The history, fabrication, theory, numerical modeling, optical properties, guidance mechanisms, and applications of photonic-crystal fibers are reviewed

Photonic-Crystal Fibers

1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

The present invention relates to a multi-core optical fiber having a structure to effectively reduce crosstalk between adjacent core regions among a plurality of core regions. The multi-core optical fiber (1) has a leakage reduction portion (50), at least a portion of which is arranged at a position on a straight line connecting adjacent core regions together among a plurality of core regions (10). The leakage reduction portion (50) reduces leakage light in the multi-core optical fiber (1) from each of the core regions (10), thereby effectively reducing crosstalk between adjacent core regions.

Multi-core optical fiber

The first rare-earth-doped fiber lasers were operated in the early 1960s, and produced a few milliwatts at a wavelength around 1 mum. Since the beginning of the decade, an enormous increase of fiber laser output power has been reported, the realm of kilowatt power has been entered, and power levels as high as 100 kW are envisaged. Apart from the power, fiber laser systems are renowned for their inherent compactness, monolithic architecture, and a power-independent beam quality. This paper reviews the challenges, achievements, and perspectives of high-power continuous-wave (CW) laser generation and amplification in fibers.

The Rising Power of Fiber Lasers and Amplifiers

Fiber lasers are well suited to scaling to high average power using beam-combining techniques. For coherent combining, optical phase-noise characterization of a ytterbium fiber amplifier is required to perform a critical evaluation of various approaches to coherent combining. For wavelength beam combining, we demonstrate good beam quality from the combination of three fiber amplifiers, and we discuss system scaling and design trades between laser linewidth, beam width, grating dispersion, and beam quality.

Beam combining of ytterbium fiber amplifiers (Invited)

We report on the laser properties of multicore photonic crystal fiber lasers. A stable phase locking of six- and seven-core structures through evanescent coupling is observed. Effective supermode selection is obtained by using both diffraction losses and the Talbot effect. A pure in-phase supermode is obtained (1.1 times diffraction limited). The laser operating in this mode has a slope efficiency of 70% with up to 44 W of output power. The modal area of the in-phase supermode multicore fiber is 1150 microm2, which makes it, to our knowledge, the single-mode fiber laser with the largest mode field area. In-phase laser action is stable when the fiber is bent.

Phase locking and supermode selection in multicore photonic crystal fiber lasers with a large doped area.

In this paper, the authors discuss the modal and lasing properties of multicore photonic crystal fiber lasers in the context of high power/energy production from fiber cores with very large mode area. Supermode selection methods like Talbot imaging or far-field aperturing are tested using 6-, 7-, and 18-core fibers. It is shown that in-phase mode selection is achieved efficiently by using either method. The fibers have been tested in continuous-wave (CW) and Q-switched laser operation. The mode field area is as large as 4240 mum2 for one of the fibers, providing up to 2 mJ of pulse energy in Q-switched operations with 30 ns pulse duration.

Multicore Photonic Crystal Fiber Lasers for High Power/Energy Applications

We model and characterize the behavior of a Q-switched fiber laser. The fiber is a doped multicore photonic crystal fiber having six cores in a ring-type geometry. The fiber laser is Q-switched using an intracavity acousto-optic modulator. Using a mode filtering technique in the far field, a mode very close to the fundamental in-phase supermode is obtained with a mode field area of 4200 microm(2) and a divergence of 9 mrad. Pulses with energies of up to 2.2 mJ and durations of 26 ns (limited by end facet damage) at a repetition rate of 10 kHz are obtained.

Characteristics of a Q-switched multicore photonic crystal fiber laser with a very large mode field area.

A novel microstructured fibre has been created for use in an optical interconnection system. The fibre has low crosstalk with a high density of cores corresponding to 1150 channels/mm/sup 2/. A repeating pseudorandom binary sequence has been used to demonstrate a four-channel transmit/receive system using vertical cavity surface emitting lasers as both emitters and detectors.

Demonstration of multi-core photonic crystal fibre in an optical interconnect

Laser damage thresholds of 8 μm- and 22 μm-core diameter solid-core photonic crystal fibres (PCF) and hollow-core photonic band gap (PBG) fibres have been measured. The studies were carried out using a 1.06 μm Nd:YAG laser (30 nsec pulses at 10 Hz), which is optimally coupled into these fibres by careful mode matching, providing a coupling efficiency greater than 90%. It has been shown that the damage threshold of the 8 μm core PBG fibre occurs at pulse energies close to 1 mJ, equivalent to a fluence well in excess of 1 kJ/cm 2 propagating down the fibre. This is a factor of 4 larger than the damage threshold of a solid-core PCF of similar core diameter. In comparison, the damage threshold of the large-core PBG is smaller than that of the equivalent PCF. Theoretical modelling based only on the optical modal properties of the single-mode PBG fibre shows that an enhancement by a factor of 25 should be obtainable. Thus there are different damage mechanisms potentially responsible for the fragility of larger-core PBG fibres. In an experimental study of bend losses it has been found that it is possible to bend the 8 μm PBG fibre up to the breaking point bend radius (<1 mm). The critical bend radius for the 22 μm core PBG is close to 2 mm, which is 50 times smaller than the critical bend radius of a 20 μm core PCF.

Charlotte R. Bennett

Papers

Phase locking and supermode selection in multicore photonic crystal fiber lasers with a large doped area.

Multicore Photonic Crystal Fiber Lasers for High Power/Energy Applications

Characteristics of a Q-switched multicore photonic crystal fiber laser with a very large mode field area.

Demonstration of multi-core photonic crystal fibre in an optical interconnect

Damage threshold and bending properties of photonic crystal and photonic band-gap optical fibers