Modal cutoff and the V parameter in photonic crystal fibers

Abstract

We address the long-standing unresolved problem concerning the V -parameter in a photonic crystal fiber (PCF). Formulate the parameter appropriate for a core-defect in a periodic structure we argue that the multi-mode cut-off occurs at a wavelength λ * which satisfies VPCF(λ * ) = π. Comparing to numerics and recent cut-off calculations we confirm this result.In photonic crystal fibers (PCFs) an arrangement of air-holes running along the full length of the fiber provides the confinement and guidance of light. The airholes of diameter d are typically arranged in a triangular lattice[1] with a pitch Λ (see insert in Fig. 2), but e.g. honey-comb[2] and kagome [3,4] arrangements are other options. By making a defect in the lattice, light can be confined and guided along the fiber axis. The guidance mechanism depends on the nature of the defect and the air-hole arrangement. For the triangular lattice with a silica-core light is confined by total-internal reflection [1] whereas for an air-core a photonic-bandgap confines light to the defect.[5] For recent reviews we refer to Ref. 6 and references therein.Both type of PCFs have revealed surprising and novel optical properties. In this work we consider the silicacore PCF (see insert in Fig. 2) which was the one first reported.[1] This structure provides the basis of a variety of phenomena including the endlessly single-mode behaviour, [7] large-mode area PCFs,[8] as well as highly non-linear PCF with unique dispersion properties. [9,10,11] Properties of standard fibers are often parametrized by the so-called V -parameter and the entire concept is very close to the heart of the majority of the optical fiber community (see e.g. Refs. 12, 13). The cut-off properties and the endlessly single-mode phenomena of PCFs can also be qualitatively understood within this framework. [1,7,14,15,16] However, the proper choice of the correct length scale for the V -parameter has, until now, remained unsolved as well as the value of V * that marks the second-order cut-off. In this Letter we clarify this problem and also put recent work on multi-mode cut-off [17,18] into the context of the V -parameter.The tradition of parametrizing the optical properties in terms of the V -parameter stems from analysis of the step-index fiber (SIF). The SIF is characterized by the core radius ρ, the core index n c , and the cladding index n cl which all enter into the parameter V SIF given byBecause of its inverse dependence on the wavelength λ, this quantity is often referred to as the normalized frequency. However, in a more general context, this is somewhat misleading (especially if n c and/or n cl has a strong wavelength dependence) and in this Letter we would like to emphasize a more physical interpretation. To do this, we first introduce the numerical aperture NA (or the angle of divergence θ) given bywhich follows from use of Snell's law for critical incidence at the interface between the n c and n cl regions (see e.g. Refs. 12, 13). Next, we introduce the free-space wavenumber k = 2π/λ and its tr...

Design and optimization of photonic crystal fiber based sensor for gas condensate and air pollution monitoring

“…The V eff parameter can be expressed by (6). With approximate perfect electric and perfect magnetic conductor boundary condition, FEM is used at the outer enclosure to achieve the index of space-filling mode [39]. At operating wavelength 1.33 m, the desired agreement for operating as an SMF is V eff ≤ 2.405 [14].…”

Numerical modelling of self-heating effects on guiding modes of high-power photonic crystal fibre lasers

“…Due to a complex structure of the holey fibre, the numerical method of finite element is adopted to raise the reliability of the results. where T(x, y) is temperature in Kelvin, K(T) is temperature dependent thermal conductivity in W/m/K, and Q(x, y) is heat source density in W/m 3 . Although temperature independent thermal conductivity may suffice [8,9,19,20], in this work we have used the experimental data of Jund and Jullien [21] to comprehensively cover the temperature dependence of thermal conductivity.…”

“…The ratio of the hole diameter (d) to the hole-to-hole distance (Λ) plays a crucial role in determining the optical properties of photonic crystal fibres (PCFs). It has been proved that for a ratio of d/Λ = 0.45 the one-hole missing PCF acts as a single-mode fibre regardless of the wavelength of the propagating light [3][4][5]. In fibre lasers, to suppress unwanted nonlinear effects when scaling the delivered powers, one can increase the core area.…”

The Influence of Core Diameter on Endlessly Single Mode Properties for Index Guiding Photonic Crystal Fiber

“…The tradition of parametrizing the optical properties in terms of the V-parameter (normalized frequency) stems from analysis of the step index fiber (SIF). The SIF is characterized by the core radius (r), the core index (n c ), and the cladding index (n cl ), which all enter into the parameter V SIF , given by [8]:…”

“…However, a simple translation is not straight forward since no wavelengthindependent core-or cladding index can be defined. Mortensen et al proposed a formulation of the V-parameter for a PCF given by [8]:…”