L27 · Lasers powered by scattering

Raman & Brillouin Lasers

Can transparent glass become a laser gain medium? Yes. A strong pump scatters off vibrations in the glass, molecular vibrations for Raman and sound waves for Brillouin, and amplifies light shifted to a lower frequency, called Stokes light. No population inversion is needed. Above threshold, the next Stokes order can grow, drain the previous one and hold it at a fixed level.

Pump a silica fiber past a Stokes threshold and watch the next order clamp the one before it. Capture a transient and calculate a steady pump sweep.

First Stokes steady noise-floor linewidth $\text{—}$

Second Stokes steady noise-floor linewidth $\text{—}$

Third Stokes steady noise-floor linewidth $\text{—}$

Recorded phase-diffusion linewidth $\text{—}$

Recorded phase samples $\text{—}$

Scattering process $\text{—}$

Elapsed round trips $\text{—}$

Physical elapsed time $\text{—}$

First Stokes frequency shift $\text{—}$

First Stokes wavelength $\text{—}$

Effective gain bandwidth $\text{—}$

Feedback free spectral range $\text{—}$

Gain overlap fraction $\text{—}$

First oscillation threshold $\text{—}$

Recorded pump in the fiber $\text{—}$

First-order extracted power $\text{—}$

Second-order extracted power $\text{—}$

Third-order extracted power $\text{—}$

Recorded phonon heat power $\text{—}$

Recorded passive loss power $\text{—}$

Recorded total Stokes output $\text{—}$

Separate steady output reference $\text{—}$

Integrated energy residual $\text{—}$

Captured transient samples $\text{—}$

Computed equilibrium samples $\text{—}$

Frozen captured Stokes output $\text{—}$

Stokes propagation $\text{—}$

First-threshold regime $\text{—}$

L27

Can transparent glass become a laser gain medium?

Raman / Brillouin

m

0

Optical pump power

P_{\rm in}

3\,\mathrm{W}

Pump wavelength

\lambda_0

1064\,\mathrm{nm}

Silica gain fiber length

L

100\,\mathrm{m}

Effective mode area

A_{\rm eff}

60\,\mathrm{\mu m^2}

Stokes output coupling

T

10\,\mathrm{\%}

Additional round-trip loss

\ell

2\,\mathrm{\%}

Allowed Stokes orders

M

3

Spacing error in gain FWHM units

\delta/\Gamma

0

Prescribed Brillouin pump linewidth

\Delta\nu_p

1\,\mathrm{MHz}

Detail: fiber / backward / forward

j

1

The scene shows guided fiber with ideal wavelength-routing couplers. Brightness uses a fixed logarithmic power scale; fiber turns and dimensions are schematic. Each setting records six hundred round trips. Switching process sets a typical pump of three watts for Raman or eighty milliwatts for Brillouin, whose slider spans zero to three hundred milliwatts.

Compare the recorded cascade with the separate steady pump sweep. A broader Brillouin pump raises the first threshold even at the same total pump power.

The model uses spatially uniform, mean-field power equations. The pump is continually replenished and is not resonant, and there are up to three set Stokes modes. Raman light travels with the pump; bulk Brillouin orders alternate direction. This teaching cavity is defined by assumed silica gains, fast material relaxation and logarithmic round-trip losses. Photon-energy ratios keep track of the heat left behind as phonons. The set pump spectrum broadens the Brillouin gain; that width is not the emitted linewidth. A separate model of small phase fluctuations takes the same calculated steady powers, thermal phonon occupation at 300 kelvin, vacuum noise and the anti-Stokes noise from the next order, and calculates the fundamental Lorentzian linewidth of each lasing order. You can record a Gaussian phase walk for the first order and compare its measured diffusion and field coherence with that reference. This low-offset noise floor leaves out the transfer of technical pump noise, amplitude fluctuations, material dispersion, polarization and non-Gaussian behavior near threshold. The phase record is not the power transient. Transients are frozen copies, and the steady-state sweep and phase-noise reference are calculated diagnostics, not hardware measurements. Fiber routes, colors and dimensions are schematic.

Start with the essentials

Focus question: Can transparent glass become a laser gain medium?
One-sentence intuition: When the next Stokes order starts oscillating, it drains its parent and clamps it; it does not simply add more output.

Core mathematical model

One photon becomes light and vibration

\begin{aligned}\nu_{j-1}&=\nu_j+\Omega_j\\h\nu_{j-1}&=h\nu_j+h\Omega_j\end{aligned}

Each scattering event moves one photon from an order to the next, but the photons in the two orders carry different energies.

Average gain over the fiber

\begin{aligned}C_j&=g_jL_{\rm eff}/A_{\rm eff}\\L_{\rm eff}&=(1-e^{-\alpha L})/\alpha\end{aligned}

The gain overlap includes the set error in mode spacing. A spectrally broad pump lowers the Brillouin gain.

Stokes growth and depletion

\begin{aligned}\dot P_j&=G_j-D_j\\G_j&=C_jP_{j-1}P_j-\Lambda P_j\\D_j&=r_jC_{j+1}P_jP_{j+1}\end{aligned}

Time here is counted in round trips. The frequency ratio in the depletion term accounts for the energy carried off by the emitted phonon.

First oscillation threshold

\begin{aligned}P_{0,\rm th}&=\Lambda/C_1\\P_{\rm in,th}&=a\Lambda/C_1\end{aligned}

The pump in the fiber decays with coefficient a. Each further Stokes order needs more power from its parent.

Heat left behind as phonons

\begin{aligned}Q_{\rm ph}&=\sum_j(r_{j-1}-1)S_j\\S_j&=C_jP_{j-1}P_j\\r_{j-1}&=\nu_{j-1}/\nu_j\end{aligned}

The fraction of optical energy lost is small for Brillouin scattering and much larger for Raman scattering.

In steady state the parent is clamped

\begin{aligned}C_jP_{j-1}&=\Lambda+r_jC_{j+1}P_{j+1}\\P_j&>0\end{aligned}

This relation gives every order that oscillates in a steady-state branch. The last order has no higher order to drain it.

Fundamental linewidth of each output

\begin{aligned}N_m&=P_m t_{\rm rt}/(h\nu_m)\\A_m&=\gamma(\bar n+1)\\B_m&=2\mu_mN_{m+1}(2\bar n+1)\\\Delta\nu_m&=(A_m+B_m)/(4\pi N_m)\end{aligned}

A separate model of small phase fluctuations at low offset frequency uses the same steady powers. When the next order lases, it adds anti-Stokes noise. Technical noise from the pump is left out.

Record phase, then test coherence

\begin{aligned}d\varphi&=\sqrt{2\pi\Delta\nu_m}\,dW\\g^{(1)}(t)&=e^{-\pi\Delta\nu_m|t|}\\\widehat{\Delta\nu}&=\frac{\operatorname{Var}(\delta\varphi)}{2\pi\delta t}\end{aligned}

The simulated phase record lets you check the diffusion and the coherence. The Fourier transform of the exponential coherence is a Lorentzian with this full width.

Common difficulties

The gain width is the output linewidth

Typical misconceptionThe gain bandwidth shown tells you the linewidth of the emitted laser light.

Better mental modelThe gain bandwidth belongs to the power model. The separate phase model calculates the steady, phase-matched noise floor and records how the phase diffuses. Technical pump noise and fluctuations near threshold are outside its scope.

More pump always grows the first order

Typical misconceptionEvery Stokes order keeps growing as the pump increases.

Better mental modelOnce the next order oscillates, it drains its parent, and the parent stays clamped on that branch.

Run the experiment

01
Cross the threshold
Compare Below threshold with Raman, then drag the pump dial. Each setting records six hundred round trips automatically.
What to observe: The fixed seed light dies away below threshold and grows above it, until pump depletion limits the growth.
02
Follow the energy into another order
Choose Cascaded orders and follow the three colored outputs and the pump sweep below. Open Advanced controls to compare One allowed order.
What to observe: As a new order grows, its parent is clamped. The separately calculated sweep shows the thresholds one after another.
03
Broaden the pump
Compare narrow and broad Brillouin pumping at the same power, and look at the backward and forward ports.
What to observe: Less overlap raises the threshold. Odd and even Brillouin orders leave through opposite ports.
04
Measure the output phase
Open Advanced controls, choose One allowed order and click Record output phase. Expand the separate phase-noise record below, then compare it with a cascade.
What to observe: The emitted linewidth is not the gain bandwidth, and in a cascade the next order adds its own noise channel.

Raman & Brillouin Lasers

Scattered photons can sustain an oscillator