1 line
48 KiB
Plaintext
1 line
48 KiB
Plaintext
|
{"GladTeX__cache__version": "2.0", "\\begin{aligned}\n\\beta^2 E_x - \\tilde{\\partial}_x (\n \\frac{1}{\\epsilon_{zz}} \\hat{\\partial}_x (\\epsilon_{xx} E_x)\n + \\frac{1}{\\epsilon_{zz}} \\hat{\\partial}_y (\\epsilon_{yy} E_y)\n ) &= \\omega^2 \\mu_{yy} \\epsilon_{xx} E_x\n +\\mu_{yy} \\hat{\\partial}_y \\frac{1}{\\mu_{zz}}\n(\\tilde{\\partial}_x E_y - \\tilde{\\partial}_y E_x) \\\\\n-\\beta^2 E_y + \\tilde{\\partial}_y (\n \\frac{1}{\\epsilon_{zz}} \\hat{\\partial}_x (\\epsilon_{xx} E_x)\n + \\frac{1}{\\epsilon_{zz}} \\hat{\\partial}_y (\\epsilon_{yy} E_y)\n ) &= -\\omega^2 \\mu_{xx} \\epsilon_{yy} E_y\n -\\mu_{xx} \\hat{\\partial}_x \\frac{1}{\\mu_{zz}}\n(\\tilde{\\partial}_x E_y - \\tilde{\\partial}_y E_x) \\\\\n\\end{aligned}": {"true": {"pos": {"depth": 0.6691693166041001, "width": 598.8462583621765, "height": 111.7813692054657}, "path": "_doc_mathimg/eqn037.svg"}}, "\\begin{bmatrix}\n -\\imath \\omega \\epsilon & \\nabla \\times \\\\\n \\nabla \\times & \\imath \\omega \\mu\n \\end{bmatrix}": {"true": {"pos": {"depth": 0.6691693166041001, "width": 598.8462583621765, "height": 77.3383153998754}, "path": "_doc_mathimg/eqn011.svg"}}, "\\beta^2 E_{xy} = A_E E_{xy}": {"true": {"pos": {"depth": 0.6691693166041001, "width": 598.8462583621765, "height": 72.00500353320821}, "path": "_doc_mathimg/eqn053.svg"}}, "\\mu_{yy}": {"false": {"pos": {"depth": 5.1432292047526005, "width": 23.4001260816635, "height": 12.701293015801}, "path": "_doc_mathimg/eqn050.svg"}}, "\\imath \\omega \\epsilon_{zz} E_z = \\hat{\\partial}_x H_y -\n\\hat{\\partial}_y H_x \\\\": {"true": {"pos": {"depth": 0.6691693166041001, "width": 598.8462583621765, "height": 72.00500353320821}, "path": "_doc_mathimg/eqn043.svg"}}, "\\vec{E}": {"false": {"pos": {"depth": 0.6691693166041001, "width": 13.873412986498002, "height": 16.787190246986903}, "path": "_doc_mathimg/eqn018.svg"}}, "\\imath \\beta H_y": {"false": {"pos": {"depth": 5.1432292047526005, "width": 35.7014351074641, "height": 16.923482243579603}, "path": "_doc_mathimg/eqn024.svg"}}, "\\imath \\beta \\tilde{\\partial}_x": {"false": {"pos": {"depth": 3.780253238827, "width": 31.386291215342702, "height": 19.290690184399402}, "path": "_doc_mathimg/eqn022.svg"}}, "A_E": {"false": {"pos": {"depth": 3.0691532566045, "width": 22.653136767004902, "height": 14.6716502998754}, "path": "_doc_mathimg/eqn054.svg"}}, "(\\nabla \\times (\\frac{1}{\\epsilon} \\nabla \\times) - \\omega^2 \\mu) E =\n\\imath \\omega M": {"true": {"pos": {"depth": 0.6691693166041001, "width": 598.8462583621765, "height": 75.14021678816121}, "path": "_doc_mathimg/eqn014.svg"}}, "\\begin{aligned}\nE_z &= \\frac{1}{- \\omega \\beta \\epsilon_{zz}} ((\n \\hat{\\partial}_y \\hat{\\partial}_x H_z\n -\\hat{\\partial}_x \\hat{\\partial}_y H_z)\n + \\imath \\omega (\\hat{\\partial}_x \\epsilon_{xx} E_x +\n\\hat{\\partial}_y \\epsilon{yy} E_y))\n &= \\frac{1}{\\imath \\beta \\epsilon_{zz}} (\\hat{\\partial}_x\n\\epsilon_{xx} E_x + \\hat{\\partial}_y \\epsilon{yy} E_y)\n\\end{aligned}": {"true": {"pos": {"depth": 0.6691693166041001, "width": 598.8462583621765, "height": 75.61576210960591}, "path": "_doc_mathimg/eqn045.svg"}}, "\\begin{bmatrix}\n -\\imath \\omega \\epsilon & \\nabla \\times \\\\\n \\nabla \\times & \\imath \\omega \\mu\n \\end{bmatrix}\n \\begin{bmatrix} E \\\\\n H\n \\end{bmatrix}\n = \\begin{bmatrix} J \\\\\n -M\n \\end{bmatrix}": {"true": {"pos": {"depth": 0.6691693166041001, "width": 598.8462583621765, "height": 77.3383153998754}, "path": "_doc_mathimg/eqn012.svg"}}, "\\hat{\\partial}_x": {"false": {"pos": {"depth": 3.0691532566045, "width": 16.6549675836258, "height": 19.0715941898768}, "path": "_doc_mathimg/eqn048.svg"}}, "\\begin{aligned}\n\\imath \\beta H_y &= \\imath \\omega \\epsilon_{xx} E_x -\n\\hat{\\partial}_y H_z \\\\\n\\imath \\beta H_x &= -\\imath \\omega \\epsilon_{yy} E_y -\n\\hat{\\partial}_x H_z \\\\\n\\imath \\omega E_z &= \\frac{1}{\\epsilon_{zz}} \\hat{\\partial}_x H_y -\n\\frac{1}{\\epsilon_{zz}} \\hat{\\partial}_y H_x \\\\\n\\end{aligned
|