# Lorentz

Lorentz defines a dispersive medium using Lorentz oscillator parameters.

This object corresponds to tidy3d.Lorentz (opens new window).

The Lorentz model represents bound charges in a material as damped harmonic oscillators driven by an electric field. For one oscillator, the microscopic picture is:

d2xdt2+γdxdt+ω02x=−qmE(t) \frac{d^2x}{dt^2} + \gamma\frac{dx}{dt} + \omega_0^2 x = -\frac{q}{m}E(t)

This oscillator picture maps directly to the GUI coefficients. Each row in coeffs adds one resonance to the material response: f is the resonance frequency, delta is the damping rate, and delta_eps controls how strongly that oscillator changes the permittivity. eps_inf adds the background relative permittivity away from the listed resonances.

The frequency dependence of the complex-valued permittivity is:

ϵ(f)=ϵ∞+∑iΔϵifi2fi2−2jfδi−f2 \epsilon(f) = \epsilon_\infty + \sum_i \frac{\Delta\epsilon_i f_i^2}{f_i^2 - 2jf\delta_i - f^2}

When the simulation frequency is near f, the oscillator response becomes strong, so the material permittivity changes rapidly with frequency and can become lossy. To learn more about the physical model, see the Lorentz oscillator model (opens new window).

# Name

name: Optional unique name for the medium.

# Type

type: Medium model used by this material entry.

  • Options: Lorentz

# Color

color: Display color used for the medium in the GUI.

  • Type: color
  • Default: automatically assigned by the GUI

# General Properties

coeffs: List of Lorentz oscillator coefficient rows.

  • Type: list of three-value coefficient rows
  • Required field

delta_eps: Oscillator strength, written as Δε in the GUI.

  • Type: float number
  • Unit: unitless
  • Required field

f: Resonance frequency.

  • Type: float number
  • Unit: Hz, kHz, MHz, GHz, THz, or other available frequency unit
  • Required field

delta: Damping rate, written as δ in the GUI.

  • Type: float number
  • Unit: Hz, kHz, MHz, GHz, THz, or other available frequency unit
  • Constraint: greater than or equal to 0
  • Required field

eps_inf: Relative permittivity at infinite frequency.

  • Type: float number
  • Unit: unitless
  • Constraint: greater than 0
  • Default: 1

# Advanced

set_from_global_frequency: Toggle whether the frequency range is set from the Global Settings frequency range.

  • Options:
    • True: Use the global frequency range and disable manual frequency range inputs.
    • False: Manually set frequency_range.

frequency_range: Optional range of validity for the medium.

  • Type: two float numbers
  • Unit: Hz, kHz, MHz, GHz, THz, or other available frequency unit
  • Default: None

allow_gain: Toggle whether the medium is allowed to be active.

  • Options: True/False
  • Default: False

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