Towards rigorous simulations of Kerr non-linear photonic components in frequency domain.ppt by malj

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									Comments about BEP
 Towards rigorous simulations of Kerr non-linear
   photonic components in frequency domain
Eigenmode expansion (BEP) for nonlinear structures?
             Didn’t you learn math?
       No problem for Kerr-nonlinearity, it’s just an iterative loop :)




                      Define refractive index profile




                            Linear calculation




                      Update refractive index profile
 Eigenmode expansion (BEP) for nonlinear structures?

Eigenmode expansion in each (linear) section               x


                                                           y   z




                                                 NL
                                               n changes
                                                   in z
                     Nonlinear sections are divided

Eigenmode expansion in each (linear) section                 x


                                                             y   z




                                                      NL
                                                 n changes
                                                     in z
              Nonlinear sections are divided


•   The main advantage of BEP, simple propagation in z-invariant
    sections, is lost
•   Suitable for complex structures with small number of short nonlinear
    sections.
•   For longer nonlinear structures it is probably better to use FEM (in the
    frequency domain) which is optimized for this task.
 Eigenmode expansion (BEP) for nonlinear structures?

Eigenmode expansion in each (linear) section                           x


                                                                       y   z




                                                            NL
                                                         n changes
                                                             in z




                                               The change is small (<1e-4).
                                               Couldn’t we use CMT?
                                               (Coupled Mode Theory)
                           Coupled Mode Theory

Eigenmode expansion in each (linear) section                 x


                                                             y   z




                                                   NL
                                                 n changes
                                                     in z
                   Zatím nevyřešené problémy

•   Jak určit S-matici nelineárního úseku?               x
     – přeformulovat vázané rovnice
        v rovnice pro jednotlivé složky                  y   z
        matice S, je více možností
     – ... ?
•   Pozor na součet velkých a malých čísel
•   Jak se změní S-matice na rozhraní?         NL
    (zatím změnu zanedbávám)                 n changes
                                                 in z
                              One-way technique

Eigenmode expansion in each (linear) section                  x


                                                              y   z




                                                    NL
                                                  n changes
                                                      in z
                           One-way technique

                                                            x


                                                            y   z




                                                  NL
                                                n changes
                                                    in z




- Simple solution using Runge-Kutta technique
- No iteration needed :D
- Reminiscent of BPM
Example: Nonlinear directional coupler




         FEM - Comsol RF module
Example: Nonlinear directional coupler




         FEM - Comsol RF module
Linear coupler




Nonlinear coupler




                    FEM - Comsol RF module
                 NL-BEP




Critical power
                 NL-BEP




Critical power
Example:
NL-BEP
                             Conclusions

:-) Principle of NL-BEP proposed.
:-) One-way technique successfully tested.
:-) Bidirectional technique under development.
         Example 1: Nonlinear plasmonic coupler

• two nonlinear dielectric slot waveguides with metallic
  claddings (silver at 480 nm)

  y

                 metal

 Pin      w     dielectric                             P1

          t

          w                                            P2


                                                           z
               Example 1: Nonlinear plasmonic coupler

         No loss                                   Loss




Calculation parameters:                           Coupling length decreases with loss
w = 0.06λ (λ = wavelength in vacuum), t = λ/10,
Pin = 0.1,
Pin = normalized input power = maximum of
nonlinear index change at the input
          Coupling length Lc




                                          Power at Lc of
                                          the linear device
                                          (Lc are different
                                          for each w/λ)

•   the loss significantly affects
    coupler behaviour
•   structure does not exhibit critical
    power
•   the nonlinear functionality
    (switching) is still possible
    Computational efficiency and comparison with FEM




•   NL-EME does not seem to converge for     •   Computational efficiency (memory
    (absurdly) high values of nonlinearity       requirement, speed) is one of the main
                                                 NL-EME advantages
•   For moderate nonlinearities good
    convergence and agreement with FEM       •   Computational time does not
    (COMSOL, RF module)                          significantly increase with nonlinearity
                                                 strength
•   Reasonable approximate results even
    with low number of modes used in the     •   Approximate calculations (low mode
    expansion                                    numbers) are extremely fast
               Example 2: Soliton-plasmon interaction

 nonlinear
 dielectric

 metal
(silver at 1500 nm)



The structure is
excited with
fundamental
spatial soliton                                              Psoliton

      P0
                                                        SPP may be
                D                                       created
(soliton position)
                                                             PSPP
                Example 2: Soliton-plasmon interaction
•   Conversion efficiency and coupling             Coupling length
    length strongly depend on soliton
    position D
•   The results do not appear to depend
    significantly on soliton amplitude nor
    propagation constant provided these
    parameters are near the resonance

                                         Soliton

                                                   Power at the
                                                   coupling length




                                        SPP
Example 3: Nonlinear cavity

								
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