PT-symmetric coupler with χ(2) nonlinearity
We introduce the notion of a PT -symmetric dimer with a χ(2) nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that b...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2013
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/33038/ http://irep.iium.edu.my/33038/ http://irep.iium.edu.my/33038/ http://irep.iium.edu.my/33038/1/PhysRevA.88.053820.pdf |
| Summary: | We introduce the notion of a PT -symmetric dimer with a χ(2) nonlinearity. Similarly to the Kerr case, we
argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity
and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics,
there exist in general two distinct gain and loss parameters, different values of which are considered herein. We
find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of
nonlinear modes from the linear solutions occur in two different ways depending on whether the first- or the
second-harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting
bifurcation phenomena appear to occur, including saddle-center and pitchfork bifurcations which our parametric
variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical
time-evolution simulations exploring the evolution of the different configurations, when unstable.
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