| Date | 17:05:46 15/11/2011 |
| 1. | Global Definitions | |||||
| 1.1. | Parameters 1 | |||||
| 1.2. | Functions | |||||
| 2. | Model 1 (mod1) | |||||
| 2.1. | Definitions | |||||
| 2.2. | Geometry 1 | |||||
| 2.3. | Materials | |||||
| 2.4. | Electromagnetic Waves (emw) | |||||
| 2.5. | Mesh 1 | |||||
| 3. | Study 1 | |||||
| 3.1. | Frequency Domain | |||||
| 4. | Results | |||||
| 4.1. | Electric Field (emw) | |||||
| Name | Expression | Description |
|---|---|---|
| lambda | 1064.5 [nm] | |
| T | 100 [C] | |
| d33 | 13.7 [pV/m] |
| Function name | nektp |
| Function type | Analytic |
Analytic 1
| Name | Value |
|---|---|
| Function name | nektp |
| Expression | (2.127246810298+1.184312171943/(1-0.051485232676/lambda^2)+0.660296369063/(1-100.005073661931/lambda^2)-0.009689556913*lambda^2)^0.5 + (9.9587e-6+9.9288e-6/lambda+-8.9603e-6/lambda^2+4.101e-6/lambda^3)*(T-25)+ (-1.1882e-8+10.459e-8/lambda+-9.8136e-8/lambda^2+3.1481e-8/lambda^3)*(T-25)^2 |
| Arguments | {lambda, T} |
| Arguments | um, C |
| Arguments | {{lambda, 1064.5 [nm], 1064.5 [nm]}, {T, 80, 120}} |
Geometry
| Property | Value |
|---|---|
| Space dimension | 2 |
| Number of domains | 1 |
| Number of boundaries | 4 |
| Name | Value |
|---|---|
| Position | {0, 0} |
| Base | Center |
| Width | 10 |
| Height | 5 |
| Size | {10, 5} |
Air
| Name | Value | Unit |
|---|
| Description | Value |
|---|---|
| Relative permeability | {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}} |
| Relative permittivity | {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}} |
| Dynamic viscosity | eta(T[1/K])[Pa*s] |
| Ratio of specific heats | 1.4 |
| Electrical conductivity | {{0[S/m], 0, 0}, {0, 0[S/m], 0}, {0, 0, 0[S/m]}} |
| Heat capacity at constant pressure | Cp(T[1/K])[J/(kg*K)] |
| Density | rho(pA[1/Pa],T[1/K])[kg/m^3] |
| Thermal conductivity | {{k(T[1/K])[W/(m*K)], 0, 0}, {0, k(T[1/K])[W/(m*K)], 0}, {0, 0, k(T[1/K])[W/(m*K)]}} |
| Speed of sound | cs(T[1/K])[m/s] |
| Function name | Type |
|---|---|
| eta | Piecewise |
| Cp | Piecewise |
| rho | Analytic |
| k | Piecewise |
| cs | Analytic |
eta
Cp
k
| Description | Value |
|---|---|
| Refractive index | {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}} |
| Refractive index, imaginary part | {{0i, 0, 0}, {0, 0i, 0}, {0, 0, 0i}} |
KTP (ne)
| Name | Value | Unit |
|---|---|---|
| Refractive index | nektp(lambda/1e-6,T) | 1 |
| Refractive index, imaginary part | 0i | 1 |
| Description | Value |
|---|---|
| Refractive index | {{nektp(lambda/1e-6,T), 0, 0}, {0, nektp(lambda/1e-6,T), 0}, {0, 0, nektp(lambda/1e-6,T)}} |
| Refractive index, imaginary part | {{0i, 0, 0}, {0, 0i, 0}, {0, 0, 0i}} |
Electromagnetic Waves
| Description | Value |
|---|---|
| Show equation assuming | std1/freq |
| Description | Value |
|---|---|
| Displacement field model | Refractive index |
| Property | Material | Property group |
|---|---|---|
| Refractive index | KTP (ne) | Refractive index |
| Refractive index, imaginary part | KTP (ne) | Refractive index |
Wave Equation, Electric 1
| Name | Expression | Unit | Description | Selection |
|---|---|---|---|---|
| emw.normE | sqrt(realdot(Ex,Ex)+realdot(Ey,Ey)+realdot(Ez,Ez)) | V/m | Electric field norm | Domain 1 |
| emw.curlEx | Ezy | V/m^2 | Curl of electric field, x component | Domain 1 |
| emw.curlEy | -Ezx | V/m^2 | Curl of electric field, y component | Domain 1 |
| emw.curlEz | root.mod1.curlEz | V/m^2 | Curl of electric field, z component | Domain 1 |
| emw.dBdtx | -emw.curlEx | V/m^2 | Magnetic flux density, time derivative, x component | Domain 1 |
| emw.dBdty | -emw.curlEy | V/m^2 | Magnetic flux density, time derivative, y component | Domain 1 |
| emw.dBdtz | -emw.curlEz | V/m^2 | Magnetic flux density, time derivative, z component | Domain 1 |
| emw.Bx | -emw.curlEx/emw.iomega | T | Magnetic flux density, x component | Domain 1 |
| emw.By | -emw.curlEy/emw.iomega | T | Magnetic flux density, y component | Domain 1 |
| emw.Bz | -emw.curlEz/emw.iomega | T | Magnetic flux density, z component | Domain 1 |
| emw.normB | sqrt(realdot(emw.Bx,emw.Bx)+realdot(emw.By,emw.By)+realdot(emw.Bz,emw.Bz)) | T | Magnetic flux density norm | Domain 1 |
| emw.Jx | emw.Jix+emw.Jdx | A/m^2 | Current density, x component | Domain 1 |
| emw.Jy | emw.Jiy+emw.Jdy | A/m^2 | Current density, y component | Domain 1 |
| emw.Jz | emw.Jiz+emw.Jdz | A/m^2 | Current density, z component | Domain 1 |
| emw.normJ | sqrt(realdot(emw.Jx,emw.Jx)+realdot(emw.Jy,emw.Jy)+realdot(emw.Jz,emw.Jz)) | A/m^2 | Current density norm | Domain 1 |
| emw.murxx | 1 | Relative permeability, xx component | Domain 1 | |
| emw.muryx | 0 | Relative permeability, yx component | Domain 1 | |
| emw.murzx | 0 | Relative permeability, zx component | Domain 1 | |
| emw.murxy | 0 | Relative permeability, xy component | Domain 1 | |
| emw.muryy | 1 | Relative permeability, yy component | Domain 1 | |
| emw.murzy | 0 | Relative permeability, zy component | Domain 1 | |
| emw.murxz | 0 | Relative permeability, xz component | Domain 1 | |
| emw.muryz | 0 | Relative permeability, yz component | Domain 1 | |
| emw.murzz | 1 | Relative permeability, zz component | Domain 1 | |
| emw.murinvxx | (emw.muryy*emw.murzz-emw.muryz*emw.murzy)/(emw.murxx*emw.muryy*emw.murzz+emw.murxy*emw.muryz*emw.murzx+emw.murxz*emw.muryx*emw.murzy-emw.murxx*emw.muryz*emw.murzy-emw.murxy*emw.muryx*emw.murzz-emw.murxz*emw.muryy*emw.murzx) | Inverse of relative permeability, xx component | Domain 1 | |
| emw.murinvyx | (emw.muryz*emw.murzx-emw.muryx*emw.murzz)/(emw.murxx*emw.muryy*emw.murzz+emw.murxy*emw.muryz*emw.murzx+emw.murxz*emw.muryx*emw.murzy-emw.murxx*emw.muryz*emw.murzy-emw.murxy*emw.muryx*emw.murzz-emw.murxz*emw.muryy*emw.murzx) | Inverse of relative permeability, yx component | Domain 1 | |
| emw.murinvzx | (emw.muryx*emw.murzy-emw.muryy*emw.murzx)/(emw.murxx*emw.muryy*emw.murzz+emw.murxy*emw.muryz*emw.murzx+emw.murxz*emw.muryx*emw.murzy-emw.murxx*emw.muryz*emw.murzy-emw.murxy*emw.muryx*emw.murzz-emw.murxz*emw.muryy*emw.murzx) | Inverse of relative permeability, zx component | Domain 1 | |
| emw.murinvxy | (emw.murxz*emw.murzy-emw.murxy*emw.murzz)/(emw.murxx*emw.muryy*emw.murzz+emw.murxy*emw.muryz*emw.murzx+emw.murxz*emw.muryx*emw.murzy-emw.murxx*emw.muryz*emw.murzy-emw.murxy*emw.muryx*emw.murzz-emw.murxz*emw.muryy*emw.murzx) | Inverse of relative permeability, xy component | Domain 1 | |
| emw.murinvyy | (emw.murxx*emw.murzz-emw.murxz*emw.murzx)/(emw.murxx*emw.muryy*emw.murzz+emw.murxy*emw.muryz*emw.murzx+emw.murxz*emw.muryx*emw.murzy-emw.murxx*emw.muryz*emw.murzy-emw.murxy*emw.muryx*emw.murzz-emw.murxz*emw.muryy*emw.murzx) | Inverse of relative permeability, yy component | Domain 1 | |
| emw.murinvzy | (emw.murxy*emw.murzx-emw.murxx*emw.murzy)/(emw.murxx*emw.muryy*emw.murzz+emw.murxy*emw.muryz*emw.murzx+emw.murxz*emw.muryx*emw.murzy-emw.murxx*emw.muryz*emw.murzy-emw.murxy*emw.muryx*emw.murzz-emw.murxz*emw.muryy*emw.murzx) | Inverse of relative permeability, zy component | Domain 1 | |
| emw.murinvxz | (emw.murxy*emw.muryz-emw.murxz*emw.muryy)/(emw.murxx*emw.muryy*emw.murzz+emw.murxy*emw.muryz*emw.murzx+emw.murxz*emw.muryx*emw.murzy-emw.murxx*emw.muryz*emw.murzy-emw.murxy*emw.muryx*emw.murzz-emw.murxz*emw.muryy*emw.murzx) | Inverse of relative permeability, xz component | Domain 1 | |
| emw.murinvyz | (emw.murxz*emw.muryx-emw.murxx*emw.muryz)/(emw.murxx*emw.muryy*emw.murzz+emw.murxy*emw.muryz*emw.murzx+emw.murxz*emw.muryx*emw.murzy-emw.murxx*emw.muryz*emw.murzy-emw.murxy*emw.muryx*emw.murzz-emw.murxz*emw.muryy*emw.murzx) | Inverse of relative permeability, yz component | Domain 1 | |
| emw.murinvzz | (emw.murxx*emw.muryy-emw.murxy*emw.muryx)/(emw.murxx*emw.muryy*emw.murzz+emw.murxy*emw.muryz*emw.murzx+emw.murxz*emw.muryx*emw.murzy-emw.murxx*emw.muryz*emw.murzy-emw.murxy*emw.muryx*emw.murzz-emw.murxz*emw.muryy*emw.murzx) | Inverse of relative permeability, zz component | Domain 1 | |
| emw.Hx | (emw.murinvxx*emw.Bx+emw.murinvxy*emw.By+emw.murinvxz*emw.Bz)/mu0_const | A/m | Magnetic field, x component | Domain 1 |
| emw.Hy | (emw.murinvyx*emw.Bx+emw.murinvyy*emw.By+emw.murinvyz*emw.Bz)/mu0_const | A/m | Magnetic field, y component | Domain 1 |
| emw.Hz | (emw.murinvzx*emw.Bx+emw.murinvzy*emw.By+emw.murinvzz*emw.Bz)/mu0_const | A/m | Magnetic field, z component | Domain 1 |
| emw.normH | sqrt(realdot(emw.Hx,emw.Hx)+realdot(emw.Hy,emw.Hy)+realdot(emw.Hz,emw.Hz)) | A/m | Magnetic field norm | Domain 1 |
| emw.dHdtx | (emw.murinvxx*emw.dBdtx+emw.murinvxy*emw.dBdty+emw.murinvxz*emw.dBdtz)/mu0_const | A/(m*s) | Magnetic field, time derivative, x component | Domain 1 |
| emw.dHdty | (emw.murinvyx*emw.dBdtx+emw.murinvyy*emw.dBdty+emw.murinvyz*emw.dBdtz)/mu0_const | A/(m*s) | Magnetic field, time derivative, y component | Domain 1 |
| emw.dHdtz | (emw.murinvzx*emw.dBdtx+emw.murinvzy*emw.dBdty+emw.murinvzz*emw.dBdtz)/mu0_const | A/(m*s) | Magnetic field, time derivative, z component | Domain 1 |
| emw.Mx | emw.Bx/mu0_const-emw.Hx | A/m | Magnetization, x component | Domain 1 |
| emw.My | emw.By/mu0_const-emw.Hy | A/m | Magnetization, y component | Domain 1 |
| emw.Mz | emw.Bz/mu0_const-emw.Hz | A/m | Magnetization, z component | Domain 1 |
| emw.normM | sqrt(realdot(emw.Mx,emw.Mx)+realdot(emw.My,emw.My)+realdot(emw.Mz,emw.Mz)) | A/m | Magnetization norm | Domain 1 |
| emw.Qml | real(0.5*(emw.Bx*conj(emw.Hx)+emw.By*conj(emw.Hy)+emw.Bz*conj(emw.Hz))*emw.iomega) | W/m^3 | Magnetic losses | Domain 1 |
| emw.Qsh | 0 | W/m^2 | Surface losses | Boundaries 1-4 |
| emw.Qe | emw.Qml+emw.Qrh | W/m^3 | Electromagnetic power loss density | Domain 1 |
| emw.Qh | emw.Qml+emw.Qrh | W/m^3 | Total power dissipation density | Domain 1 |
| emw.Brx | 0 | T | Remanent flux density, x component | Domain 1 |
| emw.Bry | 0 | T | Remanent flux density, y component | Domain 1 |
| emw.Brz | 0 | T | Remanent flux density, z component | Domain 1 |
| emw.normBr | 0 | T | Remanent flux density norm | Domain 1 |
| emw.wee1.input.Ex | E1 | V/m | Electric field, x component | Global |
| emw.wee1.input.Ey | E2 | V/m | Electric field, y component | Global |
| emw.wee1.input.Ez | E3 | V/m | Electric field, z component | Global |
| emw.sigmaxx | 0 | S/m | Electric conductivity, xx component | Domain 1 |
| emw.sigmayx | 0 | S/m | Electric conductivity, yx component | Domain 1 |
| emw.sigmazx | 0 | S/m | Electric conductivity, zx component | Domain 1 |
| emw.sigmaxy | 0 | S/m | Electric conductivity, xy component | Domain 1 |
| emw.sigmayy | 0 | S/m | Electric conductivity, yy component | Domain 1 |
| emw.sigmazy | 0 | S/m | Electric conductivity, zy component | Domain 1 |
| emw.sigmaxz | 0 | S/m | Electric conductivity, xz component | Domain 1 |
| emw.sigmayz | 0 | S/m | Electric conductivity, yz component | Domain 1 |
| emw.sigmazz | 0 | S/m | Electric conductivity, zz component | Domain 1 |
| emw.Jix | emw.sigmaxx*emw.wee1.input.Ex+emw.sigmaxy*emw.wee1.input.Ey+emw.sigmaxz*emw.wee1.input.Ez | A/m^2 | Induced current density, x component | Domain 1 |
| emw.Jiy | emw.sigmayx*emw.wee1.input.Ex+emw.sigmayy*emw.wee1.input.Ey+emw.sigmayz*emw.wee1.input.Ez | A/m^2 | Induced current density, y component | Domain 1 |
| emw.Jiz | emw.sigmazx*emw.wee1.input.Ex+emw.sigmazy*emw.wee1.input.Ey+emw.sigmazz*emw.wee1.input.Ez | A/m^2 | Induced current density, z component | Domain 1 |
| emw.Jdx | emw.iomega*emw.Dx | A/m^2 | Displacement current density, x component | Domain 1 |
| emw.Jdy | emw.iomega*emw.Dy | A/m^2 | Displacement current density, y component | Domain 1 |
| emw.Jdz | emw.iomega*emw.Dz | A/m^2 | Displacement current density, z component | Domain 1 |
| emw.nxx | material.parameter.n11 | 1 | Refractive index, xx component | Domain 1 |
| emw.nyx | material.parameter.n21 | 1 | Refractive index, yx component | Domain 1 |
| emw.nzx | material.parameter.n31 | 1 | Refractive index, zx component | Domain 1 |
| emw.nxy | material.parameter.n12 | 1 | Refractive index, xy component | Domain 1 |
| emw.nyy | material.parameter.n22 | 1 | Refractive index, yy component | Domain 1 |
| emw.nzy | material.parameter.n32 | 1 | Refractive index, zy component | Domain 1 |
| emw.nxz | material.parameter.n13 | 1 | Refractive index, xz component | Domain 1 |
| emw.nyz | material.parameter.n23 | 1 | Refractive index, yz component | Domain 1 |
| emw.nzz | material.parameter.n33 | 1 | Refractive index, zz component | Domain 1 |
| emw.kixx | material.parameter.ki11 | 1 | Refractive index, imaginary part, xx component | Domain 1 |
| emw.kiyx | material.parameter.ki21 | 1 | Refractive index, imaginary part, yx component | Domain 1 |
| emw.kizx | material.parameter.ki31 | 1 | Refractive index, imaginary part, zx component | Domain 1 |
| emw.kixy | material.parameter.ki12 | 1 | Refractive index, imaginary part, xy component | Domain 1 |
| emw.kiyy | material.parameter.ki22 | 1 | Refractive index, imaginary part, yy component | Domain 1 |
| emw.kizy | material.parameter.ki32 | 1 | Refractive index, imaginary part, zy component | Domain 1 |
| emw.kixz | material.parameter.ki13 | 1 | Refractive index, imaginary part, xz component | Domain 1 |
| emw.kiyz | material.parameter.ki23 | 1 | Refractive index, imaginary part, yz component | Domain 1 |
| emw.kizz | material.parameter.ki33 | 1 | Refractive index, imaginary part, zz component | Domain 1 |
| emw.epsilonrxx | (emw.nxx-emw.kixx*i)^2 | 1 | Relative permittivity, xx component | Domain 1 |
| emw.epsilonryx | (emw.nyx-emw.kiyx*i)^2 | 1 | Relative permittivity, yx component | Domain 1 |
| emw.epsilonrzx | (emw.nzx-emw.kizx*i)^2 | 1 | Relative permittivity, zx component | Domain 1 |
| emw.epsilonrxy | (emw.nxy-emw.kixy*i)^2 | 1 | Relative permittivity, xy component | Domain 1 |
| emw.epsilonryy | (emw.nyy-emw.kiyy*i)^2 | 1 | Relative permittivity, yy component | Domain 1 |
| emw.epsilonrzy | (emw.nzy-emw.kizy*i)^2 | 1 | Relative permittivity, zy component | Domain 1 |
| emw.epsilonrxz | (emw.nxz-emw.kixz*i)^2 | 1 | Relative permittivity, xz component | Domain 1 |
| emw.epsilonryz | (emw.nyz-emw.kiyz*i)^2 | 1 | Relative permittivity, yz component | Domain 1 |
| emw.epsilonrzz | (emw.nzz-emw.kizz*i)^2 | 1 | Relative permittivity, zz component | Domain 1 |
| emw.Px | epsilon0_const*((-1+emw.epsilonrxx)*emw.wee1.input.Ex+emw.epsilonrxy*emw.wee1.input.Ey+emw.epsilonrxz*emw.wee1.input.Ez) | C/m^2 | Polarization, x component | Domain 1 |
| emw.Py | epsilon0_const*(emw.epsilonryx*emw.wee1.input.Ex+(-1+emw.epsilonryy)*emw.wee1.input.Ey+emw.epsilonryz*emw.wee1.input.Ez) | C/m^2 | Polarization, y component | Domain 1 |
| emw.Pz | epsilon0_const*(emw.epsilonrzx*emw.wee1.input.Ex+emw.epsilonrzy*emw.wee1.input.Ey+(-1+emw.epsilonrzz)*emw.wee1.input.Ez) | C/m^2 | Polarization, z component | Domain 1 |
| emw.normP | sqrt(realdot(emw.Px,emw.Px)+realdot(emw.Py,emw.Py)+realdot(emw.Pz,emw.Pz)) | C/m^2 | Polarization norm | Domain 1 |
| emw.epsrAv | (emw.epsilonrxx+emw.epsilonryy+emw.epsilonrzz)/3 | 1 | Relative permittivity, average | Domain 1 |
| emw.Dx | epsilon0_const*emw.wee1.input.Ex+emw.Px | C/m^2 | Electric displacement field, x component | Domain 1 |
| emw.Dy | epsilon0_const*emw.wee1.input.Ey+emw.Py | C/m^2 | Electric displacement field, y component | Domain 1 |
| emw.Dz | epsilon0_const*emw.wee1.input.Ez+emw.Pz | C/m^2 | Electric displacement field, z component | Domain 1 |
| emw.normD | sqrt(realdot(emw.Dx,emw.Dx)+realdot(emw.Dy,emw.Dy)+realdot(emw.Dz,emw.Dz)) | C/m^2 | Displacement field norm | Domain 1 |
| emw.Weav | 0.25*(realdot(emw.Dx,E1)+realdot(emw.Dy,E2)+realdot(emw.Dz,E3)) | J/m^3 | Electric energy density time average | Domain 1 |
| emw.Wav | emw.Weav+emw.Wmav | J/m^3 | Energy density time average | Domain 1 |
| emw.intWe | emw.intwee11(emw.Weav) | J | Total electric energy | Global |
| emw.Qrh | 0.5*(realdot(emw.Jx,E1)+realdot(emw.Jy,E2)+realdot(emw.Jz,E3)) | W/m^3 | Resistive losses | Domain 1 |
| emw.Wmav | 0.25*(realdot(emw.Bx,emw.Hx)+realdot(emw.By,emw.Hy)+realdot(emw.Bz,emw.Hz)) | J/m^3 | Magnetic energy density time average | Domain 1 |
| emw.intWm | emw.intwee12(emw.Wmav) | J | Total magnetic energy | Global |
| emw.unTmx | 0.5*real(-0.5*dnx*(up(emw.Bx)*up(conj(emw.Hx))+up(emw.By)*up(conj(emw.Hy))+up(emw.Bz)*up(conj(emw.Hz)))+up(emw.Bx)*(up(conj(emw.Hx))*dnx+up(conj(emw.Hy))*dny)) | Pa | Maxwell upward magnetic surface stress tensor, x component | Boundaries 1-4 |
| emw.unTmy | 0.5*real(-0.5*dny*(up(emw.Bx)*up(conj(emw.Hx))+up(emw.By)*up(conj(emw.Hy))+up(emw.Bz)*up(conj(emw.Hz)))+up(emw.By)*(up(conj(emw.Hx))*dnx+up(conj(emw.Hy))*dny)) | Pa | Maxwell upward magnetic surface stress tensor, y component | Boundaries 1-4 |
| emw.unTmz | 0.5*real(up(emw.Bz)*(up(conj(emw.Hx))*dnx+up(conj(emw.Hy))*dny)) | Pa | Maxwell upward magnetic surface stress tensor, z component | Boundaries 1-4 |
| emw.dnTmx | 0.5*real(-0.5*unx*(down(emw.Bx)*down(conj(emw.Hx))+down(emw.By)*down(conj(emw.Hy))+down(emw.Bz)*down(conj(emw.Hz)))+down(emw.Bx)*(down(conj(emw.Hx))*unx+down(conj(emw.Hy))*uny)) | Pa | Maxwell downward magnetic surface stress tensor, x component | Boundaries 1-4 |
| emw.dnTmy | 0.5*real(-0.5*uny*(down(emw.Bx)*down(conj(emw.Hx))+down(emw.By)*down(conj(emw.Hy))+down(emw.Bz)*down(conj(emw.Hz)))+down(emw.By)*(down(conj(emw.Hx))*unx+down(conj(emw.Hy))*uny)) | Pa | Maxwell downward magnetic surface stress tensor, y component | Boundaries 1-4 |
| emw.dnTmz | 0.5*real(down(emw.Bz)*(down(conj(emw.Hx))*unx+down(conj(emw.Hy))*uny)) | Pa | Maxwell downward magnetic surface stress tensor, z component | Boundaries 1-4 |
| emw.unTx | 0 | Pa | Maxwell upward surface stress tensor, x component | Boundaries 1-4 |
| emw.unTy | 0 | Pa | Maxwell upward surface stress tensor, y component | Boundaries 1-4 |
| emw.unTz | 0 | Pa | Maxwell upward surface stress tensor, z component | Boundaries 1-4 |
| emw.dnTx | emw.dnTmx+emw.dnTex | Pa | Maxwell downward surface stress tensor, x component | Boundaries 1-4 |
| emw.dnTy | emw.dnTmy+emw.dnTey | Pa | Maxwell downward surface stress tensor, y component | Boundaries 1-4 |
| emw.dnTz | emw.dnTmz+emw.dnTez | Pa | Maxwell downward surface stress tensor, z component | Boundaries 1-4 |
| emw.unTex | 0.5*real(-0.5*dnx*(up(emw.Dx)*up(conj(root.mod1.emw.Ex))+up(emw.Dy)*up(conj(root.mod1.emw.Ey))+up(emw.Dz)*up(conj(root.mod1.emw.Ez)))+up(emw.Dx)*(up(conj(root.mod1.emw.Ex))*dnx+up(conj(root.mod1.emw.Ey))*dny)) | Pa | Maxwell upward electric surface stress tensor, x component | Boundaries 1-4 |
| emw.unTey | 0.5*real(-0.5*dny*(up(emw.Dx)*up(conj(root.mod1.emw.Ex))+up(emw.Dy)*up(conj(root.mod1.emw.Ey))+up(emw.Dz)*up(conj(root.mod1.emw.Ez)))+up(emw.Dy)*(up(conj(root.mod1.emw.Ex))*dnx+up(conj(root.mod1.emw.Ey))*dny)) | Pa | Maxwell upward electric surface stress tensor, y component | Boundaries 1-4 |
| emw.unTez | 0.5*real(up(emw.Dz)*(up(conj(root.mod1.emw.Ex))*dnx+up(conj(root.mod1.emw.Ey))*dny)) | Pa | Maxwell upward electric surface stress tensor, z component | Boundaries 1-4 |
| emw.dnTex | 0.5*real(-0.5*unx*(down(emw.Dx)*down(conj(root.mod1.emw.Ex))+down(emw.Dy)*down(conj(root.mod1.emw.Ey))+down(emw.Dz)*down(conj(root.mod1.emw.Ez)))+down(emw.Dx)*(down(conj(root.mod1.emw.Ex))*unx+down(conj(root.mod1.emw.Ey))*uny)) | Pa | Maxwell downward electric surface stress tensor, x component | Boundaries 1-4 |
| emw.dnTey | 0.5*real(-0.5*uny*(down(emw.Dx)*down(conj(root.mod1.emw.Ex))+down(emw.Dy)*down(conj(root.mod1.emw.Ey))+down(emw.Dz)*down(conj(root.mod1.emw.Ez)))+down(emw.Dy)*(down(conj(root.mod1.emw.Ex))*unx+down(conj(root.mod1.emw.Ey))*uny)) | Pa | Maxwell downward electric surface stress tensor, y component | Boundaries 1-4 |
| emw.dnTez | 0.5*real(down(emw.Dz)*(down(conj(root.mod1.emw.Ex))*unx+down(conj(root.mod1.emw.Ey))*uny)) | Pa | Maxwell downward electric surface stress tensor, z component | Boundaries 1-4 |
| emw.Poavx | real(0.5*(conj(emw.Hz)*E2-conj(emw.Hy)*E3)) | W/m^2 | Power flow, time average, x component | Domain 1 |
| emw.Poavy | real(0.5*(-conj(emw.Hz)*E1+conj(emw.Hx)*E3)) | W/m^2 | Power flow, time average, y component | Domain 1 |
| emw.Poavz | real(0.5*(conj(emw.Hy)*E1-conj(emw.Hx)*E2)) | W/m^2 | Power flow, time average, z component | Domain 1 |
| emw.nPoav | emw.nx*real(0.5*(conj(emw.Hz)*E2-conj(emw.Hy)*E3))+emw.ny*real(0.5*(-conj(emw.Hz)*E1+conj(emw.Hx)*E3))+emw.nz*real(0.5*(conj(emw.Hy)*E1-conj(emw.Hx)*E2)) | W/m^2 | Power outflow, time average | Boundaries 1-4 |
| emw.deltaS | 1/real(sqrt(emw.iomega*mu0_const*(emw.murxx+emw.muryy+emw.murzz)*(emw.sigmaxx+emw.sigmayy+emw.sigmazz+emw.iomega*epsilon0_const*(emw.epsilonrxx+emw.epsilonryy+emw.epsilonrzz))/9)) | m | Skin depth | Domain 1 |
| Name | Shape function | Unit | Description | Shape frame | Selection |
|---|---|---|---|---|---|
| Ex | Curl | V/m | Electric field, x component | Spatial | Domain 1 |
| Ey | Curl | V/m | Electric field, y component | Spatial | Domain 1 |
| Ez | Lagrange | V/m | Electric field, z component | Spatial | Domain 1 |
| Weak expression | Integration frame | Selection |
|---|---|---|
| -mu0_const*(-emw.dHdtx*test(Ezy)+emw.dHdty*test(Ezx)-emw.dHdtz*test(root.mod1.curlEz)+emw.iomega*(emw.Jx*test(Ex)+emw.Jy*test(Ey)+emw.Jz*test(Ez))) | Spatial | Domain 1 |
Perfect Electric Conductor 1
Initial Values 1
Scattering Boundary Condition 1
| Name | Expression | Unit | Description | Selection |
|---|---|---|---|---|
| emw.murScalar | (emw.nx*emw.murxx+emw.ny*emw.muryx+emw.nz*emw.murzx)*emw.nx+(emw.nx*emw.murxy+emw.ny*emw.muryy+emw.nz*emw.murzy)*emw.ny+(emw.nx*emw.murxz+emw.ny*emw.muryz+emw.nz*emw.murzz)*emw.nz | 1 | Relative permeability | Boundaries 2-4 |
| emw.sigmaScalar | (emw.nx*emw.sigmaxx+emw.ny*emw.sigmayx+emw.nz*emw.sigmazx)*emw.nx+(emw.nx*emw.sigmaxy+emw.ny*emw.sigmayy+emw.nz*emw.sigmazy)*emw.ny+(emw.nx*emw.sigmaxz+emw.ny*emw.sigmayz+emw.nz*emw.sigmazz)*emw.nz | S/m | Electrical conductivity | Boundaries 2-4 |
| emw.epsrScalar | (emw.nx*emw.epsilonrxx+emw.ny*emw.epsilonryx+emw.nz*emw.epsilonrzx)*emw.nx+(emw.nx*emw.epsilonrxy+emw.ny*emw.epsilonryy+emw.nz*emw.epsilonrzy)*emw.ny+(emw.nx*emw.epsilonrxz+emw.ny*emw.epsilonryz+emw.nz*emw.epsilonrzz)*emw.nz | 1 | Relative permittivity | Boundaries 2-4 |
| emw.r0x | 0 | m | Source point, x component | Boundaries 2-4 |
| emw.r0y | 0 | m | Source point, y component | Boundaries 2-4 |
| emw.r0z | 0 | m | Source point, z component | Boundaries 2-4 |
| emw.E0ix | 0 | V/m | Incident electric field, x component | Boundaries 2-4 |
| emw.E0iy | 0 | V/m | Incident electric field, y component | Boundaries 2-4 |
| emw.E0iz | 0 | V/m | Incident electric field, z component | Boundaries 2-4 |
| emw.H0ix | 0 | A/m | Incident magnetic field, x component | Boundaries 2-4 |
| emw.H0iy | 0 | A/m | Incident magnetic field, y component | Boundaries 2-4 |
| emw.H0iz | 0 | A/m | Incident magnetic field, z component | Boundaries 2-4 |
| emw.kdirx | -emw.nx | Wave direction, x component | Boundaries 2-4 | |
| emw.kdiry | -emw.ny | Wave direction, y component | Boundaries 2-4 | |
| emw.kdirz | -emw.nz | Wave direction, z component | Boundaries 2-4 |
| Weak expression | Integration frame | Selection |
|---|---|---|
| -((emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*tEx+emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*exp(-j*emw.k*(emw.kdirx*x+emw.kdiry*y)/sqrt(emw.kdirx^2+emw.kdiry^2+emw.kdirz^2))*((-(emw.ny-emw.kdiry)*emw.E0ix-(-emw.nx+emw.kdirx)*emw.E0iy)*emw.ny+((-emw.nz+emw.kdirz)*emw.E0ix+(emw.nx-emw.kdirx)*emw.E0iz)*emw.nz)+mean(0)*emw.ny-mean(0)*emw.nz)*test(tEx)+(emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*tEy+emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*exp(-j*emw.k*(emw.kdirx*x+emw.kdiry*y)/sqrt(emw.kdirx^2+emw.kdiry^2+emw.kdirz^2))*(((emw.ny-emw.kdiry)*emw.E0ix+(-emw.nx+emw.kdirx)*emw.E0iy)*emw.nx+(-(emw.nz-emw.kdirz)*emw.E0iy-(-emw.ny+emw.kdiry)*emw.E0iz)*emw.nz)-mean(0)*emw.nx+mean(0)*emw.nz)*test(tEy)+(emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*Ez+emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*exp(-j*emw.k*(emw.kdirx*x+emw.kdiry*y)/sqrt(emw.kdirx^2+emw.kdiry^2+emw.kdirz^2))*((-(-emw.nz+emw.kdirz)*emw.E0ix-(emw.nx-emw.kdirx)*emw.E0iz)*emw.nx+((emw.nz-emw.kdirz)*emw.E0iy+(-emw.ny+emw.kdiry)*emw.E0iz)*emw.ny)+mean(0)*emw.nx-mean(0)*emw.ny)*test(Ez))/emw.murScalar | Spatial | Boundaries 2-4 |
| Description | Value |
|---|---|
| Incident electric field | {0, 0, 1} |
Scattering Boundary Condition 2
| Name | Expression | Unit | Description | Selection |
|---|---|---|---|---|
| emw.murScalar | (emw.nx*emw.murxx+emw.ny*emw.muryx+emw.nz*emw.murzx)*emw.nx+(emw.nx*emw.murxy+emw.ny*emw.muryy+emw.nz*emw.murzy)*emw.ny+(emw.nx*emw.murxz+emw.ny*emw.muryz+emw.nz*emw.murzz)*emw.nz | 1 | Relative permeability | Boundary 1 |
| emw.sigmaScalar | (emw.nx*emw.sigmaxx+emw.ny*emw.sigmayx+emw.nz*emw.sigmazx)*emw.nx+(emw.nx*emw.sigmaxy+emw.ny*emw.sigmayy+emw.nz*emw.sigmazy)*emw.ny+(emw.nx*emw.sigmaxz+emw.ny*emw.sigmayz+emw.nz*emw.sigmazz)*emw.nz | S/m | Electrical conductivity | Boundary 1 |
| emw.epsrScalar | (emw.nx*emw.epsilonrxx+emw.ny*emw.epsilonryx+emw.nz*emw.epsilonrzx)*emw.nx+(emw.nx*emw.epsilonrxy+emw.ny*emw.epsilonryy+emw.nz*emw.epsilonrzy)*emw.ny+(emw.nx*emw.epsilonrxz+emw.ny*emw.epsilonryz+emw.nz*emw.epsilonrzz)*emw.nz | 1 | Relative permittivity | Boundary 1 |
| emw.r0x | 0 | m | Source point, x component | Boundary 1 |
| emw.r0y | 0 | m | Source point, y component | Boundary 1 |
| emw.r0z | 0 | m | Source point, z component | Boundary 1 |
| emw.E0ix | 0 | V/m | Incident electric field, x component | Boundary 1 |
| emw.E0iy | 0 | V/m | Incident electric field, y component | Boundary 1 |
| emw.E0iz | 1 | V/m | Incident electric field, z component | Boundary 1 |
| emw.H0ix | 0 | A/m | Incident magnetic field, x component | Boundary 1 |
| emw.H0iy | 0 | A/m | Incident magnetic field, y component | Boundary 1 |
| emw.H0iz | 0 | A/m | Incident magnetic field, z component | Boundary 1 |
| emw.kdirx | -emw.nx | Wave direction, x component | Boundary 1 | |
| emw.kdiry | -emw.ny | Wave direction, y component | Boundary 1 | |
| emw.kdirz | -emw.nz | Wave direction, z component | Boundary 1 |
| Weak expression | Integration frame | Selection |
|---|---|---|
| -((emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*tEx+emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*exp(-j*emw.k*(emw.kdirx*x+emw.kdiry*y)/sqrt(emw.kdirx^2+emw.kdiry^2+emw.kdirz^2))*((-(emw.ny-emw.kdiry)*emw.E0ix-(-emw.nx+emw.kdirx)*emw.E0iy)*emw.ny+((-emw.nz+emw.kdirz)*emw.E0ix+(emw.nx-emw.kdirx)*emw.E0iz)*emw.nz)+mean(0)*emw.ny-mean(0)*emw.nz)*test(tEx)+(emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*tEy+emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*exp(-j*emw.k*(emw.kdirx*x+emw.kdiry*y)/sqrt(emw.kdirx^2+emw.kdiry^2+emw.kdirz^2))*(((emw.ny-emw.kdiry)*emw.E0ix+(-emw.nx+emw.kdirx)*emw.E0iy)*emw.nx+(-(emw.nz-emw.kdirz)*emw.E0iy-(-emw.ny+emw.kdiry)*emw.E0iz)*emw.nz)-mean(0)*emw.nx+mean(0)*emw.nz)*test(tEy)+(emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*Ez+emw.iomega*sqrt(epsilon0_const*mu0_const)*sqrt(emw.murScalar)*sqrt(emw.epsrScalar+emw.sigmaScalar/(emw.iomega*epsilon0_const))*exp(-j*emw.k*(emw.kdirx*x+emw.kdiry*y)/sqrt(emw.kdirx^2+emw.kdiry^2+emw.kdirz^2))*((-(-emw.nz+emw.kdirz)*emw.E0ix-(emw.nx-emw.kdirx)*emw.E0iz)*emw.nx+((emw.nz-emw.kdirz)*emw.E0iy+(-emw.ny+emw.kdiry)*emw.E0iz)*emw.ny)+mean(0)*emw.nx-mean(0)*emw.ny)*test(Ez))/emw.murScalar | Spatial | Boundary 1 |
| Property | Value |
|---|---|
| Minimum element quality | 0.0 |
| Average element quality | 0.0 |
Mesh 1
| Name | Value |
|---|---|
| Maximum element size | 0.2 |
| Minimum element size | 7.5E-4 |
| Resolution of curvature | 0.25 |
| Maximum element growth rate | 1.2 |
| Predefined size | Extra fine |
| Geometry | Mesh |
|---|---|
| Geometry 1 (geom1) | mesh1 |
| Physics interface | Discretization |
|---|---|
| Electromagnetic Waves (emw) | physics |
freq(1)=2.816275e14 Surface: Electric field, z component (V/m)