P OSEIDON ’ S H IDDEN M YSTERIES ... Dissipative soliton resonance described by the complex cubic-quintic Ginzburg-Landau equation in the normal dispersion regime Peter Vouzas, Wonkeun Chang and Nail Akhmediev
The Art of Physics, AIP, ANU
O PTICAL S CIENCES G ROUP, Research School of Physics and Engineering, Australian National University
Dissipative soliton
Dissipative soliton resonance
A soliton (Wave of Translation) is a self-reinforcing wave structure in a conserved system, which maintains its shape while traveling at a constant speed, first described by John Scott Russell in 1834: “...a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed...“
Dissipative solitons (DS) are an extension to solitons, also propagating for extended periods of time. Their localized structure consists of components experiencing both gain and loss of energy and/or mass. They do require the presence of a continuous energy supply via an external source, where the energy gain being maintained, is counterbalanced with energy loss of the system. This phenomena occurs naturally and has received wide attention in optical fibers, laser optics, general physics, biology and medicine.
Dissipative soliton resonance (DSR) is a DS that pertains towards indefinite energy. This phenomena can be utilized in the generation of ultra short optical pulses with record-high energy, the generation of exceptionally wideband, or supercontinuum light sources, and assist in the design of equipment for more precise laser medical surgery, including manipulation of cells and tissues without destructive effects, nondestructive dentistry and delicate eye surgery. In this work new regions around DSR are explored numerically. We observe moving fronts (MF) that also include structural chaos and a new brach of DSs is identified.
Complex cubic-quintic Ginzburg-Landau equation
Shaded region
A dissipative soliton resonance in the normal dispersion regime is identified by fixing 5 parameters in the complex-quintic Ginzburg Landau equation. The quintic non-linear parameter ν is varied. z
5 0 60 40
ν ∼ quintic non-linearity is varied D ∼ dispersion parameter
20 0 15
ν = −0.0803
10 z
Pulse profiles and chirp
Solution system plot
ν = −0.08605
z
∼ non-linear gain µ ∼ non-linear gain saturation
15 10
D 2 4 4 2 iψz + ψtt + |ψ| ψ = i( δψ + βψtt + |ψ| ψ + µ|ψ| ψ ) − ν|ψ| ψ 2 ψ ∼ complex envelope of the wave field z ∼ propagating distance in a 1-D spatial dimension t ∼ moving time frame δ ∼ linear gain/loss β ∼ gain bandwidth
Figure 3 : Evolving solutions in time & frequency
5
Figure 1 : Soliton solution energy vs ν.
Figure 2 : Pulse profiles and chirp characteristics RHS
|ψ|2
0.8π
10
0
δ = −0.1
Energy
60
0 15
ν = −0.07
10 5
= 1.0
0
µ = −0.05
40
5
z
β = 0.8
0
20
Chirp
10
Chirp
D = −1
0.8π
10
|ψ|2
20
100
ν = −0.075
z
LHS
80
0 15
−2
0 t
2
−0.8π
0
0 t
2
0 15
100
ν = −0.06
10
−0.2
0.0
0.2
0.4
0.6
ν = −0.04
10
0.8
0
ν
Line embracing shaded region (RHS branch) extending towards infinity is DSR. I Along DSR, pulse width widens towards infinity (infinite energy). I Stable soliton pulse width on LHS branch is finite I Shaded region represents MF propagations; including structured Chaos. I Hopf bifurcation observed to far right. ie. pulsating solitons (PS) I
0 15
−1 0 1 Frequency detuning
0
−1 0 1 Frequency detuning
Red pulse plots are identical in energy, but differ in peak power and duration. I Chirp differs in sign and size from LHS to RHS branch. I Along DSR on RHS branch, pulse width increases, but peak power is limited. I LHS: blue plot is a DS. I RHS: blue and purple plots is energy (min/max) of a PS.
z
−0.4
50
5 0 15
ν = −0.02
I
References : [1] N. Akhmediev, J. M. Soto-Crespo, and G. Town, “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: CGLE approach,” Phys. Rev. E 63, 056602 (2001). [2] W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 70, 023830 (2008). [3] W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances in laser models with parameter management,” J. Opt. Soc. Am. B 25, 1972 (2008). [4] W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev “Dissipative soliton resonances in the anomalous dispersion regime,” Phys. Rev. A 79, 033840 (2009). [5] X. Wu, D.Y. Tang and L.M, Zao, ”Dissipative soliton resonance in an all-normal-dispersion erbium-doped fiber laser,” Optics Express17, 7, 5580 (2009). [6] P. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev “Dissipative soliton resonances as a guide for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B 27, 2336 (2010).
10 z
0 −0.6
50
5
5 0 15
ν = −0.01
10 z
20
Spectrum
Spectrum
z
100
−2
−0.8π
5 0 −20
ν = 0.65 −10
0 t
0
12
10
20 24
−2 −40
−1 0 1 Frequency detuning −20
2 0
Acknowledgments :
Contact :
The authors acknowledge the support of the Australian Research Council (Project numbers DE130101432 and DP140100265). N. A. acknowledges support from the Volkswagen Stiftung. P. V. acknowledges support of the Australian Postgraduate Award.
Peter Vouzas O PTICAL S CIENCES G ROUP Research School of Physics and Engineering Australian National University Acton ACT 2601, Australia E-mail:
[email protected]
