diff --git a/src/new/IFOs/FT_FP_sidebands.m b/src/new/IFOs/FT_FP_sidebands.m new file mode 100644 index 0000000000000000000000000000000000000000..0304a17d5b8895dee9e1a91bf7fb3422c4c63534 --- /dev/null +++ b/src/new/IFOs/FT_FP_sidebands.m @@ -0,0 +1,65 @@ +%-------------------------------------------------------------------------- +% [a_FP] = FT_FP_sidebands(fsig,a0,lambda,L,R1,T1,R2,sb_sign) +% +% A function for Matlab which calculates the amplitude and phase of the +% sidebands created and reflected from a Fabry-Perot cavity where the +% cavity space is modulated by a gravitational wave (with h=1). The +% calculation is carried out for a linear cavity on resonance. +% +% fsig: Gravitational wave frequency [Hz] +% a0: Complex number representing the amplitude and phase of the beam +% injected into the cavity [sqrt(W)]. +% lambda: Laser wavelength [m] +% L: Cavity length [m] +% R1: ITM reflection coefficient (power) +% T1: ITM transmission coefficient (power) +% R1 and T1 should satisfy R1+T1<=1 +% R2: ETM reflection coefficient (power). R2 must satisfy R2<=1. +% sb_sign: Sign of the sideband to calculate the amplitude and phase of. +% 1: upper sideband +% -1: lower sideband +% The amplitudes of the upper and lower sidebands are the same, +% the phases depend on the sign. +% +% a_FP: Returned complex coefficient describing the amplitude and phase +% of the reflected sideband [sqrt(W)]. +% +% Charlotte Bond 28.01.2013 +%-------------------------------------------------------------------------- +% + +function [a_FP] = FT_FP_sidebands(fsig,a0,lambda,L,R1,T1,R2,sb_sign) + + % Light/cavity parameters + c=299792458; + ksig = 2*pi*fsig/c; + n = 1; + + % Make the cavity space resonanat + L = round(L/lambda)*lambda; + + % Reflection amplitude coefficients + r1 = sqrt(R1); + r2 = sqrt(R2); + + % Gravitational wave amplitude = 1 + h0 = 1; + + % Amplitude of sidebands created when a beam travels through a space + % modulated by a GW + asb = FT_GW_sidebands(lambda,h0,fsig,L,n,sb_sign); + + % Sideband amplitude from round-trip of the space + a_arm = r2*asb.*(1+exp(-1i*sb_sign*ksig*L)); + + % Amplitude of sidebands reflected from the cavity + a_FP = a0 * (-T1/(1-r1*r2)) * (a_arm./(1-r1*r2*exp(-1i*2*sb_sign*ksig*L))); + + % If T1=1 (i.e. not ITM) the equation above adds an extra 180 deg + % phase, which needs to be corrected via an extra - + if T1==1 + a_FP = -a_FP; + end + +end + diff --git a/src/new/IFOs/FT_MICH_sidebands.m b/src/new/IFOs/FT_MICH_sidebands.m new file mode 100644 index 0000000000000000000000000000000000000000..a0a013749fe69a14cead5eef6c85401778b1b31a --- /dev/null +++ b/src/new/IFOs/FT_MICH_sidebands.m @@ -0,0 +1,59 @@ +%-------------------------------------------------------------------------- +% function [a_MICH] = +% FT_MICH_sidebands(fsig,a0,lambda,L,Rbs,Tbs,R1,T1,R2,sb_sign) +% +% A function for Matlab which calculates the sidebands created at the +% output (dark) port of a Michleson interferometer when a gravitational +% wave modulates the length of the arms. The Michelson is on the dark +% fringe with lx 0.25*lambda longer than ly and the arm cavities are on +% resonance. The gravitational wave is in the optimal polarisation, +% modulating the y arm 180 degrees out of phase with the x arm. +% +% fsig: Frequency of the gravitational wave [Hz] +% a0: Complex number describing the amplitude and phase of the +% input light beam [sqrt(W)]. +% lambda: Laser wavelength [m] +% L: Length of arm cavities [m] +% Rbs: Beam-splitter reflection coefficient (power) +% Tbs: Beam-splitter reflection coefficient (power) +% R1: ITM reflection coefficient (power) +% T1: ITM transmission coefficient (power) +% For the case of no arm cavities (just a single end mirror) use +% T1 = 1, R1 = 0. +% R2: ETM reflection coefficient (power) +% sb_sign: Sign of the sideband amplitude to calculate. +% 1: Upper sideband +% -1: Lower sideband +% +% a_MICH: Returned complex sideband amplitude, including the amplitude +% and phase, at the dark port of the Michleson interferometer +% [sqrt(W)]. +% +% Charlotte Bond 26.02.2013 +%-------------------------------------------------------------------------- +% + +function [a_MICH] = FT_MICH_sidebands(fsig,a0,lambda,L,Rbs,Tbs,R1,T1,R2,sb_sign) + + % Carrier and sideband parameters + c=299792458; + k0 = 2*pi/lambda; + ksig = 2*pi*fsig/c; + + % BS parameters + rbs = sqrt(Rbs); + tbs = sqrt(Tbs); + + % Calculate the amplitude of the sidebands reflected from the arms + a_FP = FT_FP_sidebands(fsig,a0,lambda,L,R1,T1,R2,sb_sign); + + % Put the Michelson on the dark fringe + lx = 0.25*lambda; + ly = 0; + + % Calculate the amplitude of the sidebands sent to the dark port + a_MICH = 1i * tbs * rbs * a0 * a_FP .* (exp(-1i*(2*k0+sb_sign*ksig)*lx)-exp(-1i*(2*k0+sb_sign*ksig)*ly)); + + +end + diff --git a/src/new/IFOs/FT_SAG_sidebands.m b/src/new/IFOs/FT_SAG_sidebands.m new file mode 100644 index 0000000000000000000000000000000000000000..2b43b8910e7b3b3aa0ca05c307d546c51e9ff5f9 --- /dev/null +++ b/src/new/IFOs/FT_SAG_sidebands.m @@ -0,0 +1,57 @@ +%-------------------------------------------------------------------------- +% function [a_SAG] = +% FT_SAG_sidebands(fsig,a0,lambda,L,Rbs,Tbs,R1,T1,R2,sb_sign) +% +% A function for Matlab which calculates the amplitude of sidebands created +% in a Sagnac interferometer at the output (dark) port when a gravitational +% wave modulates the length of the arms. The arm cavities are on resonance +% and the gravitational wave is in the optimal polarisation, modulating the +% y arm 180 degrees out of phase to the x arm. +% +% fsig: Frequency of the gravitational wave [Hz] +% a0: Complex number describing the amplitude and phase of the input +% light beam [sqrt(W)]. +% lambda: Laser wavelength [m] +% L: Length of the arms/ cavities [m] +% Rbs: Beam-splitter reflection coefficient (power) +% Tbs: Beam-splitter transmission coefficient (power) +% R1: ITM reflection coefficient (power) +% T1: ITM transmission coefficient (power) +% For no arm cavities (just a single end mirror in the arms) use +% R1 = 0, T1 = 1. +% R2: ETM reflection coefficient (power) +% sb_sign: Sign of the sidebands to calculate. +% 1: upper sideband +% -1: lower sideband +% +% a_SAG: Complex number describing the amplitude and phase of the +% sideband at the output of the Sagnac interferometer [sqrt(W)]. +% +% Charlotte Bond 26.02.2013 +%-------------------------------------------------------------------------- +% + +function [a_SAG] = FT_SAG_sidebands(fsig,a0,lambda,L,Rbs,Tbs,R1,T1,R2,sb_sign) + + % Light parameters + c=299792458; + k0 = 2*pi/lambda; + ksig = 2*pi*fsig/c; + + % Put the arm cavities on resonance + L = round(L/lambda)*lambda; + + % Calculate the amplitude of the sidebands reflected from the arms + a_FP = FT_FP_sidebands(fsig,a0,lambda,L,R1,T1,R2,sb_sign); + + % Reflection coefficients for the FP cavities for the carrier and + % sideband frequency. + rcav_k0 = FT_FP_refl(k0,L,R1,T1,R2); + rcav_ksig = FT_FP_refl(k0+sb_sign*ksig,L,R1,T1,R2); + + % Final amplitude of the sidebands at the output port of the Sagnac + % interferometer + a_SAG = a0 * a_FP .* (rcav_k0 - rcav_ksig) * (Rbs+Tbs); + +end +