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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.


Formation of a broad PT soliton.A broad Gaussian distribution populating the focusing band is excited. In the linear regime (a,b) the beam spreads, while in the nonlinear regime a broad double hump (c) or single hump (d) PT soliton forms which can propagate for 100 round trips. Note that for observing the single and double hump solitons the sign of the phase potential is switched between ϕ0=−0.4π and ϕ0=+0.4π, with G=1.4 for all cases. The estimated peak power in the experiment is about 2 mW for the nonlinear regime and below 0.5 mW for the linear regime.
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f6: Formation of a broad PT soliton.A broad Gaussian distribution populating the focusing band is excited. In the linear regime (a,b) the beam spreads, while in the nonlinear regime a broad double hump (c) or single hump (d) PT soliton forms which can propagate for 100 round trips. Note that for observing the single and double hump solitons the sign of the phase potential is switched between ϕ0=−0.4π and ϕ0=+0.4π, with G=1.4 for all cases. The estimated peak power in the experiment is about 2 mW for the nonlinear regime and below 0.5 mW for the linear regime.

Mentions: To launch wider solitons, a broad Gaussian distribution with a flat phase front is used to excite the system. In this case, because of nonlinearity, Schrödinger-like solitons29 form in the PT lattice (see Fig. 6 and Supplementary Figs 15 and 16), which are similar in shape and behaviour to solitons arising from the nonlinear Schrödinger equation. Note that, if the above mentioned phase potential (equation 6) is generated without any amplification or attenuation, the system behaves like a bi-periodic waveguide array where transport is considerably suppressed. In the nonlinear regime, discrete solitons are formed that happen to be quite immobile in a way similar to those found in waveguide arrays31 (see Supplementary Fig. 16). In the presence of PT-symmetric gain/loss, the intensity profile of the soliton is close to that of a conservative self-trapped wave and is critically determined by the phase potential. As in the previous case, these PT lattice solitons belong to a continuous parametric family of solutions. As numerical simulations indicate, mainly its phase profile adapts to gain and loss, while their interaction is still similar to that of conservative solitons (see Supplementary Fig. 17 and Supplementary Note 5). Although the observed PT solitons are stable for the complete experimental range of 100 round trips, simulations suggest that an extremely weak intrinsic instability is present due to a small imaginary part (because of nonlinearity) in the propagation constant. This instability is caused by the physical separation between amplification/attenuation and nonlinear propagation in our setup. In a sense, our mesh lattice platform can be viewed as an experimental implementation of the numerical split-step method when solving the nonlinear Schrödinger equation where errors arise due to discretization.


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 a broad PT soliton.A broad Gaussian distribution populating the focusing band is excited. In the linear regime (a,b) the beam spreads, while in the nonlinear regime a broad double hump (c) or single hump (d) PT soliton forms which can propagate for 100 round trips. Note that for observing the single and double hump solitons the sign of the phase potential is switched between ϕ0=−0.4π and ϕ0=+0.4π, with G=1.4 for all cases. The estimated peak power in the experiment is about 2 mW for the nonlinear regime and below 0.5 mW for the linear regime.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4525206&req=5

f6: Formation of a broad PT soliton.A broad Gaussian distribution populating the focusing band is excited. In the linear regime (a,b) the beam spreads, while in the nonlinear regime a broad double hump (c) or single hump (d) PT soliton forms which can propagate for 100 round trips. Note that for observing the single and double hump solitons the sign of the phase potential is switched between ϕ0=−0.4π and ϕ0=+0.4π, with G=1.4 for all cases. The estimated peak power in the experiment is about 2 mW for the nonlinear regime and below 0.5 mW for the linear regime.
Mentions: To launch wider solitons, a broad Gaussian distribution with a flat phase front is used to excite the system. In this case, because of nonlinearity, Schrödinger-like solitons29 form in the PT lattice (see Fig. 6 and Supplementary Figs 15 and 16), which are similar in shape and behaviour to solitons arising from the nonlinear Schrödinger equation. Note that, if the above mentioned phase potential (equation 6) is generated without any amplification or attenuation, the system behaves like a bi-periodic waveguide array where transport is considerably suppressed. In the nonlinear regime, discrete solitons are formed that happen to be quite immobile in a way similar to those found in waveguide arrays31 (see Supplementary Fig. 16). In the presence of PT-symmetric gain/loss, the intensity profile of the soliton is close to that of a conservative self-trapped wave and is critically determined by the phase potential. As in the previous case, these PT lattice solitons belong to a continuous parametric family of solutions. As numerical simulations indicate, mainly its phase profile adapts to gain and loss, while their interaction is still similar to that of conservative solitons (see Supplementary Fig. 17 and Supplementary Note 5). Although the observed PT solitons are stable for the complete experimental range of 100 round trips, simulations suggest that an extremely weak intrinsic instability is present due to a small imaginary part (because of nonlinearity) in the propagation constant. This instability is caused by the physical separation between amplification/attenuation and nonlinear propagation in our setup. In a sense, our mesh lattice platform can be viewed as an experimental implementation of the numerical split-step method when solving the nonlinear Schrödinger equation where errors arise due to discretization.

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.