Space-Time Modulation

In active nanophotonic devices such as electro-optical modulators, materials can be modulated in both space and time. In Tidy3D, space-time modulations can be applied to a regular Medium, or a dispersive medium such as Lorentz, or even a spatially varying medium such as CustomMedium.

To apply spatio-temporal modulations to permittivity and/or electric conductivity, you have to check the Space-Time Modulation option in medium definition. Then, expand the Permittivity and/or Conductivity menus to set the modulation parameters.

The full space-time modulation is $A(r, t) = Re[A_t(t) A_s(r)]$.

Time Modulation

Modulation with a harmonic time dependence. If you include modulation to both permittivity and electrical conductivity, the same time modulation parameters are applied.

The time modulation is given by $A_t(t) = A e^{i \phi - 2 \pi i f t}$.

freq0 ($f$): Modulation frequency.

Type: floating-point number

• Unit: Hz (default) or THz
• Constraint: greater than or equal 0
• Required field

amplitude ($A$): Real-valued maximum amplitude of the time dependence.

Type: floating-point number

• Unit: It takes the unit of whatever is being modulated.
• Constraint: greater than or equal 0
• Default: 1

phase ($\phi$): Phase shift of the time dependence.

Type: floating-point number

• Unit: rad or degree (default)
• Default: 0

Space Modulation

The modulation profile with a uniform or user-supplied spatial distribution of amplitude and phase. You can set different space modulation parameters to permittivity and electrical conductivity.

The space modulation is given by $A_s(r) = A_0(r) e^{i \psi(r)}$.

amplitude ($A_0$): Amplitude of space modulation. To obtain a uniform space modulation throughout the medium, set a real value in the edit box. Or upload a user-supplied amplitude distribution HDF5 dataset.

Type: floating-point number

• Unit: It takes the unit of whatever is being modulated.
• Constraint: greater than or equal 0
• Default: 1

To generate a HDF5 dataset in a correct shape, create a SpaceModulation (opens new window) object using the Python interface and use the to_hdf5(filename) (opens new window) method.

phase ($\psi$): Phase of space modulation. To obtain a uniform phase throughout the medium, set a real value in the edit box. Or upload a user-supplied phase distribution HDF5 dataset.

Type: floating-point number

• Unit: rad or degree (default)
• Default: 0

To generate a HDF5 dataset in a correct shape, create a SpaceModulation (opens new window) object using the Python interface and use the to_hdf5(filename) (opens new window) method.

interp_method: Interpolation method used to obtain the values at spatial locations on the Yee grid.

Options:

• nearest (default)
• linear

Notes

• Currently, these mediums DO NOT support space-time modulation:
  • PECMedium
  • Anisotropic Medium
  • Custom Anisotropic Medium
  • Fully Anisotropic Medium
  • Medium2D
• Make allow_gain=True to set space-time modulation for dispersive medium.
• Nonlinearity and Space-Time Modulation are not simultaneously supported.
• The value of $A(r, t)$ must be higher than medium permittivity.

Related Content:

• Applying time modulation to materials (opens new window)
• Modeling dispersive materials (opens new window)