Attachment 'lcgt_param.m'
Download 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;
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