A photonic crystal fiber (PCF) with high-quality graphene nano-particles uniformly dispersed in the hole cladding are demonstrated to passively mode-lock the erbium-doped fiber laser (EDFL) by evanescent-wave interaction. The few-layer graphene nano-particles are obtained by a stabilized electrochemical exfoliation at a threshold bias. These slowly and softly exfoliated graphene nano-particle exhibits an intense 2D band and an almost disappeared D band in the Raman scattering spectrum. The saturable phenomena of the extinction coefficient β in the cladding provides a loss modulation for the intracavity photon intensity by the evanescent-wave interaction. The evanescent-wave mode-locking scheme effectively enlarges the interaction length of saturable absorption with graphene nano-particle to provide an increasing transmittance ΔT of 5% and modulation depth of 13%. By comparing the core-wave and evanescent-wave mode-locking under the same linear transmittance, the transmittance of the graphene nano-particles on the end-face of SMF only enlarges from 0.54 to 0.578 with ΔT = 3.8% and the modulation depth of 10.8%. The evanescent wave interaction is found to be better than the traditional approach which confines the graphene nano-particles at the interface of two SMF patchcords. When enlarging the intra-cavity gain by simultaneously increasing the pumping current of 980-nm and 1480-nm pumping laser diodes (LDs) to 900 mA, the passively mode-locked EDFL shortens its pulsewidth to 650 fs and broadens its spectral linewidth to 3.92 nm. An extremely low carrier amplitude jitter (CAJ) of 1.2-1.6% is observed to confirm the stable EDFL pulse-train with the cladding graphene nano-particle based evanescent-wave mode-locking.

Eigenvalue equations for solving full-vector modes of optical waveguides are formulated using Yee-mesh-based finite difference algorithms and incorporated with perfectly matched layer absorbing boundary conditions. The established method is thus able to calculate the complex propagation constants and the confinement losses of leaky waveguide modes. Proper matching of dielectric interface conditions through the Taylor series expansion of the fields is adopted in the formulation to achieve high numerical accuracy. The method is applied to the study of the holey fiber with triangular lattice, the two-core holey fiber, and the air-guiding photonic crystal fiber.

A finite-difference frequency-domain method based on the Yee's cell is utilized to analyze the band diagrams of two-dimensional photonic crystals with square or triangular lattice. The differential operator is replaced by the compact scheme and the index average scheme is introduced to deal with the curved dielectric interfaces in the unit cell. For the triangular lattice, the hexagonal unit cell is converted into a rectangular one for easier mesh generation. The band diagrams for both square and triangular lattices are obtained and the numerical convergence of computed eigen frequencies is examined and compared with other methods.

We have theoretically investigated the dispersion characteristics of dispersion compensating fibers based on dual-core liquid-filled PCFs. A very high negative chromatic dispersion value D = -19000 ps/(nm-km) can be achieved at 1.55-microm wavelength by an appropriate design. By varying the geometry of the PCF and the index of the filling liquid, the phase-matching wavelength and dispersion values are shown to be well tuned to desired values. The proposed structure also demonstrates good tunable properties with operation temperature for optical communication systems.

We have theoretically investigated the propagation properties of two kinds of selectively liquid-filled PCFs. For internally liquid-filled PCFs, the outer air-hole layers function as the second cladding to reduce the penetration of the light field while the inner liquid-hole layers can still induce the tunable PBG effect. The complementary structures, externally liquid-filled PCFs, can be used in long-period fiber gratings to decrease the utilization of the lossy liquids and remain single-mode operation for the existence of the inner air-hole layers. The confinement losses of both selectively liquid-filled PCFs are shown to be efficiently reduced due to the outer or inner air-hole layers, which is quite useful for further applications.