W-type optical fiber: relation between refractive index difference and transmission bandwidth

Toshiki P. Tanaka, Sei-ichi Onoda, and Masao Sumi Hitachi Ltd., Central Research Laboratory, Kokubunji, Tokyo 185, Japan. Received 30 September 1975.

The doubly clad fiber whose geometry and refraqtive index profile are shown in Fig. 1 is known as a W-type fiber.1'2 A W-type fiber can be regarded as a perturbed system comprising a reference singly clad (SC1) fiber with an outer layer with a high refractive index. By perturba­tion theory,3 it is shown that:

(1) The higher order modes turn out to be leaky, so the number of guided modes is smaller than in the SC1 fiber.

(2) The field distributions of the guided modes are al­most equal to those of the corresponding guided modes in the SC1 fiber.

The attenuation constants of the leaky modes strongly depend on the thickness of the intermediate layer; it can be made large enough by arranging the thickness. In this case, a fiber whose bandwidth is almost equal to that of the other reference singly clad (SC2) fiber can be obtained. This fiber also features tight confinement of the light power of the guided modes to the core.

In this Letter, the experimental results on the relation between the refractive index difference and the transmis­sion bandwidth of multimode W-type fibers are described.

Samples with various refractive index differences have been fabricated. The index difference between the core and cladding of the samples was 0.26% for the largest and 0.03% for the smallest. The index difference between the core and the intermediate layer was in the region from 0.40% to 0.62%. The refractive indices were measured using an interference microscope with sliced and polished samples of preforms. In the measurement on the fibers themselves, the refractive indices of the intermediate layers could not be measured accurately because the spatial reso­lution was insufficient. The error of the measured value is ±0.01%. The core diameters were about 50 μm; and the el-lipticity of the core, defined by 2(α - b)/(a + b) (a and b are the major and minor radii of the core, respectively), was below 5%. The fluctuation of the diameter of each sample was within ±5%. The thickness of the intermediate layer was ~4-6 μm (δ 0.17-0.23).

The bandwidth was measured by the frequency sweeping method.4 A sinusoidally modulated optical signal whose modulating frequency was swept from 100 kHz to 500 MHz was launched into the fiber. By comparing the frequency spectra of the detected signals at different transmission lengths of the fiber, the amplitude response was obtained. The optical source was a GaAlAs semiconductor laser with a 0.835-μm wavelength. The optical beam from the laser was collimated and focused into the fiber with a 10X micro­scope objective lens. The exciting was done so as to maxi­mize the output power from the fiber. An Si avalanche photodiode was used as the detector. The measured lengths were about 1 km.

The experimental results are shown in Fig. 2. The hori­zontal axis indicates the refractive index difference be­tween the core and cladding, and the vertical axis denotes the 3-dB bandwidth at 1 km (3-dB bandwidth-length product). The dashed curve shows the theoretical value of a singly clad fiber with a 50-μm core diameter, which corre­sponds to the SC2 fiber. The small circles show the theo­retical value of the samples, and black points indicate the measured values. The theoretical values are calculated as-

Fig. 1. Geometry and refractive index profile of a W-type fiber.

Fig. 2. Refractive index difference between the core and cladding vs 3-dB bandwidth-length product of W-type fibers.

suming that each guided mode propagates independently with uniform modal power; the influence of the leaky modes is neglected in W-type fibers. The increase of the bandwidth of W-type fibers closely follows the curve of the SC2 fiber as the refractive index difference between the core and cladding decreases. It is almost completely inde­pendent of the index difference between the core and inter­mediate layer.

May 1976 / Vol. 15, No. 5 / APPLIED OPTICS 1121

The measured bandwidths are wider than the theoretical values where the index differences are rather large. How­ever, in fibers with index differences of abqut 0.03%, the measured values are narrower than the theoretical values. This fact can be explained as follows:

(1) In a fiber whose index difference is large, many guided modes can propagate. However, at the input end, the power distribution of the excited modes localizes in the lower order modes. Consequently, the bandwidth is wider when measured. Mode coupling5 due to the inhomgeneity of the structure along the fiber is one possible reason for the widening of the bandwidth. However, since the length dependencies of the pulse broadening were linear up to full length (1 km), the mode coupling is not considered to be the main reason for this result.

(2) In a fiber with small index differences, all guided modes and lower leaky modes are excited. The attenua­tion of the leaky modes is not large enough because the thickness of the intermediate layer is not suitable. For this reason, the measured bandwidth is narrower than the theoretical value, which is derived neglecting the influence of the leaky modes.

The above interpretations are still assumptions to be proved. However, the following facts endorse these inter­pretations. When the refractive index difference was large, the bandwidth characteristics varied considerably as the exciting condition changed; but this phenomenon was not conspicuous in a fiber whose index difference was small. And in a fiber with a small index difference, the launching loss penalty due to the excitation of leaky modes was observed along the fiber near the input end.

The authors wish to thank S. Kawakami for his useful discussions and T. Suganuma and K. Ishida for their con­tributions in preparing the samples.

References 1. S. Kawakami and S. Nishida, Electron. Lett. 10, 38 (1974). 2. S. Kawakami and S. Nishida, IEEE J. Quantum Electron. QE-

10, 879 (1974). 3. S. Kawakami and S. Nishida, IEEE J. Quantum Electron. QE-

11,130(1975). 4. S. D. Personick, W. M. Hubbard, D. Gloge, W. S. Holden, R. W.

Dawson, E. L. Chinnock, and T. P. Lee, in IEEE/OSA 1973 Di­gest of Technical Papers, paper 3.4.

5. D. Gloge, Bell Syst. Tech. J. 52, 801 (1973).

1122 APPLIED OPTICS / Vol. 15, No. 5 / May 1976