ElectroAbsorptionModTimeStepper

ElectroAbsorptionModTimeStepper(
    *,
    absorption: photonforge.Interpolator,
    length: Annotated[float, exclusiveMinimum=0, units='μm'],
    confinement_factor: Annotated[float, maximum=1, minimum=0] = 1.0,
    bias: Annotated[float, units='V'] = 0.0,
    residual_loss: Annotated[float, minimum=0, units='dB'] = 0.0,
    chirp: float = 0.0,
    f_3dB: Annotated[
        Annotated[float, minimum=0, units='Hz'] | None, _
    ] = None,
    quantum_efficiency: Annotated[float, maximum=1, minimum=0] = 1.0,
    n_group: Annotated[float, minimum=0] = 0.0,
    voltage_samples: Annotated[int, minimum=2] = 401,
    z0: Annotated[complex, units='Ω'] | None = None,
    ports: Annotated[collections.abc.Sequence[str], maxItems=2, minItems=2]
    | None = None,
) -> None

Time-stepper for an electro-absorption modulator (EAM).

Reverse-biased absorbing waveguide driven by one electrical port. The absorption table is sliced at the carrier wavelength during setup, giving $\alpha(V)$, and the field transfer:

$$A_{\rm out} = A_{\rm in}\,10^{-L_0/20} \exp\!\left[-\frac{\Gamma\alpha(V)\ell}{2} \left(1 - j\alpha_c\right)\right]$$

Transmission is exponential in $\alpha$ while $\alpha(V)$ itself rises then saturates, so the transfer curve in dB is S-shaped. The phase term makes the instantaneous frequency of the output follow its power, $\delta\nu = (\alpha_c/4\pi)\,{\rm d}\ln P/{\rm d}t$.

The drive passes through an optional first-order low-pass representing the junction RC. Absorbed light produces photocurrent

$$I_{ph} = \eta\frac{q}{h\nu}P_{\rm in} \left(1 - e^{-\Gamma\alpha(V)\ell}\right)$$

emitted on the electrical port as $-I_{ph}\sqrt{\Re Z_0}$.

Args

• absorption: Material absorption in 1/μm, as an Interpolator over voltage and wavelength.
• length: Interaction length.
• confinement_factor: Fraction of the optical mode overlapping the absorbing region.
• bias: Constant bias, in V, added to the voltage read from the electrical port. Reverse bias is negative.
• residual_loss: Bias-independent insertion loss, in dB.
• chirp: Chirp parameter $\alpha_c$ as quoted on modulator datasheets: the output frequency deviates by $\delta\nu = (\alpha_c/4\pi)\,{\rm d}\ln P/{\rm d}t$. Positive values blue-shift the rising optical edge and red-shift the falling one.
• f_3dB: -3 dB cutoff of the junction RC low-pass on the drive. Only active for positive values.
• quantum_efficiency: Fraction of absorbed photons collected as photocurrent. Set to 0 to disable the photocurrent output.
• n_group: Group index for the optical transit delay. A value of 0 disables the delay.
• voltage_samples: Number of points used to resample alpha(V) at the carrier during setup. The original sample points are always kept, so this only adds fill between them.
• z0: Characteristic impedance of the electrical port, used to convert the input field amplitude to a voltage. If None, taken from the port spec impedance, else 50 Ohm.
• ports: Optical input and output port names, in that order. If not set, the sorted list of optical port names is used.

Important

The electrical input $A$ becomes a voltage through the port impedance, $V = \Re\{A\}\sqrt{\Re Z_0}$, and the applied bias is bias plus that voltage. Reverse bias is negative.

Important

chirp takes the value quoted on a datasheet unchanged, and it has the same sign convention as linewidth_enhancement_factor in the laser and semiconductor amplifier models: in every one of them a positive value shifts the light to higher frequency while its power rises. Values measured with the opposite sign convention must be negated.

Note

PhotonForge uses the $e^{-j\omega t}$ time convention, so an envelope $e^{-j2\pi\Delta f\,t}$ is light at $f_c + \Delta f$, with $f_c$ the carrier frequency. The instantaneous frequency deviation of an output envelope a is therefore $-(1/2\pi)\,{\rm d}\arg a/{\rm d}t$, for example -numpy.gradient(numpy.unwrap(numpy.angle(a)), time_step) / (2 * numpy.pi), and the frequency axis of a numpy.fft spectrum must be reversed.

Note

A single band at the carrier is assumed: the absorption edge varies over terahertz while the signal occupies tens of gigahertz, so $\alpha$ is evaluated once at the carrier wavelength. Absorption saturation from state filling is not modelled, and mode-solving for z0 is not supported here.

See Also

franz_keldysh_absorption can be used to generate absorption from tabular data.

Methods

Method	Description
bind_native	Bind a compiled step function.
reset	Reset internal state.
setup	Initialize the time stepper.
setup_state	Initialize internal state.
step	Compute the outputs of this time stepper, given inputs.
step_single	Take a single time step on the given inputs.
update	Update this time stepper.
write_verilog_a	Write this configured time stepper as one Verilog-A module.

bind_native

bind_native(self, step, keys, state=None, cstate=None, context=None)

Bind a compiled step function.

Instead of implementing step_single, a time stepper can hand the simulator the address of a C function with the signature:

int64 step(inputs, outputs, time_index, update_state, shutdown,
           context, state, cstate)

inputs and outputs are complex128 arrays with one entry per key, state and cstate are the float64 and complex128 arrays, and a nonzero return signals failure. The function must overwrite every element of outputs and only modify the state arrays when update_state is true. The arrays must not be reallocated after binding; reset restores them to the values given here, so a subclass overriding reset must call super().reset().

Calls with update_state false must give the same outputs: circuits may call the function several times in a time step, and setup checks this for steppers that declare path_delays. Random numbers must therefore come from a generator whose state lives in the arrays (e.g., a seed and a counter): output a draw kept there and draw the next one only when update_state is true, which also makes reset replay the stream. Do not use numpy.random in the function: numba draws it from a global stream that differs on every call and survives a reset.

The function can be compiled with numba (when available).

Args

• step (int | object): Address of the step function, or an object with an address attribute such as a numba cfunc.
• keys (Sequence[str]): Input/output keys.
• state (ndarray | None): Contiguous float64 array the function may use.
• cstate (ndarray | None): Contiguous complex128 array the function may use.
• context (int | None): Opaque pointer passed to the function.

Example

A two-port element that leaks the field entering its first port out of its second one:

>>> from numba import cfunc
>>> from photonforge.time_steppers import STEP_SIGNATURE
>>>
>>> @cfunc(STEP_SIGNATURE, cache=True)  # doctest: +SKIP
... def leaky_step(inputs, outputs, time_index, update_state,
...                shutdown, context, state, cstate):
...     # state[0]: decay per step
...     # cstate[0]: field leaving the second port
...     outputs[0] = 0j
...     outputs[1] = cstate[0] * state[0] + inputs[0]
...     if update_state:
...         cstate[0] = outputs[1]
...     return 0
...
>>> class LeakyTimeStepper(pf.TimeStepper):
...     def __init__(self, *, k=0.5):
...         super().__init__(k=k)
...
...     def setup_state(self, *, component, time_step, **kwargs):
...         keys = tuple(f"{p}@0" for p in sorted(component.ports))
...         state = numpy.array([
...             self.parametric_kwargs["k"] ** time_step
...         ])
...         self.bind_native(
...             leaky_step, keys, state, numpy.zeros(1, complex)
...         )
...
>>> pf.register_time_stepper_class(LeakyTimeStepper)

reset

reset(self) -> None

Reset internal state.

setup

setup(
    self,
    component,
    time_step,
    *,
    carrier_frequency=0,
    show_progress=True,
    **kwargs,
)

Initialize the time stepper.

Args

• component (Component): Component for the time stepper.
• time_step (float): The interval between time steps (in seconds).
• carrier_frequency (float): The carrier frequency used to construct the time stepper. The carrier should be omitted from the input signals, as it is handled automatically by the time stepper.
• show_progress (bool): If True, show setup progress.
• **kwargs (object): Keyword args forwarded to setup_state.

Returns

TimeStepper: This time stepper.

setup_state

setup_state(
    self,
    *,
    component: photonforge.Component,
    time_step: Annotated[float, minimum=0, units='s'],
    carrier_frequency: Annotated[float, minimum=0, units='Hz'],
    **kwargs: object,
) -> None

Initialize internal state.

Args

• component: Component representing the modulator.
• time_step: The interval between time steps (in seconds).
• carrier_frequency: Carrier frequency. Sets the wavelength at which the absorption table is sliced and the photon energy used for the photocurrent.
• kwargs: Unused.

step

step(self, inputs=None, steps=0, time_step=0, show_progress=True)

Compute the outputs of this time stepper, given inputs.

Args

• inputs (TimeSeries): Inputs to the time stepper.
• steps (int): The number of time steps to execute. If inputs is defined, this value is not used.
• time_step (float): The interval between time steps (in seconds). If inputs is a defined, this value is not used.
• show_progress (bool): If True, show computation progress.

Returns

TimeSeries: Computed outputs.

step_single

step_single(self, inputs, outputs, time_index, update_state, shutdown)

Take a single time step on the given inputs.

Important

Derived classes must implement this method unless they bind a compiled step with bind_native, in which case the default implementation calls it and, when shutdown is set, the optional _after_native_run hook.

The method takes the inputs as a numpy array of type complex with values in the order defined by keys. It advances a single time step, updating its internal state (if any) according to the update_state flag. It writes the outputs in-place to the pre-allocated, zero-initialized outputs array in the same order.

Args

• inputs (ndarray): Input values at the current time step. Must be a 1D array of complex values ordered according to keys.
• outputs (ndarray): Pre-allocated output array where results will be stored. Same size and type as inputs.
• time_index (int): Time series index for the current input.
• update_state (bool): Whether to update the internal stepper state.
• shutdown (bool): Whether this is the last call to the single stepping function for the original TimeSeries.

update

update(self, *args, **kwargs)

Update this time stepper.

All contents of the time stepper are updated with the contents from the updated version. Object contents or modifications introduced after the time stepper creation (outside of the original parametric function) are not propagated.

Args

• *args (object): Positional arguments to the parametric time stepper function.
• **kwargs (object): Keyword arguments to the parametric time stepper function.

Returns

TimeStepper: This time stepper.

Note

The original keyword arguments used to generate the time stepper are stored and updated with the passed kwargs. This updated version is used in the function call and will be stored for future updates. Positional arguments are not stored.

write_verilog_a

write_verilog_a(
    self,
    path,
    *,
    backend='openvaf',
    port_convention='travelling_wave',
    module_name=None,
    z0=50.0,
    field_impedance=None,
)

Write this configured time stepper as one Verilog-A module.

The time stepper must first be configured with setup or Component.setup_time_stepper. The writer creates source only; it does not compile the model or create a simulator deck. Requires a PhotonForge Photonic Canvas license.

Args

• path (str | os.PathLike): Destination .va file.
• backend (Literal[“openvaf”, “spectre”]): Compiler capability target recorded in the source.
• port_convention (Literal[“travelling_wave”, “gf_45spclo_npe”]): External optical port convention. GF packed ports require the Spectre backend.
• module_name (str | None): Module identifier derived from path when omitted.
• z0 (float): Travelling-wave optical reference impedance.
• field_impedance (float | None): GF electric-field scaling.

Returns

pathlib.Path: Absolute destination path.

Attributes

Attribute	Description
parametric_function	str: Function used to update the time stepper.
parametric_kwargs	dict[str, object]: Keyword arguments used to update the time stepper.
path_delays	dict[tuple[str, str], int] | None: Minimum delay in time steps of each (input key, output key) signal path; missing pairs have no path and None means every input reaches every output within the time step.
properties	Properties: Object properties.
random_variables	list[RandomVariable]: Random variables associated to the time stepper’s parameters.

parametric_function

str: Function used to update the time stepper.

parametric_kwargs

dict[str, object]: Keyword arguments used to update the time stepper.

path_delays

dict[tuple[str, str], int] | None: Minimum delay in time steps of each (input key, output key) signal path; missing pairs have no path and None means every input reaches every output within the time step.

properties

Properties: Object properties.

random_variables

list[RandomVariable]: Random variables associated to the time stepper’s parameters.