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    "# Laser Pulse with user-defined longitudinal profile\n",
    "\n",
    "In this example we show how to define a custom longitudinal profile based on an analytical expression (in this case a \"flat-top\" profile that rises smoothly from zero to one as a squared cosine, stays constant for some time, and then goes smoothly to zero as a squared cosine)."
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    "## Define a derived class of LongitudinalProfile: MyOwnLongitudinalProfile\n",
    "First, we define a new class `MyOwnLongitudinalProfile`, inheriting the `LongitudinalProfile` class. We need to implement the `__init__` method to record the parameters of the custom profile, and the `evaluate` method that should return the envelope as a function of the time."
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    "from lasy.profiles.longitudinal import LongitudinalProfile\n",
    "\n",
    "\n",
    "# User-defined profile\n",
    "class MyOwnLongitudinalProfile(LongitudinalProfile):\n",
    "    r\"\"\"\n",
    "    Derived class for the analytic longitudinal flat-top profile of a laser pulse.\n",
    "\n",
    "    i.e., a longitudinal profile that rises smoothly from zero to one (as a squared cosine),\n",
    "    stays constant for some time and then goes down smoothly to zero (as a squared cosine).\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    wavelength : float (in meter)\n",
    "        The main laser wavelength :math:`\\lambda_0` of the laser.\n",
    "    t_start : float (in seconds)\n",
    "        The starting time of the pulse,\n",
    "    t_rise : float (in seconds)\n",
    "        The rise time of the pulse envelope,\n",
    "    t_flat : float (in seconds)\n",
    "        The duration of the flat part of the pulse envelope,\n",
    "    t_down : float (in seconds)\n",
    "        The duration of the decreasing part of the pulse envelope,\n",
    "    cep_phase : float (in radian), optional\n",
    "        The Carrier Enveloppe Phase (CEP)\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, wavelength, t_start, t_rise, t_flat, t_down, cep_phase):\n",
    "        super().__init__(wavelength)\n",
    "        self.t_start = t_start\n",
    "        self.t_rise = t_rise\n",
    "        self.t_flat = t_flat\n",
    "        self.t_down = t_down\n",
    "        self.cep_phase = cep_phase\n",
    "\n",
    "    def evaluate(self, t):\n",
    "        \"\"\"\n",
    "        Return the longitudinal envelope.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        t : ndarrays of floats\n",
    "            Define points on which to evaluate the envelope\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        envelope : ndarray of complex numbers\n",
    "            Contains the value of the longitudinal envelope at the\n",
    "            specified points. This array has the same shape as the array t.\n",
    "        \"\"\"\n",
    "        t1 = self.t_start\n",
    "        t2 = t1 + self.t_rise\n",
    "        t3 = t2 + self.t_flat\n",
    "        t4 = t3 + self.t_down\n",
    "        tcep = 0.5 * (t3 + t2)\n",
    "\n",
    "        envelope = (\n",
    "            (t >= t1) * (t < t2) * np.cos(0.5 * np.pi * (t - t2) / (t2 - t1)) ** 2\n",
    "            + (t >= t2) * (t < t3)\n",
    "            + (t >= t3) * (t < t4) * np.cos(0.5 * np.pi * (t - t3) / (t3 - t4)) ** 2\n",
    "        ) * np.exp(+1.0j * (self.cep_phase + self.omega0 * tcep))\n",
    "\n",
    "        return envelope"
   ]
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   "source": [
    "## Use MyOwnLongitudinalProfile as a regular longitudinal profile\n",
    "The new class `MyOwnLongitudinalProfile` can be used just like any other longitudinal profile"
   ]
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    "wavelength = 800e-6\n",
    "t_start = 0\n",
    "t_rise = 20e-15\n",
    "t_flat = 20e-15\n",
    "t_down = 10e-15\n",
    "cep_phase = 0\n",
    "longitudinal_profile = MyOwnLongitudinalProfile(\n",
    "    wavelength, t_start, t_rise, t_flat, t_down, cep_phase\n",
    ")"
   ]
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   "source": [
    "# test the custom longitudinal profile\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "times = np.linspace(0.0, 55e-15, 300)\n",
    "plt.plot(times, np.abs(longitudinal_profile.evaluate(times)))"
   ]
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