## Attachment 'lcgt_param.m'

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```   1 function dat=lcgt_param(Rf)
2
3 % Parameters of LCGT Interferometer
4 %      ( conventional configulation ,  finite contrast)
5 %     Original :  Masaki Ando  June 18, 2001 for Mathematica
6 %     Modified :            October 02, 2002 for Matlab
7
8 % Constants
9 format short e
10
11 %if nargin==0; Rf=0.995; end;
12 if nargin==0; Rf=0.996; end;
13
14 lambda = 1064e-9;              % Wavelength of a laser source [m]
15 c = 2.99792458e8;              % Speed of light [m/s]
16 ee = 1.60217733e-19;           % Elementary charge [C]
17 L = 3000;                      % Baseline length [m]
18 %P = 100;                       % Lase power [W]
19 P = 75;
20 eta = 1;                       % Quantum efficiency [A/W]
21 gdet = 1e3 * sqrt(2);          % Photo detector effective impedance [Ohm]
22 El = sqrt(P * eta);            % Effective laser power [A]
23 Omega = (2 * pi * c)/lambda;   % Angular frequency of laser [Hz]
24
25 % Losses
26
27 contrast = 0.995;
28 CavRefLoss  = 1000 * 1e-6;
29 loss = 10 * 1e-6;
30 BSloss = 100 * 1e-6;
31 ARloss = 0.001;
32 BSAR  = ARloss;
33 Rst = 1;
34 Tcont = (1 - contrast)/(1 + contrast);
35 Rcont = (2 * contrast)/(1 + contrast);
36 tcont = sqrt(Tcont);
37 rcont  = sqrt(Rcont);
38 tcavloss = sqrt(1 - CavRefLoss/2);
39 rst = sqrt(Rst);
40
41 % Mirrors
42
43 %rf = sqrt(0.994);       % Front mirror
44 rf = sqrt(Rf);
45 re = sqrt(0.99995);     % End mirror
46 %rr = sqrt(0.76);        % PRM
47 %rs = sqrt(0.68);        % SEM
48 rr = sqrt(0.80);
49 rs = sqrt(0.77);
50 rp = sqrt(0.001);       % Pick-off mirror
51
52 tf = sqrt(1 - rf^2 - loss);
53 te = sqrt(1 - re^2 - loss);
54 tr = sqrt(1 - rr^2 - loss);
55 ts = sqrt(1 - rs^2 - loss);
56 tp = sqrt((1 - rp^2) * (1 - loss) * (1 - ARloss));
57
58 tar = sqrt(1 - ARloss);
59 tbs = sqrt((1 - BSAR) * (1 - BSloss));
60 tst = sqrt(1 - Rst);
61
62 % Modulation
63
64 wm = 15e6;             % Modulation frequency [rad]
65 delta = 0.25;          % Asymmetry [m]
66 m = 0.9;               % Modulation index [rad]
67 j0 = BesselJ(0, m);    % Bessel function
68 j1 = BesselJ(1, m);
69 Con = El^2 * j0 * j1;
70 alpha = (2 *pi * wm * delta)/c;
71 lplus = 5;            % Recycling cavity length
72
73 % Caliculated parameters
74 %% Parameters of arm cavity reflectivity etc.
75
76 rreso = tcavloss^2 * tar^2 * (-rf + tf^2 * re/(1 - rf * re) );
77 ranti = tcavloss^2 * tar^2 * (-rf - tf^2 * re/(1 + rf * re) );
78 rdreso =tcavloss^2 * tar^2 * tf^2 * re / (1 - rf * re)^2;
79 rdanti =tcavloss^2 * tar^2 * tf^2 * re / (1 + rf * re)^2;
80 gcav =  tcavloss * tar * tf / (1 - rf * re);
81
82 %% Finesse etc.
83
84 fine = pi * sqrt(rf * re) / (1 - rf * re);
85 tau = 2 * L * fine / (pi * c);
86 cutoff = 1 / (tau * 2 * pi);
87 NFP = 2 * fine / pi;
88
89 %% parameters of Fabry-Perot-Michelson inteferometer reflectivity
90
91 rfpm0 =  tbs^2 * rreso * rcont;
92 rfpm1 = -tbs^2 * ranti * cos(alpha) * rcont;
93 rfpmp0 = tbs^2 * tp^2 * rreso * rcont * rst^4;
94 rfpmp1 =-tbs^2 * tp^2 * ranti * cos(alpha) * rcont * rst^4;
95 %
96 % % Optimal recycling gain case
97 % rr = abs(rfpmp0);
98 % tr = sqrt(1 - rr^2 - loss);
99 % ((rr^2 + tr^2) * rfpmp1)^2;
100
101 % Parameters of power recycling
102 %% Gain
103
104 g0 = tar * tr / (1 - rr * rfpmp0);
105 g1 = tar * tr / (1 - rr * rfpmp1);
106 Gp = g0^2;
107 Gs = g0 * g1;
108 Pbs = g0^2 * P;
109 Pcav = tbs * tp * gcav^2 * Pbs;
110
111 %% Reflectivity
112
113 rrfpm0 = tar^2 * (-rr + tr^2 * rfpmp0 / (1 - rr * rfpmp0) );
114 rrfpm1 = tar^2 * (-rr + tr^2 * rfpmp1 / (1 - rr * rfpmp1) );
115
116 % Parameters of signal recycling
117
118 ers = tcavloss^2 * tar^2 * tbs^2 * rcont * rs;
119 ets = tcavloss * tar * tbs * rcont * ts;
120
121 erf = rf - tf^2 * ers/(1 - rf * ers);
122 etf= tf * ets /(1 - rf * ers);
123
124 efine = pi * sqrt(erf * re) / (1 - erf * re);
125 etau = 2 * L * efine / (pi * c);
126 ecutoff = 1 / (etau * 2 * pi);
127 eNFP = 2 * efine / pi;
128
129 sbg = fine/efine;                % Signal bandwidth gain
130 sigloss = 1 - etf^2 / (1 - (erf * re)^2);    % Signal loss
131
132 % Signal
133 %% Signal size
134
135 %%% v1
136 v1Lm = Con * g0 * g1 * abs(rdreso) * ranti * sin(alpha) * tp^2 * tbs^4 * Rcont * rst^4;
137 v1ellm =  Con * g0 * g1 * rreso * ranti * sin(alpha) * tp^2 * tbs^4 * Rcont * rst^4;
138
139 %%% v2
140 v2Lm = Con * rrfpm0 * g1^2 * abs(rdanti) * sin(alpha) * tp^2 * tbs^2 * rcont * rst^4;
141 v2ellm = -Con * rrfpm0 * g1^2 * ranti * sin(alpha) * tp^2 * tbs^2 * rcont * rst^4;
142
143 %%% v3
144 v3Lp = Con * g0^2 * g1 * abs(rdreso) * ranti * cos(alpha) ...
145    * tp^2 * rp^2 * tbs^4/tr * Rcont * rst^4;
146 v3ellp = Con * g0 * g1 * rreso * ranti * (g0 - g1) * cos(alpha) ...
147    * tp^2 * rp^2 * tbs^4/ tr * Rcont * rst^4;
148
149 %%% v4
150 v4Lp = Con * ( -rrfpm1 * g0^2 * abs(rdreso) + rrfpm0 * g1^2 * abs(rdanti)) ...
151    * tp^2 * tbs^2 * rcont * rst^4;
152 v4ellp = -Con * (rrfpm1 * g0^2 * rreso + g1^2 * rrfpm0 * ranti * cos(alpha)) ...
153    * tp^2 * tbs^2 * rcont * rst^4;
154
155 %% Calibration
156
157 alpha1 = (v1Lm   * gdet * 4 * pi)/lambda;
158 alpha2 = (v2ellm * gdet * 4 * pi)/lambda;
159 alpha4 = (v4Lp   * gdet * 4 * pi)/lambda;
160 alpha3 = (v3ellp * gdet * 4 * pi)/lambda;
161
162 %% Signal ratio
163
164 sig = (1/v1Lm) * [[v1Lm, v1ellm,    0,      0]; ...
165        [v2Lm, v2ellm,    0,      0]; ...
166        [   0,      0, v3Lp, v3ellp]; ...
167        [   0,      0, v4Lp, v4ellp]];
168 sigr = [(1/v1Lm) * [v1Lm, v1ellm, 0, 0]; ...
169        (1/v2ellm)* [v2Lm, v2ellm, 0, 0]; ...
170        (1/v3Lp)  * [0, 0, v3Lp, v3ellp]; ...
171        (1/v4ellp)* [0, 0, v4Lp, v4ellp]];
172
173 % Shot noise
174 %% Shot noise
175
176 v1shot = sqrt( ee * El^2 * tp^2 * tbs^4 * Rcont * rst^2)...
177    * sqrt(        2 * ( j1 * g1 * ranti * sin(alpha) )^2 ...
178    + Tcont * ( ( j0 * g0 * rreso )^2  ...
179    + 2 * ( j1 * g1 * ranti * cos(alpha) )^2 ) );
180 v2shot = sqrt( ee * ( (j0 * rrfpm0)^2 + 2 * (j1 * rrfpm1)^2 ) * El^2);
181 v3shot = sqrt( ee * ( (j0 * g0 * rreso)^2 + 2 * ( j1 * g1 * ranti * cos(alpha) )^2) ...
182    * rp^2 * tp^2 * tbs^4 * rst^2 * El^2 * Rcont);
183 v4shot =  v2shot;
184
185 %% Shot noise ( V/rt[Hz] )
186 v1shot * gdet ;
187 v2shot * gdet ;
188 v3shot * gdet ;
189 v4shot * gdet ;
190
191 %% Shot noise level ( m/rt[Hz] )
192 shotlevel = lambda/(4 * pi) ...
193    * [[abs(v1shot/v1Lm), abs(v1shot/v1ellm), 0, 0]; ...
194        [abs(v2shot/v2Lm), abs(v2shot/v2ellm), 0, 0]; ...
195        [ 0, 0, abs(v3shot/v3Lp), abs(v3shot/v3ellp)]; ...
196        [ 0, 0, abs(v4shot/v4Lp), abs(v4shot/v4ellp)]];
197
198 % Frequency response
199 %% Cavity cut-off
200
201 omegac = (1 - rf * re)/(rf * re * 2 * L) * c;
202 nuc = omegac/(2 * pi);
203
204 %% Coupled cavity cut-off
205
206 omegacc = (1 - rr * rfpmp0) * omegac / (1 + rr * rfpmp0);
207 nucc =omegacc/(2 *pi);
208
209 %% Recycling cavity cut-off
210
211 omegarec = - (1 + rr * tp^2 * ranti * cos(alpha) * rcont) ...
212    / ( (rr * tp^2 * ranti * cos(alpha) * lplus)/c) ;
213 nurec = omegarec/(2 *pi);
214
215 dat=[Rf,Pcav, Pcav/g0^2 , fine, g0^2];
216
217 if nargin==0,
218
219    % Parameters
220    %% Print Out
221    disp(' ')
222    disp(['Laser Power                 : ', num2str(P), ' W'] );
223    disp(['Wave Length                 : ', num2str(lambda * 1e9),' nm']);
224    disp(['Reflectivity of the Mirrors']);
225    disp(['   Front Mirror             : ', num2str(100 * rf^2), ' %']);
226    disp(['   End Mirror               : ', num2str(100 * re^2), ' %']);
227    disp(['   Power Recycling Mirror   : ', num2str(100 * rr^2), ' %']);
228    disp(['   Signal Extraction Mirror : ', num2str(100 * rs^2), ' %']);
229    disp(['   Pick-off Mirror          : ', num2str(100 * rp^2), ' %']);
230    disp(['   Steering Mirror          : ', num2str(100 * Rst),  ' %']);
231    disp(['Modulation Frequency        : ', num2str(wm/1e6), ' MHz']);
232    disp(['Mudulation Index            : ', num2str(m)]);
233    disp(['Asymmetry                   : ', num2str(delta), ' m']);
234    disp(['The ¿ parameter            : ', num2str(alpha)]);
235    disp(['Effective Mudulation Index  : ', num2str(m*sin(alpha))]);
236    disp(['Recycing Cavity Length      : ', num2str(lplus), ' m']);
237    disp(['Loss in an Optical Component: ', num2str(loss * 1e6), ' ppm']);
238    disp(['Reflectivity of an AR coat  : ', num2str(100 * ARloss), ' %']);
239    disp(['Beam Splitter AR coat       : ', num2str(100 * BSAR), ' %']);
240    disp(['Contrast of the Fringe      : ', num2str(100 * contrast), ' %']);
241    disp(['Arm Cavity']);
242    disp(['    Length                  : ', num2str(L), ' m']);
243    disp(['    Reflectivity']);
244    disp(['          for the Carrier   : ', num2str(100 * rreso^2), ' %']);
245    disp(['          for the Sidebands : ', num2str(100 * ranti^2), ' %']);
246    disp(['    Power in a cavity       : ', num2str(Pcav/1e3), ' kW']);
247    disp(['    Phase Change Enhancement ']);
248    disp(['          for the Carrier   : ', num2str(rdreso)]);
249    disp(['          for the Sidebands : ', num2str(rdanti)]);
250    disp(['    Finesse                 : ', num2str(fine)]);
251    disp(['    Cut-off Frequency       : ', num2str(cutoff), ' Hz']);
252    disp(['    Loss on the Reflection  : ', num2str(100 * CavRefLoss),' %']);
253    disp(['Fabry-Perot-Michelson interferometer']);
254    disp(['    Reflectivity']);
255    disp(['          for the Carrier   : ', num2str(100 * rfpmp0^2),' %']);
256    disp(['          for the Sidebands : ', num2str(100 * rfpmp1^2),' %']);
257    disp(['Power Recycled Interferometer']);
258    disp(['    Recycling Gain']);
259    disp(['          for the Carrier   : ', num2str(g0^2)]);
260    disp(['          for the Sidebands : ', num2str(g1^2)]);
261    disp(['    Power on BS             : ', num2str(Pbs),' W']);
262    disp(['    Reflectivity']);
263    disp(['          for the Carrier   : ', num2str(100 * rrfpm0^2), ' %']);
264    disp(['          for the Sidebands : ', num2str(100 * rrfpm1^2),  ' %']);
265    disp(['    Coupled Cavity cutoff   : ', num2str(nucc), ' Hz']);
266    disp(['    Recycling Cavity cutoff : ', num2str(nurec/1e6),  ' MHz']);
267    disp(['Signal Extraction Cavity']);
268    disp(['    Compound Front Mirror   : ', num2str(100 * erf^2), ' %']);
269    disp(['    Signal Band Gain        : ', num2str(sbg)]);
270    disp(['    Signal band             : ', num2str(ecutoff), ' Hz']);
271    disp(['    Signal loss             : ', num2str(100 * sigloss ), ' %']);
272
273 %     disp(['Signals']);
274 %     disp(['    Signal Ratio Matrix : ']);
275 %     disp(sig);
276 %     disp(['    Signal Ratio Matrix with nomalization: ']);
277 %     disp(sigr);
278 %     disp(['    Shot-noise Level : ', ' m/sqrt(Hz)']);
279 %     disp(shotlevel);
280 end;
```

## Attached Files

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• [get | view] (2011-04-29 22:27:53, 141274.6 KB) [[attachment:20060710_e2e_AdLIGO_arm_cavity.zip]]
• [get | view] (2011-04-29 22:27:53, 1976.9 KB) [[attachment:20090605_loopnoise255_LCGT.zip]]
• [get | view] (2011-04-29 22:27:49, 1879.7 KB) [[attachment:20090605_loopnoise255_LCGT_result.zip]]
• [get | view] (2011-04-29 22:27:49, 2212.7 KB) [[attachment:20090702_loopnoise255c_LCGT_Sato_model.zip]]
• [get | view] (2011-04-29 22:27:53, 17087.3 KB) [[attachment:20090806_loopnoise260_LCGT2009.zip]]
• [get | view] (2011-04-29 22:27:49, 3481.6 KB) [[attachment:20090831_loopnoise274_LCGT2009_new2.zip]]
• [get | view] (2011-04-29 22:27:53, 330.4 KB) [[attachment:LCGT_default_withYamamotoSuspTN.nb]]
• [get | view] (2011-04-29 22:27:53, 9.6 KB) [[attachment:lcgt_param.m]]
• [get | view] (2011-04-29 22:27:49, 4.6 KB) [[attachment:noise_lcgt.m]]
• [get | view] (2011-04-29 22:27:53, 191.8 KB) [[attachment:rho086BBH.nb]]
• [get | view] (2011-04-29 22:27:49, 419.3 KB) [[attachment:rho086BNS.nb]]
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