4: Laser Dynamics (single-mode)
- Page ID
- 44650
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Before we start to look into the dynamics of a multi-mode laser, we should recall the technically important regimes of operation of a ”single-mode” laser. The term ”single-mode” is set in apostrophes, since it doesn’t have to be really single-mode. There can be several modes running, for example due to spatial holeburning, but in an incoherent fashion, so that only the average power of the beam matters. For a more detailed account on single-mode laser dynamics and Q-Switching the following references are recommended [1][3][16][4][5].
- 4.1: Rate Equations
- This page discusses the interaction between a two-level atom and a laser field, covering equations of motion and key variables like energy relaxation rate, group velocity, and saturation fluence. It derives population inversion and photon density dynamics, emphasizing factors that influence laser performance.
- 4.2: Built-up of Laser Oscillation and Continuous Wave Operation
- This page explores laser power dynamics, detailing the transition from vacuum fluctuations to saturation. It illustrates how instantaneous power \(P(t)\) increases exponentially until it hits the saturation level \(P_{sat}\), with the saturation time \(T_B\) calculated based on round-trip time and gain parameters. In steady-state, it defines the saturated gain \(g_s\) in relation to steady-state power \(P_s\) and saturation power, excluding spontaneous emission effects.
- 4.3: Stability and Relaxation Oscillations
- This page examines the return of a laser system to steady state post-perturbation, emphasizing gain and power behavior via differential equations. It determines relaxation rates and eigen frequencies, establishing stability criteria at various pump levels. Findings indicate stationary states are stable, while above-threshold pumping leads to complex relaxation rates and oscillations.
- 4.4: Q-Switching
- This page covers the operation and dynamics of actively Q-switched lasers, emphasizing energy extraction efficiency, pulse characteristics, and the influence of saturable absorbers. It details how Q-switching creates intense light pulses through changes in cavity loss and gain, while passive Q-switching modulates losses for pulse generation.
- 4.5: Example- Single Mode CW-Q-Switched Microchip Lasers
- This page focuses on Q-switched microchip lasers, emphasizing their compact design, high peak powers, and short pulse widths achieved through passive Q-switching mechanisms. It covers the dynamics of pulse energy extraction, highlighting the balance between gains and losses to maximize pulse energy.
- 4.6: Q-Switched Mode Locking
- This page covers the mechanics of Q-switched mode locking in lasers, detailing the relevant rate equations and the role of saturable absorbers in energy loss. It highlights the necessary driving force for stability and the trade-offs between mode locking and absorption. Figures illustrate these dynamics and boundaries for stability, emphasizing the importance of balancing parameters to achieve optimal laser performance and self-starting mode locking while preventing unwanted Q-switching.
- 4.7: Summary
- This page covers the dynamics of solid-state lasers, emphasizing mode-locked and Q-switched lasers that use a saturable absorber, with a detailed examination of energy build-up and pulse shaping in various regimes. It includes the effectiveness of semiconductor absorbers for mode-locking and discusses pulsing phenomena at picosecond and femtosecond scales.