From 6a4cae3f628769798f238c782a1fbe80dc5ea3a1 Mon Sep 17 00:00:00 2001 From: Ardavan Oskooi Date: Sun, 9 Aug 2020 17:20:44 -0700 Subject: [PATCH 1/7] Python interface for Gaussian beam source --- python/meep.i | 12 ++++++++++++ python/simulation.py | 30 ++++++++++++++++++++++++++++-- python/source.py | 36 ++++++++++++++++++++++++++++++++++++ 3 files changed, 76 insertions(+), 2 deletions(-) diff --git a/python/meep.i b/python/meep.i index 8ab010cd9..efb35fe73 100644 --- a/python/meep.i +++ b/python/meep.i @@ -1029,6 +1029,17 @@ void _get_gradient(PyObject *grad, PyObject *fields_a, PyObject *fields_f, PyObj } +// typemaps for gaussianbeam + +%typecheck(SWIG_TYPECHECK_POINTER, fragment="NumPy_Fragments") std::complex beam_E0[3] { + $1 = is_array($input); +} + +%typemap(in) std::complex beam_E0[3] { + std::complex *pyE0 = (std::complex *)array_data($input); + $1[0] = pyE0[0]; $1[1] = pyE0[1]; $1[2] = pyE0[2]; +} + //-------------------------------------------------- // typemaps needed for get_eigenmode_coefficients //-------------------------------------------------- @@ -1648,6 +1659,7 @@ PyObject *_get_array_slice_dimensions(meep::fields *f, const meep::volume &where Source, SourceTime, check_positive, + GaussianBeamSource, ) from .visualization import ( plot2D, diff --git a/python/simulation.py b/python/simulation.py index 6c3f80859..e6fe610a6 100644 --- a/python/simulation.py +++ b/python/simulation.py @@ -18,7 +18,7 @@ import meep as mp from meep.geom import Vector3, init_do_averaging -from meep.source import EigenModeSource, check_positive +from meep.source import EigenModeSource, GaussianBeamSource, check_positive import meep.visualization as vis from meep.verbosity_mgr import Verbosity @@ -1997,7 +1997,7 @@ def get_epsilon_point(self, pt, frequency=0, omega=0): Given a frequency `frequency` and a `Vector3` `pt`, returns the average eigenvalue of the permittivity tensor at that location and frequency. If `frequency` is non-zero, the result is complex valued; otherwise it is the real, - frequency-independent part of ε (the $\\omega\\to\\infty$ limit). + frequency-independent part of $\\varepsilon$ (the $\\omega\\to\\infty$ limit). """ v3 = py_v3_to_vec(self.dimensions, pt, self.is_cylindrical) if omega != 0: @@ -2005,6 +2005,19 @@ def get_epsilon_point(self, pt, frequency=0, omega=0): warnings.warn("get_epsilon_point: omega has been deprecated; use frequency instead", RuntimeWarning) return self.fields.get_eps(v3,frequency) + def get_mu_point(self, pt, frequency=0, omega=0): + """ + Given a frequency `frequency` and a `Vector3` `pt`, returns the average eigenvalue + of the permeability tensor at that location and frequency. If `frequency` is + non-zero, the result is complex valued; otherwise it is the real, + frequency-independent part of $\\mu$ (the $\\omega\\to\\infty$ limit). + """ + v3 = py_v3_to_vec(self.dimensions, pt, self.is_cylindrical) + if omega != 0: + frequency = omega + warnings.warn("get_mu_point: omega has been deprecated; use frequency instead", RuntimeWarning) + return self.fields.get_mu(v3,frequency) + def get_filename_prefix(self): """ Return the current prefix string that is prepended, by default, to all file names. @@ -2234,6 +2247,19 @@ def add_source(self, src): add_eig_src() else: add_eig_src(src.amp_func) + elif isinstance (src, GaussianBeamSource): + gaussianbeam_args = [ + py_v3_to_vec(self.dimensions, src.beam_x0, is_cylindrical=self.is_cylindrical), + py_v3_to_vec(self.dimensions, src.beam_kdir, is_cylindrical=self.is_cylindrical), + src.beam_w0, + src.src.swigobj.frequency().real, + get_epsilon_point(src.center), + get_mu_point(src.center), + [src.beam_E0.x, src.beam_E0.y, src.beam_E0.z] + ] + gaussianbeam = functools.partial(self.gaussianbeam, *gaussianbeam_args) + add_vol_src_args = [src.component, src.src.swigobj, where, gaussianbeam] + add_vol_src = functools.partial(self.fields.add_volume_source, *add_vol_src_args) else: add_vol_src_args = [src.component, src.src.swigobj, where] add_vol_src = functools.partial(self.fields.add_volume_source, *add_vol_src_args) diff --git a/python/source.py b/python/source.py index ea5c34fc8..2d54fd2f0 100644 --- a/python/source.py +++ b/python/source.py @@ -526,3 +526,39 @@ def eig_power(self,freq): if callable(getattr(self.src, "fourier_transform", None)): amp *= self.src.fourier_transform(freq) return abs(amp)**2 + + +class GaussianBeamSource(Source): + + def __init__(self, + src, + center=None, + volume=None, + component=mp.ALL_COMPONENTS, + beam_x0=Vector3(), + beam_kdir=Vector3(), + beam_w0=None, + beam_E0=Vector3(), + **kwargs): + + super(GaussianBeamSource, self).__init__(src, component, center, volume, **kwargs) + self.beam_x0 = beam_x0 + self.beam_kdir = beam_kdir + self.beam_w0 = beam_w0 + self.beam_E0 = beam_E0 + + @property + def beam_x0(self): + return self._beam_x0 + + @property + def beam_kdir(self): + return self._beam_kdir + + @property + def beam_w0(self): + return self._beam_w0 + + @property + def E0(self): + return Vector3(self._beam_E0[0],self._beam_E0[1],self._beam_E0[2]) From 2d38f78307c51e5666e32e8a31757e5b92b83c90 Mon Sep 17 00:00:00 2001 From: Ardavan Oskooi Date: Sun, 9 Aug 2020 22:20:36 -0700 Subject: [PATCH 2/7] create gaussianbeam object in Python using functools.partial --- python/meep.i | 4 ++-- python/simulation.py | 9 +++++---- python/source.py | 12 ++++++------ 3 files changed, 13 insertions(+), 12 deletions(-) diff --git a/python/meep.i b/python/meep.i index efb35fe73..79d3966d0 100644 --- a/python/meep.i +++ b/python/meep.i @@ -1031,11 +1031,11 @@ void _get_gradient(PyObject *grad, PyObject *fields_a, PyObject *fields_f, PyObj // typemaps for gaussianbeam -%typecheck(SWIG_TYPECHECK_POINTER, fragment="NumPy_Fragments") std::complex beam_E0[3] { +%typecheck(SWIG_TYPECHECK_POINTER, fragment="NumPy_Fragments") std::complex E0[3] { $1 = is_array($input); } -%typemap(in) std::complex beam_E0[3] { +%typemap(in) std::complex E0[3] { std::complex *pyE0 = (std::complex *)array_data($input); $1[0] = pyE0[0]; $1[1] = pyE0[1]; $1[2] = pyE0[2]; } diff --git a/python/simulation.py b/python/simulation.py index e6fe610a6..3f311fe7c 100644 --- a/python/simulation.py +++ b/python/simulation.py @@ -2253,13 +2253,14 @@ def add_source(self, src): py_v3_to_vec(self.dimensions, src.beam_kdir, is_cylindrical=self.is_cylindrical), src.beam_w0, src.src.swigobj.frequency().real, - get_epsilon_point(src.center), - get_mu_point(src.center), + self.fields.get_eps(py_v3_to_vec(self.dimensions, src.center, self.is_cylindrical)).real, + self.fields.get_mu(py_v3_to_vec(self.dimensions, src.center, self.is_cylindrical)).real, [src.beam_E0.x, src.beam_E0.y, src.beam_E0.z] ] - gaussianbeam = functools.partial(self.gaussianbeam, *gaussianbeam_args) - add_vol_src_args = [src.component, src.src.swigobj, where, gaussianbeam] + gaussianbeam = functools.partial(mp.gaussianbeam, *gaussianbeam_args) + add_vol_src_args = [src.src.swigobj, where, gaussianbeam()] add_vol_src = functools.partial(self.fields.add_volume_source, *add_vol_src_args) + add_vol_src() else: add_vol_src_args = [src.component, src.src.swigobj, where] add_vol_src = functools.partial(self.fields.add_volume_source, *add_vol_src_args) diff --git a/python/source.py b/python/source.py index 2d54fd2f0..960b1f0d1 100644 --- a/python/source.py +++ b/python/source.py @@ -542,10 +542,10 @@ def __init__(self, **kwargs): super(GaussianBeamSource, self).__init__(src, component, center, volume, **kwargs) - self.beam_x0 = beam_x0 - self.beam_kdir = beam_kdir - self.beam_w0 = beam_w0 - self.beam_E0 = beam_E0 + self._beam_x0 = beam_x0 + self._beam_kdir = beam_kdir + self._beam_w0 = beam_w0 + self._beam_E0 = beam_E0 @property def beam_x0(self): @@ -560,5 +560,5 @@ def beam_w0(self): return self._beam_w0 @property - def E0(self): - return Vector3(self._beam_E0[0],self._beam_E0[1],self._beam_E0[2]) + def beam_E0(self): + return self._beam_E0 From e27dd59cd859fc4de87d75876330126073e043eb Mon Sep 17 00:00:00 2001 From: Ardavan Oskooi Date: Mon, 10 Aug 2020 10:16:45 -0700 Subject: [PATCH 3/7] rename gaussianbeam constructor argument EO to E0 --- python/meep.i | 1 - python/simulation.py | 4 ++-- src/meep.hpp | 2 +- 3 files changed, 3 insertions(+), 4 deletions(-) diff --git a/python/meep.i b/python/meep.i index 79d3966d0..6002d465d 100644 --- a/python/meep.i +++ b/python/meep.i @@ -1028,7 +1028,6 @@ void _get_gradient(PyObject *grad, PyObject *fields_a, PyObject *fields_f, PyObj $1 = (std::complex *)array_data($input); } - // typemaps for gaussianbeam %typecheck(SWIG_TYPECHECK_POINTER, fragment="NumPy_Fragments") std::complex E0[3] { diff --git a/python/simulation.py b/python/simulation.py index 3f311fe7c..4f26aee76 100644 --- a/python/simulation.py +++ b/python/simulation.py @@ -2257,8 +2257,8 @@ def add_source(self, src): self.fields.get_mu(py_v3_to_vec(self.dimensions, src.center, self.is_cylindrical)).real, [src.beam_E0.x, src.beam_E0.y, src.beam_E0.z] ] - gaussianbeam = functools.partial(mp.gaussianbeam, *gaussianbeam_args) - add_vol_src_args = [src.src.swigobj, where, gaussianbeam()] + gaussianbeam = mp.gaussianbeam(*gaussianbeam_args) + add_vol_src_args = [src.src.swigobj, where, gaussianbeam] add_vol_src = functools.partial(self.fields.add_volume_source, *add_vol_src_args) add_vol_src() else: diff --git a/src/meep.hpp b/src/meep.hpp index 74b0464a4..f8fd74efa 100644 --- a/src/meep.hpp +++ b/src/meep.hpp @@ -1488,7 +1488,7 @@ class gaussianbeam { public: gaussianbeam(const vec &x0, const vec &kdir, double w0, double freq, - double eps, double mu, std::complex EO[3]); + double eps, double mu, std::complex E0[3]); void get_fields(std::complex *EH, const vec &x) const; std::complex get_E0(int n) const { return E0[n]; }; From 9f2d2b4dd5a3d54be3ba95c6040b98f77caba9c3 Mon Sep 17 00:00:00 2001 From: Ardavan Oskooi Date: Mon, 10 Aug 2020 11:02:34 -0700 Subject: [PATCH 4/7] pass E0 from Python as NumPy array --- python/meep.i | 3 +-- python/simulation.py | 2 +- 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/python/meep.i b/python/meep.i index 6002d465d..0b1d2fab2 100644 --- a/python/meep.i +++ b/python/meep.i @@ -1035,8 +1035,7 @@ void _get_gradient(PyObject *grad, PyObject *fields_a, PyObject *fields_f, PyObj } %typemap(in) std::complex E0[3] { - std::complex *pyE0 = (std::complex *)array_data($input); - $1[0] = pyE0[0]; $1[1] = pyE0[1]; $1[2] = pyE0[2]; + $1 = (std::complex *)array_data($input); } //-------------------------------------------------- diff --git a/python/simulation.py b/python/simulation.py index 4f26aee76..41838eb82 100644 --- a/python/simulation.py +++ b/python/simulation.py @@ -2255,7 +2255,7 @@ def add_source(self, src): src.src.swigobj.frequency().real, self.fields.get_eps(py_v3_to_vec(self.dimensions, src.center, self.is_cylindrical)).real, self.fields.get_mu(py_v3_to_vec(self.dimensions, src.center, self.is_cylindrical)).real, - [src.beam_E0.x, src.beam_E0.y, src.beam_E0.z] + np.array([src.beam_E0.x, src.beam_E0.y, src.beam_E0.z], dtype=np.complex128) ] gaussianbeam = mp.gaussianbeam(*gaussianbeam_args) add_vol_src_args = [src.src.swigobj, where, gaussianbeam] From 21b7e94e0ef9daf4cdc1a5130645c1cf4ab328b1 Mon Sep 17 00:00:00 2001 From: Ardavan Oskooi Date: Tue, 11 Aug 2020 17:09:24 -0700 Subject: [PATCH 5/7] add documentation, tutorial example, and test (Python) --- doc/docs/FAQ.md | 6 +-- doc/docs/Python_User_Interface.md | 53 +++++++++++++++++++++++- doc/docs/images/gaussian_beam.png | Bin 208285 -> 226313 bytes python/Makefile.am | 1 + python/examples/gaussian-beam.py | 66 ++++++++++++++---------------- python/source.py | 18 ++++++++ python/tests/gaussianbeam.py | 62 ++++++++++++++++++++++++++++ 7 files changed, 165 insertions(+), 41 deletions(-) create mode 100644 python/tests/gaussianbeam.py diff --git a/doc/docs/FAQ.md b/doc/docs/FAQ.md index 173d063bb..fe52c91cb 100644 --- a/doc/docs/FAQ.md +++ b/doc/docs/FAQ.md @@ -142,15 +142,13 @@ For an example of the second approach, see [Tutorial/Eigenmode Source/Planewaves ### How do I create a focused beam with a Gaussian envelope? -A focused beam with a Gaussian envelope can be created using the amplitude function (`amp_func`) of the [`Source`](Python_User_Interface.md#source) object. Examples are provided for [Python](https://github.com/NanoComp/meep/blob/master/python/examples/gaussian-beam.py) and [Scheme](https://github.com/NanoComp/meep/blob/master/scheme/examples/gaussian-beam.ctl). Four snapshots of the resulting field profile generated using this script for different values of the beam width (`sigma`) and rotation angle (`tilt_angle`) are shown in the following image: +A focused beam with a Gaussian envelope can be created using the [`GaussianBeamSource`](Python_User_Interface.md#gaussianbeamsource) as demonstrated in this [script](https://github.com/NanoComp/meep/blob/master/python/examples/gaussian-beam.py). The following are four snapshots of the resulting field profile generated using a line source (red line) in 2d for different values of the beam waist radius/width $w_0$ (`beam_w0`), propagation direction $\vec{k}$ (`beam_kdir`), and focus (`beam_x0`):
![](images/gaussian_beam.png)
-Beams in a homogeneous material do not have a fixed width in Maxwell's equations; they always spread out during propagation. The [numerical aperture (NA)](https://en.wikipedia.org/wiki/Gaussian_beam#Beam_divergence) of a Gaussian beam of width w (2*`sigma` from the example script) and vacuum wavelength $\lambda$ in a medium of index $n$ is $n\sin(\lambda/(\pi nw))$. - -Note: in this example, the beam waist is at the source position (i.e., top center of the cell). If you want the beam waist to be at a position other than the position of the source, you need to adjust the *phase* of the beam accordingly. If you assume you have a Gaussian beam profile with zero phase at some plane $y=y_0$, then you can work out the beam profile (including phase) at any other plane $y=y_1$ by taking the Fourier transform and looking at the propagation of each planewave component, and then inverse Fourier transforming. In this way, you can work out the desired source profile at any plane $y=y_1$ to get a Gaussian beam waist at $y=y_0$. +Note: beams in a homogeneous material do *not* have a fixed width in Maxwell's equations; they always spread out during propagation (i.e., diffraction). The [numerical aperture (NA)](https://en.wikipedia.org/wiki/Gaussian_beam#Beam_divergence) of a Gaussian beam with waist radius $w$ and vacuum wavelength $\lambda$ within a medium of index $n$ is $n\sin(\lambda/(\pi nw))$. ### How do I create a circularly polarized planewave source in cylindrical coordinates? diff --git a/doc/docs/Python_User_Interface.md b/doc/docs/Python_User_Interface.md index be4e2f6d4..a310cba98 100644 --- a/doc/docs/Python_User_Interface.md +++ b/doc/docs/Python_User_Interface.md @@ -5832,7 +5832,7 @@ it does support anisotropic ε. Any nonlinearities, magnetic responses μ, conductivities σ, or dispersive polarizations in your materials will be *ignored* when computing the eigenmode source. PML will also be ignored. -The `src_time` object (`Source.src`), which specifies the time dependence of the +The `SourceTime` object (`Source.src`), which specifies the time dependence of the source, can be one of `ContinuousSource`, `GaussianSource` or `CustomSource`. @@ -5961,6 +5961,57 @@ Returns the total power of the fields from the eigenmode source at frequency `fr + +--- + + +### GaussianBeamSource + +```python +class GaussianBeamSource(Source): +``` + +
+ +This is a subclass of `Source` and has **all of the properties** of `Source` above. However, the `component` parameter of the `Source` object is ignored. The [Gaussian beam](https://en.wikipedia.org/wiki/Gaussian_beam) is a transverse electromagnetic mode for which the source region must be a *line* (in 2d) or *plane* (in 3d). For a beam polarized in the $x$ direction with propagation along $+z$, the electric field is defined by $\mathbf{E}(r,z)=E_0\hat{x}\frac{w_0}{w(z)}\exp\left(\frac{-r^2}{w(z)^2}\right)\exp\left(-i\left(kz + k\frac{r^2}{2R(z)}\right)\right)$ where $r$ is the radial distance from the center axis of the beam, $z$ is the axial distance from the beam's focus (or "waist"), $k=2\pi n/\lambda$ is the wavenumber (for a free-space wavelength $\lambda$ and refractive index $n$ of the homogeneous, lossless medium in which the beam propagates), $E_0$ is the electric field amplitude at the origin, $w(z)$ is the radius at which the field amplitude decays by $1/e$ of its axial values, $w_0$ is the beam waist radius, and $R(z)$ is the radius of curvature of the beam's wavefront at $z$. The only independent parameters that need to be specified are $w_0$, $E_0$, $k$, and the location of the beam focus (i.e., the origin: $r=z=0$). + +The `SourceTime` object (`Source.src`), which specifies the time dependence of the source, can be one of `ContinuousSource` or `GaussianSource`. + +
+ + + +
+ +```python +def __init__(self, + src, + center=None, + volume=None, + component=mp.ALL_COMPONENTS, + beam_x0=Vector3(), + beam_kdir=Vector3(), + beam_w0=None, + beam_E0=Vector3(), + **kwargs): +``` + +
+ +Construct a `GaussianBeamSource`. + ++ **`beam_x0` [`Vector3`]** — The location of the beam focus *relative* to the center of the source. This does *not* need to lie within the source region (i.e., the beam focus can be anywhere, inside or outside the cell, independent of position of the source). + ++ **`beam_kdir` [`Vector3`]** — The propagation direction of the beam. The length is *ignored*. The wavelength of the beam is determined by the center frequency of the `Source.src` object and the refractive index of the homogeneous medium by its value at the center of the source region. + ++ **`beam_w0` [`number`]** — The beam waist radius. + ++ **`beam_E0` [`Vector3`]** — The polarization vector of the beam. Elements can be complex valued (i.e., for circular polarization). The polarization vector must be *parallel* to the source region in order to generate a transverse mode. + +
+ +
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a/python/examples/gaussian-beam.py +++ b/python/examples/gaussian-beam.py @@ -1,48 +1,42 @@ -## generate a titled Gaussian beam profile by defining the amplitude function of the source +## launch a Gaussian beam import meep as mp import math -import cmath -import numpy as np +import matplotlib +matplotlib.use('agg') import matplotlib.pyplot as plt -resolution = 40 # pixels/μm +s = 14 +resolution = 50 +dpml = 2 -cell_size = mp.Vector3(20,10,0) +cell_size = mp.Vector3(s,s) -pml_layers = [mp.PML(thickness=1.0,direction=mp.Y)] +boundary_layers = [mp.PML(thickness=dpml)] -fcen = 1.0 # center frequency of CW source (wavelength is 1 μm) +beam_x0 = mp.Vector3(0,3.0) # beam focus (relative to source center) +rot_angle = 0 # CCW rotation angle about z axis (0: +y axis) +beam_kdir = mp.Vector3(0,1,0).rotate(mp.Vector3(0,0,1),math.radians(rot_angle)) # beam propagation direction +beam_w0 = 0.8 # beam waist radius +beam_E0 = mp.Vector3(0,0,1) +fcen = 1 +sources = [mp.GaussianBeamSource(src=mp.ContinuousSource(fcen), + center=mp.Vector3(0,-0.5*s+dpml+1.0), + size=mp.Vector3(s), + beam_x0=beam_x0, + beam_kdir=beam_kdir, + beam_w0=beam_w0, + beam_E0=beam_E0)] -tilt_angle = math.radians(-10) # angle of tilted beam -k = mp.Vector3(y=1).rotate(mp.Vector3(z=1),tilt_angle).scale(fcen) +sim = mp.Simulation(resolution=resolution, + cell_size=cell_size, + boundary_layers=boundary_layers, + sources=sources) -sigma = 1.5 # beam width +sim.run(until=20) -def gaussian_beam(sigma, k, x0): - def _gaussian_beam(x): - return cmath.exp(1j*2*math.pi*k.dot(x-x0)-(x-x0).dot(x-x0)/(2*sigma**2)) - return _gaussian_beam +sim.plot2D(fields=mp.Ez, + output_plane=mp.Volume(center=mp.Vector3(), + size=mp.Vector3(s-2*dpml,s-2*dpml))) -src_pt = mp.Vector3(y=4) -sources = [mp.Source(src=mp.ContinuousSource(fcen, fwidth=0.2*fcen), - component=mp.Ez, - center=src_pt, - size=mp.Vector3(20), - amp_func=gaussian_beam(sigma,k,src_pt))] - -sim = mp.Simulation(cell_size=cell_size, - sources=sources, - k_point=k, - boundary_layers=pml_layers, - resolution=resolution) - -non_pml_vol = mp.Volume(center=mp.Vector3(), size=mp.Vector3(20,8,0)) -sim.run(until=50) - -ez_data = sim.get_array(vol=non_pml_vol, component=mp.Ez) - -plt.figure() -plt.imshow(np.flipud(np.transpose(np.real(ez_data))), interpolation='spline36', cmap='RdBu') -plt.axis('off') -plt.show() +plt.savefig('Ez_angle{}.png'.format(rot_angle),bbox_inches='tight',pad_inches=0) diff --git a/python/source.py b/python/source.py index 960b1f0d1..ae3cbea10 100644 --- a/python/source.py +++ b/python/source.py @@ -529,6 +529,13 @@ def eig_power(self,freq): class GaussianBeamSource(Source): + """ + This is a subclass of `Source` and has **all of the properties** of `Source` above. + + The [Gaussian beam](https://en.wikipedia.org/wiki/Gaussian_beam) is a transverse electromagnetic mode for which the source region *must* be a line in 2d or plane in 3d. For a beam polarized in the $x$ direction with propagation along $+z$, the electric field is defined by $\\mathbf{E}(r,z)=E_0\\hat{x}\\frac{w_0}{w(z)}\\exp\\left(\\frac{-r^2}{w(z)^2}\\right)\\exp\\left(-i\\left(kz + k\\frac{r^2}{2R(z)}\\right)\\right)$ where $r$ is the radial distance from the center axis of the beam, $z$ is the axial distance from the beam's focus (or "waist"), $k=2\pi n/\lambda$ is the wavenumber (for a free-space wavelength $\lambda$ and refractive index $n$ of the homogeneous, lossless medium in which the beam propagates), $E_0$ is the electric field amplitude at the origin, $w(z)$ is the radius at which the field amplitude decays by $1/e$ of its axial values, $w_0$ is the beam waist radius, and $R(z)$ is the radius of curvature of the beam's wavefront at $z$. In Meep, the only parameters that need to be specified are $w_0$, $E_0$, $k$, and the location of the beam focus (i.e., the origin $r=z=0$ from the previous formula). The `component` parameter of the `Source` object is ignored. + + The `src_time` object (`Source.src`), which specifies the time dependence of the source, can be one of `ContinuousSource` or `GaussianSource`. + """ def __init__(self, src, @@ -540,6 +547,17 @@ def __init__(self, beam_w0=None, beam_E0=Vector3(), **kwargs): + """ + Construct an `GaussianBeamSource`. + + + **`beam_x0` [`Vector3`]** — The location of the beam focus. This does *not* need to lie within the source region (i.e., the beam can be focused at any arbitrary point, inside or outside the cell, independent of where the source is positioned). + + + **`beam_kdir` [`Vector3`]** — The propagation direction of the beam. The length is *ignored*. (The wavelength of the beam is determined by the center frequency of the `src_time` object and the refractive index of the homogeneous medium by its value at the center of the source region.) + + + **`beam_w0` [`number`]** — The beam waist radius. + + + **`beam_E0` [`Vector3`]** — The polarization vector of the beam. Elements can be complex valued (i.e., for circular polarization). The polarization vector must be *parallel* to the source region (i.e., in order to generate a transverse mode). + """ super(GaussianBeamSource, self).__init__(src, component, center, volume, **kwargs) self._beam_x0 = beam_x0 diff --git a/python/tests/gaussianbeam.py b/python/tests/gaussianbeam.py new file mode 100644 index 000000000..9595f6e03 --- /dev/null +++ b/python/tests/gaussianbeam.py @@ -0,0 +1,62 @@ +from __future__ import division + +import unittest +import meep as mp +import math +import numpy as np + +class TestGaussianBeamSource(unittest.TestCase): + + def gaussian_beam(self, rot_angle): + + s = 14 + resolution = 25 + dpml = 2 + + cell_size = mp.Vector3(s,s) + boundary_layers = [mp.PML(thickness=dpml)] + + beam_x0 = mp.Vector3(0,7.0) # beam focus (relative to source center) + beam_kdir = mp.Vector3(0,1,0).rotate(mp.Vector3(0,0,1),math.radians(rot_angle)) # beam propagation direction + beam_w0 = 0.8 # beam waist radius + beam_E0 = mp.Vector3(0,0,1) + beam_x0 = beam_x0.rotate(mp.Vector3(0,0,1),math.radians(rot_angle)) + fcen = 1 + src_x = 0 + src_y = -0.5*s+dpml+1.0 + sources = [mp.GaussianBeamSource(src=mp.GaussianSource(fcen,fwidth=0.2*fcen), + center=mp.Vector3(src_x,src_y), + size=mp.Vector3(s), + beam_x0=beam_x0, + beam_kdir=beam_kdir, + beam_w0=beam_w0, + beam_E0=beam_E0)] + + sim = mp.Simulation(resolution=resolution, + cell_size=cell_size, + boundary_layers=boundary_layers, + sources=sources) + + cell_dft_fields = sim.add_dft_fields([mp.Ez], fcen, 0, 1, center=mp.Vector3(), size=mp.Vector3(s-2*dpml,s-2*dpml)) + + sim.run(until_after_sources=50) + + Ez_cell = sim.get_dft_array(cell_dft_fields, mp.Ez, 0) + [x,y,z,w] = sim.get_array_metadata(dft_cell=cell_dft_fields) + + tol = 0.05 + idx_x = np.nonzero((np.squeeze(x) > (src_x+beam_x0.x-tol)) & (np.squeeze(x) < (src_x+beam_x0.x+tol))) + idx_y = np.nonzero((np.squeeze(y) > (src_y+beam_x0.y-tol)) & (np.squeeze(y) < (src_y+beam_x0.y+tol))) + + Ez_beam_x0 = Ez_cell[np.squeeze(idx_x)[0],np.squeeze(idx_y)[0]] + + frac = np.abs(Ez_beam_x0)**2 / np.amax(np.abs(Ez_cell)**2) + print("ratio of the Gaussian beam energy at the focus over the maximum beam energy for the entire cell: {}".format(frac)) + + self.assertGreater(frac, 0.99) + + def test_gaussian_beam(self): + self.gaussian_beam(-40) + +if __name__ == '__main__': + unittest.main() From 3fe179a7a027154385800ab4c11d068c452e3fe9 Mon Sep 17 00:00:00 2001 From: "Steven G. Johnson" Date: Tue, 11 Aug 2020 21:53:54 -0400 Subject: [PATCH 6/7] Update Python_User_Interface.md --- doc/docs/Python_User_Interface.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/doc/docs/Python_User_Interface.md b/doc/docs/Python_User_Interface.md index a310cba98..5da9af982 100644 --- a/doc/docs/Python_User_Interface.md +++ b/doc/docs/Python_User_Interface.md @@ -5975,6 +5975,8 @@ class GaussianBeamSource(Source): This is a subclass of `Source` and has **all of the properties** of `Source` above. However, the `component` parameter of the `Source` object is ignored. The [Gaussian beam](https://en.wikipedia.org/wiki/Gaussian_beam) is a transverse electromagnetic mode for which the source region must be a *line* (in 2d) or *plane* (in 3d). For a beam polarized in the $x$ direction with propagation along $+z$, the electric field is defined by $\mathbf{E}(r,z)=E_0\hat{x}\frac{w_0}{w(z)}\exp\left(\frac{-r^2}{w(z)^2}\right)\exp\left(-i\left(kz + k\frac{r^2}{2R(z)}\right)\right)$ where $r$ is the radial distance from the center axis of the beam, $z$ is the axial distance from the beam's focus (or "waist"), $k=2\pi n/\lambda$ is the wavenumber (for a free-space wavelength $\lambda$ and refractive index $n$ of the homogeneous, lossless medium in which the beam propagates), $E_0$ is the electric field amplitude at the origin, $w(z)$ is the radius at which the field amplitude decays by $1/e$ of its axial values, $w_0$ is the beam waist radius, and $R(z)$ is the radius of curvature of the beam's wavefront at $z$. The only independent parameters that need to be specified are $w_0$, $E_0$, $k$, and the location of the beam focus (i.e., the origin: $r=z=0$). +(In 3d, we use a ["complex point-source" method](https://doi.org/10.1364/JOSAA.16.001381) to define a source that generates an exact Gaussian-beam solution. In 2d, we currently use the simple approximation of taking a cross-section of the 3d beam.) + The `SourceTime` object (`Source.src`), which specifies the time dependence of the source, can be one of `ContinuousSource` or `GaussianSource`. From 8329a199f6b9b319c4f0bfc5534a809fed94e751 Mon Sep 17 00:00:00 2001 From: "Steven G. Johnson" Date: Tue, 11 Aug 2020 21:57:52 -0400 Subject: [PATCH 7/7] Update Python_User_Interface.md --- doc/docs/Python_User_Interface.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/docs/Python_User_Interface.md b/doc/docs/Python_User_Interface.md index 5da9af982..d48dac143 100644 --- a/doc/docs/Python_User_Interface.md +++ b/doc/docs/Python_User_Interface.md @@ -5975,9 +5975,9 @@ class GaussianBeamSource(Source): This is a subclass of `Source` and has **all of the properties** of `Source` above. However, the `component` parameter of the `Source` object is ignored. The [Gaussian beam](https://en.wikipedia.org/wiki/Gaussian_beam) is a transverse electromagnetic mode for which the source region must be a *line* (in 2d) or *plane* (in 3d). For a beam polarized in the $x$ direction with propagation along $+z$, the electric field is defined by $\mathbf{E}(r,z)=E_0\hat{x}\frac{w_0}{w(z)}\exp\left(\frac{-r^2}{w(z)^2}\right)\exp\left(-i\left(kz + k\frac{r^2}{2R(z)}\right)\right)$ where $r$ is the radial distance from the center axis of the beam, $z$ is the axial distance from the beam's focus (or "waist"), $k=2\pi n/\lambda$ is the wavenumber (for a free-space wavelength $\lambda$ and refractive index $n$ of the homogeneous, lossless medium in which the beam propagates), $E_0$ is the electric field amplitude at the origin, $w(z)$ is the radius at which the field amplitude decays by $1/e$ of its axial values, $w_0$ is the beam waist radius, and $R(z)$ is the radius of curvature of the beam's wavefront at $z$. The only independent parameters that need to be specified are $w_0$, $E_0$, $k$, and the location of the beam focus (i.e., the origin: $r=z=0$). -(In 3d, we use a ["complex point-source" method](https://doi.org/10.1364/JOSAA.16.001381) to define a source that generates an exact Gaussian-beam solution. In 2d, we currently use the simple approximation of taking a cross-section of the 3d beam.) +(In 3d, we use a ["complex point-source" method](https://doi.org/10.1364/JOSAA.16.001381) to define a source that generates an exact Gaussian-beam solution. In 2d, we currently use the simple approximation of taking a cross-section of the 3d beam. In both cases, the beam is most accurate near the source's center frequency.) -The `SourceTime` object (`Source.src`), which specifies the time dependence of the source, can be one of `ContinuousSource` or `GaussianSource`. +The `SourceTime` object (`Source.src`), which specifies the time dependence of the source, should normally be a narrow-band `ContinuousSource` or `GaussianSource`. (For a `CustomSource`, the beam frequency is determined by the source's `center_frequency` parameter.)