From eee8a30024c1339478b2067bf523dae960224c8c Mon Sep 17 00:00:00 2001
From: Jameson Graef Rollins <jrollins@finestructure.net>
Date: Fri, 20 Sep 2019 00:43:02 -0700
Subject: [PATCH] substrate carrier density noise simplification
substrate_carrierdensity() function updated to calculate thermal noise
of a single suspended optic.
ifo ITMCarrierDensity Noise class modified to handle specific case of
Fabry-Perot Michelson.
---
gwinc/ifo/noises.py | 7 ++-
gwinc/noise/substratethermal.py | 97 ++++++++++++++-------------------
2 files changed, 46 insertions(+), 58 deletions(-)
diff --git a/gwinc/ifo/noises.py b/gwinc/ifo/noises.py
index dacb91c8..406919e3 100644
--- a/gwinc/ifo/noises.py
+++ b/gwinc/ifo/noises.py
@@ -1,3 +1,5 @@
+import numpy as np
+
from .. import nb
from .. import noise
@@ -176,7 +178,10 @@ class ITMCarrierDensity(nb.Noise):
)
def calc(self):
- return noise.substratethermal.carrierdensity(self.freq, self.ifo)
+ gPhase = self.ifo.gwinc.finesse * 2/np.pi
+ n = noise.substratethermal.substrate_carrierdensity(
+ self.freq, self.ifo.Materials, self.ifo.Optics.ITM.BeamRadius)
+ return n * 2 / (gPhase)**2 * self.ifo.gwinc.dhdl_sqr
class SubstrateBrownian(nb.Noise):
diff --git a/gwinc/noise/substratethermal.py b/gwinc/noise/substratethermal.py
index 5f832315..8686a617 100644
--- a/gwinc/noise/substratethermal.py
+++ b/gwinc/noise/substratethermal.py
@@ -1,3 +1,7 @@
+'''Functions to calculate substrate thermal noise
+
+'''
+
from __future__ import division, print_function
from numpy import exp, inf, pi, sqrt
import numpy as np
@@ -9,71 +13,50 @@ from ..const import BESSEL_ZEROS as zeta
from ..const import J0M as j0m
-def carrierdensity_adiabatic(f, ifo):
- """strain noise psd arising from charge carrier density
- fluctuations in ITM substrate (for semiconductor substrates)."""
-
- Omega = 2*pi*f
- H = ifo.Materials.MassThickness
- gammaElec = ifo.Materials.Substrate.ElectronIndexGamma
- gammaHole = ifo.Materials.Substrate.HoleIndexGamma
- diffElec = ifo.Materials.Substrate.ElectronDiffusion
- diffHole = ifo.Materials.Substrate.HoleDiffusion
- cdDens = ifo.Materials.Substrate.CarrierDensity
- r0 = ifo.Optics.ITM.BeamRadius/np.sqrt(2)
- gPhase = ifo.gwinc.finesse*2/pi
-
- psdElec = 4*H*gammaElec**2*cdDens*diffElec/(pi*r0**4*Omega**2) # units are meters
- psdHole = 4*H*gammaHole**2*cdDens*diffHole/(pi*r0**4*Omega**2) # units are meters
- psdMeters = 2 * (psdElec + psdHole) # electrons and holes for two ITMs
- n = psdMeters / (gPhase)**2 * ifo.gwinc.dhdl_sqr
- return n
+def substrate_carrierdensity(f, materials, wBeam, exact=False):
+ """Substrate thermal displacement noise spectrum from charge carrier density fluctuations
+ For semiconductor substrates.
-def carrierdensity_exact(f, ifo):
- """Strain noise arising from charge carrier density fluctuations in ITM substrate
+ :f: frequency array in Hz
+ :materials: gwinc optic materials structure
+ :wBeam: beam radius (at 1 / e^2 power)
+ :exact: whether to use adiabatic approximation or exact calculation (False)
- For semiconductor substrates
+ :returns: displacement noise power spectrum at :f:, in meters
"""
- w = ifo.Optics.ITM.BeamRadius
- H = ifo.Materials.MassThickness
- kBT = const.kB * ifo.Materials.Substrate.Temp
- hbar = const.hbar
- c = const.c
-
- diffElec = ifo.Materials.Substrate.ElectronDiffusion
- diffHole = ifo.Materials.Substrate.HoleDiffusion
- mElec = ifo.Materials.Substrate.ElectronEffMass
- mHole = ifo.Materials.Substrate.HoleEffMass
- cdDens = ifo.Materials.Substrate.CarrierDensity
- gammaElec = ifo.Materials.Substrate.ElectronIndexGamma
- gammaHole = ifo.Materials.Substrate.HoleIndexGamma
- gPhase = ifo.gwinc.finesse*2/pi
-
+ H = materials.MassThickness
+ diffElec = materials.Substrate.ElectronDiffusion
+ diffHole = materials.Substrate.HoleDiffusion
+ mElec = materials.Substrate.ElectronEffMass
+ mHole = materials.Substrate.HoleEffMass
+ cdDens = materials.Substrate.CarrierDensity
+ gammaElec = materials.Substrate.ElectronIndexGamma
+ gammaHole = materials.Substrate.HoleIndexGamma
+ r0 = wBeam/np.sqrt(2)
omega = 2*pi*f
- def integrand(k, om, D):
- return D * k**3 * exp(-k**2 * w**2/4) / (D**2 * k**4 + om**2)
+ if exact:
+ def integrand(k, om, D):
+ return D * k**3 * exp(-k**2 * wBeam**2/4) / (D**2 * k**4 + om**2)
- integralElec = np.array([scipy.integrate.quad(lambda k: integrand(k, om, diffElec), 0, inf)[0] for om in omega])
- integralHole = np.array([scipy.integrate.quad(lambda k: integrand(k, om, diffHole), 0, inf)[0] for om in omega])
-
- # From P1400084 Heinert et al. Eq. 15
- #psdCD = @(gamma,m,int) 2*(3/pi^7)^(1/3)*kBT*H*gamma^2*m/hbar^2*cdDens^(1/3)*int; %units are meters
- def psdCD(gamma,m,int_):
- return 2/pi * H * gamma**2 * cdDens * int_ #units are meters
-
- psdElec = psdCD(gammaElec, mElec, integralElec)
- psdHole = psdCD(gammaHole, mHole, integralHole)
-
- psdMeters = 2 * (psdElec + psdHole)
-
- n = psdMeters / (gPhase)**2 * ifo.gwinc.dhdl_sqr
-
- return n
-
-carrierdensity = carrierdensity_adiabatic
+ integralElec = np.array([scipy.integrate.quad(lambda k: integrand(k, om, diffElec), 0, inf)[0] for om in omega])
+ integralHole = np.array([scipy.integrate.quad(lambda k: integrand(k, om, diffHole), 0, inf)[0] for om in omega])
+
+ # From P1400084 Heinert et al. Eq. 15
+ #psdCD = @(gamma,m,int) 2*(3/pi^7)^(1/3)*kBT*H*gamma^2*m/hbar^2*cdDens^(1/3)*int; %units are meters
+ # FIXME: why the unused argument here?
+ def psdCD(gamma, m, int_):
+ return 2/pi * H * gamma**2 * cdDens * int_
+
+ psdElec = psdCD(gammaElec, mElec, integralElec)
+ psdHole = psdCD(gammaHole, mHole, integralHole)
+ else:
+ psdElec = 4*H*gammaElec**2*cdDens*diffElec/(pi*r0**4*omega**2)
+ psdHole = 4*H*gammaHole**2*cdDens*diffHole/(pi*r0**4*omega**2)
+
+ return psdElec + psdHole
def thermorefractiveITM_adiabatic(f, ifo):
--
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