Glossary entry

TEM00 mode

The fundamental transverse mode of a laser cavity, with a Gaussian intensity profile and the lowest divergence achievable for a given beam waist. The desired output mode for nearly all laser applications.

Lasers & gain Optics fundamentalsUpdated October 2026

The TEM₀₀ mode is the fundamental transverse electromagnetic mode of a laser cavity: the Gaussian-profile beam with no nodes in either transverse direction. It is the lowest-order transverse mode in the Hermite-Gaussian basis ( $m = 0$ , $n = 0$ ) and equivalent to the LG₀₀ Laguerre-Gaussian mode.

Field profile. The TEM₀₀ intensity distribution is a 2D Gaussian:

I (x, y, z) = \frac{2 P}{π w (z)^{2}} \exp ⁣ [- \frac{2 (x^{2} + y^{2})}{w (z)^{2}}],

where $P$ is the total beam power and $w (z)$ is the $1 / e^{2}$ beam radius at position $z$ . The beam profile evolves with $z$ via the standard Gaussian-beam formulas:

w (z) = w_{0} \sqrt{1 + (z / z_{R})^{2}}, z_{R} = \frac{π w_{0}^{2}}{λ},

where $w_{0}$ is the beam waist (minimum spot size) and $z_{R}$ is the Rayleigh range.

Why TEM₀₀ is special.

Diffraction-limited propagation: TEM₀₀ has the minimum divergence achievable for a given beam waist; $M^{2} = 1$ exactly. Higher-order modes have $M^{2} > 1$ and diverge more.
Lowest divergence-times-spot product: the product $w_{0} θ = λ / π$ for TEM₀₀ is the smallest physically possible (the "diffraction limit").
Self-similar propagation: TEM₀₀ retains its Gaussian shape during propagation through ideal optics; only its width changes. Other modes change shape with propagation.
Cleanest focusing: TEM₀₀ focuses to a smooth Gaussian spot with no rings; a collimated beam of $1 / e^{2}$ radius $W$ on a lens of focal length $f$ gives a waist radius $λ f / (π W)$ . The rings and the $1.22 λ / NA$ first-null diameter of an Airy disk belong to a uniformly filled aperture, not to a Gaussian beam.
Best fiber coupling: TEM₀₀ couples to single-mode fiber's LP₀₁ mode with near-perfect overlap; higher-order modes couple poorly.

Standard parameters.

Beam parameter	Symbol	Significance
Beam waist	$w_{0}$	Minimum $1 / e^{2}$ radius along the beam
Divergence half-angle	$θ = λ / (π w_{0})$	Asymptotic far-field angle
Rayleigh range	$z_{R} = π w_{0}^{2} / λ$	Distance over which beam doubles in area
Confocal parameter	$b = 2 z_{R}$	Length of "in-focus" region
Beam quality	$M^{2} = 1$	Diffraction-limited, by definition

Practical TEM₀₀ characterization. A laser is verified to be TEM₀₀ by:

Beam profile imaging: a CCD or beam profiler captures the 2D intensity distribution; a TEM₀₀ beam has a smooth Gaussian shape with no internal structure
$M^{2}$ measurement: standardized ISO 11146 procedure measures the beam-quality parameter; ideal TEM₀₀ gives $M^{2} = 1.0$ , in practice TEM₀₀ lasers achieve $M^{2} = 1.0 - 1.2$
Beam divergence consistency: the far-field divergence should match $θ = λ / (π w_{0})$ from the measured beam waist
Fiber-coupling efficiency: high coupling (>90%) to a known single-mode fiber confirms TEM₀₀ purity

TEM₀₀ vs single-mode fiber LP₀₁. Both are Gaussian-like fundamental modes, but they differ in important ways:

Boundary conditions: TEM₀₀ exists in free space (or in stable laser cavity); LP₀₁ exists in a guiding fiber
Exact profile: TEM₀₀ is purely Gaussian; LP₀₁ in step-index fiber is approximately Gaussian with corrections from the boundary conditions
Coupling efficiency: TEM₀₀ → LP₀₁ coupling is theoretically above 99% efficient with optimum focusing (about 99.7% for a step-index fiber at $V = 2.4$ ); residual loss is from the slight profile difference and any wavefront aberrations
Polarization: TEM₀₀ has a definite polarization state; LP₀₁ is degenerate in two orthogonal polarization states

Beam quality requirements by application.

Application	Required $M^{2}$
Single-mode fiber coupling	$\leq 1.2$
Microscopy (diffraction-limited focus)	$\leq 1.2$
Holography	$\leq 1.1$
Laser cutting (sharp kerf)	$\leq 2$
Laser welding (deep penetration)	$\leq 3$
Laser marking	$\leq 5$
Pumping fiber amplifiers	unconstrained
Direct illumination	unconstrained

TEM₀₀ from semiconductor lasers. Single-mode edge-emitting semiconductor lasers (ridge Fabry-Perot, DFB) produce elliptical, astigmatic beams: the output is close to Gaussian along both axes, but it diverges much faster along the fast axis than along the slow axis, and the two axes have their waists at different positions. Broad-area devices are strongly multimode along the slow axis. Beam-shaping optics (anamorphic prism pairs, cylindrical lenses) circularize the beam for single-mode fiber coupling.

Small-aperture single-mode VCSELs produce circular TEM₀₀ output due to their circular aperture, simplifying coupling but at the cost of lower output power per device.

TEM₀₀ from external-cavity lasers. Larger cavity volumes and intracavity apertures readily produce clean TEM₀₀ output. ECDLs, fiber lasers, and Ti:sapphire lasers routinely achieve $M^{2} < 1.1$ .

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 3 (Gaussian beams); Siegman, Lasers (University Science Books, 1986), Ch. 17 (transverse mode analysis); ISO 11146 for the standard beam-quality measurement protocol.