Tapered single-mode fibers: external refractive-index dependence

Suzanne Lacroix, Richard J. Black, Christian Veilleux, and Jean Lapierre

Ecole Polytechnique, Department of Engineering Physics, P.O. Box 6079, Station A, Montreal, Quebec H3C 3A7. Received 19 April 1986. 0003-6935/86/152468-02$02.00/0. © 1986 Optical Society of America.

Biconically tapered single-mode fibers can be considered as basic elements in understanding fused fiber couplers.1,2

These have been modeled under the assumption that the cores do not play a significant role in the power coupling mechanism.3 This point of view provides a useful first ap­proximation, particularly for highly tapered fibers; however, in some cases, the influence of the residual core must be accounted for. In fact, a tapered fiber strictly should be regarded as a three-layer structure: core-cladding-external medium.4-5 Herein we report experimental results which support the importance of using models that account for the presence of the core for small taper elongations. Moreover, these results allow us to draw some general conclusions with regard to the coupler-modeling problem and certain applica­tions of tapered fibers.

Three biconical tapers with different elongations, la, lb, and lc, were made from a matched-cladding step-index fiber having cladding and core diameters of 70 and 4.3 μm, respec­tively, and a second-mode cutoff wavelength of 566 nm. A narrow flame (<2 mm) was used so that the nonadiabatic1,4

behavior of the tapered waveguides could be observed as in Fig. 1. All three tapers were immersed in a container filled with a graded water-glycerol mixture prepared by liquid-liquid diffusion so that the refractive index of the mixture varied from 1.33 (pure water) at the surface of the mixture to 1.47 (pure glycerol) at the bottom of the container. By lowering each taper down into such a mixture parallel to its surface, the refractive index surrounding the taper (external index) could be varied continuously from 1.33 to 1.47 mainly in the vicinity of the diffusion interface. No attempt was made to establish a true scale of the index variation with depth, but the results reported in Fig. 2 are sufficient for the purpose of our discussion.

For each of the three elongations, la, lb, and lc, we have recorded the core-mode output power as a function of refrac­tive index.

For external index values below the cladding index of 1.46, in each case oscillations in core-mode output were observed. These oscillations are due to a change in the phase matching condition between the modes involved in the process when the external index is varied. The oscillatory dependence becomes increasingly rapid as the external index approaches the cladding index. Also the more elongated and thinner the taper the more pronounced is this effect.

As the external index approaches the cladding index (= 1.46), the core-mode output power decreases suddenly in all three cases. For this matched condition the optical wave­guide is essentially step index with an infinite cladding; i.e., it is the core that plays the guiding role. However, this guid­ance is very weak, and the HEn local mode is for all intents and purposes cut off over much of the taper region; that is, we have the condition1 that the standard waveguide parameter V < 1, making waveguiding very sensitive to radiation losses due to tapering and other perturbations. Furthermore, for a more elongated taper, we encounter an increasingly small

Fig. 1. Transmitted fundamental core-mode power in a single step-index biconically tapered "monomode" fiber. Cladding modes were stripped at the input and output using an index-matching oil. The elongations la, lb, and lc refer to Figs. 2(a), (b), and (c), respectively.

Fig. 2. Transmitted core-mode power as a function of external index: (a) small elongation; (b) medium elongation; (c) large elon­gation. The taper waist diameters were (a) 25, (b) 14, and (c) 10 μm.

waveguide parameter and have a larger interaction length; thus the above loss effect is accentuated.

Above the index "cutoff value (1.46), some of the core-mode power is gradually recovered as n increased due to the additional guidance provided by Fresnel reflections at the cladding-external medium interface. No oscillations occur in the n > 1.46 region, i.e., the three-layer structure, schemat­ically represented at the top of Fig. 2, behaves as if it were essentially monomode.

Given these results, especially the fact that for tapers (a) and (b) some power remains guided at the "cutoff value, it is clear that the residual core influence cannot be ignored if a

2468 APPLIED OPTICS / Vol. 25, No. 15 / 1 August 1986

complete account of mode propagation in a tapered fiber is contemplated. However, as expected, this effect tends to be negligible for tapers with smaller waists as can be seen in Fig. 2(c). In the case of our experiments, guiding by the residual core is fairly important for taper elongations <3 mm, which corresponds to taper waist diameters >15% of the initial untapered value. For a coupler this corresponds typically to the first maximum of power transfer. Therefore, especially for small elongations, the calculated coupling coefficient of a coupler should take into account the residual core influence. This is a possible explanation of the discrepancy at small elongations between theory and experiment reported in Ref. 3. Indeed, we have observed the residual core guiding effect, i.e., power recovery at and above the "cutoff index, for couplers with small elongations.

In conclusion, it appears that tapered single-mode fibers may be regarded as devices that can be highly sensitive to external index variations.

Below the "cutoff value the throughput power oscillates with changes in index, and there is the possibility of using tapered fibers instead of couplers as sensors1 or simple switches.

Above this value transmitted core-mode power is also sen­sitive to external index variation but is a monotonically increasing function. This dependence is of some interest in the application to electrooptical devices involving fibers and common liquid crystals6 which typically have indices above that of fused silica.7

We thank Francois Gonthier for experimental measure­ment and Jacques Bures for helpful discussion.

References 1. D. T. Cassidy, D. C. Johnson, and K. 0. Hill, "Wavelength-

Dependent Transmission of Monomode Optical Fiber Tapers," Appl. Opt. 24, 945 (1985).

2. G. Georgiou and A. C. Boucouvalas, "Low-Loss Single-Mode Optical Couplers," IEE Proc. Part J 132, 297 (1985).

3. J. Bures, S. Lacroix, et J. Lapierre, "Analyse d'un coupleur bidir-ectionnel à fibres optiques monomodes fusionnées," Appl. Opt. 22, 1918 (1983).

4. W. J. Stewart and J. D. Love, "Design Limitations on Tapers and Couplers in Single Mode Fibers," in Technical Digest, Fifth International Conference on Integrated Optics and Optical Fi­ber Communication-Eleventh European Conference on Optical Communication, Venice (1985).

5. J. V. Wright, "Variational Analysis of Fused Taper Couplers," Electron. Lett. 21, 1064 (1985).

6. R. J. Black, C. Veilleux, J. Bures, and J. Lapierre, "Radially Anisotropic Lightguide Mode Selector," Electron. Lett. 21, 987 (1985).

7. After submission of this Letter, a paper that gives somewhat similar responses for coaxial couplers came to our attention: A. C. Boucouvalas and G. Georgiou, "External Refractive-Index Response of Tapered Coaxial Couplers," Opt. Lett. 11, 257 (1986).

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