tidy3d.TwoPhotonAbsorption#

class TwoPhotonAbsorption[source]#

Bases: NonlinearModel

Model for two-photon absorption (TPA) nonlinearity which gives an intensity-dependent absorption of the form $\alpha ={\alpha }_0+\beta I$. Also includes free-carrier absorption (FCA) and free-carrier plasma dispersion (FCPD) effects. The expression for the nonlinear polarization is given below.

Parameters:

• beta (Union[float, tidycomplex, ComplexNumber] = 0) – [units = um / W]. Coefficient for two-photon absorption (TPA).

• tau (NonNegativeFloat = 0) – [units = sec]. Lifetime for the free carriers created by two-photon absorption (TPA).

• sigma (NonNegativeFloat = 0) – [units = um^2]. Total cross section for free-carrier absorption (FCA). Contains contributions from electrons and from holes.

• e_e (NonNegativeFloat = 1) – Exponent for the free electron refractive index shift in the free-carrier plasma dispersion (FCPD).

• e_h (NonNegativeFloat = 1) – Exponent for the free hole refractive index shift in the free-carrier plasma dispersion (FCPD).

• c_e (float = 0) – [units = um^(3 e_e)]. Coefficient for the free electron refractive index shift in the free-carrier plasma dispersion (FCPD).

• c_h (float = 0) – [units = um^(3 e_h)]. Coefficient for the free hole refractive index shift in the free-carrier plasma dispersion (FCPD).

• n0 (Union[tidycomplex, ComplexNumber, NoneType] = None) – Complex linear refractive index of the medium, computed for instance using ‘medium.nk_model’. If not provided, it is calculated automatically using the central frequencies of the simulation sources (as long as these are all equal).

• freq0 (Optional[PositiveFloat] = None) – Central frequency, used to calculate the energy of the free-carriers excited by two-photon absorption. If not provided, it is obtained automatically from the simulation sources (as long as these are all equal).

Note

$$\begin{array}{r}{P}_{NL}=P_{TPA}+P_{FCA}+P_{FCPD}\\ P_{TPA}=-\frac{c_0^2{\epsilon }_0^2{n}_0\mathrm{Re}(n_0)\beta }{2i\omega }|E{|}^{2}E\\ P_{FCA}=-\frac{c_0{\epsilon }_0{n}_0\sigma N_f}{i\omega }E\\ \frac{d{N}_f}{dt}=\frac{c_0^2{\epsilon }_0^2{n}_0^2\beta }{8q_e\hslash \omega }|E{|}^4-\frac{N_f}{\tau }\\ N_e=N_h=N_f\\ P_{FCPD}={\epsilon }_{0}2n_0\mathrm{\Delta }n(N_f)E\\ \mathrm{\Delta }n(N_f)=(c_e{N}_e^{e_e}+c_h{N}_h^{e_h})\end{array}$$

Note

This frequency-domain equation is implemented in the time domain using complex-valued fields.

Note

Different field components do not interact nonlinearly. For example, when calculating $P_{NL,x}$, we approximate $|E{|}^2\approx |E_x{|}^2$. This approximation is valid when the E field is predominantly polarized along one of the x, y, or z axes.

Note

The implementation is described in:

N. Suzuki, "FDTD Analysis of Two-Photon Absorption and Free-Carrier Absorption in Si
High-Index-Contrast Waveguides," J. Light. Technol. 25, 9 (2007).

Example

>>> tpa_model = TwoPhotonAbsorption(beta=1)

Attributes

complex_fields

Whether the model uses complex fields.

Methods

beta#

tau#

sigma#

e_e#

e_h#

c_e#

c_h#

n0#

freq0#

property complex_fields#

Whether the model uses complex fields.

__hash__()#

Hash method.