From c76890f10464193ef6fe864c1d02441eb39a3220 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=81ngel=20Ferran=20Pousa?= <angel.ferran.pousa@desy.de>
Date: Thu, 17 Aug 2023 21:17:56 +0200
Subject: [PATCH 01/30] Implement `get_spectrum`

---
 lasy/utils/laser_utils.py | 97 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 97 insertions(+)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 28c182e0..0ffcc93d 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -211,6 +211,103 @@ def get_full_field(laser, theta=0, slice=0, slice_axis="x", Nt=None):
     return env, ext
 
 
+def get_spectrum(
+    grid,
+    dim,
+    bins=20,
+    range=None,
+    is_envelope=True,
+    is_hilbert=False,
+    omega0=None,
+    phase_unwrap_1d=None
+):
+    """
+    Get the the frequency spectrum of an electric field or envelope.
+
+    Parameters
+    ----------
+    grid : a Grid object.
+        It contains a ndarrays with the field data from which the
+        spectrum is computed, and the associated metadata. The last axis must
+        be the longitudinal dimension.
+        Can be the full electric field or the envelope.
+
+    dim : string (optional)
+        Dimensionality of the array. Only used if is_envelope is False.
+        Options are:
+
+        - 'xyt': The laser pulse is represented on a 3D grid:
+                 Cartesian (x,y) transversely, and temporal (t) longitudinally.
+        - 'rt' : The laser pulse is represented on a 2D grid:
+                 Cylindrical (r) transversely, and temporal (t) longitudinally.
+
+    bins : int (optional)
+        Number of bins of the spectrum.
+
+    range : list of float (optional)
+        List of two values indicating the minimum and maximum frequency of the
+        spectrum.
+
+    is_envelope : bool (optional)
+        Whether the field provided uses the envelope representation, as used
+        internally in lasy. If False, field is assumed to represent the
+        the electric field.
+
+    is_hilbert : boolean (optional)
+        If True, the field argument is assumed to be a Hilbert transform, and
+        is used through the computation. Otherwise, the Hilbert transform is
+        calculated in the function.
+
+    omega0 : scalar
+        Angular frequency at which the envelope is defined.
+        Required if an only if is_envelope is True.
+
+    phase_unwrap_1d : boolean (optional)
+        Whether the phase unwrapping is done in 1D.
+        This is not recommended, as the unwrapping will not be accurate,
+        but it might be the only practical solution when dim is 'xyt'.
+
+    Returns
+    -------
+    spectrum : ndarray of doubles
+        Array with the spectrum amplitudes.
+
+    omega_spectrum : scalar
+        Array with the frequencies of the spectrum.
+    """
+    # Get frequency array.
+    omega, central_omega = get_frequency(
+        grid=grid,
+        dim=dim,
+        is_envelope=is_envelope,
+        is_hilbert=is_hilbert,
+        omega0=omega0,
+        phase_unwrap_1d=phase_unwrap_1d
+    )
+    # Calculate weights of each frequency (amplitude of the field).
+    if dim == "xyt":
+        dV = grid.dx[0] * grid.dx[1] * dz
+        weights = np.abs(grid.field) * dV
+    elif dim == "rt":
+        r = grid.axes[0]
+        dr = grid.dx[0]
+        dz = grid.dx[-1] * c
+        # 1D array that computes the volume of radial cells
+        dV = np.pi * ((r + 0.5 * dr) ** 2 - (r - 0.5 * dr) ** 2) * dz
+        weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
+    # Get weighted spectrum.
+    # Neglects the 2 first and last time slices, whose values seems to be
+    # slightly off (maybe due to lower order derivative at the edges).
+    spectrum, edges = np.histogram(
+        a=np.squeeze(omega)[..., 2:-2],
+        weights=np.squeeze(weights[..., 2:-2]),
+        bins=bins,
+        range=range
+    )
+    omega_spectrum = edges[1:] - (edges[1] - edges[0]) / 2
+    return spectrum, omega_spectrum
+
+
 def get_frequency(
     grid,
     dim=None,

From 551aee916d97966ad8fa9ad7b6a7e9f06a9747fd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=81ngel=20Ferran=20Pousa?= <angel.ferran.pousa@desy.de>
Date: Thu, 17 Aug 2023 22:07:07 +0200
Subject: [PATCH 02/30] Implement `get_duration`

---
 lasy/utils/laser_utils.py | 104 ++++++++++++++++++++++++++++----------
 1 file changed, 77 insertions(+), 27 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 0ffcc93d..4ce5c6ab 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -40,16 +40,11 @@ def compute_laser_energy(dim, grid):
 
     envelope = grid.field
 
-    dz = grid.dx[-1] * c
+    dV = get_grid_cell_volume(grid, dim)
 
     if dim == "xyt":
-        dV = grid.dx[0] * grid.dx[1] * dz
         energy = ((dV * epsilon_0 * 0.5) * abs(envelope) ** 2).sum()
     elif dim == "rt":
-        r = grid.axes[0]
-        dr = grid.dx[0]
-        # 1D array that computes the volume of radial cells
-        dV = np.pi * ((r + 0.5 * dr) ** 2 - (r - 0.5 * dr) ** 2) * dz
         energy = (
             dV[np.newaxis, :, np.newaxis]
             * epsilon_0
@@ -216,13 +211,11 @@ def get_spectrum(
     dim,
     bins=20,
     range=None,
-    is_envelope=True,
-    is_hilbert=False,
     omega0=None,
     phase_unwrap_1d=None
 ):
     """
-    Get the the frequency spectrum of an electric field or envelope.
+    Get the the frequency spectrum of an envelope.
 
     Parameters
     ----------
@@ -248,16 +241,6 @@ def get_spectrum(
         List of two values indicating the minimum and maximum frequency of the
         spectrum.
 
-    is_envelope : bool (optional)
-        Whether the field provided uses the envelope representation, as used
-        internally in lasy. If False, field is assumed to represent the
-        the electric field.
-
-    is_hilbert : boolean (optional)
-        If True, the field argument is assumed to be a Hilbert transform, and
-        is used through the computation. Otherwise, the Hilbert transform is
-        calculated in the function.
-
     omega0 : scalar
         Angular frequency at which the envelope is defined.
         Required if an only if is_envelope is True.
@@ -279,21 +262,15 @@ def get_spectrum(
     omega, central_omega = get_frequency(
         grid=grid,
         dim=dim,
-        is_envelope=is_envelope,
-        is_hilbert=is_hilbert,
+        is_envelope=True,
         omega0=omega0,
         phase_unwrap_1d=phase_unwrap_1d
     )
     # Calculate weights of each frequency (amplitude of the field).
+    dV = get_grid_cell_volume(grid, dim)
     if dim == "xyt":
-        dV = grid.dx[0] * grid.dx[1] * dz
         weights = np.abs(grid.field) * dV
     elif dim == "rt":
-        r = grid.axes[0]
-        dr = grid.dx[0]
-        dz = grid.dx[-1] * c
-        # 1D array that computes the volume of radial cells
-        dV = np.pi * ((r + 0.5 * dr) ** 2 - (r - 0.5 * dr) ** 2) * dz
         weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
     # Get weighted spectrum.
     # Neglects the 2 first and last time slices, whose values seems to be
@@ -410,6 +387,32 @@ def get_frequency(
     return omega, central_omega
 
 
+def get_duration(grid, dim):
+    """Get envelope duration, measured as RMS.
+
+    Parameters
+    ----------
+    grid : Grid
+        The grid with the envelope to analyze.
+    dim : str
+        Dimensionality of the grid.
+
+    Returns
+    -------
+    float
+        RMS duration of the envelope in seconds.
+    """
+    # Calculate weights of each frequency (amplitude of the field).
+    dV = get_grid_cell_volume(grid, dim)
+    if dim == "xyt":
+        weights = np.abs(grid.field) * dV
+    elif dim == "rt":
+        weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
+    # project weights to longitudinal axes
+    weights = np.sum(weights, axis=(0, 1))
+    return weighted_std(grid.axes[-1], weights)
+
+
 def field_to_vector_potential(grid, omega0):
     """
     Convert envelope from electric field (V/m) to normalized vector potential.
@@ -518,6 +521,53 @@ def hilbert_transform(grid):
     return hilbert(grid.field[:, :, ::-1])[:, :, ::-1]
 
 
+def get_grid_cell_volume(grid, dim):
+    """Get the volume of the grid cells.
+
+    Parameters
+    ----------
+    grid : Grid
+        The grid form which to compute the cell volume
+    dim : str
+        Dimensionality of the grid.
+
+    Returns
+    -------
+    float or ndarray
+        A float with the cell volume (if dim=='xyt') or a numpy array with the
+        radial distribution of cell volumes (if dim=='rt').
+    """
+    if dim == "xyt":
+        dV = grid.dx[0] * grid.dx[1] * dz
+    elif dim == "rt":
+        r = grid.axes[0]
+        dr = grid.dx[0]
+        dz = grid.dx[-1] * c
+        # 1D array that computes the volume of radial cells
+        dV = np.pi * ((r + 0.5 * dr) ** 2 - (r - 0.5 * dr) ** 2) * dz
+    return dV
+
+
+def weighted_std(values, weights=None):
+    """Calculates the weighted standard deviation of the given values
+
+    Parameters
+    ----------
+    values: array
+        Contains the values to be analyzed
+
+    weights : array
+        Contains the weights of the values to analyze
+
+    Returns
+    -------
+    A float with the value of the standard deviation
+    """
+    mean_val = np.average(values, weights=weights)
+    std = np.sqrt(np.average((values-mean_val)**2, weights=weights))
+    return std
+
+
 def create_grid(array, axes, dim):
     """Create a lasy grid from a numpy array.
 

From 57598cbfff3c63c568ea40d4100f3eca64ffa03a Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Fri, 18 Aug 2023 07:28:35 +0000
Subject: [PATCH 03/30] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 lasy/utils/laser_utils.py | 15 ++++-----------
 1 file changed, 4 insertions(+), 11 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 4ce5c6ab..2ac6eb16 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -206,14 +206,7 @@ def get_full_field(laser, theta=0, slice=0, slice_axis="x", Nt=None):
     return env, ext
 
 
-def get_spectrum(
-    grid,
-    dim,
-    bins=20,
-    range=None,
-    omega0=None,
-    phase_unwrap_1d=None
-):
+def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=None):
     """
     Get the the frequency spectrum of an envelope.
 
@@ -264,7 +257,7 @@ def get_spectrum(
         dim=dim,
         is_envelope=True,
         omega0=omega0,
-        phase_unwrap_1d=phase_unwrap_1d
+        phase_unwrap_1d=phase_unwrap_1d,
     )
     # Calculate weights of each frequency (amplitude of the field).
     dV = get_grid_cell_volume(grid, dim)
@@ -279,7 +272,7 @@ def get_spectrum(
         a=np.squeeze(omega)[..., 2:-2],
         weights=np.squeeze(weights[..., 2:-2]),
         bins=bins,
-        range=range
+        range=range,
     )
     omega_spectrum = edges[1:] - (edges[1] - edges[0]) / 2
     return spectrum, omega_spectrum
@@ -564,7 +557,7 @@ def weighted_std(values, weights=None):
     A float with the value of the standard deviation
     """
     mean_val = np.average(values, weights=weights)
-    std = np.sqrt(np.average((values-mean_val)**2, weights=weights))
+    std = np.sqrt(np.average((values - mean_val) ** 2, weights=weights))
     return std
 
 

From 4bdd0f5750d5be3fc9283fbbea57b4be2bc997c4 Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Fri, 18 Aug 2023 09:29:50 +0200
Subject: [PATCH 04/30] Fix docstring

---
 lasy/utils/laser_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 2ac6eb16..3452a9ab 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -542,7 +542,7 @@ def get_grid_cell_volume(grid, dim):
 
 
 def weighted_std(values, weights=None):
-    """Calculates the weighted standard deviation of the given values
+    """Calculate the weighted standard deviation of the given values.
 
     Parameters
     ----------

From 07673b377add311ea886e5b52a10c4a4ce3efcbb Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Fri, 18 Aug 2023 09:32:14 +0200
Subject: [PATCH 05/30] Fix bug

---
 lasy/utils/laser_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 3452a9ab..009b939b 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -530,12 +530,12 @@ def get_grid_cell_volume(grid, dim):
         A float with the cell volume (if dim=='xyt') or a numpy array with the
         radial distribution of cell volumes (if dim=='rt').
     """
+    dz = grid.dx[-1] * c
     if dim == "xyt":
         dV = grid.dx[0] * grid.dx[1] * dz
     elif dim == "rt":
         r = grid.axes[0]
         dr = grid.dx[0]
-        dz = grid.dx[-1] * c
         # 1D array that computes the volume of radial cells
         dV = np.pi * ((r + 0.5 * dr) ** 2 - (r - 0.5 * dr) ** 2) * dz
     return dV

From 96c43f39760f147007f5f537bf77cbe1277ef81d Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Fri, 18 Aug 2023 09:45:19 +0200
Subject: [PATCH 06/30] Low-effort ifs

---
 lasy/utils/laser_utils.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 009b939b..1562b002 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -44,7 +44,7 @@ def compute_laser_energy(dim, grid):
 
     if dim == "xyt":
         energy = ((dV * epsilon_0 * 0.5) * abs(envelope) ** 2).sum()
-    elif dim == "rt":
+    else:  # dim == "rt":
         energy = (
             dV[np.newaxis, :, np.newaxis]
             * epsilon_0
@@ -263,7 +263,7 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
     dV = get_grid_cell_volume(grid, dim)
     if dim == "xyt":
         weights = np.abs(grid.field) * dV
-    elif dim == "rt":
+    else:  # dim == "rt":
         weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
     # Get weighted spectrum.
     # Neglects the 2 first and last time slices, whose values seems to be
@@ -399,7 +399,7 @@ def get_duration(grid, dim):
     dV = get_grid_cell_volume(grid, dim)
     if dim == "xyt":
         weights = np.abs(grid.field) * dV
-    elif dim == "rt":
+    else:  # dim == "rt":
         weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
     # project weights to longitudinal axes
     weights = np.sum(weights, axis=(0, 1))
@@ -533,7 +533,7 @@ def get_grid_cell_volume(grid, dim):
     dz = grid.dx[-1] * c
     if dim == "xyt":
         dV = grid.dx[0] * grid.dx[1] * dz
-    elif dim == "rt":
+    else:  # dim == "rt":
         r = grid.axes[0]
         dr = grid.dx[0]
         # 1D array that computes the volume of radial cells

From 686ffc8f7427e47d9812dc49fd7c083f7809ed16 Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Fri, 18 Aug 2023 18:02:30 +0200
Subject: [PATCH 07/30] Improve comments

---
 lasy/utils/laser_utils.py | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 1562b002..38eee0d1 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -216,7 +216,6 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
         It contains a ndarrays with the field data from which the
         spectrum is computed, and the associated metadata. The last axis must
         be the longitudinal dimension.
-        Can be the full electric field or the envelope.
 
     dim : string (optional)
         Dimensionality of the array. Only used if is_envelope is False.
@@ -236,7 +235,6 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
 
     omega0 : scalar
         Angular frequency at which the envelope is defined.
-        Required if an only if is_envelope is True.
 
     phase_unwrap_1d : boolean (optional)
         Whether the phase unwrapping is done in 1D.
@@ -251,7 +249,7 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
     omega_spectrum : scalar
         Array with the frequencies of the spectrum.
     """
-    # Get frequency array.
+    # Get the array of angular frequency.
     omega, central_omega = get_frequency(
         grid=grid,
         dim=dim,
@@ -267,7 +265,7 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
         weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
     # Get weighted spectrum.
     # Neglects the 2 first and last time slices, whose values seems to be
-    # slightly off (maybe due to lower order derivative at the edges).
+    # slightly off (maybe due to lower-order derivative at the edges).
     spectrum, edges = np.histogram(
         a=np.squeeze(omega)[..., 2:-2],
         weights=np.squeeze(weights[..., 2:-2]),

From c6ea5a596b3f0b8e88cc7d58053776af395970d3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=81ngel=20Ferran=20Pousa?= <angel.ferran.pousa@desy.de>
Date: Mon, 21 Aug 2023 21:27:10 +0200
Subject: [PATCH 08/30] Test fft

---
 lasy/utils/laser_utils.py | 89 ++++++++++++++++++++++++++++-----------
 1 file changed, 64 insertions(+), 25 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 38eee0d1..bbe1054f 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -206,7 +206,7 @@ def get_full_field(laser, theta=0, slice=0, slice_axis="x", Nt=None):
     return env, ext
 
 
-def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=None):
+def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=None, is_envelope=True, method='fft'):
     """
     Get the the frequency spectrum of an envelope.
 
@@ -249,30 +249,69 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
     omega_spectrum : scalar
         Array with the frequencies of the spectrum.
     """
-    # Get the array of angular frequency.
-    omega, central_omega = get_frequency(
-        grid=grid,
-        dim=dim,
-        is_envelope=True,
-        omega0=omega0,
-        phase_unwrap_1d=phase_unwrap_1d,
-    )
-    # Calculate weights of each frequency (amplitude of the field).
-    dV = get_grid_cell_volume(grid, dim)
-    if dim == "xyt":
-        weights = np.abs(grid.field) * dV
-    else:  # dim == "rt":
-        weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
-    # Get weighted spectrum.
-    # Neglects the 2 first and last time slices, whose values seems to be
-    # slightly off (maybe due to lower-order derivative at the edges).
-    spectrum, edges = np.histogram(
-        a=np.squeeze(omega)[..., 2:-2],
-        weights=np.squeeze(weights[..., 2:-2]),
-        bins=bins,
-        range=range,
-    )
-    omega_spectrum = edges[1:] - (edges[1] - edges[0]) / 2
+    if method == 'fft':
+
+        # spectrum = np.fft.fft(grid.field[0, 0]) * grid.dx[-1]
+        spectrum = np.fft.fft(grid.field) * grid.dx[-1]
+        dV = get_grid_cell_volume(grid, dim)
+        if dim == "xyt":
+            spectrum = np.sum(spectrum, axis=(0, 1))
+        else:
+            spectrum = np.sum(spectrum * dV[np.newaxis, :, np.newaxis] / dV[0], axis=1)[0]
+        # spectrum = np.abs(spectrum[:int(len(spectrum) / 2)])
+        freq = np.fft.fftfreq(spectrum.shape[-1], d=(grid.axes[-1][1] - grid.axes[-1][0]))
+        omega_spectrum = 2 * np.pi * freq
+        
+        if is_envelope:
+            omega_spectrum = omega0 - omega_spectrum
+
+        i_sort = np.argsort(omega_spectrum)
+        omega_spectrum = omega_spectrum[i_sort]
+        spectrum = np.abs(spectrum[i_sort])
+
+        i_keep = omega_spectrum >= 0.
+        omega_spectrum = omega_spectrum[i_keep]
+        spectrum = spectrum[i_keep]
+
+        omega_interp = np.linspace(*range, bins)
+        spectrum = np.interp(omega_interp, omega_spectrum, spectrum)
+        omega_spectrum = omega_interp
+
+        # spectrum = np.fft.fft(grid.field) * grid.dx[-1]
+        # spectrum = np.abs(spectrum[..., :int(spectrum.shape[-1] / 2)])
+        # omega_spectrum = 2 * np.pi / (grid.axes[-1][-1] - grid.axes[-1][0]) * np.arange(spectrum.shape[-1])
+        # if is_envelope:
+        #     omega_spectrum = omega_spectrum
+        # dV = get_grid_cell_volume(grid, dim)
+        # if dim == "xyt":
+        #     spectrum = np.sum(spectrum * dV, axis=(0, 1))
+        # else:
+        #     spectrum = np.sum(spectrum * dV[np.newaxis, :, np.newaxis], axis=1)[0]
+    else:
+        # Get the array of angular frequency.
+        omega, central_omega = get_frequency(
+            grid=grid,
+            dim=dim,
+            is_envelope=True,
+            omega0=omega0,
+            phase_unwrap_1d=phase_unwrap_1d,
+        )
+        # Calculate weights of each frequency (amplitude of the field).
+        dV = get_grid_cell_volume(grid, dim)
+        if dim == "xyt":
+            weights = np.abs(grid.field) * dV
+        else:  # dim == "rt":
+            weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
+        # Get weighted spectrum.
+        # Neglects the 2 first and last time slices, whose values seems to be
+        # slightly off (maybe due to lower-order derivative at the edges).
+        spectrum, edges = np.histogram(
+            a=np.squeeze(omega)[..., 2:-2],
+            weights=np.squeeze(weights[..., 2:-2]),
+            bins=bins,
+            range=range,
+        )
+        omega_spectrum = edges[1:] - (edges[1] - edges[0]) / 2
     return spectrum, omega_spectrum
 
 

From 804f4eba38ffef58a32785783552c67ff24f354b Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 21 Aug 2023 19:27:28 +0000
Subject: [PATCH 09/30] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 lasy/utils/laser_utils.py | 26 +++++++++++++++++++-------
 1 file changed, 19 insertions(+), 7 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index bbe1054f..4c5fe76b 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -206,7 +206,16 @@ def get_full_field(laser, theta=0, slice=0, slice_axis="x", Nt=None):
     return env, ext
 
 
-def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=None, is_envelope=True, method='fft'):
+def get_spectrum(
+    grid,
+    dim,
+    bins=20,
+    range=None,
+    omega0=None,
+    phase_unwrap_1d=None,
+    is_envelope=True,
+    method="fft",
+):
     """
     Get the the frequency spectrum of an envelope.
 
@@ -249,19 +258,22 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
     omega_spectrum : scalar
         Array with the frequencies of the spectrum.
     """
-    if method == 'fft':
-
+    if method == "fft":
         # spectrum = np.fft.fft(grid.field[0, 0]) * grid.dx[-1]
         spectrum = np.fft.fft(grid.field) * grid.dx[-1]
         dV = get_grid_cell_volume(grid, dim)
         if dim == "xyt":
             spectrum = np.sum(spectrum, axis=(0, 1))
         else:
-            spectrum = np.sum(spectrum * dV[np.newaxis, :, np.newaxis] / dV[0], axis=1)[0]
+            spectrum = np.sum(spectrum * dV[np.newaxis, :, np.newaxis] / dV[0], axis=1)[
+                0
+            ]
         # spectrum = np.abs(spectrum[:int(len(spectrum) / 2)])
-        freq = np.fft.fftfreq(spectrum.shape[-1], d=(grid.axes[-1][1] - grid.axes[-1][0]))
+        freq = np.fft.fftfreq(
+            spectrum.shape[-1], d=(grid.axes[-1][1] - grid.axes[-1][0])
+        )
         omega_spectrum = 2 * np.pi * freq
-        
+
         if is_envelope:
             omega_spectrum = omega0 - omega_spectrum
 
@@ -269,7 +281,7 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
         omega_spectrum = omega_spectrum[i_sort]
         spectrum = np.abs(spectrum[i_sort])
 
-        i_keep = omega_spectrum >= 0.
+        i_keep = omega_spectrum >= 0.0
         omega_spectrum = omega_spectrum[i_keep]
         spectrum = spectrum[i_keep]
 

From 9ce1bceaefdfaee7cbc596f439761f7b40bb543b Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 09:41:58 +0200
Subject: [PATCH 10/30] Use range only when it's not None

---
 lasy/utils/laser_utils.py | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index bbe1054f..03ec58e8 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -273,9 +273,10 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
         omega_spectrum = omega_spectrum[i_keep]
         spectrum = spectrum[i_keep]
 
-        omega_interp = np.linspace(*range, bins)
-        spectrum = np.interp(omega_interp, omega_spectrum, spectrum)
-        omega_spectrum = omega_interp
+        if range is not None:
+            omega_interp = np.linspace(*range, bins)
+            spectrum = np.interp(omega_interp, omega_spectrum, spectrum)
+            omega_spectrum = omega_interp
 
         # spectrum = np.fft.fft(grid.field) * grid.dx[-1]
         # spectrum = np.abs(spectrum[..., :int(spectrum.shape[-1] / 2)])

From 8b30a0b350e011c2985d476abc3685903e036fb9 Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 09:42:36 +0200
Subject: [PATCH 11/30] Divide spectrum by 2 when is envelope

---
 lasy/utils/laser_utils.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 03ec58e8..217bfe33 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -264,6 +264,7 @@ def get_spectrum(grid, dim, bins=20, range=None, omega0=None, phase_unwrap_1d=No
         
         if is_envelope:
             omega_spectrum = omega0 - omega_spectrum
+            spectrum /= 2
 
         i_sort = np.argsort(omega_spectrum)
         omega_spectrum = omega_spectrum[i_sort]

From 265fe234e1230b6c3ec6e43d2ca627b83bbcb4d1 Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 17:09:25 +0200
Subject: [PATCH 12/30] Improve FFT implementation

---
 lasy/utils/laser_utils.py | 146 ++++++++++++++++++--------------------
 1 file changed, 68 insertions(+), 78 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 1b6cdf71..2d391c7b 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -209,12 +209,11 @@ def get_full_field(laser, theta=0, slice=0, slice_axis="x", Nt=None):
 def get_spectrum(
     grid,
     dim,
-    bins=20,
     range=None,
-    omega0=None,
-    phase_unwrap_1d=None,
+    bins=20,
     is_envelope=True,
-    method="fft",
+    omega0=None,
+    on_axis=False,
 ):
     """
     Get the the frequency spectrum of an envelope.
@@ -235,97 +234,88 @@ def get_spectrum(
         - 'rt' : The laser pulse is represented on a 2D grid:
                  Cylindrical (r) transversely, and temporal (t) longitudinally.
 
-    bins : int (optional)
-        Number of bins of the spectrum.
-
     range : list of float (optional)
         List of two values indicating the minimum and maximum frequency of the
-        spectrum.
+        spectrum. If provided, only the FFT spectrum within this range
+        will be returned using interpolation.
 
-    omega0 : scalar
-        Angular frequency at which the envelope is defined.
+    bins : int (optional)
+        Number of bins of to which to interpolate the spectrum if a `range`
+        is given.
 
-    phase_unwrap_1d : boolean (optional)
-        Whether the phase unwrapping is done in 1D.
-        This is not recommended, as the unwrapping will not be accurate,
-        but it might be the only practical solution when dim is 'xyt'.
+    is_envelope : bool (optional)
+        Whether the field provided uses the envelope representation, as used
+        internally in lasy. If False, field is assumed to represent the
+        the electric field.
+
+    omega0 : scalar (optional)
+        Angular frequency at which the envelope is defined. Required if
+        `is_envelope=True`.
+
+    on_axis : bool (optional)
+        Whether to get the spectrum on axis or, otherwise, the summed spectrum
+        along the transverse direction(s).
 
     Returns
     -------
     spectrum : ndarray of doubles
-        Array with the spectrum amplitudes.
+        Array with the spectrum amplitudes (FFT amplitude * dt).
 
     omega_spectrum : scalar
         Array with the frequencies of the spectrum.
     """
-    if method == "fft":
-        # spectrum = np.fft.fft(grid.field[0, 0]) * grid.dx[-1]
-        spectrum = np.fft.fft(grid.field) * grid.dx[-1]
-        dV = get_grid_cell_volume(grid, dim)
+    # Get the frequencies of the fft output.
+    freq = np.fft.fftfreq(
+        grid.field.shape[-1], d=(grid.axes[-1][1] - grid.axes[-1][0])
+    )
+    omega_spectrum = 2 * np.pi * freq
+
+    # Get on axis or full field.
+    if on_axis:
         if dim == "xyt":
-            spectrum = np.sum(spectrum, axis=(0, 1))
+            nx, ny, nt = grid.field.shape
+            field = grid.field[nx//2, ny//2]
         else:
-            spectrum = np.sum(spectrum * dV[np.newaxis, :, np.newaxis] / dV[0], axis=1)[
-                0
-            ]
-        # spectrum = np.abs(spectrum[:int(len(spectrum) / 2)])
-        freq = np.fft.fftfreq(
-            spectrum.shape[-1], d=(grid.axes[-1][1] - grid.axes[-1][0])
-        )
-        omega_spectrum = 2 * np.pi * freq
-
-        if is_envelope:
-            omega_spectrum = omega0 - omega_spectrum
-            spectrum /= 2
-
-        i_sort = np.argsort(omega_spectrum)
-        omega_spectrum = omega_spectrum[i_sort]
-        spectrum = np.abs(spectrum[i_sort])
-
-        i_keep = omega_spectrum >= 0.0
-        omega_spectrum = omega_spectrum[i_keep]
-        spectrum = spectrum[i_keep]
-
-        if range is not None:
-            omega_interp = np.linspace(*range, bins)
-            spectrum = np.interp(omega_interp, omega_spectrum, spectrum)
-            omega_spectrum = omega_interp
-
-        # spectrum = np.fft.fft(grid.field) * grid.dx[-1]
-        # spectrum = np.abs(spectrum[..., :int(spectrum.shape[-1] / 2)])
-        # omega_spectrum = 2 * np.pi / (grid.axes[-1][-1] - grid.axes[-1][0]) * np.arange(spectrum.shape[-1])
-        # if is_envelope:
-        #     omega_spectrum = omega_spectrum
-        # dV = get_grid_cell_volume(grid, dim)
-        # if dim == "xyt":
-        #     spectrum = np.sum(spectrum * dV, axis=(0, 1))
-        # else:
-        #     spectrum = np.sum(spectrum * dV[np.newaxis, :, np.newaxis], axis=1)[0]
+            field = grid.field[0, 0]
     else:
-        # Get the array of angular frequency.
-        omega, central_omega = get_frequency(
-            grid=grid,
-            dim=dim,
-            is_envelope=True,
-            omega0=omega0,
-            phase_unwrap_1d=phase_unwrap_1d,
-        )
-        # Calculate weights of each frequency (amplitude of the field).
+        field = grid.field
+
+    # Get spectrum.
+    if is_envelope:
+        # Assume that the FFT of the envelope and the FFT of the complex
+        # conjugate of the envelope do not overlap. Then we only need
+        # one of them.
+        spectrum = 0.5 * np.abs(np.fft.fft(field)) * grid.dx[-1]
+        omega_spectrum = omega0 - omega_spectrum
+    else:
+        spectrum = np.fft.fft(field) * grid.dx[-1]
+        # Keep only positive frequencies.
+        i_keep = spectrum.shape[-1] // 2
+        spectrum = np.abs(spectrum[:i_keep])
+        omega_spectrum = omega_spectrum[:i_keep]
+
+    # Sum spectrum transversely.
+    if not on_axis:
         dV = get_grid_cell_volume(grid, dim)
         if dim == "xyt":
-            weights = np.abs(grid.field) * dV
-        else:  # dim == "rt":
-            weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
-        # Get weighted spectrum.
-        # Neglects the 2 first and last time slices, whose values seems to be
-        # slightly off (maybe due to lower-order derivative at the edges).
-        spectrum, edges = np.histogram(
-            a=np.squeeze(omega)[..., 2:-2],
-            weights=np.squeeze(weights[..., 2:-2]),
-            bins=bins,
-            range=range,
-        )
-        omega_spectrum = edges[1:] - (edges[1] - edges[0]) / 2
+            spectrum = np.sum(spectrum, axis=(0, 1))
+        else:
+            spectrum = np.sum(
+                spectrum * dV[np.newaxis, :, np.newaxis] / dV[0],
+                axis=1
+            )[0]
+
+    # Sort freqency array (and the spectrum accordingly).
+    i_sort = np.argsort(omega_spectrum)
+    omega_spectrum = omega_spectrum[i_sort]
+    spectrum = np.abs(spectrum[i_sort])
+
+    # If the user specified a frequency range, interpolate into it.
+    if range is not None:
+        omega_interp = np.linspace(*range, bins)
+        spectrum = np.interp(omega_interp, omega_spectrum, spectrum)
+        omega_spectrum = omega_interp
+
     return spectrum, omega_spectrum
 
 

From b18861bb84dec52492898b8f162043ed869e68c3 Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 17:12:00 +0200
Subject: [PATCH 13/30] Fix description

---
 lasy/utils/laser_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 2d391c7b..804cccd7 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -436,7 +436,7 @@ def get_duration(grid, dim):
     float
         RMS duration of the envelope in seconds.
     """
-    # Calculate weights of each frequency (amplitude of the field).
+    # Calculate weights of each grid cell (amplitude of the field).
     dV = get_grid_cell_volume(grid, dim)
     if dim == "xyt":
         weights = np.abs(grid.field) * dV

From 2888b52148b4ac292316d55e3e190d3c8e9ecf6a Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 22 Aug 2023 15:14:12 +0000
Subject: [PATCH 14/30] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 lasy/utils/laser_utils.py | 13 +++++--------
 1 file changed, 5 insertions(+), 8 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 804cccd7..2a1e77ad 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -265,16 +265,14 @@ def get_spectrum(
         Array with the frequencies of the spectrum.
     """
     # Get the frequencies of the fft output.
-    freq = np.fft.fftfreq(
-        grid.field.shape[-1], d=(grid.axes[-1][1] - grid.axes[-1][0])
-    )
+    freq = np.fft.fftfreq(grid.field.shape[-1], d=(grid.axes[-1][1] - grid.axes[-1][0]))
     omega_spectrum = 2 * np.pi * freq
 
     # Get on axis or full field.
     if on_axis:
         if dim == "xyt":
             nx, ny, nt = grid.field.shape
-            field = grid.field[nx//2, ny//2]
+            field = grid.field[nx // 2, ny // 2]
         else:
             field = grid.field[0, 0]
     else:
@@ -300,10 +298,9 @@ def get_spectrum(
         if dim == "xyt":
             spectrum = np.sum(spectrum, axis=(0, 1))
         else:
-            spectrum = np.sum(
-                spectrum * dV[np.newaxis, :, np.newaxis] / dV[0],
-                axis=1
-            )[0]
+            spectrum = np.sum(spectrum * dV[np.newaxis, :, np.newaxis] / dV[0], axis=1)[
+                0
+            ]
 
     # Sort freqency array (and the spectrum accordingly).
     i_sort = np.argsort(omega_spectrum)

From 3fa9c66b422583a97d5c73809d4ebe748d5e9f7a Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 17:21:58 +0200
Subject: [PATCH 15/30] Fix docstring

---
 lasy/utils/laser_utils.py | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 804cccd7..5a649714 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -216,18 +216,17 @@ def get_spectrum(
     on_axis=False,
 ):
     """
-    Get the the frequency spectrum of an envelope.
+    Get the the frequency spectrum of an envelope or electric field.
 
     Parameters
     ----------
     grid : a Grid object.
-        It contains a ndarrays with the field data from which the
+        It contains an ndarray with the field data from which the
         spectrum is computed, and the associated metadata. The last axis must
         be the longitudinal dimension.
 
     dim : string (optional)
-        Dimensionality of the array. Only used if is_envelope is False.
-        Options are:
+        Dimensionality of the array. Options are:
 
         - 'xyt': The laser pulse is represented on a 3D grid:
                  Cartesian (x,y) transversely, and temporal (t) longitudinally.

From f96edfe9cb1095ad7e99775049e3aec010070b14 Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 17:27:19 +0200
Subject: [PATCH 16/30] Shorten line

---
 lasy/utils/laser_utils.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index c10402af..5560ed6c 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -297,9 +297,7 @@ def get_spectrum(
         if dim == "xyt":
             spectrum = np.sum(spectrum, axis=(0, 1))
         else:
-            spectrum = np.sum(spectrum * dV[np.newaxis, :, np.newaxis] / dV[0], axis=1)[
-                0
-            ]
+            spectrum = np.sum(spectrum[0] * dV[:, np.newaxis] / dV[0], axis=0)
 
     # Sort freqency array (and the spectrum accordingly).
     i_sort = np.argsort(omega_spectrum)

From a56c599fa7c75218e113c40618c489289a84d14d Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 18:05:22 +0200
Subject: [PATCH 17/30] Square spectrum

---
 lasy/utils/laser_utils.py | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 5560ed6c..c6a476c1 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -291,6 +291,9 @@ def get_spectrum(
         spectrum = np.abs(spectrum[:i_keep])
         omega_spectrum = omega_spectrum[:i_keep]
 
+    # Square to get energy-like spectrum (check if appropriate).
+    spectrum = spectrum ** 2
+
     # Sum spectrum transversely.
     if not on_axis:
         dV = get_grid_cell_volume(grid, dim)

From 4e26ba85ace65a857ec96ffb4192e47fbc941dba Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 22 Aug 2023 16:05:49 +0000
Subject: [PATCH 18/30] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 lasy/utils/laser_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index c6a476c1..0cdcff68 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -292,7 +292,7 @@ def get_spectrum(
         omega_spectrum = omega_spectrum[:i_keep]
 
     # Square to get energy-like spectrum (check if appropriate).
-    spectrum = spectrum ** 2
+    spectrum = spectrum**2
 
     # Sum spectrum transversely.
     if not on_axis:

From 651f401365dbe722862b4f43d062aecc71cc7618 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=81ngel=20Ferran=20Pousa?= <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 22:56:42 +0200
Subject: [PATCH 19/30] Implement spectrum "mode" + fixes

---
 lasy/utils/laser_utils.py | 46 ++++++++++++++++++++++++---------------
 1 file changed, 29 insertions(+), 17 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index c6a476c1..59c73bf9 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -213,7 +213,7 @@ def get_spectrum(
     bins=20,
     is_envelope=True,
     omega0=None,
-    on_axis=False,
+    mode='sum'
 ):
     """
     Get the the frequency spectrum of an envelope or electric field.
@@ -251,14 +251,15 @@ def get_spectrum(
         Angular frequency at which the envelope is defined. Required if
         `is_envelope=True`.
 
-    on_axis : bool (optional)
-        Whether to get the spectrum on axis or, otherwise, the summed spectrum
-        along the transverse direction(s).
+    mode : {'sum', 'on_axis', 'full'} (optional)
+        Whether to return the summed spectrum along the transverse direction(s),
+        the on-axis spectrum, or the full (unsumed) spectrum in the whole
+        transverse domain.
 
     Returns
     -------
     spectrum : ndarray of doubles
-        Array with the spectrum amplitudes (FFT amplitude * dt).
+        Array with the spectral density in J/(rad/s).
 
     omega_spectrum : scalar
         Array with the frequencies of the spectrum.
@@ -268,7 +269,7 @@ def get_spectrum(
     omega_spectrum = 2 * np.pi * freq
 
     # Get on axis or full field.
-    if on_axis:
+    if mode == 'on_axis':
         if dim == "xyt":
             nx, ny, nt = grid.field.shape
             field = grid.field[nx // 2, ny // 2]
@@ -295,17 +296,28 @@ def get_spectrum(
     spectrum = spectrum ** 2
 
     # Sum spectrum transversely.
-    if not on_axis:
-        dV = get_grid_cell_volume(grid, dim)
+    dV = get_grid_cell_volume(grid, dim)
+    if mode == 'on_axis':
         if dim == "xyt":
-            spectrum = np.sum(spectrum, axis=(0, 1))
+            spectrum *= dV
         else:
-            spectrum = np.sum(spectrum[0] * dV[:, np.newaxis] / dV[0], axis=0)
-
-    # Sort freqency array (and the spectrum accordingly).
+            spectrum *= dV[0]
+    else:
+        if dim == "xyt":
+            spectrum = spectrum * dV
+        else:
+            spectrum = spectrum[0] * dV[:, np.newaxis]
+        if mode == 'sum':
+            if dim == "xyt":
+                spectrum = np.sum(spectrum, axis=(0, 1))
+            else:
+                spectrum = np.sum(spectrum, axis=0)
+    spectrum *= epsilon_0 / grid.dx[-1] / np.pi
+
+    # Sort frequency array (and the spectrum accordingly).
     i_sort = np.argsort(omega_spectrum)
     omega_spectrum = omega_spectrum[i_sort]
-    spectrum = np.abs(spectrum[i_sort])
+    spectrum = spectrum[..., i_sort]
 
     # If the user specified a frequency range, interpolate into it.
     if range is not None:
@@ -419,7 +431,7 @@ def get_frequency(
 
 
 def get_duration(grid, dim):
-    """Get envelope duration, measured as RMS.
+    """Get duration of the intensity of the envelope, measured as RMS.
 
     Parameters
     ----------
@@ -431,14 +443,14 @@ def get_duration(grid, dim):
     Returns
     -------
     float
-        RMS duration of the envelope in seconds.
+        RMS duration of the envelope intensity in seconds.
     """
     # Calculate weights of each grid cell (amplitude of the field).
     dV = get_grid_cell_volume(grid, dim)
     if dim == "xyt":
-        weights = np.abs(grid.field) * dV
+        weights = np.abs(grid.field)**2 * dV
     else:  # dim == "rt":
-        weights = np.abs(grid.field) * dV[np.newaxis, :, np.newaxis]
+        weights = np.abs(grid.field)**2 * dV[np.newaxis, :, np.newaxis]
     # project weights to longitudinal axes
     weights = np.sum(weights, axis=(0, 1))
     return weighted_std(grid.axes[-1], weights)

From d9fce8129e7f676e5126f80f8ba4b54e1c423a7d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=81ngel=20Ferran=20Pousa?= <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 22:57:18 +0200
Subject: [PATCH 20/30] Add tests

---
 tests/test_laser_utils.py | 71 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 71 insertions(+)
 create mode 100644 tests/test_laser_utils.py

diff --git a/tests/test_laser_utils.py b/tests/test_laser_utils.py
new file mode 100644
index 00000000..faeb9329
--- /dev/null
+++ b/tests/test_laser_utils.py
@@ -0,0 +1,71 @@
+import numpy as np
+
+from lasy.laser import Laser
+from lasy.profiles.gaussian_profile import GaussianProfile
+from lasy.utils.laser_utils import (get_spectrum, compute_laser_energy, get_duration)
+
+
+def get_gaussian_profile():
+    # Cases with Gaussian laser
+    wavelength = 0.8e-6
+    pol = (1, 0)
+    laser_energy = 1.0  # J
+    t_peak = 0.0e-15  # s
+    tau = 30.0e-15  # s
+    w0 = 5.0e-6  # m
+    profile = GaussianProfile(wavelength, pol, laser_energy, w0, tau, t_peak)
+
+    return profile
+
+
+def get_gaussian_laser(dim):
+    # - Cylindrical case
+    if dim == "rt":
+        lo = (0e-6, -60e-15)
+        hi = (25e-6, +60e-15)
+        npoints = (100, 100)
+    elif dim == "xyt":
+        lo = (-25e-6, -25e-6, -60e-15)
+        hi = (+25e-6, +25e-6, +60e-15)
+        npoints = (100, 100, 100)
+    return Laser(dim, lo, hi, npoints, get_gaussian_profile())
+
+
+def test_laser_analysis_utils():
+    """Test the different laser analysis utilities in both geometries."""
+    for dim in ["xyt", 'rt']:
+        laser = get_gaussian_laser(dim)
+
+        # Check that energy computed from spectrum agrees with `compute_laser_energy`.
+        spectrum, omega = get_spectrum(laser.grid, dim, is_envelope=True,
+                                       omega0=laser.profile.omega0)
+        d_omega = omega[1] - omega[0]
+        spectrum_energy = np.sum(spectrum) * d_omega
+        energy = compute_laser_energy(dim, laser.grid)
+        np.testing.assert_approx_equal(spectrum_energy, energy, significant=14)
+
+        # Check that:
+        # 1. The on-axis spectrum agrees with the on-axis value of the full spectrum
+        # 2. The summed full spectrum agrees with the summed spectrum.
+        spectrum_oa, omega = get_spectrum(laser.grid, dim, is_envelope=True,
+                                          omega0=laser.profile.omega0, mode='on_axis')
+        spectrum_full, omega = get_spectrum(laser.grid, dim, is_envelope=True,
+                                            omega0=laser.profile.omega0, mode='full')
+        if dim == "xyt":
+            nx, ny, nt = laser.grid.field.shape
+            spectrum_oa_from_full = spectrum_full[nx // 2, ny // 2]
+            spectrum_sum_from_full = np.sum(spectrum_full, axis=(0, 1))
+        else:
+            spectrum_oa_from_full = spectrum_full[0, 0]
+            spectrum_sum_from_full = np.sum(spectrum_full, axis=(0))
+        np.testing.assert_allclose(spectrum_oa_from_full, spectrum_oa, rtol=1e-13)
+        np.testing.assert_allclose(spectrum_sum_from_full, spectrum, rtol=1e-13)
+
+        # Check that laser duration agrees with the given one.
+        tau_rms = get_duration(laser.grid, dim)
+        np.testing.assert_approx_equal(2*tau_rms, laser.profile.long_profile.tau, significant=3)
+        
+
+
+if __name__ == "__main__":
+    test_laser_analysis_utils()

From 5fd62e815c91a4feb01e7ea8ea38af7f9f2d0f26 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 22 Aug 2023 20:58:38 +0000
Subject: [PATCH 21/30] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 lasy/utils/laser_utils.py | 18 ++++++------------
 tests/test_laser_utils.py | 28 ++++++++++++++++++----------
 2 files changed, 24 insertions(+), 22 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 6b14a27a..799f167c 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -207,13 +207,7 @@ def get_full_field(laser, theta=0, slice=0, slice_axis="x", Nt=None):
 
 
 def get_spectrum(
-    grid,
-    dim,
-    range=None,
-    bins=20,
-    is_envelope=True,
-    omega0=None,
-    mode='sum'
+    grid, dim, range=None, bins=20, is_envelope=True, omega0=None, mode="sum"
 ):
     """
     Get the the frequency spectrum of an envelope or electric field.
@@ -269,7 +263,7 @@ def get_spectrum(
     omega_spectrum = 2 * np.pi * freq
 
     # Get on axis or full field.
-    if mode == 'on_axis':
+    if mode == "on_axis":
         if dim == "xyt":
             nx, ny, nt = grid.field.shape
             field = grid.field[nx // 2, ny // 2]
@@ -297,7 +291,7 @@ def get_spectrum(
 
     # Sum spectrum transversely.
     dV = get_grid_cell_volume(grid, dim)
-    if mode == 'on_axis':
+    if mode == "on_axis":
         if dim == "xyt":
             spectrum *= dV
         else:
@@ -307,7 +301,7 @@ def get_spectrum(
             spectrum = spectrum * dV
         else:
             spectrum = spectrum[0] * dV[:, np.newaxis]
-        if mode == 'sum':
+        if mode == "sum":
             if dim == "xyt":
                 spectrum = np.sum(spectrum, axis=(0, 1))
             else:
@@ -448,9 +442,9 @@ def get_duration(grid, dim):
     # Calculate weights of each grid cell (amplitude of the field).
     dV = get_grid_cell_volume(grid, dim)
     if dim == "xyt":
-        weights = np.abs(grid.field)**2 * dV
+        weights = np.abs(grid.field) ** 2 * dV
     else:  # dim == "rt":
-        weights = np.abs(grid.field)**2 * dV[np.newaxis, :, np.newaxis]
+        weights = np.abs(grid.field) ** 2 * dV[np.newaxis, :, np.newaxis]
     # project weights to longitudinal axes
     weights = np.sum(weights, axis=(0, 1))
     return weighted_std(grid.axes[-1], weights)
diff --git a/tests/test_laser_utils.py b/tests/test_laser_utils.py
index faeb9329..ed04c282 100644
--- a/tests/test_laser_utils.py
+++ b/tests/test_laser_utils.py
@@ -2,7 +2,7 @@
 
 from lasy.laser import Laser
 from lasy.profiles.gaussian_profile import GaussianProfile
-from lasy.utils.laser_utils import (get_spectrum, compute_laser_energy, get_duration)
+from lasy.utils.laser_utils import get_spectrum, compute_laser_energy, get_duration
 
 
 def get_gaussian_profile():
@@ -33,12 +33,13 @@ def get_gaussian_laser(dim):
 
 def test_laser_analysis_utils():
     """Test the different laser analysis utilities in both geometries."""
-    for dim in ["xyt", 'rt']:
+    for dim in ["xyt", "rt"]:
         laser = get_gaussian_laser(dim)
 
         # Check that energy computed from spectrum agrees with `compute_laser_energy`.
-        spectrum, omega = get_spectrum(laser.grid, dim, is_envelope=True,
-                                       omega0=laser.profile.omega0)
+        spectrum, omega = get_spectrum(
+            laser.grid, dim, is_envelope=True, omega0=laser.profile.omega0
+        )
         d_omega = omega[1] - omega[0]
         spectrum_energy = np.sum(spectrum) * d_omega
         energy = compute_laser_energy(dim, laser.grid)
@@ -47,10 +48,16 @@ def test_laser_analysis_utils():
         # Check that:
         # 1. The on-axis spectrum agrees with the on-axis value of the full spectrum
         # 2. The summed full spectrum agrees with the summed spectrum.
-        spectrum_oa, omega = get_spectrum(laser.grid, dim, is_envelope=True,
-                                          omega0=laser.profile.omega0, mode='on_axis')
-        spectrum_full, omega = get_spectrum(laser.grid, dim, is_envelope=True,
-                                            omega0=laser.profile.omega0, mode='full')
+        spectrum_oa, omega = get_spectrum(
+            laser.grid,
+            dim,
+            is_envelope=True,
+            omega0=laser.profile.omega0,
+            mode="on_axis",
+        )
+        spectrum_full, omega = get_spectrum(
+            laser.grid, dim, is_envelope=True, omega0=laser.profile.omega0, mode="full"
+        )
         if dim == "xyt":
             nx, ny, nt = laser.grid.field.shape
             spectrum_oa_from_full = spectrum_full[nx // 2, ny // 2]
@@ -63,8 +70,9 @@ def test_laser_analysis_utils():
 
         # Check that laser duration agrees with the given one.
         tau_rms = get_duration(laser.grid, dim)
-        np.testing.assert_approx_equal(2*tau_rms, laser.profile.long_profile.tau, significant=3)
-        
+        np.testing.assert_approx_equal(
+            2 * tau_rms, laser.profile.long_profile.tau, significant=3
+        )
 
 
 if __name__ == "__main__":

From 629a3a1865c5c1a49458849413742523d66b90b7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=81ngel=20Ferran=20Pousa?= <angel.ferran.pousa@desy.de>
Date: Tue, 22 Aug 2023 23:13:13 +0200
Subject: [PATCH 22/30] Fix codeQL

---
 tests/test_laser_utils.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/tests/test_laser_utils.py b/tests/test_laser_utils.py
index ed04c282..d47961a7 100644
--- a/tests/test_laser_utils.py
+++ b/tests/test_laser_utils.py
@@ -23,8 +23,8 @@ def get_gaussian_laser(dim):
     if dim == "rt":
         lo = (0e-6, -60e-15)
         hi = (25e-6, +60e-15)
-        npoints = (100, 100)
-    elif dim == "xyt":
+        npoints = (100, 100)    
+    else:  # dim == "xyt":
         lo = (-25e-6, -25e-6, -60e-15)
         hi = (+25e-6, +25e-6, +60e-15)
         npoints = (100, 100, 100)

From 8054d3132a65f14e6bed1b97fe5238c5e6fb067f Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 22 Aug 2023 21:14:03 +0000
Subject: [PATCH 23/30] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 tests/test_laser_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/test_laser_utils.py b/tests/test_laser_utils.py
index d47961a7..9136b1c0 100644
--- a/tests/test_laser_utils.py
+++ b/tests/test_laser_utils.py
@@ -23,7 +23,7 @@ def get_gaussian_laser(dim):
     if dim == "rt":
         lo = (0e-6, -60e-15)
         hi = (25e-6, +60e-15)
-        npoints = (100, 100)    
+        npoints = (100, 100)
     else:  # dim == "xyt":
         lo = (-25e-6, -25e-6, -60e-15)
         hi = (+25e-6, +25e-6, +60e-15)

From e9559d9d37b25110879854205b4a79aac0bef458 Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Wed, 23 Aug 2023 15:41:42 +0200
Subject: [PATCH 24/30] Change output depending on calculation method

---
 lasy/utils/laser_utils.py | 107 +++++++++++++++++++++++---------------
 1 file changed, 65 insertions(+), 42 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 799f167c..d07adf17 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -207,11 +207,41 @@ def get_full_field(laser, theta=0, slice=0, slice_axis="x", Nt=None):
 
 
 def get_spectrum(
-    grid, dim, range=None, bins=20, is_envelope=True, omega0=None, mode="sum"
+    grid, dim, range=None, bins=20, is_envelope=True, omega0=None, method="sum"
 ):
-    """
+    r"""
     Get the the frequency spectrum of an envelope or electric field.
 
+    The spectrum can be calculated in three different ways, depending on the
+    `method` specified by the user:
+
+    Initially, the spectrum is calculated as the Fourier transform of the
+    electric field :math:`E(t)`.
+
+    ..math::
+        \int E(t) e^{-i \omega t} dt
+
+    neglecting the negative frequencies. If ``method=="raw"``, no further
+    processing is done and the returned spectrum is a complex array with the
+    same transverse dimensions as the input grid. The units are
+    :math:`\mathrm{V / Hz}`.
+
+    For the other methods, the spectral energy density is calculated as
+
+    ..math::
+        \frac{\epsilon_0 c}{2\pi} |\int E(t) e^{-i \omega t} dt| ^ 2
+
+    If ``method=="on_axis"``, a 1D real array with on-axis value of the
+    equation above is returned. The units are :math:`\mathrm{J / (rad Hz m^2)}`.
+
+    Otherwise, if ``method=="sum"`` (default), the transverse integral of the
+    spectral energy density is calculated:
+
+    ..math::
+        \frac{\epsilon_0 c}{2\pi} \int |\int E(t) e^{-i \omega t} dt| ^ 2 dx dy
+
+    The units of this array are :math:`\mathrm{J / (rad Hz)}`
+
     Parameters
     ----------
     grid : a Grid object.
@@ -245,25 +275,24 @@ def get_spectrum(
         Angular frequency at which the envelope is defined. Required if
         `is_envelope=True`.
 
-    mode : {'sum', 'on_axis', 'full'} (optional)
-        Whether to return the summed spectrum along the transverse direction(s),
-        the on-axis spectrum, or the full (unsumed) spectrum in the whole
-        transverse domain.
+    method : {'sum', 'on_axis', 'raw'} (optional)
+        Determines the type of spectrum that is returned as described above.
+        By default 'sum'.
 
     Returns
     -------
-    spectrum : ndarray of doubles
-        Array with the spectral density in J/(rad/s).
+    spectrum : ndarray
+        Array with the spectrum (units and array type depend on ``method``).
 
-    omega_spectrum : scalar
-        Array with the frequencies of the spectrum.
+    omega : ndarray
+        Array with the angular frequencies of the spectrum.
     """
     # Get the frequencies of the fft output.
     freq = np.fft.fftfreq(grid.field.shape[-1], d=(grid.axes[-1][1] - grid.axes[-1][0]))
-    omega_spectrum = 2 * np.pi * freq
+    omega = 2 * np.pi * freq
 
     # Get on axis or full field.
-    if mode == "on_axis":
+    if method == "on_axis":
         if dim == "xyt":
             nx, ny, nt = grid.field.shape
             field = grid.field[nx // 2, ny // 2]
@@ -277,49 +306,43 @@ def get_spectrum(
         # Assume that the FFT of the envelope and the FFT of the complex
         # conjugate of the envelope do not overlap. Then we only need
         # one of them.
-        spectrum = 0.5 * np.abs(np.fft.fft(field)) * grid.dx[-1]
-        omega_spectrum = omega0 - omega_spectrum
+        spectrum = 0.5 * np.fft.fft(field) * grid.dx[-1]
+        omega = omega0 - omega
+        # Sort frequency array (and the spectrum accordingly).
+        i_sort = np.argsort(omega)
+        omega = omega[i_sort]
+        spectrum = spectrum[..., i_sort]
+        # Keep only positive frequencies.
+        i_keep = omega >= 0
+        omega = omega[i_keep]
+        spectrum = spectrum[..., i_keep]
     else:
         spectrum = np.fft.fft(field) * grid.dx[-1]
         # Keep only positive frequencies.
         i_keep = spectrum.shape[-1] // 2
-        spectrum = np.abs(spectrum[:i_keep])
-        omega_spectrum = omega_spectrum[:i_keep]
+        omega = omega[:i_keep]
+        spectrum = spectrum[:i_keep]
 
-    # Square to get energy-like spectrum (check if appropriate).
-    spectrum = spectrum**2
+    # Convert to spectral energy density (J/(m^2 rad Hz)).
+    if method != "raw":
+        spectrum = np.abs(spectrum)**2 * epsilon_0 * c / np.pi
 
-    # Sum spectrum transversely.
-    dV = get_grid_cell_volume(grid, dim)
-    if mode == "on_axis":
-        if dim == "xyt":
-            spectrum *= dV
-        else:
-            spectrum *= dV[0]
-    else:
+    # Integrate transversely.
+    if method == "sum":
+        dV = get_grid_cell_volume(grid, dim)
+        dz = grid.dx[-1] * c
         if dim == "xyt":
-            spectrum = spectrum * dV
+            spectrum = np.sum(spectrum * dV / dz, axis=(0, 1))
         else:
-            spectrum = spectrum[0] * dV[:, np.newaxis]
-        if mode == "sum":
-            if dim == "xyt":
-                spectrum = np.sum(spectrum, axis=(0, 1))
-            else:
-                spectrum = np.sum(spectrum, axis=0)
-    spectrum *= epsilon_0 / grid.dx[-1] / np.pi
-
-    # Sort frequency array (and the spectrum accordingly).
-    i_sort = np.argsort(omega_spectrum)
-    omega_spectrum = omega_spectrum[i_sort]
-    spectrum = spectrum[..., i_sort]
+            spectrum = np.sum(spectrum[0] * dV[:, np.newaxis] / dz, axis=0)
 
     # If the user specified a frequency range, interpolate into it.
     if range is not None:
         omega_interp = np.linspace(*range, bins)
-        spectrum = np.interp(omega_interp, omega_spectrum, spectrum)
-        omega_spectrum = omega_interp
+        spectrum = np.interp(omega_interp, omega, spectrum)
+        omega = omega_interp
 
-    return spectrum, omega_spectrum
+    return spectrum, omega
 
 
 def get_frequency(

From 6e485b5644c5aaac54e24461568577d5a0f72e25 Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Wed, 23 Aug 2023 15:41:51 +0200
Subject: [PATCH 25/30] Update test

---
 tests/test_laser_utils.py | 25 +------------------------
 1 file changed, 1 insertion(+), 24 deletions(-)

diff --git a/tests/test_laser_utils.py b/tests/test_laser_utils.py
index 9136b1c0..15e13f81 100644
--- a/tests/test_laser_utils.py
+++ b/tests/test_laser_utils.py
@@ -43,30 +43,7 @@ def test_laser_analysis_utils():
         d_omega = omega[1] - omega[0]
         spectrum_energy = np.sum(spectrum) * d_omega
         energy = compute_laser_energy(dim, laser.grid)
-        np.testing.assert_approx_equal(spectrum_energy, energy, significant=14)
-
-        # Check that:
-        # 1. The on-axis spectrum agrees with the on-axis value of the full spectrum
-        # 2. The summed full spectrum agrees with the summed spectrum.
-        spectrum_oa, omega = get_spectrum(
-            laser.grid,
-            dim,
-            is_envelope=True,
-            omega0=laser.profile.omega0,
-            mode="on_axis",
-        )
-        spectrum_full, omega = get_spectrum(
-            laser.grid, dim, is_envelope=True, omega0=laser.profile.omega0, mode="full"
-        )
-        if dim == "xyt":
-            nx, ny, nt = laser.grid.field.shape
-            spectrum_oa_from_full = spectrum_full[nx // 2, ny // 2]
-            spectrum_sum_from_full = np.sum(spectrum_full, axis=(0, 1))
-        else:
-            spectrum_oa_from_full = spectrum_full[0, 0]
-            spectrum_sum_from_full = np.sum(spectrum_full, axis=(0))
-        np.testing.assert_allclose(spectrum_oa_from_full, spectrum_oa, rtol=1e-13)
-        np.testing.assert_allclose(spectrum_sum_from_full, spectrum, rtol=1e-13)
+        np.testing.assert_approx_equal(spectrum_energy, energy, significant=10)
 
         # Check that laser duration agrees with the given one.
         tau_rms = get_duration(laser.grid, dim)

From 1b0f5ab391bcca0efb0bca75c684f75403d86d84 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 23 Aug 2023 13:42:27 +0000
Subject: [PATCH 26/30] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 lasy/utils/laser_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index d07adf17..fd0dc96e 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -325,7 +325,7 @@ def get_spectrum(
 
     # Convert to spectral energy density (J/(m^2 rad Hz)).
     if method != "raw":
-        spectrum = np.abs(spectrum)**2 * epsilon_0 * c / np.pi
+        spectrum = np.abs(spectrum) ** 2 * epsilon_0 * c / np.pi
 
     # Integrate transversely.
     if method == "sum":

From 85e4fc1d00a4d8d958cc7e4f6408a1f6c5c09df2 Mon Sep 17 00:00:00 2001
From: Angel Ferran Pousa <angel.ferran.pousa@desy.de>
Date: Wed, 23 Aug 2023 15:55:35 +0200
Subject: [PATCH 27/30] Fix bug

---
 lasy/utils/laser_utils.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index fd0dc96e..01924cbb 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -321,7 +321,7 @@ def get_spectrum(
         # Keep only positive frequencies.
         i_keep = spectrum.shape[-1] // 2
         omega = omega[:i_keep]
-        spectrum = spectrum[:i_keep]
+        spectrum = spectrum[..., :i_keep]
 
     # Convert to spectral energy density (J/(m^2 rad Hz)).
     if method != "raw":
@@ -337,7 +337,7 @@ def get_spectrum(
             spectrum = np.sum(spectrum[0] * dV[:, np.newaxis] / dz, axis=0)
 
     # If the user specified a frequency range, interpolate into it.
-    if range is not None:
+    if method in ["sum", "on_axis"] and range is not None:
         omega_interp = np.linspace(*range, bins)
         spectrum = np.interp(omega_interp, omega, spectrum)
         omega = omega_interp

From 75116977614bfccacece0d71a596905a5cdc48b0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=81ngel=20Ferran=20Pousa?= <angelmail_97@msn.com>
Date: Wed, 23 Aug 2023 16:27:04 +0200
Subject: [PATCH 28/30] Update lasy/utils/laser_utils.py
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-authored-by: Maxence Thévenet <maxence.thevenet@desy.de>
---
 lasy/utils/laser_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 01924cbb..e48c6a64 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -210,7 +210,7 @@ def get_spectrum(
     grid, dim, range=None, bins=20, is_envelope=True, omega0=None, method="sum"
 ):
     r"""
-    Get the the frequency spectrum of an envelope or electric field.
+    Get the frequency spectrum of an envelope or electric field.
 
     The spectrum can be calculated in three different ways, depending on the
     `method` specified by the user:

From 07c8f71cec29ea6c27151e61df5ba5371705ff2b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=81ngel=20Ferran=20Pousa?= <angelmail_97@msn.com>
Date: Wed, 23 Aug 2023 16:27:21 +0200
Subject: [PATCH 29/30] Update lasy/utils/laser_utils.py
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-authored-by: Maxence Thévenet <maxence.thevenet@desy.de>
---
 lasy/utils/laser_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index e48c6a64..4b140e65 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -263,7 +263,7 @@ def get_spectrum(
         will be returned using interpolation.
 
     bins : int (optional)
-        Number of bins of to which to interpolate the spectrum if a `range`
+        Number of bins into which to interpolate the spectrum if a `range`
         is given.
 
     is_envelope : bool (optional)

From e18c7b484524351a08f771a1ba612ea3158a7c03 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=81ngel=20Ferran=20Pousa?= <angelmail_97@msn.com>
Date: Wed, 23 Aug 2023 16:27:32 +0200
Subject: [PATCH 30/30] Update lasy/utils/laser_utils.py
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Co-authored-by: Maxence Thévenet <maxence.thevenet@desy.de>
---
 lasy/utils/laser_utils.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lasy/utils/laser_utils.py b/lasy/utils/laser_utils.py
index 4b140e65..b86e9673 100644
--- a/lasy/utils/laser_utils.py
+++ b/lasy/utils/laser_utils.py
@@ -269,7 +269,7 @@ def get_spectrum(
     is_envelope : bool (optional)
         Whether the field provided uses the envelope representation, as used
         internally in lasy. If False, field is assumed to represent the
-        the electric field.
+        the full electric field (with fast oscillations).
 
     omega0 : scalar (optional)
         Angular frequency at which the envelope is defined. Required if