# Knowledge Base

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Unless otherwise stated, Lumerical's optical solvers used SI units at all times.

### General

 Quantity Description Units Unit description f=ω/2π Frequency Hz Hertz x,y,z Position m Meter t Time s Seconds

### Time domain electromagnetic fields

 Quantity Description Units Unit description E(t) Electric field as function of time V/m Volts per meter |E(t)|2 Electric field intensity as a function of time (V/m)2 Volts squared per meter squared H(t) Magnetic field as a function A/m Amperes per meter |H(t)|2 Magnetic field intensity as a function of time (A/m)2 Amperes squared per meter squared P(t) Poynting vector as a function of time W/m2 Watts per meter squared Power(t) Power as a function of time W Watts

### Dipole moments

 Quantity Description Units Unit description p Electric dipole in 3D Cm Coulomb meters m Magnetic dipole in 3D Am2 Ampere meters squared p Electric field in 2D Cm/m Coulomb meters per meter m Magnetic dipole in 2D Am2/m Ampere meters squared per meter

### Frequency domain electromagnetic fields - Steady state, single frequency, cwnorm data

 Quantity Description Units Unit description E(ω) Electric field as a function of angular frequency V/m Volts per meter |E(ω)|2 Electric field intensity as a function of angular frequency (V/m)2 Volts squared per meter squared H(ω) Magnetic field as a function of angular frequency A/m Amperes per meter |H(ω)|2 Magnetic field intensity as a function of angular frequency (A/m)2 Amperes squared per meter squared P(ω) Poynting vector as a function of angular frequency W/m2 Watts per meter squared Power(ω) Power as a function of angular frequency W Watts Power(ω) 2D Power as a function of angular frequency W/m Watts per meter

### Frequency domain electromagnetic fields - nonorm data

 Quantity Description Units Unit description E(ω) Electric field as a function of angular frequency V/m/Hz Volts per meter per Hertz |E(ω)|2 Electric field intensity as a function of angular frequency (V/m/Hz)2 Volts squared per meter squared per Hertz squared H(ω) Magnetic field as a function of angular frequency A/m/Hz Amperes per meter per Hertz |H(ω)|2 Magnetic field intensity as a function of angular frequency (A/m/Hz)2 Amperes squared per meter squared per Hertz squared P(ω) Poynting vector as a function of angular frequency W/m2/Hz2 Watts per meter squared per Hertz squared Power(ω) Power as a function of angular frequency W/Hz2 Watts per Hertz squared Power(ω) 2D Power as a function of angular frequency W/Hz2/m Watts per Hertz squared per meter

### Source amplitudes

Beam sources

When specifying the amplitude for beam sources, the "amplitude" refers to the peak electric field amplitude in units of V/m. For example, if a Gaussian beam has the following electric field distribution in time and space:

$$E(x, y, z, t)=E_{0} \sin \left(\omega_{0}\left(t-t_{0}\right)\right) \exp \left(-\frac{\left(t-t_{0}\right)^{2}}{2(\Delta t)^{2}}\right) \exp \left(-\frac{\left(x^{2}+y^{2}\right)}{w_{0}^{2}}\right)$$

Then the "amplitude" refers to the value of E0 and has units of V/m.  It is worth noting that different beams will inject different amounts of power for a given source amplitude.

Dipole sources

For dipole sources, amplitude refers to the amplitude of the point source whose units are listed below. Base amplitude refers to the amplitude that will generate a radiated CW power of 10 nW/m in 2D simulations and 1 fW in 3D simulations, and total amplitude refers to the amplitude actually used in the simulations which is the product of the amplitude and the base amplitude.

Dipole source amplitude units are

Cm for 3D electric dipole sources

Am2 for 3D magnetic dipole sources

Cm/m for 2D electric dipole sources

Am2/m for 2D magnetic dipole sources

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