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Observation of optical solitons in PT-symmetric lattices.

Wimmer M, Regensburger A, Miri MA, Bersch C, Christodoulides DN, Peschel U - Nat Commun (2015)

Bottom Line: Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation.Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions.The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.

View Article: PubMed Central - PubMed

Affiliation: 1] Institute of Optics, Information and Photonics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7/B2, 91058 Erlangen, Germany [2] Erlangen Graduate School in Advanced Optical Technologies (SAOT), 91058 Erlangen, Germany.

ABSTRACT
Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.

No MeSH data available.


Related in: MedlinePlus

Formation of the double-discrete soliton on a passive lattice.(a) The band structure is split into two bands, separated by a gap of width π/2. The excitation of a single-lattice site in the long loop initiates a light walk for linear power levels P≈13 mW (b,e). If the input power is increased P≈65 mW (c,f), one of the two branches bends towards the center and repels the remaining light. At high powers P≈130 mW (d,g) a soliton is formed, which is dominated by a single pulse, which switches between loops. The insets at P≈130 mW show the temporal dynamics over five time steps around m=25. Only pulses propagating in the short loop are shown. (h) Comparison between a numerically (bars) and an experimentally (markers) determined soliton profile in the longer (v, cross) and in the shorter (u, circle) loop. (i), numerically determined phase distribution along the exact soliton profile. The values for the propagation constant of the soliton are lying inside the band gap. From the lower to the upper edge of the band gap the total energy E monotonically increases (j). At the edge of the band gap the width w of the soliton tends to infinity, while at the center of the gap the soliton has a minimum width <1 position (k). (j,k) are based on numerically determined soliton solutions.
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f2: Formation of the double-discrete soliton on a passive lattice.(a) The band structure is split into two bands, separated by a gap of width π/2. The excitation of a single-lattice site in the long loop initiates a light walk for linear power levels P≈13 mW (b,e). If the input power is increased P≈65 mW (c,f), one of the two branches bends towards the center and repels the remaining light. At high powers P≈130 mW (d,g) a soliton is formed, which is dominated by a single pulse, which switches between loops. The insets at P≈130 mW show the temporal dynamics over five time steps around m=25. Only pulses propagating in the short loop are shown. (h) Comparison between a numerically (bars) and an experimentally (markers) determined soliton profile in the longer (v, cross) and in the shorter (u, circle) loop. (i), numerically determined phase distribution along the exact soliton profile. The values for the propagation constant of the soliton are lying inside the band gap. From the lower to the upper edge of the band gap the total energy E monotonically increases (j). At the edge of the band gap the width w of the soliton tends to infinity, while at the center of the gap the soliton has a minimum width <1 position (k). (j,k) are based on numerically determined soliton solutions.

Mentions: Here θ and Q stand for the longitudinal propagation constant and the transverse Bloch momentum respectively. The band structure depicted in Fig. 2a consists of two bands, which are separated by a gap of π/2. Due to different dispersion characteristics, the Kerr nonlinearity32 of the fibre has a focusing effect on the field distribution populating the upper band, and a defocusing one on pulses in the lower band5262. By injecting a single low-intensity pulse at one lattice site, all states of the band structure are excited simultaneously (see Fig. 2b,e). In this linear regime, the field spreads ballistically34 between two intensity lobes formed by waves having zero group velocity dispersion (Fig. 2a). As we will show, this so-called classical light walk is considerably modified in the presence of nonlinearity.


Observation of optical solitons in PT-symmetric lattices.

Wimmer M, Regensburger A, Miri MA, Bersch C, Christodoulides DN, Peschel U - Nat Commun (2015)

Formation of the double-discrete soliton on a passive lattice.(a) The band structure is split into two bands, separated by a gap of width π/2. The excitation of a single-lattice site in the long loop initiates a light walk for linear power levels P≈13 mW (b,e). If the input power is increased P≈65 mW (c,f), one of the two branches bends towards the center and repels the remaining light. At high powers P≈130 mW (d,g) a soliton is formed, which is dominated by a single pulse, which switches between loops. The insets at P≈130 mW show the temporal dynamics over five time steps around m=25. Only pulses propagating in the short loop are shown. (h) Comparison between a numerically (bars) and an experimentally (markers) determined soliton profile in the longer (v, cross) and in the shorter (u, circle) loop. (i), numerically determined phase distribution along the exact soliton profile. The values for the propagation constant of the soliton are lying inside the band gap. From the lower to the upper edge of the band gap the total energy E monotonically increases (j). At the edge of the band gap the width w of the soliton tends to infinity, while at the center of the gap the soliton has a minimum width <1 position (k). (j,k) are based on numerically determined soliton solutions.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
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getmorefigures.php?uid=PMC4525206&req=5

f2: Formation of the double-discrete soliton on a passive lattice.(a) The band structure is split into two bands, separated by a gap of width π/2. The excitation of a single-lattice site in the long loop initiates a light walk for linear power levels P≈13 mW (b,e). If the input power is increased P≈65 mW (c,f), one of the two branches bends towards the center and repels the remaining light. At high powers P≈130 mW (d,g) a soliton is formed, which is dominated by a single pulse, which switches between loops. The insets at P≈130 mW show the temporal dynamics over five time steps around m=25. Only pulses propagating in the short loop are shown. (h) Comparison between a numerically (bars) and an experimentally (markers) determined soliton profile in the longer (v, cross) and in the shorter (u, circle) loop. (i), numerically determined phase distribution along the exact soliton profile. The values for the propagation constant of the soliton are lying inside the band gap. From the lower to the upper edge of the band gap the total energy E monotonically increases (j). At the edge of the band gap the width w of the soliton tends to infinity, while at the center of the gap the soliton has a minimum width <1 position (k). (j,k) are based on numerically determined soliton solutions.
Mentions: Here θ and Q stand for the longitudinal propagation constant and the transverse Bloch momentum respectively. The band structure depicted in Fig. 2a consists of two bands, which are separated by a gap of π/2. Due to different dispersion characteristics, the Kerr nonlinearity32 of the fibre has a focusing effect on the field distribution populating the upper band, and a defocusing one on pulses in the lower band5262. By injecting a single low-intensity pulse at one lattice site, all states of the band structure are excited simultaneously (see Fig. 2b,e). In this linear regime, the field spreads ballistically34 between two intensity lobes formed by waves having zero group velocity dispersion (Fig. 2a). As we will show, this so-called classical light walk is considerably modified in the presence of nonlinearity.

Bottom Line: Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation.Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions.The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.

View Article: PubMed Central - PubMed

Affiliation: 1] Institute of Optics, Information and Photonics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7/B2, 91058 Erlangen, Germany [2] Erlangen Graduate School in Advanced Optical Technologies (SAOT), 91058 Erlangen, Germany.

ABSTRACT
Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.

No MeSH data available.


Related in: MedlinePlus