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S + Autograd + XLA :: S-parameter based frequency domain circuit simulations and optimizations using JAX.

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# SAX

> 0.18.2

![SAX LOGO](https://raw.githubusercontent.com/gdsfactory/sax/main/docs/assets/logo.svg)

SAX: S-Matrices with Autograd and XLA - a scatter parameter circuit simulator and
optimizer for the frequency domain based on [JAX](https://github.com/google/jax).

The simulator was developed for simulating Photonic Integrated Circuits but in fact is
able to perform any S-parameter based circuit simulation. The goal of SAX is to be a
thin wrapper around JAX with some basic tools for S-parameter based circuit simulation
and optimization. Therefore, SAX does not define any special datastructures and tries to
stay as close as possible to the functional nature of JAX. This makes it very easy to
get started with SAX as you only need functions and standard python dictionaries. Let's
dive in...

## Quick Start

[Full Quick Start page](https://gdsfactory.github.io/sax/nbs/examples/01_quick_start) - [Documentation](https://gdsfactory.github.io/sax).

Let's first import the SAX library, along with JAX and the JAX-version of numpy:

```python
import sax
import jax
import jax.numpy as jnp
```

Define a model function for your component. A SAX model is just a function that returns
an 'S-dictionary'. For example a directional coupler:

```python
def coupler(coupling=0.5):
    kappa = coupling**0.5
    tau = (1-coupling)**0.5
    sdict = sax.reciprocal({
        ("in0", "out0"): tau,
        ("in0", "out1"): 1j*kappa,
        ("in1", "out0"): 1j*kappa,
        ("in1", "out1"): tau,
    })
    return sdict

coupler(coupling=0.3)
```

{('in0', 'out0'): 0.8366600265340756,
     ('in0', 'out1'): 0.5477225575051661j,
     ('in1', 'out0'): 0.5477225575051661j,
     ('in1', 'out1'): 0.8366600265340756,
     ('out0', 'in0'): 0.8366600265340756,
     ('out1', 'in0'): 0.5477225575051661j,
     ('out0', 'in1'): 0.5477225575051661j,
     ('out1', 'in1'): 0.8366600265340756}

Or a waveguide:

```python
def waveguide(wl=1.55, wl0=1.55, neff=2.34, ng=3.4, length=10.0, loss=0.0):
    dwl = wl - wl0
    dneff_dwl = (ng - neff) / wl0
    neff = neff - dwl * dneff_dwl
    phase = 2 * jnp.pi * neff * length / wl
    amplitude = jnp.asarray(10 ** (-loss * length / 20), dtype=complex)
    transmission =  amplitude * jnp.exp(1j * phase)
    sdict = sax.reciprocal({("in0", "out0"): transmission})
    return sdict

waveguide(length=100.0)
```

{('in0', 'out0'): 0.97953-0.2013j, ('out0', 'in0'): 0.97953-0.2013j}

These component models can then be combined into a circuit:

```python
mzi, _ = sax.circuit(
    netlist={
        "instances": {
            "lft": coupler,
            "top": waveguide,
            "rgt": coupler,
        },
        "connections": {
            "lft,out0": "rgt,in0",
            "lft,out1": "top,in0",
            "top,out0": "rgt,in1",
        },
        "ports": {
            "in0": "lft,in0",
            "in1": "lft,in1",
            "out0": "rgt,out0",
            "out1": "rgt,out1",
        },
    }
)

type(mzi)
```

function

As you can see, the mzi we just created is just another component model function! To simulate it, call the mzi function with the (possibly nested) settings of its subcomponents. Global settings can be added to the 'root' of the circuit call and will be distributed over all subcomponents which have a parameter with the same name (e.g. 'wl'):

```python
wl = jnp.linspace(1.53, 1.57, 1000)
result = mzi(wl=wl, lft={'coupling': 0.3}, top={'length': 200.0}, rgt={'coupling': 0.8})

plt.plot(1e3*wl, jnp.abs(result['in0', 'out0'])**2, label="in0->out0")
plt.plot(1e3*wl, jnp.abs(result['in0', 'out1'])**2, label="in0->out1", ls="--")
plt.xlabel("λ [nm]")
plt.ylabel("T")
plt.grid(True)
plt.figlegend(ncol=2, loc="upper center")
plt.show()
```

![output](https://raw.githubusercontent.com/gdsfactory/sax/main/docs/assets/output_10_0.png)

Those are the basics. For more info, check out the **full**
[SAX Quick Start page](https://gdsfactory.github.io/sax/nbs/examples/01_quick_start) or the rest of the [Documentation](https://gdsfactory.github.io/sax).

## Installation

You can install SAX with pip:

```sh
pip install sax
```

If you want to be able to run all the example notebooks, you'll need python>=3.10 and
you should install the development version of SAX:

```sh
pip install 'sax[dev]'
```

## License

sax

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