Add laser model description to docs #5397
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| .. math:: | ||
| \varphi |_{z=0} = \varphi(x,\Omega) |_{z=0} = k_x(\Omega) \cdot x\,, | ||
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| where :math:`k_x = \tfrac{\Omega}{c} \vec{\mathrm e}_\Omega \cdot \vec{\mathrm e}_x = -\tfrac{\Omega}{c}\sin\theta` with :math:`\theta=\theta(\Omega)` being the angle enclosed by the propagation directions of frequency :math:`\Omega` and the central laser frequency :math:`\Omega_0`. |
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I would have loved to see the symmetry $\vec{\mathrm e}\Omega \cdot \vec{\mathrm e}{\Omega_0}$ exposed here but I agree that for the rest of the text choosing that direction to be
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Yes, and it is also the way PIConGPU internally implements the lasers. They propagate along x and the internal system is rotated according to the users choice of PropagationDirection in params.
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| ^^^^^^ | ||
| According to the definitions above | ||
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| .. math:: | ||
| \hat E(x,y,z,\Omega) = \hat E_x \cdot \hat E_y\,. | ||
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This currently provides very little additional value as a separate section. I'd either drop the section heading or expand on this further by, e.g., providing the full formula plugged in with the various terms.
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Well you probably find it obvious since it is written this explicitly. But I am afraid it wouldn't be that obvious when removing the section title. It is only this high in document hierarchy because of its importance.
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@steindev what is the status of this PR? |
Co-authored-by: chillenzer <107195608+chillenzer@users.noreply.github.com>
Co-authored-by: chillenzer <107195608+chillenzer@users.noreply.github.com>
Co-authored-by: chillenzer <107195608+chillenzer@users.noreply.github.com>
| .. math:: | ||
| \hat{\vec E}(\vec r, \Omega) = \hat E_\mathrm{A}(\vec r, \Omega) e^{-\imath \varphi(\vec r, \Omega)}\vec{\mathrm e}_x\,, | ||
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| where :math:`\Omega=2\pi\nu` is the angular frequency and :math:`\vec r` the position considered, :math:`\hat E_\mathrm{A}` is the spectral amplitude and |
| :math:`\varphi=\tfrac{\Omega}{c} \vec{\mathrm e}_\Omega \cdot \vec r` | ||
| the spectral phase of the pulse, | ||
| with :math:`\vec{\mathrm e}_\Omega` being the propagation direction of frequency :math:`\Omega`. | ||
| Dispersions are assumed to occur only in the plane spanned by the direction of pulse propagation :math:`\vec{\mathrm e}_z`, being equal to the direction of propagation of the central frequency :math:`\Omega_0`, and polarization :math:`\vec{\mathrm e}_x`, i.e. :math:`\vec{\mathrm e}_\Omega \cdot \vec{\mathrm e}_y = 0`. |
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Is this generally true or only for
| Dispersions are assumed to occur only in the plane spanned by the direction of pulse propagation :math:`\vec{\mathrm e}_z`, being equal to the direction of propagation of the central frequency :math:`\Omega_0`, and polarization :math:`\vec{\mathrm e}_x`, i.e. :math:`\vec{\mathrm e}_\Omega \cdot \vec{\mathrm e}_y = 0`. | |
| Dispersions are assumed to occur only in the plane spanned by the direction of pulse propagation :math:`\vec{\mathrm e}_z`, being equal to the direction of propagation of the central frequency :math:`\Omega_0`, and polarization :math:`\vec{\mathrm e}_x`, i.e. :math:`\vec{\mathrm e}_{\Omega_0} \cdot \vec{\mathrm e}_y = 0`. |
| This last exponential simply contributes a term to :math:`\gamma_4`, which is located between eqs. (13) and (14) in [Steiniger2024]_, in the form of | ||
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| .. math:: | ||
| \gamma_4\; +\negthickspace= -\frac{y^2 R_y^{-1}(z)}{2c}\frac{1}{\tau_0}\,. |
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This renders as
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Updates? |
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@steindev what is the status of this PR? |
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Work in progress. Might come back to it this or next week. |
PR adds analytic formulas, which are the basis of the implementation of the
GaussianPulseandDispersivePulse, to the docs.I see this as a first version. Feedback is welcome!