Units & Conversions — Abridged Guide

Quick-reference equations, tables, and rules of thumb for photonics unit conversions. For full derivations, worked examples, and diagrams, see the Comprehensive Guide.

1.Overview

Photonics uses multiple unit systems because different subfields describe the same physical phenomena in different ways: wavelength (nm) in laser optics, frequency (THz) in RF/telecom, wavenumber (cm⁻¹) in spectroscopy, and photon energy (eV) in semiconductor physics.

Key constants:

c = 2.998 \times 10^8 \text{ m/s}

h = 6.626 \times 10^{-34} \text{ J·s}

hc = 1240 \text{ eV·nm}

(memory shortcut).

2.SI Prefixes

Prefix	Symbol	Factor	Photonics Use
femto	f	10⁻¹⁵	fs (pulse widths)
pico	p	10⁻¹²	ps (pulse widths), pW (detector NEP)
nano	n	10⁻⁹	nm (wavelength), nrad (pointing)
micro	µ	10⁻⁶	µm (IR wavelength), µrad (divergence), µW
milli	m	10⁻³	mm (optic sizes), mrad (divergence), mW
kilo	k	10³	kHz (rep rate), kW (fiber lasers)
mega	M	10⁶	MHz (rep rate), MW (peak power)
giga	G	10⁹	GHz (FSR, linewidth), GW (peak power)
tera	T	10¹²	THz (optical frequency)

Most common in optics: nm for wavelength (UV-Vis-NIR), µm for IR/telecom, mrad for beam divergence, fs/ps for ultrafast pulse widths.

3.Wavelength, Frequency & Wavenumber

Wavelength ↔ Frequency

\lambda = \frac{c}{\nu} \qquad \nu = \frac{c}{\lambda}

Wavenumber (Spectroscopic)

\tilde{\nu} = \frac{1}{\lambda} = \frac{\nu}{c} \quad \text{[cm}^{-1}\text{]}

Use λ in cm: 532 nm = 5.32 × 10⁻⁵ cm → ν̃ = 18,797 cm⁻¹

Quick Conversions

\lambda \text{ (nm)} = \frac{10^7}{\tilde{\nu} \text{ (cm}^{-1}\text{)}} \qquad \nu \text{ (THz)} = \frac{c}{\lambda \text{ (µm)}} \approx \frac{299.79}{\lambda \text{ (µm)}}

Laser	λ (nm)	ν (THz)	ν̃ (cm⁻¹)
ArF excimer	193	1553	51,813
Nd:YAG 2ω	532	563.5	18,797
HeNe	632.8	473.8	15,803
Nd:YAG 1ω	1064	281.8	9,398
CO₂	10,600	28.3	943

4.Photon Energy

Planck's Relation

E = h\nu = \frac{hc}{\lambda}

The 1240 Rule

E \text{ (eV)} = \frac{1240}{\lambda \text{ (nm)}} \qquad \lambda \text{ (nm)} = \frac{1240}{E \text{ (eV)}}

Works because hc ≈ 1240 eV·nm (exact: 1239.842)

Shorter wavelength = higher photon energy. UV photons carry enough energy to break chemical bonds (>3 eV), while IR photons primarily cause molecular vibrations (<1 eV).

5.Power, Energy & Photon Flux

CW Power

P = \frac{E}{t} = \Phi_p \cdot \frac{hc}{\lambda} \;\; \text{[W]}

P = power, Φₚ = photon flux (photons/s)

Photon Flux

\Phi_p = \frac{P\lambda}{hc} = 5.034 \times 10^{15} \times P\,(\text{W}) \times \lambda\,(\text{nm}) \;\; \text{[photons/s]}

Longer wavelength = more photons per watt (each photon carries less energy). A 1 W source at 1550 nm produces ~6× more photons/s than a 1 W source at 250 nm.

For pulsed laser quantities (peak power, fluence, pulse energy scaling), see the Pulsed Lasers guide.

6.Radiometric Units

Radiometry measures electromagnetic radiation physically, across all wavelengths.

Quantity	Symbol	SI Unit	Meaning
Radiant flux	Φₑ	W	Total optical power
Radiant intensity	Iₑ	W/sr	Power per solid angle
Irradiance	Eₑ	W/m²	Power per area (incident)
Radiant exitance	Mₑ	W/m²	Power per area (emitted)
Radiance	Lₑ	W/(m²·sr)	Power per area per solid angle

Solid Angle

\Omega = \frac{A}{r^2} \;\text{[sr]} \qquad \text{Cone: } \Omega = 2\pi(1-\cos\theta) \qquad \text{Full sphere: } 4\pi \text{ sr}

"Intensity" is ambiguous. SI defines it as W/sr, but many optics texts use it for W/m². Always check the units on any datasheet specifying "intensity."

Radiance is conserved along a ray in a lossless medium — it is the fundamental quantity in radiative transfer.

7.Photometric Units

Photometry weights radiation by human visual response V(λ), peaking at 555 nm.

Photometric	Symbol	SI Unit	Radiometric Equiv.
Luminous flux	Φᵥ	lm (lumen)	Radiant flux (W)
Luminous intensity	Iᵥ	cd (candela)	Radiant intensity (W/sr)
Illuminance	Eᵥ	lx (lux)	Irradiance (W/m²)
Luminance	Lᵥ	cd/m² (nit)	Radiance (W/m²/sr)

Luminous Efficacy

K(\lambda) = 683 \times V(\lambda) \;\;\text{[lm/W]}

Maximum 683 lm/W at 555 nm. At 532 nm: 589 lm/W. At 635 nm: 148 lm/W.

A 5 mW green (532 nm) laser pointer produces ~2.9 lumens — 4× brighter to the eye than a 5 mW red (635 nm) pointer at ~0.74 lumens, despite equal optical power.

8.Radiometric ↔ Photometric Conversion

General Conversion (Broadband)

X_v = 683 \int_{380}^{780} X_{e,\lambda}(\lambda)\,V(\lambda)\,d\lambda

Monochromatic Shortcut

\Phi_v = 683 \times V(\lambda_0) \times \Phi_e

Works for any corresponding pair (irradiance → illuminance, etc.)

Photometric units are meaningless for UV and IR. V(λ) = 0 outside 380–780 nm, so a 10 W CO₂ laser (10.6 µm) has exactly zero lumens. Use radiometric units for non-visible radiation.

Use Case	System	Why
Laser power	Radiometric (W)	Physical energy
Detector spec	Radiometric (A/W)	Wavelength-dependent
Room lighting	Photometric (lux)	Human comfort
Display brightness	Photometric (nit)	Perceived brightness
UV/IR sources	Radiometric only	No visual response

9.Angular & Spatial Units

Radian ↔ Degree

1 \text{ rad} = 57.296° \qquad 1° = 0.01745 \text{ rad} \qquad 1° = 60' = 3600''

Milliradian Conversions

1 \text{ mrad} = 0.0573° = 3.44' = 206.3'' \qquad 1 \text{ rad} = 206\,265''

Beam divergence is specified in mrad. Pointing stability is specified in µrad. One µrad = 1 µm displacement per 1 m distance.

Small-angle approximation:

\sin\theta \approx \tan\theta \approx \theta

(in radians) for

\theta \lesssim 10°

. This underpins all of paraxial optics.

10.Practical Conversion Reference

Laser	λ (nm)	ν (THz)	ν̃ (cm⁻¹)	E (eV)
ArF excimer	193	1553	51,813	6.424
KrF excimer	248	1209	40,323	5.000
Ar-ion	488	614.5	20,492	2.541
Nd:YAG 2ω	532	563.5	18,797	2.331
HeNe	632.8	473.8	15,803	1.960
Ti:Sapph	800	374.7	12,500	1.550
Nd:YAG 1ω	1064	281.8	9,398	1.165
Er:fiber	1550	193.4	6,452	0.800
CO₂	10,600	28.27	943.4	0.117

Imperial	Metric	Context
¼"-20 thread	M6 × 1.0	Posts, holders, table mount
8-32 thread	M4 × 0.7	Small components, cage
1" optic Ø	25.4 mm	Standard optic/mount
½" optic Ø	12.7 mm	Compact/cage system
2" optic Ø	50.8 mm	Large aperture

Temperature

T(K) = T(°C) + 273.15 \qquad T(°F) = \tfrac{9}{5}\,T(°C) + 32

Key lengths: 1 inch = 25.4 mm (exact). 1 Å = 0.1 nm. Room temperature ≈ 20–25 °C = 293–298 K. Standardise on one thread system (¼-20 or M6) per lab — never mix.

Continue Learning

Comprehensive Units & Conversions Guide →Spectral Unit Converter →Photon Flux Calculator →Radiometric ↔ Photometric Converter →Angular Unit Converter →Laser Line Quick Reference →

The Comprehensive Guide includes 6 worked examples, SVG diagrams, full explanations of radiometric and photometric systems, and detailed derivations for every formula on this page.