Abstract

A novel approach to the application of an adaptive pre-shaping algorithm for ultrashort pulse distortion compensation during the propagation in AZO/ZnO multilayered metamaterials (thickness 300-700 nm) at the epsilon-near-zero spectral point is investigated. We show that using the Broyden-Fletcher-Goldfarb-Shanno algorithm to minimize the residual between frequency-resolved optical gating traces of the distorted output pulse and the zero phase pulse of 100 fs duration can yield increased output pulse field strength and a central frequency shift towards the epsilon-near-zero spectral point, which can be of future use for applications in ultrafast communication, signal processing, and super resolution imaging.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

2018 (4)

P. Kelly and L. Kuznetsova, “Pulse shaping in the presence of enormous second-order dispersion in Al: ZnO/ZnO epsilon-near-zero metamaterial,” Appl. Phys. B 124(4), 60 (2018).
[Crossref]

A. D. Neira, G. A. Wurtz, and A. V. Zayats, “All-optical switching in silicon photonic waveguides with an epsilon-near-zero resonant cavity,” Photonics Res. 6(5), B1 (2018).
[Crossref]

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[Crossref]

C. Rizza, X. Li, A. Di Falco, E. Palange, A. Marini, and A. Ciattoni, “Enhanced asymmetric transmission in hyperbolic epsilon-near-zero slabs,” J. Opt. 20(8), 085001 (2018).
[Crossref]

2017 (2)

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

M. A. Vincenti, M. Kamandi, D. de Ceglia, C. Guclu, M. Scalora, and F. Capolino, “Second-harmonic generation in longitudinal epsilon-near-zero materials,” Phys. Rev. B 96(4), 045438 (2017).
[Crossref]

2016 (5)

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced Nonlinear Refractive Index in ɛ-Near-Zero Materials,” Phys. Rev. Lett. 116(23), 233901 (2016).
[Crossref]

P. Kelly, M. Liu, and L. Kuznetsova, “Designing optical metamaterial with hyperbolic dispersion based on an Al:ZnO/ZnO nano-layered structure using the atomic layer deposition technique,” Appl. Opt. 55(11), 2993–2997 (2016).
[Crossref]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref]

C. Bacco, P. Kelly, and L. Kuznetsova, “Optical mode confinement in the Al/SiO2 disk nano cavities with hyperbolic dispersion in the infrared spectral region,” J. Nanophotonics 10(4), 046003 (2016).
[Crossref]

M. Javani and M. Stockman, “Real and Imaginary Properties of Epsilon-Near-Zero Materials,” Phys. Rev. Lett. 117(10), 107404 (2016).
[Crossref]

2015 (3)

C. Rizza, A. Di Falco, M. Scalora, and A. Ciattoni, “One-Dimensional Chirality: Strong Optical Activity in Epsilon-Near-Zero Metamaterials,” Phys. Rev. Lett. 115(5), 057401 (2015).
[Crossref]

A. K. Pradhan, R. M. Mundle, K. Santiago, J. R. Skuza, B. Xiao, K. D. Song, M. Bahoura, R. Cheaito, and P. E. Hopkins, “Extreme tunability in aluminum doped Zinc Oxide plasmonic materials for near-infrared applications,” Sci. Rep. 4(1), 6415 (2015).
[Crossref]

E. Capretti, Y. Wang, N. Engheta, and L. Dal Negro, “Enhanced third-harmonic generation in Si-compatible epsilonnear-zero indium tin oxide nanolayers,” Opt. Lett. 40(7), 1500–1503 (2015).
[Crossref]

2014 (1)

C. T. Riley, T. A. Kieu, J. S. T. Smalley, S. H. A. Pan, S. J. Kim, K. W. Post, A. Kargar, D. N. Basov, X. Pan, Y. Fainman, D. Wang, and D. J. Sirbuly, “Plasmonic tuning of aluminum doped zinc oxide nanostructures by atomic layer deposition,” Phys. Status Solidi RRL 8(11), 948–952 (2014).
[Crossref]

2013 (2)

S. Campione, D. de Ceglia, M. A. Vincenti, M. Scalora, and F. Capolino, “Electric field enhancement in -near-zero slabs under TM-polarized oblique incidence,” Phys. Rev. B 87(3), 035120 (2013).
[Crossref]

W. Chang, T. Zhou, L. A. Siiman, and A. Galvanauskas, “Femtosecond pulse spectral synthesis in coherently-spectrally combined multi-channel fiber chirped pulse amplifiers,” Opt. Express 21(3), 3897–3910 (2013).
[Crossref]

2012 (1)

D. A. Ciattoni and E. Spinozzi, “Efficient second-harmonic generation in micrometer-thick slabs with indefinite permittivity,” Phys. Rev. A 85(4), 043806 (2012).
[Crossref]

2011 (2)

C. A. Vincenti, D. de Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second- and third-harmonic generation at ɛ -near-zero crossing points,” Phys. Rev. A 84(6), 063826 (2011).
[Crossref]

G. V. Naik, J. Kim, and A. Boltasseva, “Oxides and nitrides as alternative plasmonic materials in the optical range,” Opt. Mater. Express 1(6), 1090–1099 (2011).
[Crossref]

2010 (3)

A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. 35(13), 2130–2132 (2010).
[Crossref]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

J. Khurgin, “Slow light in various media: a tutorial,” Adv. Opt. Photonics 2(3), 287–318 (2010).
[Crossref]

2009 (1)

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical Nonlocalities and Additional Waves in Epsilon-Near-Zero Metamaterials,” Phys. Rev. Lett. 102(12), 127405 (2009).
[Crossref]

2008 (1)

2007 (3)

2006 (2)

N. Silveirinha and Engheta, “Tunneling of Electromagnetic Energy through Subwavelength Channels and Bends using ɛ-Near-Zero Materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[Crossref]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref]

2005 (1)

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref]

2002 (1)

R. Boyd and D. Gauthier, ““Slow” and “fast” light,” Prog. Opt. 43, 497–530 (2002).
[Crossref]

2000 (2)

J. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref]

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70(S1), S119–S124 (2000).
[Crossref]

1997 (3)

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[Crossref]

Y. Yoshikawa and S. Adachi, “Optical Constants of ZnO,” Jpn. J. Appl. Phys. 36(Part 1, No. 10), 6237–6243 (1997).
[Crossref]

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw. 23(4), 550–560 (1997).
[Crossref]

1990 (1)

Adachi, S.

Y. Yoshikawa and S. Adachi, “Optical Constants of ZnO,” Jpn. J. Appl. Phys. 36(Part 1, No. 10), 6237–6243 (1997).
[Crossref]

Alam, M. Z.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref]

Alekseyev, L. V.

Alù, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

Atkinson, R.

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical Nonlocalities and Additional Waves in Epsilon-Near-Zero Metamaterials,” Phys. Rev. Lett. 102(12), 127405 (2009).
[Crossref]

Bacco, C.

C. Bacco, P. Kelly, and L. Kuznetsova, “Optical mode confinement in the Al/SiO2 disk nano cavities with hyperbolic dispersion in the infrared spectral region,” J. Nanophotonics 10(4), 046003 (2016).
[Crossref]

Bahoura, M.

A. K. Pradhan, R. M. Mundle, K. Santiago, J. R. Skuza, B. Xiao, K. D. Song, M. Bahoura, R. Cheaito, and P. E. Hopkins, “Extreme tunability in aluminum doped Zinc Oxide plasmonic materials for near-infrared applications,” Sci. Rep. 4(1), 6415 (2015).
[Crossref]

Barty, C. P. J.

Basov, D. N.

C. T. Riley, T. A. Kieu, J. S. T. Smalley, S. H. A. Pan, S. J. Kim, K. W. Post, A. Kargar, D. N. Basov, X. Pan, Y. Fainman, D. Wang, and D. J. Sirbuly, “Plasmonic tuning of aluminum doped zinc oxide nanostructures by atomic layer deposition,” Phys. Status Solidi RRL 8(11), 948–952 (2014).
[Crossref]

Baumert, T.

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[Crossref]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Boltasseva, A.

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced Nonlinear Refractive Index in ɛ-Near-Zero Materials,” Phys. Rev. Lett. 116(23), 233901 (2016).
[Crossref]

G. V. Naik, J. Kim, and A. Boltasseva, “Oxides and nitrides as alternative plasmonic materials in the optical range,” Opt. Mater. Express 1(6), 1090–1099 (2011).
[Crossref]

Boyd, R.

R. Boyd and D. Gauthier, ““Slow” and “fast” light,” Prog. Opt. 43, 497–530 (2002).
[Crossref]

Boyd, R. W.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref]

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media, 2nd edn. (Academic, London, 1980).

Brixner, T.

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70(S1), S119–S124 (2000).
[Crossref]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[Crossref]

Byrd, R. H.

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization,” ACM Trans. Math. Softw. 23(4), 550–560 (1997).
[Crossref]

Campione, S.

S. Campione, D. de Ceglia, M. A. Vincenti, M. Scalora, and F. Capolino, “Electric field enhancement in -near-zero slabs under TM-polarized oblique incidence,” Phys. Rev. B 87(3), 035120 (2013).
[Crossref]

Capolino, F.

M. A. Vincenti, M. Kamandi, D. de Ceglia, C. Guclu, M. Scalora, and F. Capolino, “Second-harmonic generation in longitudinal epsilon-near-zero materials,” Phys. Rev. B 96(4), 045438 (2017).
[Crossref]

S. Campione, D. de Ceglia, M. A. Vincenti, M. Scalora, and F. Capolino, “Electric field enhancement in -near-zero slabs under TM-polarized oblique incidence,” Phys. Rev. B 87(3), 035120 (2013).
[Crossref]

Capretti, E.

Caspani, L.

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced Nonlinear Refractive Index in ɛ-Near-Zero Materials,” Phys. Rev. Lett. 116(23), 233901 (2016).
[Crossref]

Chang, W.

Cheaito, R.

A. K. Pradhan, R. M. Mundle, K. Santiago, J. R. Skuza, B. Xiao, K. D. Song, M. Bahoura, R. Cheaito, and P. E. Hopkins, “Extreme tunability in aluminum doped Zinc Oxide plasmonic materials for near-infrared applications,” Sci. Rep. 4(1), 6415 (2015).
[Crossref]

Ciattoni, A.

C. Rizza, X. Li, A. Di Falco, E. Palange, A. Marini, and A. Ciattoni, “Enhanced asymmetric transmission in hyperbolic epsilon-near-zero slabs,” J. Opt. 20(8), 085001 (2018).
[Crossref]

C. Rizza, A. Di Falco, M. Scalora, and A. Ciattoni, “One-Dimensional Chirality: Strong Optical Activity in Epsilon-Near-Zero Metamaterials,” Phys. Rev. Lett. 115(5), 057401 (2015).
[Crossref]

C. A. Vincenti, D. de Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second- and third-harmonic generation at ɛ -near-zero crossing points,” Phys. Rev. A 84(6), 063826 (2011).
[Crossref]

A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. 35(13), 2130–2132 (2010).
[Crossref]

Ciattoni, D. A.

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[Crossref]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65(6), 779–782 (1997).
[Crossref]

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70(S1), S119–S124 (2000).
[Crossref]

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Opt. Express (4)

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Opt. Mater. Express (1)

Photonics Res. (1)

A. D. Neira, G. A. Wurtz, and A. V. Zayats, “All-optical switching in silicon photonic waveguides with an epsilon-near-zero resonant cavity,” Photonics Res. 6(5), B1 (2018).
[Crossref]

Phys. Rev. A (2)

C. A. Vincenti, D. de Ceglia, A. Ciattoni, and M. Scalora, “Singularity-driven second- and third-harmonic generation at ɛ -near-zero crossing points,” Phys. Rev. A 84(6), 063826 (2011).
[Crossref]

D. A. Ciattoni and E. Spinozzi, “Efficient second-harmonic generation in micrometer-thick slabs with indefinite permittivity,” Phys. Rev. A 85(4), 043806 (2012).
[Crossref]

Phys. Rev. B (3)

S. Campione, D. de Ceglia, M. A. Vincenti, M. Scalora, and F. Capolino, “Electric field enhancement in -near-zero slabs under TM-polarized oblique incidence,” Phys. Rev. B 87(3), 035120 (2013).
[Crossref]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

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[Crossref]

Phys. Rev. Lett. (6)

M. Javani and M. Stockman, “Real and Imaginary Properties of Epsilon-Near-Zero Materials,” Phys. Rev. Lett. 117(10), 107404 (2016).
[Crossref]

N. Silveirinha and Engheta, “Tunneling of Electromagnetic Energy through Subwavelength Channels and Bends using ɛ-Near-Zero Materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
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C. Rizza, A. Di Falco, M. Scalora, and A. Ciattoni, “One-Dimensional Chirality: Strong Optical Activity in Epsilon-Near-Zero Metamaterials,” Phys. Rev. Lett. 115(5), 057401 (2015).
[Crossref]

R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical Nonlocalities and Additional Waves in Epsilon-Near-Zero Metamaterials,” Phys. Rev. Lett. 102(12), 127405 (2009).
[Crossref]

Phys. Status Solidi RRL (1)

C. T. Riley, T. A. Kieu, J. S. T. Smalley, S. H. A. Pan, S. J. Kim, K. W. Post, A. Kargar, D. N. Basov, X. Pan, Y. Fainman, D. Wang, and D. J. Sirbuly, “Plasmonic tuning of aluminum doped zinc oxide nanostructures by atomic layer deposition,” Phys. Status Solidi RRL 8(11), 948–952 (2014).
[Crossref]

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R. Boyd and D. Gauthier, ““Slow” and “fast” light,” Prog. Opt. 43, 497–530 (2002).
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Sci. Rep. (1)

A. K. Pradhan, R. M. Mundle, K. Santiago, J. R. Skuza, B. Xiao, K. D. Song, M. Bahoura, R. Cheaito, and P. E. Hopkins, “Extreme tunability in aluminum doped Zinc Oxide plasmonic materials for near-infrared applications,” Sci. Rep. 4(1), 6415 (2015).
[Crossref]

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[Crossref]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. (a) Input pulse with an initial guess for the temporal phase. (b) Schematic of the adaptive pre-shaping approach. (c) The FROG trace of the zero-phase 100 fs Gaussian pulse with reference points for optimization.
Fig. 2.
Fig. 2. (a) Transmittance of the AZO/ZnO metamaterial with various damping frequency γ vs. propagation distance. (b-d). The real part of the electric field for a 100 fs Gaussian pulse propagated through 500 nm of AZO/ZnO with various damping frequency γ . The propagation distance of 500 nm is within fabrication limits [11-14].
Fig. 3.
Fig. 3. Results of the FDTD simulations with spectral tuning: (a-c) initial spectra (dotted line) and real part of the out-of-plane optical permittivity (solid line) (γ=1011 Hz); (d-f) the real part of the electric field for a 100 fs Gaussian pulse at different central frequencies (shown in (a-c) respectively) propagated through 500 nm of AZO/ZnO and their associated FROG traces (g-i). ENZ frequency is 1.686 × 1014 Hz (1778nm).
Fig. 4.
Fig. 4. Results of the FDTD simulations for the real part of the electric fields (a-c) for a 100 fs Gaussian pulse with a zero phase propagated through 300, 500, and 700 nm of the AZO/ZnO metamaterial (γ=1011 Hz) and their associated FROG traces (d-f).
Fig. 5.
Fig. 5. Results of the FDTD simulations and the adaptive pre-shaping approach for the real part of the electric fields (a-c) for a 100 fs Gaussian pulse propagated through 300, 500, and 700 nm of the AZO/ZnO metamaterial (γ=1011 Hz) and their associated FROG traces (d-f). The output pulse was obtained using adaptive pre-shaping approach illustrated in Fig. 1.
Fig. 6.
Fig. 6. The final temporal phase used as the initial phase for the pre-shaped pulse for each propagation distance in AZO/ZnO multilayered metamaterial.

Tables (1)

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Table 1. Terms for the 5th-degree polynomial final phase for pre-shaping in time domain for various propagation distances. The time variable for each term is in femtoseconds.

Equations (1)

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ε ( ω ) = ε f ω p 2 ω 2 + i ω γ ,

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