Units & Conversions for Photonics

1Introduction to Units in Photonics

Photonics spans an extraordinary range of physical scales. Wavelengths of interest extend from sub-nanometre X-rays to millimetre-wave terahertz radiation. Pulse durations range from continuous wave through milliseconds down to attoseconds. Optical powers span from single-photon detection thresholds (sub-femtowatt) to multi-petawatt ultrafast laser systems. Navigating this landscape requires fluency with the unit systems, prefixes, and conversion relationships that connect these diverse quantities.

This guide serves as a foundational reference for the units encountered throughout optics and photonics. It covers the core interconversions — wavelength, frequency, wavenumber, and photon energy — along with the radiometric and photometric measurement systems, angular units, and practical laboratory conversions. Laser-specific units such as pulse duration metrics, fluence, group velocity dispersion, and beam quality parameters are covered in their respective sections within the Lasers category, where those units are presented alongside the physics that defines them.

1.1The SI System

The International System of Units (SI), maintained by the Bureau International des Poids et Mesures (BIPM), defines seven base units from which all other physical quantities are derived [7]. The base units most relevant to photonics work are the metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (thermodynamic temperature), and candela (luminous intensity). The mole appears primarily in photochemistry and spectroscopy contexts.

Following the 2019 SI redefinition, all seven base units are now defined in terms of fixed numerical values of fundamental physical constants. The speed of light in vacuum is exactly $c = 299\,792\,458$ m/s, Planck's constant is exactly $h = 6.626\,070\,15 \times 10^{-34}$ J·s, and the elementary charge is exactly $e = 1.602\,176\,634 \times 10^{-19}$ C. These exact definitions underpin every conversion in this guide.

1.2Why Photonics Uses So Many Units

Different subfields within photonics adopted different unit conventions because different physical descriptions are most natural for different phenomena. Infrared spectroscopists describe absorption features in wavenumber (cm⁻¹) because wavenumber is linearly proportional to energy, making spectral interpretation more intuitive. Laser engineers specify wavelength in nanometres because optical coatings, diffraction gratings, and detector responsivity are most directly related to wavelength. Radio-frequency and microwave engineers work in frequency (Hz) because their circuits and antennas are designed around temporal oscillation rates.

Compounding this, the optics community straddles the boundary between SI and legacy conventions. The inch persists in optomechanical hardware (25.4 mm = 1 inch optics, ¼-20 threads), the ångström (1 Å = 0.1 nm) appears in crystallography and some spectroscopy literature, and the centimetre remains embedded in the spectroscopic wavenumber (cm⁻¹). The photometric system adds another layer, weighting radiometric quantities by human visual response to produce units like lumens, lux, and candelas that have no direct physical analogue in radiometry.

Mastering these conversions eliminates a persistent source of errors in optical design. A misplaced factor of 2π between angular and spectroscopic wavenumber, a confusion between vacuum and air wavelength, or an incorrect radiometric-to-photometric conversion can propagate through an entire system design. This guide provides the relationships and worked examples needed to convert confidently between all commonly encountered photonics units.

2SI Prefixes for Photonics

The SI prefix system provides a standardised way to express quantities that span many orders of magnitude. In photonics, the practical range extends from femto (10⁻¹⁵) through tera (10¹²) — a span of 27 orders of magnitude encountered in everyday laboratory work. Understanding which prefixes attach to which quantities is essential for reading datasheets, specifying components, and communicating results without ambiguity.

2.1The Prefix Table

The prefixes quetta (10³⁰), ronna (10²⁷), yotta (10²⁴), zetta (10²¹), and exa (10¹⁸) exist in the SI system but rarely appear in photonics literature. At the small end, zepto (10⁻²¹) and yocto (10⁻²⁴) are occasionally encountered in fundamental physics contexts but not in practical optical engineering.

2.2Common Photonics Prefix Usage

Certain prefix–unit combinations are so ubiquitous in photonics that they function as the de facto standard units for their respective quantities. Wavelength is almost universally reported in nanometres (nm) for the UV through near-infrared range and in micrometres (µm) for the mid- and far-infrared. Laser power is reported in milliwatts (mW) for low-power sources and watts (W) for higher-power systems. Pulse durations are reported in the appropriate time prefix: nanoseconds (ns) for Q-switched lasers, picoseconds (ps) for mode-locked solid-state lasers, and femtoseconds (fs) for ultrafast Ti:sapphire and ytterbium fibre systems.

Frequency descriptions similarly follow convention: laser linewidth is typically quoted in MHz or GHz, acousto-optic modulator drive frequencies in MHz, optical chopper frequencies in Hz or kHz, and terahertz radiation in THz. Repetition rates for pulsed lasers span from single-shot through Hz, kHz, and MHz depending on the technology. Beam divergence is typically expressed in milliradians (mrad), while pointing stability specifications use microradians (µrad).

3Wavelength, Frequency & Wavenumber

The three most fundamental spectral descriptors in photonics — wavelength, frequency, and wavenumber — are different ways of characterising the same physical property of electromagnetic radiation. Converting fluently between them is one of the most frequently needed skills in the optics laboratory. Each quantity offers a natural description in different contexts, and all three appear routinely in datasheets, publications, and specifications [1, 3].

3.1Wavelength–Frequency Relationship

The wavelength $\lambda$ and frequency $\nu$ of electromagnetic radiation in vacuum are related by the speed of light:

where $c = 299\,792\,458$ m/s (exact). This relationship is strictly valid in vacuum. In a material medium with refractive index $n$, the wavelength shortens to $\lambda_\text{medium} = \lambda_\text{vac} / n$, while the frequency remains unchanged. This distinction matters in precision spectroscopy: the standard spectral lines catalogued by NIST are quoted as vacuum wavelengths (or equivalently, frequencies), while air-wavelength values require a correction using the refractive index of air at standard conditions (approximately $n_\text{air} \approx 1.000\,29$ at 15 °C and 101.325 kPa for visible wavelengths) [1, 7].

For practical photonics work with lasers and broadband sources, the vacuum speed of light is generally used in conversions. The distinction between vacuum and air wavelength becomes significant primarily in high-resolution spectroscopy, wavelength metrology, and interferometric measurements.

3.2Wavenumber

Two distinct wavenumber conventions exist in physics, and confusing them introduces a factor of 2π error. The spectroscopic wavenumber $\tilde{\nu}$ is the reciprocal of the wavelength:

The SI unit of spectroscopic wavenumber is m⁻¹, but the universally used unit in spectroscopy is the reciprocal centimetre (cm⁻¹). When wavelength is expressed in centimetres, $\tilde{\nu}\,(\text{cm}^{-1}) = 1 / \lambda\,(\text{cm})$. To convert from wavelength in nanometres: $\tilde{\nu}\,(\text{cm}^{-1}) = 10^7 / \lambda\,(\text{nm})$. The spectroscopic wavenumber is proportional to photon energy, which is why infrared and Raman spectroscopists prefer it — energy differences between spectral features appear as linear separations on a wavenumber axis [1, 8].

The angular wavenumber (or simply "wavenumber" in theoretical physics) is defined as:

where $\omega = 2\pi\nu$ is the angular frequency. The angular wavenumber has units of rad/m and appears in wave equations, propagation constants, and spatial Fourier analysis. In optical design and spectroscopy, the spectroscopic wavenumber $\tilde{\nu}$ is far more common. The relationship between the two is simply $k = 2\pi\tilde{\nu}$.

3.3Worked Example: Spectral Unit Conversion

4Photon Energy

The quantum nature of light means that electromagnetic radiation carries energy in discrete packets — photons. The energy of a single photon is determined entirely by its frequency (or equivalently, its wavelength). This relationship, established by Planck and Einstein, is fundamental to understanding photodetection, photochemistry, laser–matter interaction, and semiconductor physics [1, 3].

4.1Planck's Relation

The energy of a single photon is given by Planck's relation:

where $h = 6.626\,070\,15 \times 10^{-34}$ J·s is Planck's constant (exact since the 2019 SI redefinition). In SI units, photon energy is expressed in joules (J), but the joule is inconveniently large for individual photons. A 500 nm photon carries approximately $3.97 \times 10^{-19}$ J — a number that conveys little intuitive meaning.

For this reason, photon energy is almost universally expressed in electron volts (eV) in photonics. One electron volt is the energy gained by an electron traversing a potential difference of one volt:

The electron volt provides a natural energy scale for photonics: visible photons span approximately 1.6 to 3.3 eV, near-infrared telecom wavelengths (1550 nm) correspond to 0.80 eV, and UV excimer laser photons (193 nm ArF) carry 6.4 eV. These values relate directly to semiconductor bandgaps, chemical bond energies, and detector thresholds [3, 8].

4.2The 1240 eV·nm Rule

A widely used shortcut for converting between wavelength in nanometres and photon energy in electron volts comes from combining Planck's relation with the SI definitions:

The exact value of the numerator is $hc/e = 1239.841\,984\ldots$ eV·nm, which is conventionally rounded to 1240 for rapid mental calculations with accuracy better than 0.02%. This single number should be committed to memory — it is the most frequently used conversion factor in photonics [1, 3].

4.3Worked Example: Photon Energy at Common Wavelengths

5Power, Energy & Photon Flux

Power and energy are among the most commonly specified laser and source parameters, yet confusion between the two — and between average and peak values — is a persistent source of errors in photonics. This section establishes the fundamental relationships. Pulsed laser-specific quantities such as fluence, peak power, and pulse energy scaling are covered in the Pulsed Lasers guide.

5.1Power vs. Energy

Power is the rate of energy transfer. The SI unit is the watt (W), defined as one joule per second:

For a continuous-wave (CW) laser emitting at constant power $P$, the total energy delivered to a target over time $t$ is simply $E = Pt$. A 1 W CW laser delivers 1 J every second, 60 J every minute.

For pulsed lasers, the distinction between average power and peak power becomes critical. The average power $P_\text{avg}$ is the time-averaged energy delivery rate:

where $E_\text{pulse}$ is the energy per pulse and $f_\text{rep}$ is the repetition rate. A laser producing 1 mJ pulses at 1 kHz has an average power of 1 W — the same average power as the CW laser above, but the energy is concentrated into brief pulses, producing much higher instantaneous power during each pulse. The detailed treatment of peak power, pulse shape factors, and fluence is covered in the Pulsed Lasers guide (Section 4.4).

5.2Photon Flux

Photon flux is the number of photons per unit time. It provides a particle-based description of optical power that is essential for photodetection, where each detected photon generates one electron–hole pair (in an ideal detector). The conversion from radiometric power to photon flux uses Planck's relation [4]:

where $\Phi_p$ is the photon flux in photons/s, $P$ is the optical power in watts, and $\lambda$ is the wavelength. Note that for a given power level, longer-wavelength sources produce more photons per second because each photon carries less energy. A 1 W source at 1550 nm (telecom) produces approximately 7.8 × 10¹⁸ photons/s, while a 1 W source at 250 nm (UV) produces only 1.26 × 10¹⁸ photons/s — about six times fewer.

A useful numerical form for practical calculations with wavelength in nm and power in watts:

This constant, $1/(hc) = 5.034 \times 10^{24}$ photons/(J·m), becomes $5.034 \times 10^{15}$ when power is in watts and wavelength is in nanometres. Dividing by further factors gives photon irradiance (photons/s/m²) or photon flux density as needed [4, 5].

5.3Worked Example: Photon Flux from a HeNe Laser

6Radiometric Units

Radiometry is the science of measuring electromagnetic radiation across all wavelengths, without weighting by human visual response. Radiometric units describe the objective physical properties of optical radiation — how much energy is emitted, transmitted, or received, and how it is distributed in space and angle. Every quantitative measurement in photonics — from laser power meters to spectroradiometers — ultimately reports in radiometric units [4, 5].

6.1Radiometric Quantity Hierarchy

Radiometric quantities form a logical hierarchy, each built by adding a geometric constraint to the previous quantity. Understanding this hierarchy is the key to correctly interpreting datasheet specifications and selecting appropriate measurement instruments [5, 8].

Radiant flux (Φₑ) is the total optical power, measured in watts. This is what a power meter reads when it captures an entire beam. Radiant intensity (Iₑ) describes how power is distributed over direction — watts per steradian. It characterises point-like sources and is independent of distance. Irradiance (Eₑ) is the power density arriving at a surface, measured in W/m². It decreases with distance from a point source following the inverse-square law. Radiance (Lₑ) is the most complete radiometric descriptor: it specifies how much power is emitted (or received) per unit projected area per unit solid angle. Radiance is conserved along a ray in a lossless medium, making it the fundamental quantity in radiative transfer calculations [5].

A common source of confusion is the term "intensity." In the SI system, radiant intensity is specifically defined as W/sr. However, many optics texts and laser datasheets use "intensity" loosely to mean irradiance (W/m²) or even radiance (W/m²/sr). When reading specifications, always check the units to determine which quantity is actually being reported [5, 8].

6.2Spectral Quantities

Any radiometric quantity can be resolved spectrally by expressing it as a function of wavelength (or frequency or wavenumber). The spectral quantity represents the amount of that radiometric quantity per unit wavelength interval. For example, spectral irradiance is the irradiance per unit wavelength:

The total irradiance is recovered by integrating the spectral irradiance over all wavelengths: $E_e = \int_0^\infty E_{e,\lambda}\,d\lambda$. Spectral irradiance is the most commonly specified quantity for broadband light sources such as quartz-tungsten-halogen (QTH) lamps, xenon arc lamps, and solar simulators. Datasheets typically plot spectral irradiance in mW/m²/nm at a specified distance from the source [4].

Similarly, spectral radiance ($L_{e,\lambda}$, W/m²/sr/nm) is the wavelength-resolved version of radiance. Spectral quantities can also be expressed per unit frequency ($E_{e,\nu}$, W/m²/Hz) or per unit wavenumber ($E_{e,\tilde{\nu}}$, W/m²/cm⁻¹). Care is needed when converting between these forms, because $d\lambda$ and $d\nu$ are not linearly related — the conversion involves a $\lambda^2/c$ factor arising from $|d\nu/d\lambda| = c/\lambda^2$.

6.3Solid Angle & the Steradian

The steradian (sr) is the SI unit of solid angle — the three-dimensional analogue of the radian. A solid angle $\Omega$ describes the two-dimensional angular area subtended by a surface as seen from a point. It is defined as the area $A$ on a sphere of radius $r$ divided by $r^2$:

A full sphere subtends $4\pi$ sr (approximately 12.566 sr). A hemisphere subtends $2\pi$ sr. For a cone of half-angle $\theta$, the solid angle is:

For small angles ($\theta \lesssim 10°$), this simplifies to $\Omega \approx \pi\theta^2$ (with $\theta$ in radians). The solid angle is essential for converting between radiant intensity (W/sr) and irradiance (W/m²), and for calculating the collection efficiency of optical systems defined by their numerical aperture or f-number [1, 5].

7Photometric Units

Photometry measures light as perceived by the human eye. Unlike radiometry, which treats all wavelengths equally, photometry weights each wavelength according to the spectral sensitivity of human vision. This makes photometric quantities essential for lighting design, display engineering, and laser safety classification, but irrelevant for purely physical measurements of optical radiation outside the visible range [4, 5, 6].

7.1The Photopic Response

The photopic luminous efficiency function $V(\lambda)$ describes the relative spectral sensitivity of the light-adapted (cone-mediated) human eye. It is a bell-shaped curve peaking at 555 nm (yellow-green) with a value of 1.0, and falling to approximately zero below 380 nm and above 780 nm. This function was standardised by the CIE in 1924 based on experiments with a population of observers, and updated in 1988. The scotopic function $V'(\lambda)$, describing dark-adapted (rod-mediated) vision, peaks at 507 nm and is used for low-light conditions [6].

7.2Photometric Quantity Hierarchy

Every radiometric quantity has a photometric counterpart, obtained by weighting the spectral distribution by $V(\lambda)$ and multiplying by the luminous efficacy constant. The correspondence is one-to-one [5, 6]:

The lumen (lm) is the unit of luminous flux — the photometric equivalent of the watt. The candela (cd) is the SI base unit, defined as the luminous intensity of a monochromatic 540 THz source (approximately 555 nm) with a radiant intensity of 1/683 W/sr. The lux (lx) is one lumen per square metre, used to specify illumination levels for workspaces, displays, and laser safety calculations. One foot-candle, still used in some North American lighting standards, equals approximately 10.764 lux [6, 7].

7.3The Luminous Efficacy

The maximum luminous efficacy $K_m = 683$ lm/W occurs at 555 nm, where $V(\lambda) = 1$. This value is exact by definition — it is built into the SI definition of the candela. At any other wavelength, the luminous efficacy is reduced by the value of $V(\lambda)$ at that wavelength:

For example, at 632.8 nm (HeNe red), $V(632.8) \approx 0.247$, giving $K(632.8) = 683 \times 0.247 = 168.7$ lm/W. At 532 nm (green laser pointer), $V(532) \approx 0.862$, giving $K(532) = 683 \times 0.862 = 589$ lm/W. This explains why green laser pointers appear dramatically brighter than red ones at the same optical power [5, 6].

7.4Worked Example: Laser Pointer Brightness

8Radiometric ↔ Photometric Conversion

Converting between radiometric and photometric quantities requires knowledge of the spectral distribution of the source. The conversion is straightforward for monochromatic sources and more involved for broadband sources. The direction from radiometric to photometric is always well-defined; the reverse direction (photometric to radiometric) is generally not unique without additional spectral information [5, 6].

8.1The Conversion Integral

For a source with known spectral power distribution, the general conversion from any radiometric spectral quantity $X_{e,\lambda}$ to its photometric equivalent $X_v$ is:

The integration limits are 380–780 nm because $V(\lambda)$ is effectively zero outside this range. The constant 683 lm/W converts the integral from the "light-watt" (the intermediate product of the spectral quantity times $V(\lambda)$) into lumens. In practice, this integral is evaluated numerically by summing the product $X_{e,\lambda}(\lambda_i) \times V(\lambda_i) \times \Delta\lambda$ over wavelength bins, typically at 1 nm or 5 nm intervals, then multiplying by 683 [4, 5].

8.2Monochromatic Sources

For a monochromatic source at wavelength $\lambda_0$ (such as a laser), the integral collapses to a simple multiplication:

where $\Phi_e$ is the radiant flux in watts and $\Phi_v$ is the luminous flux in lumens. This same relationship applies to all corresponding pairs: multiply the radiometric value by $683 \times V(\lambda_0)$ to obtain the photometric value. For example, the irradiance (W/m²) of a laser spot on a screen can be converted to illuminance (lux) by the same factor [5].

8.3When to Use Which System

The choice between radiometric and photometric units is determined by the application:

A key principle: photometric units are meaningless for infrared and ultraviolet radiation. A 10 W CO₂ laser at 10.6 µm has exactly zero lumens of output, because $V(\lambda)$ is zero at that wavelength. Radiometric units are the only valid description for radiation outside the visible range. Within the visible range, both systems are valid, and the choice depends on whether you care about the physics (radiometric) or the perception (photometric) [5, 6].

9Angular & Spatial Units

Angles appear throughout photonics in beam divergence, pointing stability, mirror mount resolution, grating equations, and field-of-view specifications. Four angular units are commonly encountered, and converting between them correctly is essential for specification interpretation and system design [1].

9.1Radian vs. Degree

The radian (rad) is the SI unit of plane angle. One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. The degree (°) is the historical unit, dividing a full circle into 360 equal parts. The conversions are:

In photonics, radians are the natural unit for wave propagation calculations (phase $\phi = kz$, where $k$ is in rad/m), while degrees are used conversationally and in some mechanical specifications. The small-angle approximation — valid when $\theta \lesssim 10°$ (0.17 rad) — states that $\sin\theta \approx \theta$ and $\tan\theta \approx \theta$ when $\theta$ is in radians. This approximation is foundational to paraxial optics and Gaussian beam theory [1].

9.2Milliradians & Microradians

Beam divergence is almost universally specified in milliradians (mrad). A typical HeNe laser has a full-angle divergence of approximately 1.0–1.5 mrad. Diode lasers diverge more rapidly, with fast-axis divergences often exceeding 100 mrad. Collimated beams from well-designed beam expanders may achieve divergences below 0.1 mrad.

Pointing stability — the angular jitter of a beam direction over time — is typically specified in microradians (µrad). Precision mirror mounts (e.g., Newport Suprema or Thorlabs Polaris series) specify drift in µrad/°C. Actively stabilised beams achieve pointing stabilities in the sub-µrad range. One microradian corresponds to a beam displacement of 1 µm at a distance of 1 metre, or 1 mm at a distance of 1 km.

where ′ denotes arc-minutes and ″ denotes arc-seconds. The factor 206,265 (the number of arc-seconds in one radian) is useful to remember: $1 \text{ rad} = 206\,265''$.

9.3Arc-seconds & Arc-minutes

Arc-minutes (′) and arc-seconds (″) subdivide the degree into 60 arc-minutes and 3600 arc-seconds:

These units appear in precision optomechanical specifications. Kinematic mirror mount angular resolution is often quoted in arc-seconds per graduation or arc-seconds per actuator count. Wedge angle tolerance on optical windows is specified in arc-minutes or arc-seconds. Autocollimator measurements report angular deviation in arc-seconds. The Rayleigh criterion for diffraction-limited angular resolution of a circular aperture ($\theta = 1.22\lambda/D$) is sometimes expressed in arc-seconds for astronomical applications [1, 8].

9.4Worked Example: Beam Divergence Conversion

For a deeper treatment of angular measurement in the context of optical alignment — including pitch, yaw, and roll, angular error propagation, and the small-angle (paraxial) approximation — see the Geometry for Optical Alignment comprehensive guide. The Optical Geometry Calculator provides a multi-mode angle converter alongside beam displacement, solid angle, and error propagation calculations.

10Practical Conversion Reference

This section collects the most frequently needed conversion tables for daily use in the optics laboratory. These tables are designed to be bookmarked and referenced quickly during design work, purchasing, and system specification.

10.1Master Conversion Table

The following table provides all four spectral descriptors for commonly encountered laser wavelengths, calculated using the exact values of $c$ and $h$ from the 2019 SI redefinition:

10.2Length Unit Conversions

Length units in photonics span from sub-nanometre (coating thickness, atomic bonds) to kilometres (free-space optical links, fibre runs). The following conversion factors cover the commonly encountered units:

Key conversions to memorise: 1 inch = 25.4 mm (exact, by definition). Standard optic diameters of 0.5″, 1″, and 2″ correspond to 12.7, 25.4, and 50.8 mm respectively. The ångström (Å) is not an SI unit but persists in some crystallography and thin-film literature; 1 nm = 10 Å.

10.3Imperial ↔ Metric for the Optics Lab

Despite the universal adoption of SI units in scientific publication, imperial measurements persist in optomechanical hardware, particularly in North American labs. The two threading standards coexist on nearly every optical table:

Both Thorlabs and Newport/MKS sell essentially identical product lines in imperial (¼-20) and metric (M6) thread standards. Within a single lab, it is critical to standardise on one threading system to avoid the frustration and potential damage of mixing incompatible posts and holders. Most US academic and industrial labs use ¼-20; European and Asian labs predominantly use M6.

10.4Temperature Scales

Temperature appears in thermal specifications for optical components (operating range, CTE), laser diode specifications (junction temperature, TEC set points), and environmental requirements for cleanrooms and storage. Three scales are in common use:

The kelvin is the SI unit and is used in all scientific calculations (blackbody radiation, thermal noise, CTE calculations). Celsius is standard for component specifications and operating temperatures. Fahrenheit appears only in some North American HVAC and environmental specifications. Key reference points: room temperature is approximately 20–25 °C (293–298 K), liquid nitrogen is 77 K (−196 °C), and absolute zero is 0 K (−273.15 °C).

References

1. [1]E. Hecht, Optics, 5th ed. Pearson, 2017.
2. [2]F. L. Pedrotti, L. M. Pedrotti, and L. S. Pedrotti, Introduction to Optics, 3rd ed. Cambridge University Press, 2017.
3. [3]B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. Wiley, 2019.
4. [4]Newport Corporation, "Optical Radiation Terminology and Units," Technical Note. Available: newport.com.
5. [5]J. M. Palmer and B. G. Grant, The Art of Radiometry, SPIE Press, 2009.
6. [6]CIE, "The Basis of Physical Photometry," CIE 018:2019.
7. [7]BIPM, The International System of Units (SI), 9th ed., 2019.
8. [8]M. Bass et al., Handbook of Optics, Vol. I, 3rd ed. McGraw-Hill, 2010.