Update documentation

kthpanor · Jul 1, 2024 · 5aedc46 · 5aedc46
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diff --git a/.buildinfo b/.buildinfo
@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: a690d6b237e74cc2a5c5a47d5f425538
+config: 1730e940bd0f5a51009b164991c631c2
 tags: 645f666f9bcd5a90fca523b33c5a78b7
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diff --git a/_sources/docs/spec_prop/birefring.ipynb b/_sources/docs/spec_prop/birefring.ipynb
@@ -0,0 +1,217 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "349b6c4d-ddbd-4f51-844e-2dfbf626cbde",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "remove-output"
+    ]
+   },
+   "source": [
+    "# Birefringences and dichroisms"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dbc9eb5d-2031-4607-969b-20c501481643",
+   "metadata": {},
+   "source": [
+    "Light experienced in everyday life is mostly non-polarized - that is, the\n",
+    "tip of the electric or magnetic field vectors moves randomly in the\n",
+    "plane perpendicular to the propagation direction. With the use of\n",
+    "appropriate tools, unpolarized light can be turned into a wide\n",
+    "variety of polarization states, becoming linearly, elliptically or\n",
+    "circularly polarized. In these cases, the tip of the field vector(s)\n",
+    "oscillates in the plane containing the direction of propagation\n",
+    "(linear polarization) or rotates along a circle (circular\n",
+    "polarization) or an ellipse (elliptical polarization) in the plane\n",
+    "perpendicular to it. The polarization of light plays an important\n",
+    "role in the interactions of light with a\n",
+    "molecule.\n",
+    "\n",
+    "Birefringences and dichroisms are two aspects of this interaction\n",
+    "which are closely related to the polarization status of light.\n",
+    "They arise through a variety of different mechanisms and\n",
+    "interactions between the electromagnetic field and the molecule,\n",
+    "but they are all characterized by the simultaneous measurements of \n",
+    "the refractive (birefringences) or absorptive (dichroisms) index\n",
+    "of light along two directions, different with respect to some\n",
+    "predefined laboratory or molecular frame. The difference in the \n",
+    "dispersion or absorption at these two directions is described by a \n",
+    "quantity of a specific sign and magnitude.  All these properties \n",
+    "give detailed information about the molecular structure, and\n",
+    "in particular some of them can distinguish between \n",
+    "a sample and its mirror \n",
+    "image. Distinguishable mirror images can occur naturally, in *chiral* \n",
+    "molecules where the mirror image of the molecule cannot\n",
+    "be superimposed on the original molecule itself - that is, for\n",
+    "so-called _enantiomers_ - or they can occur by introducing an asymmetry in\n",
+    "the experimental set-up that makes the mirror image of the\n",
+    "experimental design impossible to superimpose on the original\n",
+    "set-up. In the latter case, since the experimental design is\n",
+    "itself chiral, the observed effect does not vanish even if the\n",
+    "molecule is not chiral.\n",
+    "Note that only molecules possessing no improper or\n",
+    "rotation-reflection axes may be chiral.\n",
+    "\n",
+    "# Linear birefringence\n",
+    "\n",
+    "Let us consider first an isotropic \n",
+    "liquid sample  subject to a strong external static electric \n",
+    "field. The refractive index $n_\\|$ experienced\n",
+    "by the component of the polarization vector aligned parallel to\n",
+    "the direction of the external field $\\mathbf{F}$ in this case differs\n",
+    "from the index of refraction $n_\\bot$ for the\n",
+    "component aligned perpendicular to the direction of the vector\n",
+    "$\\mathbf{F}$.  As a consequence, the \n",
+    "initially linearly polarized light beam will exit the region of the\n",
+    "sample with an ellipticity. This is an example of a \n",
+    "*linear birefringence*,\n",
+    "\n",
+    "$$\n",
+    "\\Delta n^{\\rm lin} = n_\\| - n_\\bot,\n",
+    "$$\n",
+    "\n",
+    "and the effect is known as *electric-field-induced optical \n",
+    "birefringence* or more often as the *Kerr (electro-optical) \n",
+    "effect*.  It exhibits a quadratic dependence on the strength of\n",
+    "the applied electric field. Its existence is due mainly to the \n",
+    "fact that the external electric field, in a system possessing an \n",
+    "anisotropic electric dipole polarizability\n",
+    "tensor, tends to align \n",
+    "the molecules preferentially in its\n",
+    "direction.\n",
+    "\n",
+    "Other mechanisms in general\n",
+    "also contribute to the emergence of an anisotropy, the most \n",
+    "important being the effect of electronic rearrangements.\n",
+    "They play a role through the higher-order polarizabilities of the system, in \n",
+    "particular by the second electric-dipole hyperpolarizability\n",
+    "$\\gamma$ and, \n",
+    "in the presence of permanent electric dipoles,\n",
+    "by the first electric-dipole hyperpolarizability\n",
+    "$\\beta$.\n",
+    "Other examples of linear\n",
+    "birefringences are the *Cotton-Mouton*, the *Buckingham effects, the *Jones* and\n",
+    "*magneto-electric* birefringences, the latter occurring when linearly\n",
+    "polarized light goes through an isotropic fluid perpendicularly to\n",
+    "both electric and magnetic static fields.\n",
+    "\n",
+    "# Circular birefringence\n",
+    "\n",
+    "*Circular birefringence* is observed when the two circular components of\n",
+    "a linearly polarized beam propagate with different circular\n",
+    "velocities, and therefore an anisotropy arises between the two\n",
+    "refractive indices $n_+$ and $n_-$:\n",
+    "\n",
+    "$$\n",
+    "\\Delta n^{\\rm circ} = n_+ - n_-.\n",
+    "$$\n",
+    "\n",
+    "The net result is a rotation of the plane of polarization.  An \n",
+    "example of a circular birefringence is *optical\n",
+    "activity*,\n",
+    "which is observed when a medium composed of chiral \n",
+    "molecules (with an excess of one enantiomer)\n",
+    "is \n",
+    "subject to linearly polarized electromagnetic radiation. The \n",
+    "dependence of the corresponding anisotropy on the wavelength \n",
+    "is described by the \n",
+    "*optical rotatory dispersion* (ORD). The *Faraday effect* is another \n",
+    "well-known example of a circular birefringence.\n",
+    "\n",
+    "# Axial birefringence\n",
+    "\n",
+    "An *axial birefringence* occurs with *unpolarized*\n",
+    "light, and an example is the so-called *magnetochiral\n",
+    "birefringence*. It can be seen in \n",
+    "isotropic samples composed of chiral molecules, and it is observed\n",
+    "when a static magnetic induction field is switched on parallel to\n",
+    "the direction of propagation of the unpolarized probe beam. The\n",
+    "refractive index experienced by the beam propagating parallel to\n",
+    "the external magnetic field, $n_{\\uparrow\\uparrow}$, becomes\n",
+    "different from that experienced by a beam propagating antiparallel\n",
+    "to the field, $n_{\\uparrow\\downarrow}$\n",
+    "\n",
+    "$$\n",
+    "\\Delta n^{\\rm ax} = n_{\\uparrow\\uparrow} - n_{\\uparrow\\downarrow}.\n",
+    "$$\n",
+    "\n",
+    "The corresponding anisotropy has a different sign for the different\n",
+    "enantiomers.\n",
+    "\n",
+    "An external field will have an orientational effect on the\n",
+    "molecules of the sample, and this is a mechanism responsible for\n",
+    "the emergence of birefringences. In the presence of external\n",
+    "fields the sample becomes anisotropic, and the extent to which\n",
+    "this happens depends on the temperature.  Indeed, the general form \n",
+    "of the optical anisotropy (for measurements taken at a fixed \n",
+    "pressure) is usually of the form\n",
+    "\n",
+    "$$\n",
+    "\\Delta n \\propto A_0 + \\frac{A_1}{T} + \\frac{A_2}{T^2} + \\cdots,\n",
+    "$$\n",
+    "\n",
+    "where the term $A_0$ includes all contributions arising from the\n",
+    "reorganization of the electrons due to the action of the external\n",
+    "field(s), whereas the terms $A_1$, $A_2$, $\\ldots$ are connected\n",
+    "to different mechanisms of reorientation of the molecules,\n",
+    "involving the interaction of the field(s) with permanent electric\n",
+    "or magnetic multipole moments. The temperature-dependent\n",
+    "terms\n",
+    "vanish for systems of spherical symmetry; the \n",
+    "contributions exhibiting a nonlinear dependence \n",
+    "are usually connected to the presence of permanent\n",
+    "electric or magnetic dipole moments, or higher-order processes\n",
+    "involving more complicated interactions between fields and \n",
+    "multipoles.\n",
+    "\n",
+    "When the inducing field is time-dependent, the birefringence is \n",
+    "said to be *optically induced*. In general, the information\n",
+    "provided by birefringences induced by static fields can differ\n",
+    "from that obtained observing the corresponding optically induced\n",
+    "phenomena. For example, in the static Kerr effect of dipolar\n",
+    "molecules, an important role is played by the permanent dipoles,\n",
+    "which tend to be aligned by the static field. This contribution\n",
+    "vanishes for dynamic inducing fields, where the birefringence\n",
+    "arises only from the rearrangement of the anisotropy of the\n",
+    "electric dipole polarizability. The contribution resulting from\n",
+    "the interaction with permanent multipoles averages over time to zero.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "061503b1-0397-4b39-a551-42173f9e093e",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/_sources/docs/spec_prop/dichroism.ipynb b/_sources/docs/spec_prop/dichroism.ipynb
@@ -0,0 +1,39 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "938884bc-61c0-4eb9-95f6-e7f5ed3918dc",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "# Dichroism"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
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+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
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+   "mimetype": "text/x-python",
+   "name": "python",
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+   "pygments_lexer": "ipython3",
+   "version": "3.10.12"
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