22 t0=300;
  23 
  24 fr_i=[-1:0.01:5]';
  25 fr=10.^fr_i;
  26 %fr=[1:5:5e3]';
  27 
  28 [num,c]=size(fr);
  29 
  30 %
  31 
  32 kb=1.381e-23;                % Boltzmann's constant [J/K]
  33 g=9.8;                       % Acceleration of the gravity [m/s^2]
  34 c=2.99792458e8;              % Speed of light [m/s]
  35 hb=1.05457266912510183e-34;  % Reduced Planck constant [J s]
  36 eta=0.9;                     % Quantum efficiency [electron/photon]
  37 
  38 % LCGT parameters
  39 
  40 %m=50;                       % Mass of a mirror [kg]
  41 l=3000;                      % Length of an arm [m]
  42 lambda=1064e-9;              % Laser wavelength [m]
  43 %p0=100;                      % Laser power [W]
  44 %prg=50;                        % Power recycling gain  
  45 w0=3e-2;                     % Beam radius on a mirror [m]
  46 %finesse=100;                 % Finesse
  47 
  48 % Seismic noise
  49 
  50 Gseismic=1e-9./fr.^2;        % Seismic motion [m/Hz^(1/2)]
  51 %Hiso=10^(-3)./fr.^10;        % total isolation ratio 
  52 Hiso=10^(-3)./fr.^6;  
  53 hseis=2./l.*Gseismic.*Hiso;
  54 
  55 
  56 % Mirror Thermal noise
  57 
  58 qm=1e8;                       % Q-value of a mirror mass
  59 rho=4.0*10^3;                 % density [kg/m^3]
  60 %radius=15*10^(-2);            % radius [m]
  61 %height=18*10^(-2);            % height [m] 
  62 radius=12.5*10^(-2);            
  63 height=15*10^(-2);            
  64 mass= rho*pi*radius^2*height; % Mass [kg] 
  65 E0=4.0e11;               % Young's modulus [Pa] 
  66 sigma = 0.29;                 % Poisson ratio 
  67 dcoa=5e-6;             % Thickness of coating [m] 
  68 phicoa=4e-4;               % Loss angle of coating
  69 Tm=20;                        % Temperature of mirror [K] 
  70 
  71 phimir=1/qm;
  72 
  73 hmirrorhomo=2/l*sqrt(4*kb*Tm*(1-sigma^2)*phimir./(sqrt(pi)*E0*w0*2*pi.*fr));     
  74 
  75 hthermoe = 9.4e-25.*(Tm/20).*(rho./4.0e3).^(1/4).*(3e3./l).*(100./fr).^(1/4);
  76 
  77 hmirrorcoa= 1.2e-24.*(phicoa./4e-4).^(1/2).*(dcoa./5e-6).^(1/2) ...
  78   .*(Tm./20).^(1/2).*(3e-2./w0).*...
  79    (4e11/E0).^(1/2).*(3e3/l).*(100./fr).^(1/2);
  80 
  81 hmirror=sqrt(hmirrorhomo.^2+ hthermoe.^2 + hmirrorcoa.^2);      
  82 
  83 
  84 % Pendulum Thermal noise
  85 
  86 qp=2e8;                      % Q-value of a pendulum
  87 %qv=qp/2;
  88 lsus=0.40;                   % Length of wire [m]
  89 fp=1/(2*pi)*sqrt(g/lsus);    % Resonant frequency of suspension [Hz]
  90 tp=13;                       % Temperature of a pendulum [K]
  91 
  92 hpen=2/l*sqrt(4*kb*tp./mass./qp./(2*pi)^3./fp.^2./fr./...
  93                 abs(1+i./qp-(fr./fp).^2).^2);
  94 
  95 %for j=1:1000
  96 %   fn=514*j;
  97 %   mn=1.034/2*(fn/fp)^2;
  98 %   th_p=sqrt(th_p.^2+4*kb*t./mn./qv./(2*pi)^3./fn.^2./fr./...
  99 %      abs(1+i./qv-(fr./fn).^2).^2);
 100 %end
 101 
 102 % Shot noise
 103 
 104 pin=p0*prg;
 105 fcut=c/4/l/finesse*sbg;
 106 tau=2*l*finesse/(pi*c)/sbg;
 107 
 108 %hshot=sqrt(hb*lambda/(4*pi*c*pin*tau^2).*(1+(fr./fcav).^2));
 109 %hshot=sqrt(hb*lambda/(4*pi*c*pin*tau^2).*(1+(fr./fcav).^2))*sqrt(3/2);
 110 hshot=sqrt(hb*lambda*fcut/(2*parm*l).*(1+(fr./fcut).^2))*sqrt(3/2)/sqrt(eta);
 111 
 112 % Radiation pressure noise
 113 
 114 %hradi=4/l*(finesse/sbg/pi)./(mass*(2*pi.*fr).^2)...
 115 %    .*sqrt(16.*pi.*hb.*pin./(c.*lambda)./(1+(fr./fcut).^2));
 116 
 117 hradi=4/l./(mass*(2*pi.*fr).^2)...
 118    .*sqrt(2*hb.*parm./(lambda*l*fcut)./(1+(fr./fcut).^2))/sqrt(eta);
 119 
 120 % Total noise
 121 
 122 tot=sqrt(hmirror.^2+hpen.^2+hshot.^2+hradi.^2+hseis.^2);
 123 %tot=sqrt(hshot.^2);
 124 
 125 dat=[fr,hseis,hpen,hmirror,hradi,hshot,tot];
 126 
 127 if nargin==0
 128 %   Save and plot data
 129 
 130    loglog(fr,hmirrorhomo,fr,hpen,fr,hradi,fr,hshot,fr,hseis,fr,hmirror,fr,tot,'k.')
 131    axis([1,1e5,1e-25,1e-18])
 132    grid on
 133 
 134    save lcgt050704.spe dat -ascii
 135 end;
 136 
 137 
 138 
 139 % %%%%%%%%%%%
 140 % 
 141 % T=2*pi/finesse*sbg;
 142 % gam=T*c/(4*l);
 143 % %I0= 1000*T/0.0511;
 144 % I0= 10000*T/0.0511;
 145 % 
 146 % ISQL= mass*l^2*gam^4/4/(c/lambda*2*pi);
 147 % Omega=2*pi*fr;
 148 % beta=atan(Omega/gam);
 149 % kappa=2*(I0/ISQL)*gam^4./(Omega.^2.*(gam.^2+Omega.^2));
 150 % 
 151 % hSQL=sqrt(8*hb./(mass*(Omega*l).^2));
 152 % 
 153 % Phi=0;
 154 % phi=pi/2;  %%;
 155 % 
 156 % rho0=0.; %%
 157 % tau0=sqrt(1-rho0);
 158 % 
 159 % c11=(1+rho0^2)*(cos(2*phi)+kappa/2*sin(2*phi))-2*rho0*cos(2*(beta+Phi));
 160 % c12=-tau0^2*(sin(2*phi)+kappa*sin(phi)^2);
 161 % c21= tau0^2*(sin(2*phi)-kappa*cos(phi)^2);
 162 % c22=c11;
 163 % 
 164 % D1=-( 1+rho0*exp(2*i * (beta+Phi))) *sin(phi);
 165 % D2=-(-1+rho0*exp(2*i * (beta+Phi))) *cos(phi);
 166 % 
 167 % zeta=pi/2;
 168 % 
 169 % Sh= hSQL.^2./(2* kappa) ...
 170 %      .* ( (c11 * sin(zeta) + c21 * cos(zeta)).^2 + ...
 171 %           (c12 * sin(zeta) + c22 * cos(zeta)).^2 ) ...
 172 %           ./(tau0^2 * abs(D1 * sin(zeta) + D2 * cos(zeta)).^2);
 173 % 
 174 % if nargin==0
 175 %    hold on
 176 %    loglog(fr,sqrt(Sh)); grid on
 177 %    hold off
 178 % end;