Singularity-driven second- and third-harmonic generation at $\ensuremath{\epsilon}$-near-zero crossing points

Singularity-driven second- and third-harmonic generation at $ε$ -near-zero crossing points

M. A. Vincenti, D. de Ceglia, A. Ciattoni, and M. Scalora

Phys. Rev. A 84, 063826 – Published 12 December 2011

Abstract

We show an alternative path to efficient second- and third-harmonic generation in proximity of the zero crossing points of the dielectric permittivity in conjunction with low absorption. Under these circumstances, any material, either natural or artificial, will show similar degrees of field enhancement followed by strong harmonic generation, without resorting to any resonant mechanism. The results presented in this paper provide a general demonstration of the potential that the zero-crossing-point condition holds for nonlinear optical phenomena. We investigate a generic Lorentz medium and demonstrate that a singularity-driven enhancement of the electric field may be achieved even in extremely thin layers of material. We also discuss the role of nonlinear surface sources in a realistic scenario where a 20-nm layer of CaF $_{2}$ is excited at 21 μm, where ε ∼ 0. Finally, we show similar behavior in an artificial composite material that includes absorbing dyes in the visible range, provide a general tool for the improvement of harmonic generation using the ε ∼ 0 condition, and illustrate that this singularity-driven enhancement of the field lowers the thresholds for a plethora of nonlinear optical phenomena.

Received 7 September 2011

DOI:https://doi.org/10.1103/PhysRevA.84.063826

Authors & Affiliations

M. A. Vincenti¹, D. de Ceglia¹, A. Ciattoni², and M. Scalora³

¹AEgis Technologies Inc., Huntsville, Alabama 35806, USA
²Consiglio Nazionale delle Ricerche, CNR-SPIN, I-67100 L’Aquila, Italy
³Charles M. Bowden Research Center, RDECOM, Redstone Arsenal, Alabama 35898-5000, USA

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Vol. 84, Iss. 6 — December 2011

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Figure 1
(a) A pump (FF) is incident on a 20-nm-thick layer of uniform material composed of Lorentz oscillators that have a strong absorption peak at 2 μm. (b) Material dispersion and (c) detail of the ε $=$ 0 crossing region.Reuse & Permissions
Figure 2
(a) Intensity of the longitudinal electric field recorded inside the 20-nm layer of Fig. 1 as a function of wavelength and incident angle, normalized with respect to the incident electric field intensity. The intensity is distributed uniformly inside the layer with an amplification factor of ∼400. (b) Transmission and absorption versus wavelength when the field is incident at 12°. The peculiarity here is that maximum amplification occurs near the bottom of the transmission curve, (i.e., a rudimentary gap that forms when ε and μ have opposite signs) where absorption is also a maximum: nearly 50 $%$ of the incident light is lost; (c) Longitudinal electric field enhancement inside the 20 nm layer as a function of incident angle: red and blue curves quantify field amplification for second and third order nonlinear processes, respectively, and predict where the respective maxima of conversion efficiency are found by varying the angle of incidence.Reuse & Permissions
Figure 3
(a) SH and TH conversion efficiencies versus incident angle for the 20 nm layer of Fig. 1a. (b) Emitted spectra for SH and TH fields centered at 242 nm and 161 nm at 18°. χ $^{(2)}$ $=$ 20 pm/V and χ $^{(3)}$ $=$ 10 $^{- 20}$ (m/V) $^{2}$ . This spectral width (∼10 nm) could easily accommodate a 100 fs incident pulse.Reuse & Permissions
Figure 4
Longitudinal electric field intensity calculated inside a 20 nm CaF $_{2}$ layer as a function of wavelength and incident angle, normalized with respect to the incident electric field intensity. The intensity is distributed uniformly inside the layer with an amplification factor of ∼32. We used actual data for CaF $_{2}$ found in reference [25].Reuse & Permissions
Figure 5
Dispersion profile of NIR790B dye [33] diluted in polymer $($ ε(∞) $=$ 1.5 $)$ at concentrations of 86g/L. The inset shows details of the ε $=$ 0 crossing region. These curves may be modified almost at will by changing the dye concentration.Reuse & Permissions
Figure 6
Longitudinal electric field intensity calculated inside a 20 nm of the dye-based composite that displays the dispersion of Fig. 5, as a function of wavelength and incident angle, normalized with respect to the incident electric field intensity. The intensity is distributed uniformly inside the layer with an amplification factor of ∼80.Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information

Singularity-driven second- and third-harmonic generation at $ε$ -near-zero crossing points

M. A. Vincenti, D. de Ceglia, A. Ciattoni, and M. Scalora

Phys. Rev. A 84, 063826 – Published 12 December 2011

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Physical Review A

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Singularity-driven second- and third-harmonic generation at ε-near-zero crossing points

M. A. Vincenti, D. de Ceglia, A. Ciattoni, and M. Scalora

Phys. Rev. A 84, 063826 – Published 12 December 2011

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Singularity-driven second- and third-harmonic generation at $ε$ -near-zero crossing points