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11. Reflection/Transmission spectra

11. Reflection/Transmission spectra. Contents Normal incidence on a simple dielectric slab 2. Normal incidence on a photonic crystal slab 3. Normal incidence on a Distributed Bragg mirror 4. Normal incidence on a 1-D photonic crystal cavity. 1. Simple dielectric slab. Without slab.

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11. Reflection/Transmission spectra

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  1. 11. Reflection/Transmission spectra • Contents • Normal incidence on a simple dielectric slab • 2. Normal incidence on a photonic crystal slab • 3. Normal incidence on a Distributed Bragg mirror • 4. Normal incidence on a 1-D photonic crystal cavity

  2. 1. Simple dielectric slab Without slab Planewave source Slab (T=1a) With slab Detect

  3.  We will not use DS in this example  DD shouldn’t be this much long because the simple Fabry-Perot slab does not have a high-Q resonance. As we can see from the field data, DD may be set 4000.  (1,1) may be set (0.1, 0.1).  Gamma point periodic boundary condition. The use of the planewave source ensures that the result will be only for the exact kx=ky=0 point.

  4.  Two point detectors were set, one after the slab and the other between the planewave source and the slab

  5. ** How to obtain R & T spectra 1) We now have modeR.dat and modeT.dat 2) We must run another simulation in the absence of the dielectric slab. Then, we get modeR0.dat and modeT0.dat, which will be used as reference data. 3) Let’s denote modeR.dat = R(t) modeT.dat = T(t) modeR0.dat = R0(t) modeT0.dat = T0(t) Now let’s perform the following calculations. FT[ R(t)-R0(t) ] / FT[ R0(t)] = Refelctance spectrum in w FT[ T(t)] / FT[ T0(t)] = Transmission spectrum in w ,where FT denotes Fourier Transformation. (Important Node ) One must remember that the resolution of discrete FT will depend on the length of input data. We must add null values at the end of all ***.dat file before performing FT. I typically make the entire length of the input data file to be about 1 million (should be 2n format for accurate result)

  6. Result

  7. 2. Square lattice photonic crystal slab

  8.  We will not use DS in this example  In this example, DD should be carefully chosen. The 2-D photonic-crystal slab may contain very high-Q resonances(See the Fan’s paper)  You cannot change this (1,1)

  9.  Two point detectors were set, one after the slab and the other between the planewave source and the slab

  10. Result

  11. 3. Distributed Bragg Reflector PML PML GaAs AlAs z Planewave source 20 pairs of AlAs/GaAs Target wavelength = 950 nm Grid resolution ∆z = 2.5 nm Periodic boundary condition for x-y directions

  12.  We will not use DS in this example  In this example, DD should be carefully chosen. The time required to reach the steady-state could be longer than you initially thought.  You can change this as 0.1

  13.  In this example, we will only get reflectance spectrum

  14. Result

  15. m Exact FDTD 10 14 20 0.832424 0.83231 0.947996 0.94795 0.991636 0.99162 Accuracy Analytic expression (at the Bragg condition) Errors less than 1 part per 10,000 !

  16. 4. 1-D photonic-crystal cavity GaAs AlAs A cavity is formed by the two Bragg mirrors

  17. Result

  18. Single excitation (950nm) 3 QWs Ey field

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