Using the formalism of mode overlap, a theoretical analysis of optically pumped fiber laser amplifiers and oscillators is developed. The concept of normalized overlap coefficients is introduced to account for the effects of the transverse structure of the interacting signal and pump modes on the device characteristics. Simple and accurate closed-form expressions are derived for the gain of fiber amplifiers and the threshold and energy conversion efficiency of fiber laser oscillators in terms of the fiber and laser material parameters and the pump and signal modes. When applied to step-index Nd:YAG fiber lasers, this study predicts optimum fundamental mode oscillation in fibers with a V number of 5-25 with submilliwatt thresholds and nearly quantum-limited conversion efficiencies.

Theoretical analysis of optical fiber laser amplifiers and oscillators

In this paper we present a new development of the distributed-index planar microlens of 2.5-3-mm focal length and 0.15 N.A. and also show that it is usable with optical components in fiber communications. We then propose a concept of stacked planar optics consisting of a stack of arrayed planar microlenses and other optical components. From this configuration a 2-D array of optical devices is monolithically available, and many discrete components can be separated from the array. An optical tap array has been fabricated as an example of stacked planar optics.

Stacked planar optics: an application of the planar microlens

Graded-refractive-index-rod lenses (GRIN-rod lenses) have a number of features that make them particularly suitable for use in optical devices for manipulating and processing the optical signals in fiber communication systems. Such lenses can be cemented directly to the other elements of a device, thus giving a structure that is compact, solid, stable, and rugged. They also have significantly smaller aberrations than equivalent simple homogeneous lenses, and this results in lower insertion losses. Designs for various GRIN-rod lens devices, including connectors, attenuators, directional couplers, switches, isolators and wavelength-division multiplexers are reviewed. A consistent set of loss estimates is provided for all the device designs considered.

Applications of GRIN-rod lenses in optical fiber communication systems.

As new optical devices for increasing further the utility of and to expand the application of fiber-optic communications, grating multiplexers and isolators have been developed for 0.8 μm band employing microoptic approach. The development of these devices is the subject of this paper. The devices have desirable features of small size, compactness, high optical performances, and high reliability. The grating multiplexer consists of a graded-index rod, a blazed reflection grating replicated onto the graded-index rod slanting facet or a wedge facet, and an input-output fiber array. Simple calculations have been done to determine necessary element parameters for a given channel spacing. Experimental results are presented for five-channel multiplexers devised using a SELFOC®lens. Around 3 dB insertion loss and less than -30 dB crosstalk have been obtained for about 35 nm channel spacing in overall device size of 18 \times 13 \times 50 mm. Faraday rotation optical isolators for 0.8 μm band have been miniaturized by employing an efficient paramagnetic glass Faraday rotator, a magnet with a through hole and a folded optics in the Faraday rotator. The path number in the folded optics has been optimized in terms of trading-off between the magnet size and the insertion loss. A 0.9 dB insertion loss including fiber coupling loss and 36 dB isolation have been obtained in overall device size of 24 \times 24.5 \times 42 mm. Results on the temperature and wavelength dependence of the isolation are also presented. In addition, fundamental properties of optical circulators for 0.8 μm band and optical isolators and circulators both for 1.3 μm band, developed as extended modifications of the optical isolators for 0.8 μm band, are briefly described.

Microoptic grating multiplexers and optical isolators for fiber-optic communications

GRIN-rod lenses, ball lenses, and plano-convex rod lenses are currently proposed for fiber-optic devices. From analyses of the aberrations of these lens types it turned out that equivalent lenses in a well-designed coupling have nearly the same aberration. We derive valuable relations between the coupling efficiency and the optimal lens parameters. For each above-mentioned lens type, coupling efficiencies of 95% (0.2-dB insertion loss) can be obtained if typical communication fibers are incorporated. We also present a lens connector that has been fabricated in a factory-type production line. Its performance reaches the theoretical limits. Finally the influence of misalignments in the lens coupling system is investigated.

Lens coupling in fiber-optic devices: efficiency limits.

A novel approach, “micro-optics”, is proposed to realize coupling/branching in fiber-optic communications. The operation is based on the beam transformation in a graded index rod (beam undulation and beam size change), in association with reflection or refraction at a graded index rod facet. Small-size couplers/dividers have been devised by inserting a semitransparent mirror between the facets of two graded index rods with a length of a quarter of the undulation period. Their best features are small size, simple structure, low insertion loss, and wide application areas. An excess insertion loss as low as 0.5 dB has been realized in a 3-dB divider with SELFOC® rods. As further applications of them, wavelength division multiplexers/demultiplexers have been developed by replacing the semitransparent mirror with a dielectric interference filter. An insertion loss of as low as 1.2 dB and isolation of more than 20 dB for wavelength separation of 20 nm have been realized. Results are also shown on the o...

R. Ishikawa

Papers

Micro-optic devices for fiber-optic communications