---
title: "Fiber Laser & FBG Cavity Interactive Lab | Sandbox Physics"
description: "Does more fiber always give more useful output? No. The pump is absorbed as it travels along the fiber."
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language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/fiber-fbg-laser/"
last_modified: "2026-10-27"
---

L21 · Distributed gain and feedback

# Fiber Laser & FBG Cavity

**Does more fiber always give more useful output?** No. The pump is absorbed as it travels along the fiber. Past the point where it is used up, extra fiber adds loss instead of gain. The gratings at the two ends must also reflect the same wavelength; shift the output grating's wavelength and the feedback can fail completely.

Build a fiber laser between two fiber Bragg gratings, check the pump and signal power at any point along the fiber, and record output versus pump. Shift the output grating to take away the feedback at the fixed laser wavelength.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

This steady-state teaching model works at a single signal wavelength with ytterbium-like parameters. At each point a balance between two energy manifolds is coupled to a forward pump wave and to signal waves travelling both ways. The pump is at 976 nanometres and the signal is held at 1064 nanometres. Dopant density, cross-sections and lifetime are fixed illustrative values, not fitted to a real fiber product. The core is uniformly doped. The pump fills a fixed 125-micrometre cladding, and the signal overlap is 0.8. Stimulated emission at the pump wavelength and reabsorption of the signal are included. A fourth-order integration along the fiber, with shooting on the signal amplitude, meets the power conditions at both gratings. Below the zero-field threshold the coherent signal is zero; fluorescence and amplified spontaneous emission (ASE) are left out. The rear grating has a fixed strength of four, and the output grating is adjustable. Both are lossless, uniform, one centimetre long and have an index of 1.45. The signal stays at the rear grating's Bragg wavelength. Shifting the front grating changes its reflection at that wavelength, but the model does not solve for wavelength selection or competition between longitudinal modes. The probe reads the same steady profile. The 21 points of a sweep are independent solutions of the boundary problem, not measured hardware data or startup dynamics. The slope is taken over the last one-watt step. The quantum-defect readout is only the minimum power set by the energy difference between absorbed pump photons and signal photons; it is not the total heat or a temperature. The forward nonlinear phase is a diagnostic integral using an illustrative nonlinear index for silica. It does not feed back into the linear cavity, does not predict a damage threshold and does not simulate Raman, Brillouin, thermal or modal instabilities. The drawing straightens the fiber, enlarges the core and the grating periods, and uses visible colors for infrared light.

Laser foundations · Light, gain and feedback

[L01 · Compare sources](https://sandboxphysics.com/labs/laser-source-comparison/) [L02 · Count transitions](https://sandboxphysics.com/labs/light-matter-transitions/) [L03 · Build inversion](https://sandboxphysics.com/labs/population-inversion/) [L04 · Amplify once](https://sandboxphysics.com/labs/single-pass-amplifier/) [L05 · Add feedback](https://sandboxphysics.com/labs/passive-optical-resonator/) [L06 · Start from noise](https://sandboxphysics.com/labs/laser-noise-startup/) [L07 · Build and debug](https://sandboxphysics.com/labs/build-debug-laser/) [L08 · Measure and diagnose](https://sandboxphysics.com/labs/laser-diagnostic-bench/) [L09 · Select axial modes](https://sandboxphysics.com/labs/gain-longitudinal-modes/) [L10 · Confine the beam](https://sandboxphysics.com/labs/stable-resonator-geometry/) [L11 · Select spatial modes](https://sandboxphysics.com/labs/transverse-laser-modes/) [L12 · Propagate and measure](https://sandboxphysics.com/labs/gaussian-beam-quality/) [L13 · Align and match](https://sandboxphysics.com/labs/alignment-mode-matching/) [L14 · Optimize extraction](https://sandboxphysics.com/labs/output-coupler-optimization/) [L15 · Drive the dynamics](https://sandboxphysics.com/labs/laser-dynamics-relaxation/) [L16 · Store and release](https://sandboxphysics.com/labs/q-switched-giant-pulse/) [L17 · Lock phases into pulses](https://sandboxphysics.com/labs/mode-locking-frequency-comb/) [L18 · Calibrate the comb](https://sandboxphysics.com/labs/optical-frequency-comb/) [L19 · Inject carriers](https://sandboxphysics.com/labs/semiconductor-laser-diode/) [L20 · Compare gain media](https://sandboxphysics.com/labs/laser-medium-zoo/) [L21 · Distributed gain](https://sandboxphysics.com/labs/fiber-fbg-laser/) [L22 · Choose feedback](https://sandboxphysics.com/labs/laser-feedback-architectures/) [L23 · Balance ultrafast pulses](https://sandboxphysics.com/labs/ti-sapphire-oscillator/) [L24 · Stretch and compress](https://sandboxphysics.com/labs/chirped-pulse-amplification/) [L25 · Trap and extract](https://sandboxphysics.com/labs/regenerative-multipass-amplifier/) [L26 · Convert frequencies](https://sandboxphysics.com/labs/nonlinear-frequency-conversion/) [L27 · Scatter and cascade](https://sandboxphysics.com/labs/raman-brillouin-lasers/) [L28 · Synchronize a slave](https://sandboxphysics.com/labs/injection-locking/) [L29 · Lock to a reference](https://sandboxphysics.com/labs/pdh-frequency-lock/) [L30 · Measure phase noise](https://sandboxphysics.com/labs/laser-linewidth-phase-noise/) [L31 · Scatter for feedback](https://sandboxphysics.com/labs/random-laser/) [L32 · Diagnose thermal scaling](https://sandboxphysics.com/labs/thermal-lensing/) [L33 · Combine coherent fields](https://sandboxphysics.com/labs/coherent-beam-combining/) [L34 · Sustain a Kerr pulse](https://sandboxphysics.com/labs/microresonator-kerr-comb/) [L35 · Return a delayed field](https://sandboxphysics.com/labs/external-feedback-chaos/) [L36 · Scan without mode hops](https://sandboxphysics.com/labs/tunable-laser-scan/)

Physical basis: [MIT: coherence and spectrum](https://ocw.mit.edu/courses/res-6-006-video-demonstrations-in-lasers-and-optics-spring-2008/resources/coherence-length-and-source-spectrum/) · [Rate equations](https://ocw.mit.edu/courses/6-977-ultrafast-optics-spring-2005/resources/chapter2/) · [Pumping and gain media (§7.2)](https://ocw.mit.edu/courses/6-974-fundamentals-of-photonics-quantum-electronics-spring-2006/bf3bdeb971819ddc9c68719d28bb2745_classnotes.pdf) · [Laser dynamics](https://ocw.mit.edu/courses/6-977-ultrafast-optics-spring-2005/resources/chapter4/)

Physics tutorial

## Distributed reservoirs and mirror boundaries

**Background** In a fiber laser the gain is spread along the doped fiber, and two fiber Bragg gratings at the ends provide the feedback. Look at the pump and signal power at any point, record output versus pump, and shift the output grating to remove the feedback at the signal wavelength.

**Why it matters** Before you draw a conclusion about a design, link each part of the fiber to the powers the model actually computes there.

Start with the essentials

- **Focus question**: Does more fiber always give more useful output?
- **One-sentence intuition**: The laser runs only when the gain along the fiber and the reflections at both gratings together bring the signal back to the same power after a round trip.

### Core mathematical model

#### Population balance at each point

$$
\begin{aligned}f&=\frac{W_{pa}+W_{sa}}{W_{pa}+W_{pe}+W_{sa}+W_{se}+\tau^{-1}}\\ W_{jk}&=\frac{\Gamma_j\sigma_{jk}P_j}{h\nu_j A}\end{aligned}
$$

Absorption fills the upper manifold; stimulated and spontaneous emission empty it. The signal power here is the sum of both directions.

#### One population sets pump absorption and signal gain

$$
\begin{aligned}\frac{dP_p}{dz}&=-\Gamma_pN[\sigma_{pa}(1-f)-\sigma_{pe}f]P_p\\ g_s&=\Gamma_sN[\sigma_{se}f-\sigma_{sa}(1-f)]-\alpha_s\end{aligned}
$$

The pump overlap is the core area divided by the cladding area. A larger core therefore changes the pump overlap as well as the signal intensity.

#### Signal waves and the two grating conditions

$$
\begin{aligned}\frac{dP_+}{dz}&=g_sP_+\\\frac{dP_-}{dz}&=-g_sP_-\\ P_+(0)&=R_1P_-(0)\\ P_-(L)&=R_2P_+(L)\end{aligned}
$$

In this model the product of the forward and backward powers stays constant along the fiber. The solver adjusts the launched forward signal until the condition at the output grating is met.

#### Threshold with no signal present

$$
\mathcal M_0=\ln(R_1R_2)+2\int_0^L g_{s,0}(z)\,dz
$$

If this zero-field round-trip margin is positive, a saturated lasing solution can exist. Reaching transparency at one point is a weaker condition than reaching threshold for the whole cavity.

#### Useful power leaves through the front grating

$$
P_{\rm out}=(1-R_2)P_+(L)
$$

Making the output grating reflect almost everything can raise the power inside the cavity and still lower the useful output.

#### Two diagnostics that do not change the solution

$$
\begin{aligned}Q_{\rm qd}&=\left(1-\frac{\lambda_p}{\lambda_s}\right)P_{p,\rm abs}\\ B_+&=\int_0^L\frac{2\pi n_2P_+(z)}{\lambda_s A}\,dz\end{aligned}
$$

The first is the minimum power set by the photon-energy difference between absorbed pump and signal. The second is the nonlinear phase of the forward signal. Neither one changes the steady cavity solution, and neither is a high-power solver.

### Common difficulties

#### More fiber is always better

**Typical misconception** A longer fiber absorbs more pump, so the output has to go up.

**Better mental model** A tail that gets almost no pump, together with background loss, can outweigh that extra absorption.

#### Mismatched gratings mean no laser

**Typical misconception** If the two gratings are offset, the laser cannot start at any pump power.

**Better mental model** This fixed-wavelength model only checks whether gain beats loss, and enough gain can make up for a weak reflection. It does not solve for other wavelengths.

### Run the experiment

1. 01

   #### Break and restore feedback

   Choose Gratings mismatched, then set Output Bragg offset to zero.

   **What to observe:** The only thing that changes is the output grating's reflection at the fixed signal wavelength.

2. 02

   #### Follow the powers along the fiber

   In Working cavity and in Long fiber, move the probe along the fiber with Probe position fraction.

   **What to observe:** The leftover pump, the local excitation and the backward signal all come from the same solution.

3. 03

   #### Measure the useful output

   Press Acquire pump sweep for Working cavity and for Nearly closed output.

   **What to observe:** The signal stored in the cavity and the useful output do not have to rise together.

Physical conclusion

When you report a result, say which wavelength it is for, how the gain is defined, how the data were taken and what the model leaves out.

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)