Dispersion tailoring in single mode optical fiber by doping silver nanoparticle

Abstract

We propose an optical fiber which has very low dispersion loss (typically ~ 6.7 ps²/km at 1,550 nm) that can be achieved by doping Ag nanoparticle into the core glass. At low absorption loss approximation, dispersion free propagation can be achieved up to 64 km for a 20 ps pulse. Enhanced third order nonlinearity due to the presence of Ag nanoparticle (typically ~ 3.82 × 10⁻²⁰ W/m²) compensates for long length dispersion broadening that is not possible in conventional fused silica step index fiber.

Appendix

All the three models have certain merits and demerits. When the doped metal particle concentration is low all three theories give similar result [10]. But when the concentration increases the Maxwell–Garnett (MG) theory becomes inaccurate as the metal particles could form a connected network in the host matrix which is not considered in the formulation. However Sheng’s model is valid when both the host and dopant are granular in nature, which does not satisfy since we consider metal particle that are doped uniformly in host matrix of silica, which is not granular in nature [19]. In such case Bruggemann’s (BG) effective medium theory is useful to calculate the permittivity of the composite structure. We have taken spherical metal particles doped in silica as dielectric medium. It can be shown that if a particle of permittivity of ε ₁ is embedded in a homogeneous medium of permittivity ε ₂ then effective permittivity ε _eff of such a composite becomes [20]

$$ f\left( {\frac{{\varepsilon_{1} - \varepsilon_{\text{eff}} }}{{\varepsilon_{1} + 2\varepsilon_{\text{eff}} }}} \right) + \left( {1 - f} \right)\left( {\frac{{\varepsilon_{2} - \varepsilon_{\text{eff}} }}{{\varepsilon_{2} + 2\varepsilon_{\text{eff}} }}} \right) = 0 $$

(8)

where f is the nanoparticle filling factor given as f = V _Ag/V _total. For small filling factor f ≪ 1, ε _eff ≈ ε ₂ and ε _eff + 2ε ₂ ≈ 3ε _eff. Under this approximation, the above equation is identical to Maxwell–Garnett equation [12]

$$ \frac{{\varepsilon_{\text{eff}} - \varepsilon_{2} }}{{\varepsilon_{\text{eff}} + 2\varepsilon_{2} }} = f\frac{{\varepsilon_{1} - \varepsilon_{2} }}{{\varepsilon_{1} + 2\varepsilon_{\text{eff}} }} $$

(9)

Since the doping of Ag nano-particle in glass host is considered to be very low (around 1–2 % volume concentration) in the present case Maxwell–Garnett theory is adopted. From Eq. (9) we get

$$ \varepsilon_{\text{eff}} = \varepsilon_{2} \frac{1 + 2\sigma f}{1 - \sigma f} $$

(10.a)

where

$$ \sigma = \frac{{\varepsilon_{1} - \varepsilon_{2} }}{{\varepsilon_{1} + 2\varepsilon_{2} }} $$

(10.b)

Equation (10.a) a, b can be used to find out the effective permittivity of the composite material. Hence the refractive index of the material can be found out from the relation n = √ε _eff. In this study ε ₁ denotes the permittivity of the silver nano-particle and ε ₂ denotes the permittivity of the fused silica. Jordi Sancho-Parramon et al. [21] used the MG formulation to describe the experimental reflectance data of a silver-glass composite film.