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15.30 o4 c aguergaray
- 11. Similariton propagation and break-up with third-order dispersion influence
- 15. Theoretical study. Our Analytical model : Similariton break-up with 3
- 17. Theoretical study. Yields to the critical distance parameter : where Similariton break-up with 3
- 18. Numerical results. Analytical expression of critical distance : 2 =0.13 ps 2 /m 3 =10 -3 ps 3 /m g=2 m -1 =2.10 -3 w -1 m -1 Similariton break-up with 3
- 19. Numerical definition of pulse break-up : ↪ Pulse experiences growth of side peak under 3 influence Numerical results. Similariton break-up with 3
- 24. Parabolic and Hyper-Gaussian similaritons propagating in fiber with saturation effect.
- 27. Similariton with gain saturation Analytical solution Peak power : Pulse duration : Analytical solution with saturation effect takes the form : Dimensionless variables Dimensionless parameters
- 28. Similariton with gain saturation Parabolic similaritons = 4000 = 400 Simulation parameters: β 2 = 0.02 ps 2 m -1 / = 2 10 -5 W -1 m -1 / g 0 = 2 m -1 . Input energy: E 0 = 200 pJ 0 = 0.02. Saturation energy: E S = 20 nJ S = 2. Temporal profile and the chirp of the pulses for two different propagation distances : Input parameters:
- 29. Similariton with gain saturation = 600 = 100 Input energy: E 0 = 10 pJ 0 = 0.001. Saturation energy: E S = 10 µJ S = 100. Results for increased saturation energy : Input parameters: Parabolic similaritons
- 31. Similariton with gain saturation Hyper Gaussian similaritons This function is a product of a Gaussian and a super-Gaussian therefore we named it Hyper-Gaussian pulse (HG pulse). Two asymptotic non-linear attractors : which route depends on S
- 33. Similariton with gain saturation Hyper-Gaussian similaritons Test for different input pulse shape : All the pulses converge towards a HG shape pulse with linear chirp ! HG pulse is a local asymptotic attractor.
- 38. Bric a brac
- 40. Numerical simulations The HG similaritons may form when : - The energy E(z) of the pulse is a slowly growing function of distance, - The peak power of the pulse is a constant or decreasing function of z.
- 42. Motivation How to predict accurately the critical distance and the pulse shape? Similariton break-up with 3
- 44. OWN1 / Finot OSA OFC 2009 Context
- 45. Theoretical study. Renormalisation procedure :
- 47. Theoretical study. No renormalisation With renormalisation procedure applied
- 49. Motivation Net cavity GVD= 0.005 ps 2 Logvin et al. OE 15, 985 (2007) SMF and Yb fibers TOD (Negligible TOD) Similariton regime: symmetric pulse, top spectrum tilted. PBF TOD = 500 fs 3 /mm Cubicon-like features: asymmetric pulse, triangular shape spectrum. PBF TOD = 1200 fs 3 /mm. Stretched Pulse regime: narrower pulse, broader spectrum with asymmetric sidebands.
- 53. Motivation Latkin et al. OE 32, 331 (2007) Intensity Time [ps] Distance [km] Intensity Wavelength [nm] Distance [km]
- 54. The Australian Optical Society
Editor's Notes
- P arabolic pulses are of wide ranging practical significance since they They are also of fundamental interest as they represent a particular class of solution of the nonlinear Schrödinger equation (NLSE) with
- The top figure shows the simulation output pulse intensity and chirp (solid lines) together with parabolic and linear fits respectively (circles). The bottom figure plots the simulation output (solid line) and parabolic fit (circles) on a logarithmic scale, and also includes gaussian (long dashes) and sech2 (short dashes) fits to illustrate the comparatively poor fits obtained using these pulse shapes compared to a parabolic pulse. The presence of GVD tends to linearise the phase accumulated by the pulse, which increases the spectral bandwidth but does not destabilize the pulse.
- Some techniques for similariton generation involve use of long length of fiber or low GVD fibers (DDF) therefore TOD becomes influent and distort similariton pulse
- From a technological viewpoint Self-similar amplifiers possess a number of very attractive features Moreover, the existence of analytic design criteria for self-similar amplifiers makes it straightforward to tailor system design to a wide range of input pulses and amplifier types.
- The fact that the output pulse chirp depends only on the amplifier gain and dispersion considerably simplifies the post-compressor design
- In the route towards ever increasing output energy laser systems, the soliton lasers have quickly been disregarded due to very stringent limitation… One demonstration pushing it 1nJ, 3ps In recent years, researchers have actively investigated mode-locked laser operations with large GVD. It has now become conventional wisdom that the compensation of group-velocity dispersion (GVD) in a laser is prerequisite to the generation of femtosecond pulses. Therefore most modern femtosecond lasers have dispersion maps, with segments of normal and anomalous GVD.
- If gvd =0… But now if gvd>0 , normal disp…
- Limit by, so it is imprtant to understand their impact, and quantify characterise it
- As a result of the TOD, the pulse shape experiences an asymmetric temporal development with the peak shifted towards the edges of the pulse, the direction of the shift depending on the sign of the TOD. For long propagation in the fibre, this development is eventually halted by pulse break-up .
- Where does that equation come from ?
- The condition : T 2 (z) = T 3 (z) ( 3 >0) or T 1 (z) = T 2 (z) ( 3 <0). Leads to the expression of Zc…
- trend
- If beta 3 effect can have effect for long amplifiers, gain saturation is important… We present in this paper a new analytical solution of NLSE describing the propagation of the parabolic similaritons including the influence of the saturation effect. Saturation for time scale longer than T1 = population relaxation time.
- suitable for further amplification.
- interest could be found
- Similariton-cubicon regime to the Stretched Pulse regime