Silica 290 K

Off[General::"spell1"]
Off[General::"spell"]

SetDirectory[NotebookDirectory[]];

1. Parameters for iKAGRA

1.1 Physical constants

hb=1.05457266912510183 (10^(-34));(* reduced Planck constant (J*s) *)
ω0=1.8 (10^15);
c=2.99792458000000117`*^8;(* speed of light (m/s) *)
Ω=2 π f;
kB=1.38*10^(-23);(* Boltzmann's constant (J/K) *)
g=9.8;(* acceleration of the gravity (m/s^2) *)
L=3000;

1.2 Laser

lambda=1064*10^(-9);(* wavelength (m) *)

1.4 Mirror

rho=2200; (* density (kg/m^3) for silica *)
radius=12.5*10^(-2);(* radius (m) *)
height=10*10^(-2);(* height (m) *)
mass= rho*Pi*radius^2*height;(* mass (kg) *)

ITM reflectivity and Input power

T=0.03;

ρ=0; (* no SRM *)
ϕ=0;
ζ=0;

4. Optical readout noise (no ζ)

4.1 Additional parameter settings

m=mass; (* test mass (kg) *)

4.2 Basic equations for RSE

hSQL=(Sqrt[((8 hb)/(m (Ω^2) (L^2)))]);

Sh=((hSQL^2)/(2 κ))(((Abs[C11 Sin[ζ]+C21 Cos[ζ]])^2)+((Abs[C12 Sin[ζ]+C22 Cos[ζ]])^2)+((Abs[P12 Sin[ζ]+P22 Cos[ζ]])^2)+((Abs[P11 Sin[ζ]+P21 Cos[ζ]])^2)+((Abs[Q12 Sin[ζ]+Q22 Cos[ζ]])^2)+((Abs[Q11 Sin[ζ]+Q21 Cos[ζ]])^2)+((Abs[N11 Sin[ζ]+N21 Cos[ζ]])^2)+((Abs[N12 Sin[ζ]+N22 Cos[ζ]])^2)+(((Abs[M]*(Sqrt[Sadd])))^2))/((τ^2) ((Abs[D1sig Sin[ζ]+D2sig Cos[ζ]])^2));

M=1+(ρ^2)Exp[4 I β]-2ρ(Cos[2ϕ]+(κ/2)Sin[2ϕ])Exp[2 I β]+λSR ρ(-ρ Exp[2 I β]+Cos[2ϕ]+(κ/2)Sin[2ϕ])Exp[2 I β]+ϵ ρ(2((Cos[β])^2)(-ρ Exp[2 I β]+Cos[2ϕ])+(κ/2)(3+Exp[2 I β])Sin[2ϕ])Exp[2 I β];
C11=(Sqrt[1-λPD])((1+(ρ^2)) (Cos[2 ϕ]+(κ/2) Sin[2 ϕ])-2 ρ Cos[2 β]-(1/4)ϵ(-2(((1+Exp[2 I β]))^2)ρ+4(1+(ρ^2))((Cos[β])^2)Cos[2ϕ]+(3+Exp[2 I β])κ(1+(ρ^2))Sin[2 ϕ])+λSR(Exp[2 I β]ρ-(1/2)(1+(ρ^2))(Cos[2 ϕ]+(κ/2)Sin[2ϕ])));
C12=(Sqrt[1-λPD])(τ^2) ( -Sin[2 ϕ]-κ  ((Sin[ϕ])^2)+(1/2)ϵ Sin[ϕ]((3+Exp[2 I β])κ Sin[ϕ]+4 ((Cos[β])^2)Cos[ϕ])+(1/2)λSR(Sin[2ϕ]+κ ((Sin[ϕ])^2)));
C21=(Sqrt[1-λPD])(τ^2) (Sin[2 ϕ]-κ  ((Cos[ϕ])^2)+(1/2)ϵ Cos[ϕ]((3+Exp[2 I β])κ Cos[ϕ]+4 ((Cos[β])^2)Sin[ϕ])+(1/2)λSR(-Sin[2ϕ]+κ ((Cos[ϕ])^2))) ;
C22=C11;
D1sig=(Sqrt[1-λPD])(-(1+ρ Exp[2 I β]) Sin[ϕ]+(1/4)ϵ(3+ρ+2ρ Exp[4 I β]+(1+5ρ)Exp[2 I β])Sin[ϕ]+(1/2)λSR Exp[2 I β]ρ Sin[ϕ]);
D2sig=(Sqrt[1-λPD])(-(-1+ρ Exp[2 I β]) Cos[ϕ]+(1/4)ϵ(-3+ρ+2ρ Exp[4 I β]+(-1+5ρ)Exp[2 I β])Cos[ϕ]+(1/2)λSR Exp[2 I β]ρ Cos[ϕ]);
P11=(1/2)(Sqrt[1-λPD])(Sqrt[λSR])τ(-2ρ Exp[2 I β]+2Cos[2ϕ]+κ Sin[2ϕ]);
P12=-(Sqrt[1-λPD])(Sqrt[λSR])τ Sin[ϕ](2Cos[ϕ]+κ Sin[ϕ]);
P21=(Sqrt[1-λPD])(Sqrt[λSR])τ Cos[ϕ](2Sin[ϕ]-κ Cos[ϕ]);
P22=P11;
Q11=(Sqrt[λPD])(Exp[-2 I β]+(ρ^2)Exp[2 I β]-ρ(2 Cos[2ϕ]+κ Sin[2 ϕ])+(1/2)ϵ ρ(Exp[-2 I β]Cos[2ϕ]+Exp[2 I β](-2ρ-2ρ Cos[2 β]+Cos[2ϕ]+κ Sin[2ϕ])+2 Cos[2ϕ]+3 κ Sin[2ϕ])-(1/2)λSR ρ(2ρ Exp[2 I β]-2 Cos[2ϕ]-κ Sin[2ϕ]));
Q12=0;
Q21=0;
Q22=Q11;
N11=(Sqrt[1-λPD])(Sqrt[(ϵ/2)])τ(κ(1+ρ Exp[2 I β])Sin[ϕ]+2Cos[β](Exp[-I β]Cos[ϕ]-ρ Exp[I β](Cos[ϕ]+κ Sin[ϕ])));
N12=-(Sqrt[1-λPD])(Sqrt[2 ϵ])τ(Exp[-I β]+ρ Exp[I β])Cos[β]Sin[ϕ];
N22=-(Sqrt[1-λPD])(Sqrt[2 ϵ])τ(-Exp[-I β]+ρ Exp[I β])Cos[β]Cos[ϕ];
N21=(Sqrt[1-λPD])(Sqrt[(ϵ/2)])τ(-κ(1+ρ)Cos[ϕ]+2Cos[β](Exp[-I β]+ρ Exp[I β])Cos[β] Sin[ϕ]);

γ=T c/(4 L);(* cavity pole *)
τ=(Sqrt[1-(ρ^2)]); (* SRM transmittance *)
β=ArcTan[Ω/γ]; (* phase shift in the arm cavity *)
κ=((2 (I0/ISQL) (γ^4))/((Ω^2) ((γ^2)+(Ω^2)))); (* coefficient that shows how much the mirror moves *)
ISQL=((m (L^2) (γ^4))/(4 ω0)); (* the power with which the quantum noise reaches the SQL at the cavity pole frequency *)

4.3 Loss parameters

roundtriploss=200*10^(-6); (* ppm *)
ϵ = 2/T*roundtriploss; (* loss parameter of arms defined in KLMTV paper *)
λSR =0.0; (* loss in power at the signal recycling mirror *)
λPD=0.1;  (* 1 - PD's quantum efficiency in power *)
Sadd= 1*((π^2)/8 - 1);

3.Observable distance (Compact binary coalescense)

7. Math to Igor

logDataOutput[filename_String, X_, {imin_, imax_}] :=
  Module[{strm},
    strm = OpenWrite[filename];
    Do[
      Do[
        Module[{},
          Map[writeList[strm, #] &, { x , X} /. x -> (10^i) 10^ j];
          writeListn[strm];
          ],
        {i, 0.001, 1, 0.001}
        ],
      {j, imin, imax}
      ];
    Close[strm];
    ]

writeList[strm_, dat_] :=
  WriteString[strm, ToString[FortranForm[dat]], " "];

writeListn[strm_] :=
  WriteString[strm, "\n"];

logDataOutput["QN1W10kgLowFinesseRFwoSRM.dat",(Sqrt[Sh])/.I0->1/.{f->x},{0,3}]

logDataOutput["QN10W10kgLowFinesseRFwoSRM.dat",(Sqrt[Sh])/.I0->10/.{f->x},{0,3}]

logDataOutput["QN200W10kgLowFinesseRFwoSRM.dat",(Sqrt[Sh])/.I0->200/.{f->x},{0,3}]

logDataOutput["QN780W10kgLowFinesseRFwoSRM.dat",(Sqrt[Sh])/.I0->780/.{f->x},{0,3}]