The wg_parameterized photonic model is best suited for waveguide models which include parameters that affect the mode properties (effective and group index, loss, or dispersion). Some applications of this photonic model include:
- Straight waveguides parameterized by width
- Arced waveguides parameterized by radius of curvature
This photonic model is more complicated to use than the waveguide_simple photonic model, but is more flexible in the sense that it allows parameters which affect mode properties. Users modelling waveguides without mode-altering properties are advised to use the waveguide_simple photonic model, for simplicity's sake.
The wg_parameterized photonic model supports statistical modeling. Users can choose an arbitrary number of statistical parameters and define their influence on the effective index, group index, dispersion, and loss of the waveguide. For information on statistical CMLs, see Statistical CMLs.
This model also supports waveguides that include backscattering effects. This advanced model requires users to provide additional backscattering loss data. For more information on the backscattering model, see Waveguide Backscatter.
Lumfoundry Templates: Waveguide Straight (Parameterized), Waveguide Arc (Parameterized), Waveguide S-Bend (Parameterized), Waveguide Bend 90, Waveguide Straight (Parameterized, Statistical), Waveguide Backscatter
Quality Assurance Test: wg_parameterized QA
Statistically Enabled Parameters: neff, ng, D, loss
Supported Parameters: User defined
Tuning Support: No.
Interoperability with Cadence Virtuoso:
- Circuit design flows using INTERCONNECT model: Yes.
- Circuit design flow using photonic Verilog-A model: Yes ( not for statistical models).
Model Information
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Mode properties:
Given a waveguide with effective index as a function of angular frequency, we can express the propagation constant in a taylor expansion:
$$\beta (\omega) \equiv {\omega \over c} = \beta_0 + \beta_1 (\omega-\omega_0) + {1 \over 2} \beta_2 (\omega-\omega_2)^2 + \cdots$$
$$\beta_m \equiv {d^m\beta \over d\omega^m}\bracevert_{\omega=\omega_0}$$
The waveguide's group index and dispersion are defined in terms of the first and second order terms of this expansion:
$$n_g = c\beta_1 \approx n_{eff}-\lambda {dn_{eff} \over d\lambda} $$
$$D = - {2\pi c \over \lambda^2 } \beta_2 = {d\beta_1 \over d\lambda} \approx -{\lambda \over c} \cdot {d^2n_{eff} \over d\lambda^2}$$
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Backscatter waveguide model properties:
Once the backscatter waveguide model is compiled, the element will have the following properties:
The backscattering enabled (true/false) property allows the user to turn the backscattering on or off.
When the backscatter model is enabled, the backscatter reflections can be monitored from the input port of the waveguide. The through port of the waveguide will be modeled based on the transmission model selected. The options are:
- standard: the waveguide transmission will be the same as if there were no backscattering, (ie the transmission will look the same whether or not backscattering is enabled)
- enforce passivity: the waveguide transmission will be the same as if there were no backscattering but, if the sum of the reflection and transmission is greater than one (R+T > 1) at any wavelength, the waveguide loss will be increased to preserve passivity at all wavelengths
- scatter model: the waveguide transmission will also become noisy because the wavelength dependent backscattering will be accounted for in the transmission
The seed property is used for random number generation in the backscattering model.
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Backscatter waveguide model limitations:
Time domain simulations: The current model only supports frequency domain simulations. Time domain simulations are not supported.
Scattering events: The current model assumes only single scattering events (i.e., light that is backscattered will not undergo any further scattering). This is reasonable in most cases, but as the length of the waveguide increases, this approximation is less accurate.
Bidirectional behavior: The current model is bidirectional. However, note that the backscattering light will always be a reflection to the input, and does not undergo backscattering itself (i.e., light that has reflected/backscattered towards the input will not undergo backscattering and will not reflect towards the output).
Length recommendations: Based on the notes above, this model loses accuracy as the waveguide length increases. This inaccuracy primarily affects the transmission of the waveguide when using the scatter or enforce passivity models (described above). It is recommended that for long waveguides lengths (>1 cm), the transmission model be set to standard.
The following graph displays the transmission of the waveguide when the scatter model is used (total loss here is 100 dB/m). We see deviations from the expected behavior begin around 5 cm for the highest backscatter loss value.