diff --git a/src/scgenerator/cache.py b/src/scgenerator/cache.py
index 61ff949..1f11bb5 100644
--- a/src/scgenerator/cache.py
+++ b/src/scgenerator/cache.py
@@ -122,11 +122,14 @@ class Cache:
         stuff = pickle.loads(fn.read_bytes())
         return stuff
 
-    @check_exists
     def save(self, key: str, value: Any):
+        self.save_raw(key, pickle.dumps(value))
+
+    @check_exists
+    def save_raw(self, key: str, value: bytes):
         key = normalize_path(key)
         fn = self.dir / key
-        fn.write_bytes(pickle.dumps(value))
+        fn.write_bytes(value)
 
     @check_exists
     def reset(self):
diff --git a/src/scgenerator/evaluator.py b/src/scgenerator/evaluator.py
index c455101..56c7957 100644
--- a/src/scgenerator/evaluator.py
+++ b/src/scgenerator/evaluator.py
@@ -528,10 +528,11 @@ default_rules: list[Rule] = [
     Rule("gamma", lambda gamma_arr: gamma_arr[0], priorities=-1),
     Rule("gamma", fiber.gamma_parameter),
     Rule("gamma_arr", fiber.gamma_parameter, ["n2", "w0", "effective_area_arr"]),
+    Rule("gamma_arr", lambda t_num, gamma: np.ones(t_num) * gamma, priorities=-1),
     # Raman
     Rule(["hr_w", "raman_fraction"], fiber.delayed_raman_w),
     Rule("raman_fraction", fiber.raman_fraction),
-    Rule("raman_fraction", lambda: 0, priorities=-1),
+    Rule("raman_fraction", lambda: 0.0, priorities=-1),
     # loss
     Rule("alpha_arr", fiber.scalar_loss),
     Rule("alpha_arr", fiber.safe_capillary_loss, conditions=dict(loss="capillary")),
diff --git a/src/scgenerator/math.py b/src/scgenerator/math.py
index 1301f00..8af17b5 100644
--- a/src/scgenerator/math.py
+++ b/src/scgenerator/math.py
@@ -131,7 +131,7 @@ def sigmoid(x):
     return 1 / (np.exp(-x) + 1)
 
 
-def to_dB(arr: np.ndarray, ref=None, axis=None) -> np.ndarray:
+def to_dB(arr: np.ndarray, ref=None, axis=None, default: float | None = None) -> np.ndarray:
     """
     converts unitless values in dB
 
@@ -151,17 +151,26 @@ def to_dB(arr: np.ndarray, ref=None, axis=None) -> np.ndarray:
         array in dB
     """
     if axis is not None and arr.ndim > 1 and ref is None:
-        return np.apply_along_axis(to_dB, axis, arr)
+        return np.apply_along_axis(to_dB, axis, arr, default=default)
 
     out = np.ones_like(arr)
+    if default is not None and math.isfinite(default):
+        out[:] *= default
+    else:
+        out *= np.nan
+
     if ref is None:
         ref = np.max(arr)
     above_0 = arr > 0
     if not np.any(above_0) or ref <= 0:
-        warnings.warn("invalid array to convert to dB, returning 0 instead")
+        warnings.warn(f"invalid array to convert to dB, returning {default} instead")
+        if default is None:
+            out *= np.nan
         return out
     m = arr / ref
-    return 10 * np.log10(m, out=out * (10 * np.log10(m[above_0].min())), where=above_0)
+    if default is None:
+        out *= 10 * np.log10(m[above_0].min())
+    return 10 * np.log10(m, out=out, where=above_0)
 
 
 def u_nm(n, m):
diff --git a/src/scgenerator/operators.py b/src/scgenerator/operators.py
index cc410e7..2934397 100644
--- a/src/scgenerator/operators.py
+++ b/src/scgenerator/operators.py
@@ -518,7 +518,7 @@ def no_linear() -> VariableQuantity:
 
 def build_envelope_nonlinear(
     w: np.ndarray, gamma: float, self_steepening: bool = True, raman: str | None = "measured"
-) -> tuple[VariableQuantity, SpecOperator]:
+) -> SpecOperator:
     w0 = w[0]
     t = math.iwspace(w)
     w_c = w - w0
@@ -528,9 +528,8 @@ def build_envelope_nonlinear(
         ss_op = constant_quantity(0.0)
 
     if gamma != 0:
-        raman_frac = fiber.raman_fraction(raman) if raman else 0.0
+        hr_w, raman_frac = fiber.delayed_raman_w(t, raman)
         spm_op = envelope_spm(raman_frac)
-        hr_w = fiber.delayed_raman_w(t, raman)
         raman_op = envelope_raman(hr_w, raman_frac, sfft.fft, sfft.ifft)
         gamma_op = constant_quantity(np.ones(len(w)) * gamma)
     else:
diff --git a/src/scgenerator/parameter.py b/src/scgenerator/parameter.py
index 6f40121..55331fc 100644
--- a/src/scgenerator/parameter.py
+++ b/src/scgenerator/parameter.py
@@ -2,6 +2,7 @@ from __future__ import annotations
 
 import datetime as datetime_module
 import json
+from operator import pos
 import os
 import tomllib
 import warnings
@@ -360,6 +361,7 @@ class Parameters:
     shape: str = Parameter(literal("gaussian", "sech"))
     wavelength: float = Parameter(in_range_incl(100e-9, 10000e-9), unit="m")
     intensity_noise: float = Parameter(in_range_incl(0, 1), unit="%")
+    ase_level: float = Parameter(positive(*number), default=1.0)
     noise_correlation: float = Parameter(in_range_incl(-10, 10))
     width: float = Parameter(positive(*number), unit="s")
     t0: float = Parameter(positive(*number), unit="s")
diff --git a/src/scgenerator/physics/fiber.py b/src/scgenerator/physics/fiber.py
index c1d3912..061f56a 100644
--- a/src/scgenerator/physics/fiber.py
+++ b/src/scgenerator/physics/fiber.py
@@ -620,7 +620,7 @@ def load_custom_effective_area(effective_area_file: DataFile, l: np.ndarray) ->
     wl, effective_area = effective_area_file.load_arrays(
         ("wavelength", "wl"), ("A_eff", "effective_area")
     )
-    return np.interp(l, wl, effective_area, left=0, right=0)
+    return np.interp(l, wl, effective_area)
 
 
 def load_custom_dispersion(
@@ -777,8 +777,7 @@ def delayed_raman_t(t: np.ndarray, raman_type: str) -> np.ndarray:
 
         hr_arr = np.interp(t, t_stored, hr_arr_stored, left=0, right=0)
     else:
-        print("invalid raman response function, aborting")
-        quit()
+        raise ValueError("invalid raman response function, aborting")
 
     return hr_arr
 
diff --git a/src/scgenerator/physics/pulse.py b/src/scgenerator/physics/pulse.py
index 8096a3a..8a1522d 100644
--- a/src/scgenerator/physics/pulse.py
+++ b/src/scgenerator/physics/pulse.py
@@ -538,7 +538,13 @@ def sech_pulse(t: np.ndarray, t0: float, P0: float, chirp: float = 0.0):
 
 
 def gaussian_pulse(t: np.ndarray, t0: float, P0: float, chirp: float = 0.0):
-    return np.sqrt(P0) * np.exp(-((t / t0) ** 2) * (1 - 1j * chirp))
+    """
+    for unchirped pulses, the following, slower, formula is equivalent
+    ```
+    return np.sqrt(P0) * 4 ** (-(t / fwhm) ** 2)
+    ```
+    """
+    return np.sqrt(P0) * np.exp((1j * chirp - 1.0) * ((t / t0) ** 2))
 
 
 def pulse_envelope(
@@ -659,10 +665,11 @@ def finalize_pulse(
     quantum_noise: ShotNoiseParameter,
     w: np.ndarray,
     input_transmission: float,
+    ase_level: float = 1.0,
 ) -> np.ndarray:
     pre_field_0 *= np.sqrt(input_transmission)
     if quantum_noise:
-        pre_field_0 = pre_field_0 + np.fft.ifft(shot_noise(w, *quantum_noise))
+        pre_field_0 = pre_field_0 + np.fft.ifft(np.sqrt(ase_level) * shot_noise(w, *quantum_noise))
 
     return pre_field_0
 
@@ -1379,3 +1386,13 @@ def remove_2nd_order_dispersion2(
 
 def gdd(w: np.ndarray, gdd: float) -> np.ndarray:
     return np.exp(0.5j * w**2 * gdd)
+
+
+def mask_with_noise(
+    w: np.ndarray,
+    spectrum: T,
+    mask: np.ndarray,
+    sn_params: ShotNoiseParameter = ShotNoiseParameter(False, False),
+) -> T:
+    sn = shot_noise(w, *sn_params)
+    return spectrum * mask + np.sqrt(1.0 - mask**2) * sn
diff --git a/src/scgenerator/plotting.py b/src/scgenerator/plotting.py
index 377a0c7..9a08b16 100644
--- a/src/scgenerator/plotting.py
+++ b/src/scgenerator/plotting.py
@@ -46,6 +46,13 @@ def alt_color(c, fac: float):
     return (*colorsys.hsv_to_rgb(h, s, min(1, v * fac)), alpha)
 
 
+def lighten_rgb(c, fac: float):
+    if isinstance(c, (list, tuple)) or (isinstance(c, np.ndarray) and c.ndim > 1):
+        return np.array([alt_color(el, fac) for el in c])
+    *color, a = ColorConverter.to_rgba(c)
+    return (*(min(max(el + (1.0 - el) * fac, 0.0), 1.0) for el in color), a)
+
+
 def get_extent(x, y, facx=1, facy=1):
     """
     returns the extent 4-tuple needed for imshow, aligning each pixel
@@ -1005,7 +1012,9 @@ def uniform_axis(
     return new_axis, values.squeeze()
 
 
-def apply_log(values: np.ndarray, log: Union[str, bool, float, int]) -> np.ndarray:
+def apply_log(
+    values: np.ndarray, log: Union[str, bool, float, int], default: float = 1.0
+) -> np.ndarray:
     """
     apply log transform
 
@@ -1034,15 +1043,15 @@ def apply_log(values: np.ndarray, log: Union[str, bool, float, int]) -> np.ndarr
 
     if log is not False:
         if isinstance(log, (float, int, np.floating, np.integer)) and log is not True:
-            values = math.to_dB(values, ref=log)
+            values = math.to_dB(values, ref=log, default=default)
         elif log == "2D":
-            values = math.to_dB(values, ref=values.max())
+            values = math.to_dB(values, ref=values.max(), default=default)
         elif log == "1D" or log is True:
-            values = math.to_dB(values, axis=1)
+            values = math.to_dB(values, axis=1, default=default)
         elif log == "smooth 1D":
             ref = np.max(values, axis=1)
             ind = np.argmax((ref[:-1] - ref[1:]) < 0)
-            values = math.to_dB(values, ref=np.max(ref[ind:]))
+            values = math.to_dB(values, ref=np.max(ref[ind:]), default=default)
         elif log == "linear 1D":
             values = (values.T / values.max(axis=1)).T
         else:
diff --git a/src/scgenerator/spectra.py b/src/scgenerator/spectra.py
index 27dd5b6..6ce49ae 100644
--- a/src/scgenerator/spectra.py
+++ b/src/scgenerator/spectra.py
@@ -151,6 +151,9 @@ class Spectrum(np.ndarray):
             + self.astype(np.complex128, subok=False).tobytes()
         )
 
+    def __reduce__(self) -> tuple[type, tuple[bytes]]:
+        return self.__class__.from_bytes, (bytes(self),)
+
     def tobytes(self, *args, **kwargs) -> bytes:
         warnings.warn(
             "Calling `tobytes` (numpy function) on Spectrum object. Did you mean `bytes(obj)`?"
@@ -205,6 +208,7 @@ class Spectrum(np.ndarray):
     def energy(self) -> np.ndarray:
         return np.trapz(self.time_int, x=self.t, axis=-1)
 
+    # FIX: rename with bandpass and make a generic wrapper of pulse.mask_with_noise
     def mask_wl(
         self,
         pos: float,
@@ -263,7 +267,7 @@ class Spectrum(np.ndarray):
         gate_width: float = 100e-15,
         wavelength: bool = True,
         autocrop: bool | float = 1e-5,
-    ) -> np.ndarray:
+    ) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
         dt = self.t[1] - self.t[0]
         sigma = gate_width / (2 * np.sqrt(2 * np.log(2))) / dt
         nperseg = int(sigma) * 16
diff --git a/tests/test_pulse.py b/tests/test_pulse.py
index 0580e52..00b0b30 100644
--- a/tests/test_pulse.py
+++ b/tests/test_pulse.py
@@ -32,3 +32,4 @@ def test_chirp():
     c2 = np.unwrap(np.angle(f2))
     c2 -= c2.min()
     assert pytest.approx(c2, rel=1e-2, abs=1e-4) == t2**2
+    assert pytest.approx(sc.abs2(f2)) == 16 ** (-((t2 / np.sqrt(2 * np.log(2))) ** 2))