Fast calculation of FP cavity for modal model

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Fast calculation of FP cavity for modal model

• Keiko Kokeyama
• Ochanomizu University
• And National Astronomical Observatory of Japan

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Contents

• Introduction
• Basic formulae
• Approximations
• Simulation result
• Summary

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Introduction

• Time domain fast module
• Modal model version (TEM00, TEM01 )
• Calculate the light field of Fabry-Perot cavity
• Total simulation time ?1 / time step t
• ? calculation points

Calculate once per 2Nts




Calculate once per ts


Laser field etc.



1step tL0/c
time

• To reduce the calculation points,
• appropriate approximations were used

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Basic formulae
P
m1
m2
r1
r2
P
L0
tL0/c
z2
z1
Matrix dimensions depend on the order of mode
P is like
r1(t) is like
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Basic formulae
(1)
P
r2
r1
L0
z1
E1(t) can be solved
z2
(2)
Recursively apply this stepwise formulae
(3)
1st terminput field at time t (current) 2nd
termN terms (steps) summation 3rd term field at
(t-2Nt)
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It takes long time to calculate N terms (steps)
summation
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Approximation
By using linear approximation, that is, by
assuming that all physics quantities change
linear in time, one step calculation gives the
current field with the field 2 N t s before
N times summation without any approximations
(3)
Linear approximation for mirror positions and
tilt angles
r1(t), r2(t) depend on tilts ?
Some further approximation are used to express
the final result in an explicit analytic from.
No summation with approximations
(4)
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Simulation Results
All parameters 0
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Simulation Results
L0resonant point 210(-6) One mirror starts
from a position slightly off from the resonance
point and moves toward the resonant point and
passes it
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Simulation Results
N20 N50 N200
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Summary

• Approximation formulae were developed
• Calculations became faster when N is big (100)

To do

• Accuracy validation is undergoing (How big N is
  available? Any reference?)
• Compare with E2E calculation using primitive
  mirrors

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