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Fast calculation of FP cavity for modal model

Learn about efficient methods for simulating Fabry-Perot cavity light fields using modal models, approximations, and linear calculations to speed up results. Explore simulation results and validation processes for accuracy.

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Fast calculation of FP cavity for modal model

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  1. Fast calculation of FP cavity for modal model Keiko Kokeyama Ochanomizu University And National Astronomical Observatory of Japan

  2. Contents • Introduction • Basic formulae • Approximations • Simulation result • Summary 1

  3. Introduction • Time domain fast module • Modal model version (TEM00, TEM01 …) • Calculate the light field of Fabry-Perot cavity] • Total simulation time ∝1 / time step τ 　　 ∝ calculation points Calculate once per 2Nτ[s] * * * * Calculate once per τ[s] * * Laser field etc. * * * 1step : τ=L0/c time • To reduce the calculation points, • appropriate approximations were used 2

  4. Ein Eout Eout E4 E3 E2 Ein E1 Basic formulae P m1 m2 r1 r2 P L0 τ=L0/c z1 z2 Matrix dimensions depend on the order of mode P is like : r1(t) is like : 3

  5. E1 Eout Ein E2 E3 E4 Basic formulae (1) P r2 r1 L0 z1 E1(t) can be solved : z2 (2) Recursively apply this stepwise formulae : (3) 1st term:input field at time t (current) 2nd term:N terms (steps) summation 3rd term: field at (t-2Nτ) 4 It takes long time to calculate N terms (steps) summation

  6. 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 τ [s] before N times summation without any approximations (3) Linear approximation for mirror positions and tilt angles r1(t), r2(t) depend on tilts θ Some further approximation are used to express the final result in an explicit analytic from. No summation with approximations (4) 5

  7. Simulation Results All parameters =0 6

  8. Simulation Results L0=resonant point +2*10^(-6) One mirror starts from a position slightly off from the resonance point and moves toward the resonant point and passes it 7

  9. Simulation Results N=20 N=50 N=200 8

  10. 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 9

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