Milti -wave interaction in metamaterials

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Milti-wave interaction in metamaterials Ildar Gabitov , Zhaxylyk Kudyshev, Andrei Maimistov SCT'12 Novosibirsk, June 4-8, 2012 ω

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ω. 2 ω. Milti -wave interaction in metamaterials. Ildar Gabitov , Zhaxylyk Kudyshev, Andrei Maimistov. Broad spectrum. Multi-wave interaction. Nonlinear phenomena in negative index materials. Nonlinearity in negative index materials. What is new?. Two general cases:. - PowerPoint PPT Presentation

Transcript of Milti -wave interaction in metamaterials

Ultra-short optical pulses in active medium with embedded metallic nano-particles

Milti-wave interaction in metamaterialsIldar Gabitov, Zhaxylyk Kudyshev, Andrei Maimistov

SCT'12 Novosibirsk, June 4-8, 2012

2Nonlinear phenomena in negative index materialsNonlinearity in negative index materials. What is new?Two general cases:Frequency interface

Broad spectrumMulti-wave interaction

SCT'12 Novosibirsk, June 4-8, 20122Three wave interaction: slowly varying amplitude approximation

SCT'12 Novosibirsk, June 4-8, 2012Simplest case of three wave interaction: Second harmonic generationA. Zakhidov, AgranovichYu. Kivshar et. al.Popov, V. ShalaevM. Scalora et. al.Zh. Kudyshev et. al.D. Smith, et. al.SCT'12 Novosibirsk, June 4-8, 2012Second Harmonics generation: Classical Case

N. Blombergen

SCT'12 Novosibirsk, June 4-8, 2012Second harmonic generation

-- boundary conditions

2SCT'12 Novosibirsk, June 4-8, 2012

If fields are periodically oscillating.Classical Case

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Here:Maimistov, Kudyshev, I.G.SCT'12 Novosibirsk, June 4-8, 2012From the first two equations follows the modified M-R relation:

In conventional case we have conservation of energy. In negative index material - conservation of total flux of the energy.

Popov, ShalaevSCT'12 Novosibirsk, June 4-8, 2012Energy of pump wave decay with z, therefore the phase difference is equal to . Exact solutions general formulae:

HereandImportant: m1 is unknown!

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Boundary conditions together with M-R relation lead to the implicit equation for :

Here e10 is an amplitude of the pump wave. This transcendental equation can be solved numerically and it has multiple branches.SCT'12 Novosibirsk, June 4-8, 2012

Solution of transcendental equation

Spatial field profilesPhysical branch: Irrelevant branches: Field is singular in between of these branches SCT'12 Novosibirsk, June 4-8, 2012

SCT'12 Novosibirsk, June 4-8, 2012Physical branch shows saturation of output power of electric field at fundamental frequency with increase of input power. This indicates that with the increase of input power all excessive energy of pump signal converts to the energy of second harmonic signal.Second harmonic generation in presence of phase mismatch

Two integrals:

SCT'12 Novosibirsk, June 4-8, 201214Second harmonic generation in presence of phase mismatch

-- critical mismatch

SCT'12 Novosibirsk, June 4-8, 2012 Exact solutions

Equation for the power of second harmonic field:

- is the Weierstrass function SCT'12 Novosibirsk, June 4-8, 2012

Numerical solution

SCT'12 Novosibirsk, June 4-8, 2012Second harmonic generation in presence of phase mismatch

SCT'12 Novosibirsk, June 4-8, 2012Second harmonic generation in presence of phase mismatch

If

then second harmonicdoes not radiate outside. Therefore, sample becomes transparent for fundamental mode.

The conversion efficiency of pump wave to second harmonic is limited by the value:SCT'12 Novosibirsk, June 4-8, 2012

Conversion efficiencySCT'12 Novosibirsk, June 4-8, 2012

Jump

Multi-stability SCT'12 Novosibirsk, June 4-8, 2012

Second harmonic generation in presence of losses

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Parametric amplification:

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Two additional integralsSCT'12 Novosibirsk, June 4-8, 2012

Numerical solution of transcendental equationFull system considerationSCT'12 Novosibirsk, June 4-8, 2012If there is non-zero output signal value corresponding to zero input signal then such branch is non physical.

Popov, Shalaev regime SCT'12 Novosibirsk, June 4-8, 2012

Spatial distribution of intensities: exampleSCT'12 Novosibirsk, June 4-8, 2012Conclusions

SCT'12 Novosibirsk, June 4-8, 2012