Straight step-index fiber, centered launch from air (n₀ = 1), geometric meridional ray. No diffraction, modal coupling or bend losses. At the acceptance boundary, the model displays the transmitted ray; reflected power is not calculated. Intended for understanding ray guidance, not predicting single-mode coupling efficiency.

NA = √(n₁² − n₂²) · θₘₐₓ = asin(NA) in air · β = asin(sin θ / n₁)

Absorption & length

Explore the relationship between absorption, fiber length and remaining optical power.

Enter a measured absorption coefficient and a length. The target shows the required length.

—P(z)

Remaining power versus distance, at the specified measurement wavelength.

Remaining power—

Absorbed fraction—

Absorbed power—

Length to target—

Model & assumptions

Constant absorption at the entered wavelength, without saturation, gain, reflections or other losses. Enter a coefficient measured for the relevant wavelength and launch geometry (core or cladding). Changing the wavelength label does not recalculate the coefficient. This is not an amplifier gain or thermal model.

P(L) = P₀ × 10^(−αL/10) · Ltarget = −10 log₁₀(1 − target/100) / α

Pulsed laser

Connect average power, pulse energy and peak power.

Enter average power, repetition rate and duration. The train shows pulse spacing; the detailed chart shows pulse duration on a physical time axis. This tool does not predict fiber amplification or power handling.

Isolated pulses · ideal temporal profile

Pulse energy—

Peak power—

Period—

FWHM / period—

Model & assumptions

All average power belongs to an identical pulse train, without a CW background. Duration is intensity FWHM. Restricted to well-separated pulses: frequency × duration ≤ 0.1. Shape factor is about 0.9394 (Gaussian), 0.8814 (sech²) or 1 (rectangular). No fiber damage threshold is inferred.

E = Pavg / f · Ppeak = k E / τ · T = 1 / f

Fiber coupling

Explore losses from MFD mismatch and lateral offset.

Enter mode field diameters at the same wavelength. Lateral offset shows the ideal overlap loss.

Overlap of two Gaussian modes

Theoretical coupling—

Total loss—

MFD contribution—

Offset contribution—

Model & assumptions

MFD = 1/e² intensity diameter for the Gaussian mode. Both values must refer to the same wavelength. Circular modes with matching polarization and planar wavefronts; no angular tilt, axial gap or reflection. Offset is lateral. Wavelength documents the supplied MFDs; it does not recalculate them. These overlap losses are neither a splice recipe nor a splice guarantee.

wᵢ = MFDᵢ / 2 · S = w₁² + w₂² · η = (2w₁w₂ / S)² exp(−2d² / S) · Loss = −10 log₁₀ η

Guidance regime

Explore the V-number and theoretical cutoff of the first higher-order mode.

Enter core diameter, NA and wavelength. V locates the regime in a step-index model.

Circular core · step index · weak guidance

V-number—

Model regime—

Estimated LP₁₁ cutoff—

LP₁₁ V threshold—

Model & assumptions

Scalar weak-guidance model for a straight, circular step-index fiber. V = 2.4048256 marks the LP₁₁ cutoff. A multimode regime means modes are supported, not necessarily excited. Constant NA is assumed for the curve and estimated cutoff; dispersion is not calculated. Not applicable to HCF, microstructured fibers or arbitrary index profiles.

V = π d NA / λ · λcutoff = π d NA / 2.4048255577

PM alignment

What does an axis alignment error change?

Choose an example, adjust the values and read the result below the chart. Formulas and limits are detailed below the tool.

ANALYTICAL MODEL

Ideal axis power ratio—

Desired axis—

Orthogonal axis—

Orthogonal-axis power—

Formulas, assumptions and limits

Perfectly linearly polarized input decomposed onto two orthogonal PM axes; no distributed coupling, loss or input polarization impurity. The calculated axis power ratio is not a complete output PER measurement: relative phase and analyzer are not modeled. At zero power the geometric ratio is shown, but PER cannot be measured.

P∥ = P₀ cos²θ · P⊥ = P₀ sin²θ · Raxes = 10 log₁₀(P∥/P⊥)

Pulse dispersion

How does the pulse change along the fiber?

Choose an example, adjust the values and read the result below the chart. Formulas and limits are detailed below the tool.

ANALYTICAL MODEL

Output duration—

Duration ratio—

Accumulated dispersion—

Output/input peak ratio—

Formulas, assumptions and limits

Gaussian pulse, constant second-order dispersion, no loss, gain, Kerr effect or higher-order dispersion. Convention: E(t) = exp[−(1+iC)t²/(2T₀²)] and added spectral phase +GDD·Ω²/2. With this convention positive C can be compensated by negative GDD. Energy is conserved. β₂ must match the operating wavelength and fiber.

T₀ = τFWHM / (2√ln2) · D = β₂L/T₀² · τout/τin = √[(1+CD)² + D²]

Mode intensity

How is power concentrated in the mode?

Choose an example, adjust the values and read the result below the chart. Formulas and limits are detailed below the tool.

ANALYTICAL MODEL

On-axis intensity—

On-axis fluence—

Gaussian effective area—

1/e² radius—

Formulas, assumptions and limits

Circular Gaussian spatial mode: I(r)=I₀ exp(−2r²/w²), MFD=2w and Aeff=πw². Power and energy are independent inputs; pulse duration is not inferred. Fluence is time-integrated energy per area. The cross-section map is normalized to its peak: use the calculated central value for absolute intensity. No damage threshold is predicted.

I₀ = 2P/(πw²) · F₀ = 2E/(πw²) · Aeff = πw²

Nonlinear phase

How much Kerr phase accumulates during propagation?

Choose an example, adjust the values and read the result below the chart. Formulas and limits are detailed below the tool.

ANALYTICAL MODEL

Accumulated modal phase—

Coefficient γ—

Effective length—

Output peak power—

Formulas, assumptions and limits

Scalar single-mode approximation in a passive fiber: constant effective area, n₂ and loss. P(z)=P₀exp(−αz). No gain, dispersion, Raman, Brillouin, self-steepening or mode evolution. Modal Kerr phase γ∫P(z)dz; distinct from an on-axis intensity B integral. No universal safety or damage threshold is inferred.

γ = 2πn₂/(λAeff) · α = ln(10)·loss/10 · Leff = (1−exp(−αL))/α · φNL = γP₀Leff

Explore. Adjust. Understand.

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Light propagation

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