The strict single-polarization requirements of coherent optical fibre systems, fibre gyroscopes and polarization-dependent fibre sensors have created a need to fabricate in-line components, such as directional couplers, which are able to preserve the required polarization state to a high degree. To this end, a growing research effort has been directed recently towards fabrication and improvement of new types of birefringent optical fibre
couplers, as well as the theoretical aspects of their development, such as modelling, analysing and designing them for optimal performance.
A variety of fabrication techniques, including fusion-tapering, etch- fusion and polishing, have been reported, and have met with varying degrees of success.
Fused isotropic couplers provide some geometric birefringence, but this is only a weak effect, visible as a modulation of the coupling cycles over a long coupler, and resulting in periodic polarization splitting at the output pons. [Love and Hall, 1985, Payne et Al, 1985a,b, Snyder, 1985] This is discussed briefly in the next chapter. Form birefringence is not sufficient to reliably maintain an input state of polarization in the presence of physical perturbations, so isotropic couplers are not practical in applications which require strict polarization maintenance. To make these couplers more useful, it is possible to modify the coupling region, e.g., by depositing a layer of metal around the coupler waist [Kawachi and Kobayashi, 1984] to absorb one state of polarization. Birefringent fibre couplers offer better prospects, however, as both polarizations may be used.
The earliest reported birefringent couplers [Kawachi et AL, 1982], made using a fused biconical taper process, resulted in 15 dB polarization isolation and 3 dB loss. Two PANDA fibres [Sasaki et Al.,1984] were fused, after aligning the optical axes and coating the fibres with a layer of glass particles by chemical vapour deposition (CVD), and then drawn in a conventional manner [Kawasaki et Al., 1981].
Fusion tapering of birefringent fibres has since been extensively developed. Another early effort [Villarruel et Al., 1983] involving an etch-fusion process with single polarization fibre (Hitachi elliptical jacket fibre), resulted in a coupler with better than 6.7 dB polarization isolation, without particular effort in optical axis alignment.
Much of the work on fused-taper couplers has involved PANDA fibres (the acronym stands for Polarization maintaining AND Absorption reducing), which consist of two circular doped stress-regions either side of a circular core, all embedded in isotropic silica cladding [Sasaki et Al.,1984, Sasaki et Al., 1986, Noda et AL, 1986]. The birefringence is a result of the large stress in the core region, and it has been shown that much stress remains even when two such fibres are fused together [Shibata et AL, 1984].
Early PANDA couplers were successful in terms of coupling ratio and isolation ratio, [Yokohama et AL, 1985] with extinction ratios of up to 40 dB possible using Single Polarization Single Mode (SPSM) PANDA fibres [Okamoto, 1984, Yokohama et Al.,1984]. However, excess loss was high, around 3.6 dB, due to the index mismatch between core and stress-applying parts [Kawachi et Al., 1982]. Development of matched index PANDA fibres offers prospects of significant improvement in this figure, e.g. [Yokohama et Al., 1986], in which excess loss was reduced to around 0.1 dB while an isolation ratio better than 30 dB was maintained. Another suggested remedy to the problem of excess loss with depressed index regions is to taper the fibres more gradually in a longer coupling region, and keep the minimum waist diameter as large as possible [Noda and Yokohama, 1988, Yokohama et AL, 1988]. This is in keeping with previous theory [Love and Henry, 1986].
Another type of fibre used to make polarization maintaining couplers is the D-fibre [Dyott and Bello, 1983], so-called because of its cross sectional shape, with an elliptical core providing geometric birefringence. The core is adjacent to the flat face and its major axis is parallel to it. This allows for lateral access to the guiding regions without severe etching or polishing (which degrade the birefringence) and enables the optical axes of two such fibres to be aligned automatically, by placing them face-to-face. Methods used in coupler fabrication with D-fibre include fusing and tapering within or adjacent to a glass tube [Dyott and Bello, 1983, 1984], and modification of the index profile by controlled heat-induced diffusion of core dopants to allow for the fields to spread and couple [Handerek and Dyott, 1985].
In the same period, development has taken place in polished-type birefringent couplers, although to a lesser extent, due to their environmental sensitivity and their limited potential for large scale production. The basic polishing technique [Bergh et AL, 1980] consists of cementing a fibre in a curved groove in a silica block and lapping away the exposed cladding region towards the core until power transmission starts to drop. Bringing the lapped surfaces of two such fibres into contact results in a tunable coupling ratio.
The first application of this technique to birefringent fibres involved the use of self-aligning fibres [Pleibel et Al., 1983]. These stress-ellipse type fibres were oval, rather
than round, with the inner optical exes parallel to the outer geometric axes. Bending automatically occurred about the major geometric axis, so that the optical axes of the two fibres were aligned in the coupling region. Polarization isolation averaged 20 dB, the polarization- dependent coupling ratio was around 50 %, with 1.6 dB excess loss.
In another early experiment [Nayar and Smith, 1983], care was taken not to lap the cladding right down to the core, in order to maximize residual birefringence. This resulted in 40 dB polarization isolation at the outputs and excess loss around 0.5 dB. The power split ratio was found to be slightly polarization-dependent, and a polarization splitter, based on this, was suggested (see next chapter).
PANDA fibres have also been employed in polished-type couplers [Arikawa et AL, 1988b] with the most important observation being that the polarization cross-talk was increased markedly by small angular misalignments between the two optical axes. The results showed degradation of isolation from around 40 dB for aligned fibres, to around 15 dB with a 9 degree misalignment.
In one case, a combination of the polishing and fusion-taper techniques has been reported [Corke et Al., 1985]. The authors used a selective cladding removal step, prior to
a fusion-taper process, to make couplers from bow-tie fibres.
The theory of optical cross-talk due to evanescent coupling between two parallel cores that are weakly-coupled and weakly-guiding is well-known [Snyder, 1972, Snyder and Young, 1978, Snyder and Love, 1983, pp. 387-399; 567-584], and is applicable to polished-type aniostropic couplers. [Snyder and Stevenson, 1985, 1986, 1988]. The problem of coupling between two anisotropic fibres has been treated elsewhere, using coupled mode theory [Chen and Bums, 1982, Grochowski et Al., 1984, Shafir et Al.,
1988], and the reader may wish to compare the following treatment with these analyses. In particular, the evolution of the state of polarization along a birefringent coupler has been determined using a Jones matrix and the equivalent lumped element representation for each path between the input and output ports [Chen and Bums, 1982] . The treatment, while involved, provides a mathematical description of couplers made from aligned, misaligned or twisted birefringent fibres and considers their polarization-holding properties.
polarization-maintaining, weakly-guiding fibres was analysed using an "improved" coupled mode theory, to calculate elements of a coupling matrix [Shafir et Al, 1988]. Eigenvectors and eigenvalues of the matrix were calculated as a function of tilt angle between the fibre optical axes, and symmetry was used to simplify the treatment. It is worth noting, at least in the weak guidance weak anisotropy limit, that the coupled mode approach is equivalent to the perturbation approach to be adopted here; the same eigenvalues (geometric modal parameters) are derived in [Shafir et AL, 1988, Eq. (17)] as were found using perturbation theory [Snyder and Stevenson, 1985] (see Eq. (5-17) below).
In this work, we have chosen to adopt the more physically intuitive normal mode approach in analysing polarization phenomena in couplers with non-aligned core stress axes, since this is likely to be more easily and widely understood.
5 .2 PHYSICAL DESCRIPTION