Researching | Parametric resonances in nonlinear plasmonics [Invited]

Journals >Chinese Optics Letters >Volume 17 >Issue 12 >Page 122402 > Article

Chinese Optics Letters
Vol. 17, Issue 12, 122402 (2019)

Parametric resonances in nonlinear plasmonics [Invited] | On the Cover

Shima Fardad^1、2, Eric Schweisberger¹, and Alessandro Salandrino^1、2、*

Author Affiliations

¹Department of Electrical Engineering and Computer Science, The University of Kansas, Lawrence, KS 66045, USA

²Information and Telecommunication Technology Center, The University of Kansas, Lawrence, KS 66045, USA

show less

DOI: 10.3788/COL201917.122402 Cite this Article Set citation alerts

Shima Fardad, Eric Schweisberger, Alessandro Salandrino. Parametric resonances in nonlinear plasmonics [Invited][J]. Chinese Optics Letters, 2019, 17(12): 122402 Copy Citation Text

show less

Abstract

In the context of nonlinear plasmonics, we review the recently introduced concept of plasmonic parametric resonance (PPR) and discuss potential applications of such phenomena. PPR arises from the temporal modulation of one or more of the parameters governing the dynamics of a plasmonic system and can lead to the amplification of high-order sub-radiant plasmonic modes. The theory of PPR is reviewed, possible schemes of implementation are proposed, and applications in optical limiting are discussed.

Keywords

190.4975 250.4390 240.6680

\frac{d^{2} X (t)}{d t^{2}} + γ \frac{d X (t)}{d t} + ω_{0}^{2} X (t) = F (t),

(1)

View in Article

\frac{d^{2} X (t)}{d t^{2}} + γ \frac{d X (t)}{d t} + {ω_{0}^{2} + 2 ω_{0} δ ω [F (t)]} X (t) = 0 .

(2)

View in Article

\frac{\partial^{2} P_{1} (r, t)}{\partial t^{2}} + γ \frac{\partial P_{1} (r, t)}{\partial t} = ε_{0} ω_{p l}^{2} E_{1} (r, t),

(3)

View in Article

P_{2} (r, t) = ε_{0} (ε_{2} - 1) E_{2} (r, t) + P_{2}^{N L} (r, t) .

(4)

View in Article

P_{1} (t) = \sum_{n, m} \nabla {\frac{r^{n}}{R^{n - 1}} [P_{n, m}^{(e)} (t) Y_{n, m}^{(e)} (θ, ϕ) + P_{n, m}^{(o)} (t) Y_{n, m}^{(o)} (θ, ϕ)]} .

(5)

View in Article

\frac{d^{2} P_{n, m}^{(e, o)} (t)}{d t^{2}} + γ \frac{d P_{n, m}^{(e, o)} (t)}{d t} + ω_{n}^{2} P_{n, m}^{(e, o)} (t) = ω_{n}^{2} \frac{S_{n, m}^{(e, o)} (t)}{n} .

(6)

View in Article

ω_{n} = \sqrt{\frac{n ω_{p l}^{2}}{n ε_{\infty} + (n + 1) ε_{2}}} .

(7)

View in Article

S_{n, m}^{(e, o)} (t) = \oint_{r = R} Y_{n, m}^{(e, o)} (θ, ϕ) P_{2}^{N L} (R, θ, ϕ, t) \cdot \hat{r} \sin (θ) d θ d ϕ .

(8)

View in Article

\frac{d^{2} P_{n, 0}^{(e)} (t)}{d t^{2}} + γ \frac{d P_{n, 0}^{(e)} (t)}{d t} + [ω_{n}^{2} - α_{1} E_{P} (t)] P_{n, 0}^{(e)} (t) = α_{2} {[P_{n, 0}^{(e)} (t)]}^{2} .

(9)

View in Article

α_{1} = - \frac{4 \sqrt{π} χ_{z z z}}{n \sqrt{3}} \frac{ω_{n}^{4}}{ω_{p l}^{2}} G_{n, 0}^{(e, e)}; α_{2} = \frac{χ_{z z z}}{n ε_{0}} \frac{ω_{n}^{6}}{ω_{p l}^{4}} F_{n, 0}^{(e, e, e)}, F_{n, 0}^{(e, e, e)} = \int_{0}^{2 π} \int_{0}^{π} {\cos θ \frac{\partial}{\partial z} {[\frac{R^{n + 2}}{r^{n + 1}} Y_{n, 0}^{(e)} (θ, ϕ)]}_{R} \times \frac{\partial}{\partial z} {[\frac{R^{n + 2}}{r^{n + 1}} Y_{n, 0}^{(e)} (θ, ϕ)]}_{R} Y_{n, 0}^{(e)} (θ, ϕ)} \sin θ d θ d ϕ, G_{n, 0}^{(e, e)} = \int_{0}^{2 π} \int_{0}^{π} {\cos θ \frac{\partial}{\partial z} {[r Y_{1, 0}^{(e)} (θ, ϕ)]}_{R} \times \frac{\partial}{\partial z} {[\frac{R^{n + 2}}{r^{n + 1}} Y_{n, 0}^{(e)} (θ, ϕ)]}_{R} Y_{n, 0}^{(e)} (θ, ϕ)} \sin θ d θ d ϕ .

(10)

View in Article

P_{n, m}^{(e, o)} (t) = p (t) \cos [ω_{n} t - θ (t)] e^{- \frac{γ}{2} t}, p (t) = p_{0} \sqrt{\cosh (\frac{α_{1} A_{p}}{2 ω_{n}} t)}; θ (t) = arccot [\exp (- \frac{α_{1} A_{p}}{2 ω_{n}} t)],

(11)

View in Article

W_{a b s} (t) = \frac{n R^{3} α_{1} A_{p} p_{0}^{2}}{32 ε_{0} ω_{p l}^{2}} [2 ω_{n} + γ \sinh (\frac{α_{1} A_{p} t}{2 ω_{n}})] e^{- γ t} \sim \frac{n R^{3} α_{1} A_{p} p_{0}^{2} γ}{64 ε_{0} ω_{p l}^{2}} \exp [(A_{p} - A_{P P R}) \frac{α_{1} t}{2 ω_{n}}] .

(12)

View in Article

P_{n, m}^{(e, o)} (t) \sim - \frac{α_{2} Q_{1}^{2}}{2 ω_{n}^{2}} + Q_{1} \cos (ω_{n} t + θ_{1}) + \frac{α_{2} Q_{1}^{2}}{6 ω_{n}^{2}} \cos (2 ω_{n} t + 2 θ_{1}), θ_{1} = \frac{1}{2} \arccos (- \frac{A_{P P R}}{A_{p}}); Q_{1} = \frac{ω_{n}}{α_{2}} \sqrt{\frac{6 γ ω_{n}}{5} \sqrt{{(\frac{A_{p}}{A_{P P R}})}^{2} - 1}} .

(13)

View in Article

{\bar{W}}_{a b s} (t \to \infty) = \frac{3}{20} n R^{3} \frac{γ}{ε_{0} ω_{p l}^{2}} \frac{ω_{n}^{3}}{α_{2}^{2}} \sqrt{{(\frac{A_{p}}{A_{P P R}})}^{2} - 1} .

(14)

View in Article

σ_{N L} = \frac{3 n R^{3}}{40 ε_{0} \sqrt{ε_{2}}} \frac{ω_{n}^{3}}{ω_{p l}^{2}} \frac{α_{1}^{2}}{α_{2}^{2}} \sqrt{\frac{I_{P P R}}{I_{p}} (1 - \frac{I_{P P R}}{I_{p}})}, I_{p} > I_{P P R} .

(15)

View in Article

Figures&Tables (6)

Copy Citation Text

Shima Fardad, Eric Schweisberger, Alessandro Salandrino. Parametric resonances in nonlinear plasmonics [Invited][J]. Chinese Optics Letters, 2019, 17(12): 122402

Download Citation

Set citation alerts for the article

Set citation alerts for the article

Save the article for my favorites

Paper Information

Recommended Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology

Set citation alerts for the article

Please enter your email address