diff --git a/src/scgenerator/math.py b/src/scgenerator/math.py
index 21be5fa..ab9860d 100644
--- a/src/scgenerator/math.py
+++ b/src/scgenerator/math.py
@@ -359,6 +359,32 @@ def _polynom_extrapolation_in_place(y: np.ndarray, left_ind: int, right_ind: int
     return y
 
 
+@numba.jit(nopython=True)
+def linear_interp_2d(old_x: np.ndarray, old_y: np.ndarray, new_x: np.ndarray):
+    new_vals = np.zeros((len(old_y), len(new_x)))
+    interpolable = (new_x > old_x[0]) & (new_x <= old_x[-1])
+    equal = new_x == old_x[0]
+    inds = np.searchsorted(old_x, new_x[interpolable])
+    for i, val in enumerate(old_y):
+        new_vals[i][interpolable] = val[inds - 1] + (new_x[interpolable] - old_x[inds - 1]) * (
+            val[inds] - val[inds - 1]
+        ) / (old_x[inds] - old_x[inds - 1])
+        new_vals[i][equal] = val[0]
+    return new_vals
+
+
+@numba.jit(nopython=True)
+def linear_interp_1d(old_x: np.ndarray, old_y: np.ndarray, new_x: np.ndarray):
+    new_vals = np.zeros(len(new_x))
+    interpolable = (new_x > old_x[0]) & (new_x <= old_x[-1])
+    inds = np.searchsorted(old_x, new_x[interpolable])
+    new_vals[interpolable] = old_y[inds - 1] + (new_x[interpolable] - old_x[inds - 1]) * (
+        old_y[inds] - old_y[inds - 1]
+    ) / (old_x[inds] - old_x[inds - 1])
+    new_vals[new_x == old_x[0]] = old_y[0]
+    return new_vals
+
+
 def envelope_ind(
     signal: np.ndarray, dmin: int = 1, dmax: int = 1, split: bool = False
 ) -> tuple[np.ndarray, np.ndarray]:
diff --git a/src/scgenerator/parameter.py b/src/scgenerator/parameter.py
index 2cdccbc..4734f69 100644
--- a/src/scgenerator/parameter.py
+++ b/src/scgenerator/parameter.py
@@ -374,7 +374,7 @@ class Parameters:
     t_num: int = Parameter(positive(int))
     z_num: int = Parameter(positive(int))
     time_window: float = Parameter(positive(float, int))
-    dt: float = Parameter(in_range_excl(0, 5e-15))
+    dt: float = Parameter(in_range_excl(0, 10e-15))
     tolerated_error: float = Parameter(in_range_excl(1e-15, 1e-3), default=1e-11)
     step_size: float = Parameter(non_negative(float, int), default=0)
     interpolation_range: tuple[float, float] = Parameter(
diff --git a/src/scgenerator/physics/pulse.py b/src/scgenerator/physics/pulse.py
index d3eff47..778cfd8 100644
--- a/src/scgenerator/physics/pulse.py
+++ b/src/scgenerator/physics/pulse.py
@@ -15,6 +15,7 @@ from dataclasses import astuple, dataclass
 from pathlib import Path
 from typing import Literal, Tuple, TypeVar
 
+import numba
 import matplotlib.pyplot as plt
 import numpy as np
 from numpy import pi
@@ -570,7 +571,9 @@ def ideal_compressed_pulse(spectra):
     return math.abs2(fftshift(ifft(np.sqrt(np.mean(math.abs2(spectra), axis=0)))))
 
 
-def spectrogram(time, values, t_res=256, t_win=24e-12, gate_width=200e-15, shift=False):
+def spectrogram(
+    time, values, t_res=256, t_win=24e-12, gate_width=200e-15, shift=False, w_ind: np.ndarray = None
+):
     """
     returns the spectorgram of the field given in values
 
@@ -594,14 +597,62 @@ def spectrogram(time, values, t_res=256, t_win=24e-12, gate_width=200e-15, shift
         delays : 1D array of size t_res
             new time axis
     """
-    t_lim = t_win / 2
-    delays = np.linspace(-t_lim, t_lim, t_res)
-    spec = np.zeros((t_res, len(time)))
+    if isinstance(t_win, tuple):
+        left, right = t_win
+    else:
+        t_lim = t_win / 2
+        left, right = -t_lim, t_lim
+
+    delays = np.linspace(left, right, t_res)
+
+    spec = np.zeros((t_res, len(time) if w_ind is None else len(w_ind)))
     for i, delay in enumerate(delays):
         masked = values * np.exp(-(((time - delay) / gate_width) ** 2))
         spec[i] = math.abs2(fft(masked))
-        if shift:
-            spec[i] = fftshift(spec[i])
+
+    if shift:
+        spec = fftshift(spec, axes=1)
+    return spec, delays
+
+
+def spectrogram_interp(
+    time: np.ndarray,
+    delays: np.ndarray,
+    values: np.ndarray,
+    old_w: np.ndarray,
+    w_ind: np.ndarray,
+    new_w: np.ndarray,
+    gate_width=200e-15,
+):
+    """
+    returns the spectorgram of the field already interpolated along the frequency axis
+
+    Parameters
+    ----------
+        time : 1D array-like
+            time in the co-moving frame of reference
+        values : 1D array-like
+            field array that matches the time array
+        t_res : int, optional
+            how many "bins" the time array is subdivided into. Default : 256
+        t_win : float, optional
+            total time window (=length of time) over which the spectrogram is computed. Default : 24e-12
+        gate_width : float, optional
+            width of the gaussian gate function (=sqrt(2 log(2)) * FWHM). Default : 200e-15
+
+    Returns
+    ----------
+        spec : 2D array
+            real 2D spectrogram
+        delays : 1D array of size t_res
+            new time axis
+    """
+
+    spec = np.zeros((len(delays), len(new_w)))
+    for i, delay in enumerate(delays):
+        masked = values * np.exp(-(((time - delay) / gate_width) ** 2))
+        spec[i] = math.linear_interp_1d(old_w, math.abs2(fft(masked)[w_ind]), new_w)
+
     return spec, delays
 
 
diff --git a/src/scgenerator/physics/simulate.py b/src/scgenerator/physics/simulate.py
index 17b7079..c607459 100644
--- a/src/scgenerator/physics/simulate.py
+++ b/src/scgenerator/physics/simulate.py
@@ -180,6 +180,7 @@ class RK4IP:
                 state, self.params.linear_operator, self.params.nonlinear_operator
             )
         with warnings.catch_warnings():
+            # catch overflows as errors
             warnings.filterwarnings("error", category=RuntimeWarning)
             for state in integrator:
 
diff --git a/src/scgenerator/physics/units.py b/src/scgenerator/physics/units.py
index f1c8348..01fa75e 100644
--- a/src/scgenerator/physics/units.py
+++ b/src/scgenerator/physics/units.py
@@ -47,6 +47,7 @@ class UnitMap(dict):
         def chained_function(x: _T) -> _T:
             return c2.inv(c1(x))
 
+        chained_function.name = f"{name_1}_to_{name_2}"
         chained_function.__name__ = f"{name_1}_to_{name_2}"
         chained_function.__doc__ = f"converts x from {name_1} to {name_2}"
 
@@ -124,17 +125,17 @@ class unit:
         return func
 
 
-@unit("WL", r"Wavelength $\lambda$ (m)")
+@unit("WL", r"Wavelength λ (m)")
 def m(l: _T) -> _T:
     return 2 * pi * c / l
 
 
-@unit("WL", r"Wavelength $\lambda$ (nm)")
+@unit("WL", r"Wavelength λ (nm)")
 def nm(l: _T) -> _T:
     return 2 * pi * c / (l * 1e-9)
 
 
-@unit("WL", r"Wavelength $\lambda$ (μm)")
+@unit("WL", r"Wavelength λ (μm)")
 def um(l: _T) -> _T:
     return 2 * pi * c / (l * 1e-6)
 
@@ -418,6 +419,10 @@ class PlotRange(tuple):
     conserved_quantity: bool = property(itemgetter(3))
     __slots__ = []
 
+    @property
+    def must_correct_wl(self) -> bool:
+        return self.unit.type == "WL" and self.conserved_quantity
+
     def __new__(cls, left, right, unit, conserved_quantity=True):
         return tuple.__new__(cls, (left, right, get_unit(unit), conserved_quantity))
 
@@ -461,8 +466,8 @@ def sort_axis(
     rw = (-4, 4, s)
     rt = (-2, 6, s)
 
-    w, cw = sort_axis(w, rw)
-    t, ct = sort_axis(t, rt)
+    w, cw, _ = sort_axis(w, rw)
+    t, ct, _ = sort_axis(t, rt)
 
     # slice y according to the given ranges
     y = y[ct][:, cw]
diff --git a/src/scgenerator/plotting.py b/src/scgenerator/plotting.py
index 6114fd5..9290424 100644
--- a/src/scgenerator/plotting.py
+++ b/src/scgenerator/plotting.py
@@ -4,6 +4,7 @@ from typing import Any, Callable, Literal, Optional, Union
 
 import matplotlib.gridspec as gs
 import matplotlib.pyplot as plt
+import numba
 import numpy as np
 from matplotlib.colors import ListedColormap
 from scipy.interpolate import UnivariateSpline
@@ -12,7 +13,7 @@ from scipy.interpolate.interpolate import interp1d
 from . import math
 from .const import PARAM_SEPARATOR
 from .defaults import default_plotting as defaults
-from .math import abs2, span
+from .math import abs2, span, linear_interp_2d
 from .parameter import Parameters
 from .physics import pulse, units
 from .physics.units import PlotRange, sort_axis
@@ -256,8 +257,10 @@ def corner_annotation(text, ax, position="tl", rel_x_offset=0.05, rel_y_offset=0
 def propagation_plot(
     values: np.ndarray,
     plt_range: Union[PlotRange, RangeType],
-    params: Parameters,
-    ax: plt.Axes,
+    x_axis: np.ndarray = None,
+    y_axis: np.ndarray = None,
+    params: Parameters = None,
+    ax: Union[plt.Axes, tuple[plt.Axes, plt.Axes]] = None,
     log: Union[int, float, bool, str] = "1D",
     renormalize: bool = False,
     vmin: float = None,
@@ -295,10 +298,12 @@ def propagation_plot(
         Axes obj on which to draw, by default None
 
     """
-    x_axis, y_axis, values = transform_2D_propagation(values, plt_range, params, log, skip)
-    if renormalize and log is False:
+    x_axis, y_axis, values = transform_2D_propagation(
+        values, plt_range, x_axis, y_axis, log, skip, params
+    )
+    if renormalize and not log:
         values = values / values.max()
-    if log is not False:
+    if log:
         vmax = defaults["vmax"] if vmax is None else vmax
         vmin = defaults["vmin"] if vmin is None else vmin
     plot_2D(
@@ -320,7 +325,7 @@ def plot_2D(
     values: np.ndarray,
     x_axis: np.ndarray,
     y_axis: np.ndarray,
-    ax: Union[plt.Axes, tuple[plt.Axes, plt.Axes]],
+    ax: Union[plt.Axes, tuple[plt.Axes, plt.Axes]] = None,
     x_label: str = None,
     y_label: str = None,
     vmin: float = None,
@@ -367,6 +372,8 @@ def plot_2D(
     cbar_ax = None
     if isinstance(ax, tuple) and len(ax) > 1:
         ax, cbar_ax = ax[0], ax[1]
+    elif ax is None:
+        ax = plt.gca()
 
     fig = ax.get_figure()
 
@@ -414,10 +421,11 @@ def plot_2D(
 def transform_2D_propagation(
     values: np.ndarray,
     plt_range: Union[PlotRange, RangeType],
-    params: Parameters,
+    x_axis: np.ndarray = None,
+    y_axis: np.ndarray = None,
     log: Union[int, float, bool, str] = "1D",
     skip: int = 1,
-    y_axis=None,
+    params: Parameters = None,
 ) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
     """transforms raws values into plottable values
 
@@ -427,7 +435,11 @@ def transform_2D_propagation(
         values to transform
     plt_range : Union[PlotRange, RangeType]
         range
-    params : Parameters
+    x_axis : np.ndarray
+        corresponding x values in SI units
+    y_axis : np.ndarray
+        corresponding y values in SI units
+    params : Parameters, optional
         parameters of the simulation
     log : Union[int, float, bool, str], optional
         see apply_log, by default "1D"
@@ -448,16 +460,17 @@ def transform_2D_propagation(
     ValueError
         incorrect shape
     """
+    x_axis = get_x_axis(plt_range, x_axis, params)
+    if y_axis is None and params is not None:
+        y_axis = params.z_targets
 
     if values.ndim != 2:
         raise ValueError(f"shape was {values.shape}. Can only plot 2D array")
-    is_complex, x_axis, plt_range = prep_plot_axis(values, plt_range, params)
+    is_complex, plt_range = prep_plot_axis(values, plt_range)
     if is_complex or any(values.ravel() < 0):
         values = abs2(values)
     # if params.full_field and plt_range.unit.type == "TIME":
     #     values = envelope_2d(x_axis, values)
-    if y_axis is None:
-        y_axis = params.z_targets
 
     x_axis, values = uniform_axis(x_axis, values, plt_range)
     y_axis, values.T[:] = uniform_axis(y_axis, values.T, None)
@@ -465,6 +478,17 @@ def transform_2D_propagation(
     return x_axis[::skip], y_axis, values[:, ::skip]
 
 
+def get_x_axis(plt_range, x_axis, params) -> np.ndarray:
+    if x_axis is None and params is not None:
+        if plt_range.unit.type in {"WL", "FREQ", "AFREQ"}:
+            x_axis = params.w.copy()
+        else:
+            x_axis = params.t.copy()
+    if x_axis is None:
+        raise ValueError("No x axis specified")
+    return x_axis
+
+
 def mean_values_plot(
     values: np.ndarray,
     plt_range: Union[PlotRange, RangeType],
@@ -538,10 +562,11 @@ def transform_mean_values(
     np.ndarray, shape (m, n)
         all the values
     """
+    AAA
     if values.ndim != 2:
         print(f"Shape was {values.shape}. Can only plot 2D arrays")
         return
-    is_complex, x_axis, plt_range = prep_plot_axis(values, plt_range, params)
+    is_complex, plt_range = prep_plot_axis(values, plt_range, params)
     if is_complex:
         values = abs2(values)
     new_axis, ind, ext = sort_axis(x_axis, plt_range)
@@ -636,8 +661,9 @@ def plot_mean(
 def single_position_plot(
     values: np.ndarray,
     plt_range: Union[PlotRange, RangeType],
-    params: Parameters,
-    ax: plt.Axes,
+    x_axis: np.ndarray = None,
+    ax: plt.Axes = None,
+    params: Parameters = None,
     log: Union[str, int, float, bool] = False,
     vmin: float = None,
     vmax: float = None,
@@ -647,8 +673,7 @@ def single_position_plot(
     y_label: str = None,
     **line_kwargs,
 ) -> tuple[plt.Figure, plt.Axes, plt.Line2D, np.ndarray, np.ndarray]:
-
-    x_axis, values = transform_1D_values(values, plt_range, params, log, spacing)
+    x_axis, values = transform_1D_values(values, plt_range, x_axis, params, log, spacing)
     if renormalize:
         values = values / values.max()
 
@@ -664,7 +689,7 @@ def single_position_plot(
 def plot_1D(
     values: np.ndarray,
     x_axis: np.ndarray,
-    ax: plt.Axes,
+    ax: Optional[plt.Axes],
     x_label: str = None,
     y_label: str = None,
     vmin: float = None,
@@ -693,11 +718,18 @@ def plot_1D(
     transpose : bool, optional
         rotate the plot 90° counterclockwise, by default False
     """
-    if transpose:
+    if ax is None:
+        ax = plt.gca()
+    if transpose == -1:
+        (line,) = ax.plot(values, x_axis, **line_kwargs)
+        ax.set_xlim(vmax, vmin)
+        ax.set_xlabel(y_label)
+        ax.set_ylabel(x_label)
+    elif transpose == 1:
         (line,) = ax.plot(values, x_axis, **line_kwargs)
         ax.yaxis.tick_right()
         ax.yaxis.set_label_position("right")
-        ax.set_xlim(vmax, vmin)
+        ax.set_xlim(vmin, vmax)
         ax.set_xlabel(y_label)
         ax.set_ylabel(x_label)
     else:
@@ -711,7 +743,8 @@ def plot_1D(
 def transform_1D_values(
     values: np.ndarray,
     plt_range: Union[PlotRange, RangeType],
-    params: Parameters,
+    x_axis: np.ndarray = None,
+    params: Parameters = None,
     log: Union[int, float, bool] = False,
     spacing: Union[int, float] = 1,
 ) -> tuple[np.ndarray, np.ndarray]:
@@ -737,9 +770,10 @@ def transform_1D_values(
     tuple[np.ndarray, np.ndarray]
         x axis and values
     """
+    x_axis = get_x_axis(plt_range, x_axis, params)
     if len(values.shape) != 1:
         raise ValueError("Can only plot 1D values")
-    is_complex, x_axis, plt_range = prep_plot_axis(values, plt_range, params)
+    is_complex, plt_range = prep_plot_axis(values, plt_range)
     if is_complex:
         values = abs2(values)
     new_axis, ind, ext = sort_axis(x_axis, plt_range)
@@ -763,17 +797,20 @@ def transform_1D_values(
 
 def plot_spectrogram(
     values: np.ndarray,
-    x_range: RangeType,
-    y_range: RangeType,
-    params: Parameters,
-    t_res: int = None,
-    gate_width: float = None,
+    x_range: PlotRange,
+    y_range: PlotRange,
+    x_axis: np.ndarray = None,
+    y_axis: np.ndarray = None,
+    t_res: int = 512,
+    w_res: int = 512,
+    gate_width: float = 200e-15,
+    params: Parameters = None,
     log: bool = "2D",
-    vmin: float = None,
-    vmax: float = None,
+    vmin: float = -50,
+    vmax: float = 0,
     cbar_label: str = "normalized intensity (dB)",
     cmap: str = None,
-    ax: plt.Axes = None,
+    ax: Union[plt.Axes, tuple[plt.Axes, plt.Axes]] = None,
 ):
     """Plots a spectrogram given a complex field in the time domain
     Parameters
@@ -781,7 +818,7 @@ def plot_spectrogram(
     values : 2D array
         axis 0 defines the position in the fiber and axis 1 the position in time, frequency or wl
         example : [[1, 2, 3], [0, 1, 0]] describes a quantity at 3 different freq/time and at two locations in the fiber
-    x_range, y_range : tupple (min, max, units)
+    x_range, y_range : PlotRange
         one of them must be time, the other one must be wl/freq
         min, max : int or float
             minimum and maximum values given in the desired units
@@ -798,10 +835,6 @@ def plot_spectrogram(
         max value of the colorbar
     cbar_label : str or None
         label of the colorbar. Will not draw colorbar if None
-    file_type : str, optional
-        usually pdf or png
-    plt_name : str, optional
-        special name to give to the plot. A name is automatically assigned anyway
     cmap : str, optional
         colormap to be used in matplotlib.pyplot.imshow
     ax : matplotlib.axes._subplots.AxesSubplot object or tupple of 2 axis objects, optional
@@ -812,35 +845,49 @@ def plot_spectrogram(
     if values.ndim != 1:
         print("plot_spectrogram can only plot 1D arrays")
         return
-    x_range: PlotRange
-    y_range: PlotRange
-    _, x_axis, x_range = prep_plot_axis(values, x_range, params)
-    _, y_axis, y_range = prep_plot_axis(values, y_range, params)
+    x_axis = get_x_axis(x_range, x_axis, params)
+    y_axis = get_x_axis(y_range, y_axis, params)
+    _, x_range = prep_plot_axis(values, x_range)
+    _, y_range = prep_plot_axis(values, y_range)
 
     if (x_range.unit.type == "TIME") == (y_range.unit.type == "TIME"):
         print("exactly one range must be a time range")
         return
 
     # 0 axis means x-axis -> determine final orientation of spectrogram
-    time_axis = 0 if x_range.unit.type not in ["WL", "FREQ", "AFREQ"] else 1
-    if time_axis == 0:
+    time_axis = 1 if x_range.unit.type not in ["WL", "FREQ", "AFREQ"] else 1
+    if time_axis == 1:
+        t_axis = x_axis
         t_range = x_range
+        w_range = y_range
+        w_axis = y_axis
     else:
+        t_axis = y_axis
         t_range = y_range
+        w_range = x_range
+        w_axis = x_axis
+
+    old_w, w_ind, _ = w_range.sort_axis(w_axis)
+    new_w = np.linspace(w_range.left, w_range.right, w_res)
 
     # Actually compute the spectrogram
-    t_win = 2 * np.max(t_range.unit(np.abs((t_range.left, t_range.right))))
-    spec_kwargs = dict(t_res=t_res, t_win=t_win, gate_width=gate_width, shift=False)
-    spec, new_t = pulse.spectrogram(
-        params.t.copy(), values, **{k: v for k, v in spec_kwargs.items() if v is not None}
+    delays = np.linspace(t_range.unit(t_range.left), t_range.unit(t_range.right), t_res)
+    spec, new_t = pulse.spectrogram_interp(
+        t_axis, delays, values, old_w, w_ind, new_w, gate_width=gate_width
     )
-    if time_axis == 0:
-        x_axis = new_t
-    else:
-        y_axis = new_t
 
-    x_axis, spec = uniform_axis(x_axis, spec, x_range)
-    y_axis, spec.T[:] = uniform_axis(y_axis, spec.T, y_range)
+    new_t = t_range.unit.inv(new_t)
+
+    if w_range.must_correct_wl:
+        spec = np.apply_along_axis(units.to_WL, 1, spec, new_w)
+
+    if time_axis == 1:
+        spec = spec.T
+        x_axis = new_t
+        y_axis = new_w
+    else:
+        x_axis = new_w
+        y_axis = new_t
 
     values = apply_log(spec, log)
 
@@ -849,8 +896,8 @@ def plot_spectrogram(
         x_axis,
         y_axis,
         ax,
-        x_range.unit.label,
-        y_range.unit.label,
+        None,
+        None,
         vmin,
         vmax,
         False,
@@ -907,7 +954,7 @@ def uniform_axis(
         if plt_range.unit.type == "WL" and plt_range.conserved_quantity:
             values[:, ind] = np.apply_along_axis(units.to_WL, 1, values[:, ind], tmp_axis)
         new_axis = np.linspace(tmp_axis.min(), tmp_axis.max(), len(tmp_axis))
-        values = np.array([interp1d(tmp_axis, v[ind])(new_axis) for v in values])
+        values = linear_interp_2d(tmp_axis, values[:, ind], new_axis)
     return new_axis, values.squeeze()
 
 
@@ -954,16 +1001,12 @@ def apply_log(values: np.ndarray, log: Union[str, bool, float, int]) -> np.ndarr
 
 
 def prep_plot_axis(
-    values: np.ndarray, plt_range: Union[PlotRange, RangeType], params: Parameters
-) -> tuple[bool, np.ndarray, PlotRange]:
+    values: np.ndarray, plt_range: Union[PlotRange, RangeType]
+) -> tuple[bool, PlotRange]:
     is_spectrum = values.dtype == "complex"
     if not isinstance(plt_range, PlotRange):
         plt_range = PlotRange(*plt_range)
-    if plt_range.unit.type in ["WL", "FREQ", "AFREQ"]:
-        x_axis = params.w.copy()
-    else:
-        x_axis = params.t.copy()
-    return is_spectrum, x_axis, plt_range
+    return is_spectrum, plt_range
 
 
 def white_bottom_cmap(name, start=0, end=1, new_name="white_background", c_back=(1, 1, 1, 1)):