1. GJ Van der Westhuizen, JP Burger, EG Rohwer, JN Maran Laser Research Institute, Department of Physics, University of Stellenbosch, South Africa NUMERICAL SIMULATION OF SOLID STATE AMPLIFIER INCORPORATING AMPLIFIED SPONTANEOUS EMISSION

2. Outline Introduction Aim of project Numerical model Theoretical predictions Sensibility check of numerical predictions –Experimental design –Comparison –Discussion Summary

3. Introduction Fibre lasers have a number of advantages over conventional solid state (SS) lasers: –Excellent beam quality –Compact –No external cooling required –High mechanical stability and low thermal load (Large surface-to-volume ratio) Solid state (SS) laser materials have a larger energy storage capacity

4. Aim of project Developing a laser system in pulsed regime for dental and industrial applications with: –Good beam quality –Pulselength ~ 1ps –Energy ~ 1mJ –Repetition rate: from 1 to 10 kHz –Materials choice: Yb:glass fibre laser oscillator Yb:YAG SS amplification stage

5. Topic of discussion We wish to obtain: –Small signal gain extractable from crystal –Influence of Amplified spontaneous emission (ASE) at high gain –Energy storage capacity of crystal Recently used existing equipment to check if the numerical simulation gives sensible results Developed numerical tool capable of simulating behaviour inside SS amplification medium for designing amplifier stage

6. Assumptions used in calculations –Steady state conditions –Very fast non radiative transitions between energy levels other than lasing transition –Uniform intensity distribution of pump light (diode) inside crystal (i.e. top hat distribution) Top hat minimizes beam distortion due to non- uniform transversal gain distribution (non-saturating) Energy extraction goes down compared to Gaussian pump profile?? Want to retain M 2 -value of input beam –ASE spectrum has Lorentzian lineshape Numerical Model

7. Numerical simulation based on rate equation formalism We first consider: Use Gaussian beam width: Power GainGeometrical Gain

8. Propagation equations: σ = Absorption / Emission cross section F = Geometrical focus terms S = Spontaneous emission term

9. Expression for upper state population :

10. Simulation algorithm Divide gain crystal into segments along optical axis Assume n 2 to be zero in each segment Numerically integrate using Runga-Kutta: I p ( n 2 ), I s ( n 2 ) Calc new n 2 ( I p,I s ) in each segment Numerically integrate using Runga –Kutta: I p ( n 2 ), I s ( n 2 ) and I ASE ( n 2 ) Process is repeated until numerical Steady State is reached ASE is resolved in 100 different λ’s

11. Convergence of calculations

12. Prediction for Amplified Spontaneous Emission (ASE)

13. Sensibility check of numerical predictions Design of experimental setup: –Pump light provided by multimode fibre coupled diode –Multimode fibre yields top hat intensity distribution (measured M 2 = 314) –Use Gaussian optics to design beamtrain for pump –Use second moment to calculate the Gaussian distribution equivalent to top hat:

14. –Trivially find that, since according to the second-moment based beam width definition –Can now design beamtrain for embedded Gaussian beam, where: –Complex amplitude of optical field given by: –Beamtrain obtained by transforming complex q - parameter by relevant ABCD matrices –Multiply all half-widths in beamtrain by M

15. Experimental design

16. Experimental Setup: L1 L2 L3 PB WP M1 Nd:YAG Laser Diode Nd:YVO 4

17. –Top hat profile predicted by GLAD and physical optics calculations: Roughly 60% of pump power under top hat in waist (ω = 200 μm ).

18. –Choose a waist of ±60 μm for Signal (Nd:YAG, M 2 = 1.14) at front surface of crystal ( D ~ 3W )

19. Comparison Pump dependence of gain

20. Saturation characteristics of amplifier

21. Discussion –Small gain → ASE not significant –Some discrepancy between model and experiment –Reason: Pump profile distorted by spherical aberrations Aberrations expected with spherical lenses used at low effective f-numbers (1.5 – 2.0) Measured M 2 –values for pump light after lenses are double that of light emitted by multimode fibre –We cannot model complex beam behavior (propagation position dependent beam profile and detailed transverse position dependent saturation)

22. M 2 Measurement

23. Predicted profile at waist

24. In front of waist Behind waist At waist Measured beam profiles z = -1 mm z = +2 mm z = 0 mm z = +1 mm

25. Discussion (continued..) –Small gain in this experiment applicable to regenerative amplifier –We will probably try to achieve higher gain ~10dB (for two-stage double pass amplification) –Use Gradium™/ aspheric lenses for pump in Yb:YAG amplifier to minimize aberrations –For Yb:YAG double-pass amplifier is preferred: Simplified experimental setup Less active switching by means of Pockels’s cells (compared to regenerative type of amplifiers/systems)

26. Summary Numerically simulated behavior inside crystal incorporating focusing effects, ASE, propagation coordinate dependent inversion (up-conversion can be added in future if needed) Designed experimental setup yielding top hat at crystal waist (for comparison) Set up experiment, and characterized the actual pump beam Obtained experimental results that shows model gives sensible numbers Software can easily be modified to model pulse amplification

27. Want to Thank: Dr. Burger and Dr. Maran You all for listening