Physical Quantities and Units #

This section describes physical quantities and their units involved in the software.

Any physical quantity is composed of a numerical value and a unit.

Based on the International System of Units (SI), and considering the unit scale characteristics of micro-nano optoelectronics, the software establishes a more commonly-used unit system as the default setting, which allows users to adjust the unit of each physical quantity individually.

Understanding the unit system used in the software facilitates the selection of appropriate units for specific physical quantities.

Definitions of Physical Quantities #

Basic Physical Quantities #

• Basic Physical Quantities 1

For the definitions of the basic quantities, the definitions specified in the SI unit system shall apply:

Name	Symbol	Show Symbol	Unit	Dimension
Length	$l$	l	Meter, m	$L$
Quality	$m$	m	Kilogram, Kg	$M$
Time	$t$	t	Second, s	$T$
Current	$I$	I	Ampere, A	$I$
Temperature	$T$	T	Kelvin, K	$\Theta$
Amount of substance	$n$	n	Mole, mol	$N$
Luminous intensity	$I_v$	Iv	Candela, cd	$J$

• Basic Physical Quantities 2

This software also specifies additional basic physical quantities based on specific needs, including:

Name	Symbol	Show Symbol	Unit	Dimension
Frequency	$f$	f	$Hz$	$T^{-1}~$
Wavelength	$\lambda$	lambda/wavelength	$m$	$L$
Conductance	$\sigma$	S	$S$	$L^{-2}M^{-1}T^{3}I^{2}~$
Resistance	$R$	R	$\Omega$	$L^2MT^{-3}I^{-2}~$

Domain Space #

For the definition of an electromagnetic field, the associated spatial dimensions vary by domain. Here are the common examples:

• Time domain electromagnetic field: For example, the coordinates of $E$ are $(x,y,z,t)$;
• Frequency domain electromagnetic field: For example, the coordinates of $E$ are $(x,y,z,f)$ or $(x,y,z,\lambda)$;
• Eigenmode field: For example, the coordinates of $E$ are $(x,y,z,\# mode,f)$或$(x,y,z,\# mode,\lambda)$.

In addition, Fourier transform also involves the spatial angular frequency domain, etc.

Derived Physical Quantities #

Name	Symbol	Show Symbol	Unit	Dimension
Electric intensity	$E$	E	V/m	$LMT^{-3}I^{-1}~$
Magnetic intensity	$H$	H	A/m	$L^{-1}I~$
Poynting vector	$P$	P	W/m^2	$MT^{-3}~$
(Average) power	power	power	W	$L^2MT^{-3}~$
Transmissivity	$T$	T	~	$1$

Common Units and Scale Relationships #

The software allows users to change the units of length, frequency, time, conductance, and resistance according to different scales, specifically as follows:

Length #

The software supports the following length units:

Name	Symbol	Show Symbol	Unit
Meter	$m$	m	meter
Centimeter	$cm$	cm	1 Centimeter = 10^-2 meter
Millimeter	$mm$	mm	1 Millimeter = 10^-3 meter
Micrometer	$\mu m$	um	1 Micrometer = 10^-6 meter
Nanometer	$nm$	nm	1 Nanometer = 10^-9 meter

Frequency #

The software supports the following frequency units:

Name	Symbol	Show Symbol	Unit
Hertz	$Hz$	Hz	Hertz
Kilohertz	$KHz$	KHz	1 Kilohertz = 10^3 Hertz
Megahertz	$MHz$	MHz	1 Megahertz = 10^6 Hertz
Gigahertz	$GHz$	GHz	1 Gigahertz = 10^9 Hertz
Terahertz	$THz$	THz	1 Terahertz = 10^12 Hertz

Time #

The software supports the following time units:

Name	Symbol	Show Symbol	Unit
Seconds	$s$	s	Seconds
Milliseconds	$ms$	ms	1 Milliseconds = 10^-3 Seconds
Nanoseconds	$ns$	ns	1 Nanoseconds = 10^-9 Seconds
Picoseconds	$ps$	ps	1 Picoseconds = 10^-12 Seconds
Femtoseconds	$fs$	fs	1 Femtoseconds = 10^-15 Seconds

Conductance #

The software supports the following conductance units:

Name	Symbol	Show Symbol	Unit
Siemens	$S$	S	Siemens
Millisiemens	$mS$	mS	1 Millisiemens = 10^-3 Siemens
Microsiemens	$\mu S$	uS	1 Microsiemens = 10^-6 Siemens

Resistance #

The software supports the following resistance units:

Name	Symbol	Show Symbol	Unit
Ohms	$\Omega$	ohm	Ohms
Milliohms	$m\Omega$	mohm	1 Milliohms = 10^-3 Ohms
Microohms	$\mu \Omega$	uohm	1 Microohms = 10^-6 Ohms

Physical Constants #

The software supports the following physical constants:

Symbol	Command	Parameter Value	Unit	Dimension	Description
$\pi$	pi	3.14159265359	1	$1$	The number $\pi$
$c$	c	2.99792458e8	$m \cdot {s^{-1}}$	$LT^{-1}~$	The speed of light in a vacuum
$\varepsilon0$	eps0	8.8541878128e-12	$F \cdot {m^{-1}}$	$L^{-3}M^{-1}T^4I^2~$	The permittivity of free space
$\mu0$	mu0	1.25663706212e-6	$N \cdot {A^{-2}}$	$LMT^{-2}I^{-2}~$	The permeability of free space
$h$	h	6.62607015e-34	$J\cdot s$	$ML^2T^{-1}~$	The Planck constant
$\hbar$	hbar	1.054571800e-34	$J\cdot s$	$ML^2T^{-1}~$	The reduced Planck constant
$e$	e	1.602176634e-19	$C$	$TI$	The electron charge

Change Units #

Interface Unit Settings #

The software allows users to change the units of length, frequency, time, conductance, and resistance according to different scales, specifically as follows:

Correlation of Physical Quantities and Independence of Units #

The software supports unit conversion for input data.

Name	Symbol	Show Symbol	Unit
frequency	$f$	f	frequency
wavelength	$\lambda$	lambda	metre

More Information #

Domain of Definition #

Definition of Special Symbols #

Character	Description
inf	Infinity
nan	Not a number
-0	Negative zero

Error Report #

• Automatic modification

• Intelligent warning

• Warning, modification

Units in Scripts #

For units in scripts, particular attention should be paid to the following:

• Scripts do not support unit settings;
• For variables created in a script, their physical meaning and units are determined by the creator;
• The units in scripts are independent of the physical units set in the software, and vice versa;
• Data transfer between scripts and the software (retrieving data from the software or importing data from scripts) is performed by default based on the SI system. For example, if the length unit is set to $\mu m$ in the software, a data value indicating a side length of $3 \mu m$ is represented as $3 \times 10^{-6}m$ in scripts, and vice versa;

Special notes:

• The built-in constants provided by scripts shall be defined in the SI system. For example, the built-in velocity of light is $c = 2.99792458 \times 10^8m/s$;
• When exchanging data between scripts and projects or using built-in physical constants, the units in scripts are always based on the SI system, unless these data or constants have been converted beforehand.