Abstract

Optical fibers that possess the characteristics of both conventional cladded fibers and of a new type of fiber have been drawn and evaluated. The core has an equilateral triangular cross section with slightly bulging curved sides. The rounded vertices are in contact with the inside of the cladding tube of lower refractive index. Most of ther periphery of the core is surrounded by air. The cavity-like waveguide modes of this new type of fiber can be described as due to skew rays being reflected systematically from the glass–to–air interfaces as they propagate along the fiber. Near-field and far-field radiation patterns have been photographed and are presented. A new type of laser based on these cavity-like waveguide modes is proposed, in which the triangular core is made of a material (e.g., neodymium-doped glass, YAG, etc.) that can be optically pumped. The normal mode of operation of the laser consists of six diverging, spatially separated output beams; it can be optically pumped axially from both ends simultaneously, while being pumped from the sides.

© 1974 Optical Society of America

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References

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  1. T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, IEEE J. Quant. Electron. 5, 331 (1969).
    [CrossRef]
  2. P. Kaiser, E. A. J. Marcatili, and S. E. Miller, Bell. Syst. Tech. J. 72, 265 (1973).
    [CrossRef]
  3. U. S. Patent No. 3,712,705 issued to E. A. J. Marcatili on 23January1973. This patent describes a generalized polygonal-cored fiber as well as the equilaterial-triangular-cored fiber.
  4. A. D. Pearson and W. G. French, Bell Lab. Rec. 50, 102 (1972).
  5. R. B. Dyott, C. R. Day, and M. C. Brain, Electron. Lett. 9, 288 (1973).
    [CrossRef]
  6. N. S. Kapany, Fiber Optics (Academic, New York, 1967), p. 9.
  7. For this purpose, Zeiss UD/20 or UD/40 objectives are convenient because a 3-mm-diam opaque mask can easily be attached to the lens surface closest to the object being viewed.
  8. The direction of rotation is arbitrary. What is clear is that the two sets of three modes rotate in opposite directions.
  9. S. D. Personick, Bell Syst. Tech. J. 50, 843 (1971).
    [CrossRef]
  10. Hans Mueller, J. Am. Ceramic Soc. 21, 27 (1938).
    [CrossRef]
  11. P. Kaiser, A. R. Tynes, H. W. Astle, A. D. Pearson, W. G. French, R. E. Jaeger, and A. H. Cherin, J. Opt. Soc. Am. 63, 1141 (1973).
    [CrossRef]
  12. Losses expressed in dB/km can be converted to cm−1 by dividing by 4.34 × 105.
  13. Reference 6, p. 10. Equation (2.7) applies to meridional rays and is only approximately true for skew rays.
  14. J. B. Keller and S. J. Rubinow, Ann Phys. 9, 24 (1960).
    [CrossRef]
  15. E. A. J. Marcatiii, Bell Syst. Tech. J. 48, 2071 (1969).
    [CrossRef]
  16. J. E. Goell, Bell Syst. Tech. J. 48, 2133 (1969).
    [CrossRef]

1973 (3)

P. Kaiser, E. A. J. Marcatili, and S. E. Miller, Bell. Syst. Tech. J. 72, 265 (1973).
[CrossRef]

R. B. Dyott, C. R. Day, and M. C. Brain, Electron. Lett. 9, 288 (1973).
[CrossRef]

P. Kaiser, A. R. Tynes, H. W. Astle, A. D. Pearson, W. G. French, R. E. Jaeger, and A. H. Cherin, J. Opt. Soc. Am. 63, 1141 (1973).
[CrossRef]

1972 (1)

A. D. Pearson and W. G. French, Bell Lab. Rec. 50, 102 (1972).

1971 (1)

S. D. Personick, Bell Syst. Tech. J. 50, 843 (1971).
[CrossRef]

1969 (3)

E. A. J. Marcatiii, Bell Syst. Tech. J. 48, 2071 (1969).
[CrossRef]

J. E. Goell, Bell Syst. Tech. J. 48, 2133 (1969).
[CrossRef]

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, IEEE J. Quant. Electron. 5, 331 (1969).
[CrossRef]

1960 (1)

J. B. Keller and S. J. Rubinow, Ann Phys. 9, 24 (1960).
[CrossRef]

1938 (1)

Hans Mueller, J. Am. Ceramic Soc. 21, 27 (1938).
[CrossRef]

Astle, H. W.

Brain, M. C.

R. B. Dyott, C. R. Day, and M. C. Brain, Electron. Lett. 9, 288 (1973).
[CrossRef]

Cherin, A. H.

Day, C. R.

R. B. Dyott, C. R. Day, and M. C. Brain, Electron. Lett. 9, 288 (1973).
[CrossRef]

Dyott, R. B.

R. B. Dyott, C. R. Day, and M. C. Brain, Electron. Lett. 9, 288 (1973).
[CrossRef]

French, W. G.

Furukawa, M.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, IEEE J. Quant. Electron. 5, 331 (1969).
[CrossRef]

Goell, J. E.

J. E. Goell, Bell Syst. Tech. J. 48, 2133 (1969).
[CrossRef]

Jaeger, R. E.

Kaiser, P.

Kapany, N. S.

N. S. Kapany, Fiber Optics (Academic, New York, 1967), p. 9.

Keller, J. B.

J. B. Keller and S. J. Rubinow, Ann Phys. 9, 24 (1960).
[CrossRef]

Kitano, I.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, IEEE J. Quant. Electron. 5, 331 (1969).
[CrossRef]

Koizumi, K.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, IEEE J. Quant. Electron. 5, 331 (1969).
[CrossRef]

Marcatiii, E. A. J.

E. A. J. Marcatiii, Bell Syst. Tech. J. 48, 2071 (1969).
[CrossRef]

Marcatili, E. A. J.

P. Kaiser, E. A. J. Marcatili, and S. E. Miller, Bell. Syst. Tech. J. 72, 265 (1973).
[CrossRef]

U. S. Patent No. 3,712,705 issued to E. A. J. Marcatili on 23January1973. This patent describes a generalized polygonal-cored fiber as well as the equilaterial-triangular-cored fiber.

Matsumura, H.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, IEEE J. Quant. Electron. 5, 331 (1969).
[CrossRef]

Miller, S. E.

P. Kaiser, E. A. J. Marcatili, and S. E. Miller, Bell. Syst. Tech. J. 72, 265 (1973).
[CrossRef]

Mueller, Hans

Hans Mueller, J. Am. Ceramic Soc. 21, 27 (1938).
[CrossRef]

Pearson, A. D.

Personick, S. D.

S. D. Personick, Bell Syst. Tech. J. 50, 843 (1971).
[CrossRef]

Rubinow, S. J.

J. B. Keller and S. J. Rubinow, Ann Phys. 9, 24 (1960).
[CrossRef]

Tynes, A. R.

Uchida, T.

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, IEEE J. Quant. Electron. 5, 331 (1969).
[CrossRef]

Ann Phys. (1)

J. B. Keller and S. J. Rubinow, Ann Phys. 9, 24 (1960).
[CrossRef]

Bell Lab. Rec. (1)

A. D. Pearson and W. G. French, Bell Lab. Rec. 50, 102 (1972).

Bell Syst. Tech. J. (3)

S. D. Personick, Bell Syst. Tech. J. 50, 843 (1971).
[CrossRef]

E. A. J. Marcatiii, Bell Syst. Tech. J. 48, 2071 (1969).
[CrossRef]

J. E. Goell, Bell Syst. Tech. J. 48, 2133 (1969).
[CrossRef]

Bell. Syst. Tech. J. (1)

P. Kaiser, E. A. J. Marcatili, and S. E. Miller, Bell. Syst. Tech. J. 72, 265 (1973).
[CrossRef]

Electron. Lett. (1)

R. B. Dyott, C. R. Day, and M. C. Brain, Electron. Lett. 9, 288 (1973).
[CrossRef]

IEEE J. Quant. Electron. (1)

T. Uchida, M. Furukawa, I. Kitano, K. Koizumi, and H. Matsumura, IEEE J. Quant. Electron. 5, 331 (1969).
[CrossRef]

J. Am. Ceramic Soc. (1)

Hans Mueller, J. Am. Ceramic Soc. 21, 27 (1938).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (6)

Losses expressed in dB/km can be converted to cm−1 by dividing by 4.34 × 105.

Reference 6, p. 10. Equation (2.7) applies to meridional rays and is only approximately true for skew rays.

N. S. Kapany, Fiber Optics (Academic, New York, 1967), p. 9.

For this purpose, Zeiss UD/20 or UD/40 objectives are convenient because a 3-mm-diam opaque mask can easily be attached to the lens surface closest to the object being viewed.

The direction of rotation is arbitrary. What is clear is that the two sets of three modes rotate in opposite directions.

U. S. Patent No. 3,712,705 issued to E. A. J. Marcatili on 23January1973. This patent describes a generalized polygonal-cored fiber as well as the equilaterial-triangular-cored fiber.

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Figures (14)

Fig. 1
Fig. 1

Fiber cross section. Side of triangular-core measures 85 μm. Near beginning end of drawing process, where third vertex is not yet fused to the cladding tube. See part (c) of Fig. 6.

Fig. 2
Fig. 2

Observation arrangement for far-field mode patterns. Cladding mode stripper (S), camera (C), fiber (F), film (f).

Fig. 3
Fig. 3

Observation arrangement for near-field mode patterns, Cladding mode stripper (S), clamp (C), fiber (F), and mask (M).

Fig. 4
Fig. 4

Fat-field mode patterns obtained with equipment of Fig. 2. (a) and (b) Full-mode spectrum; (c) and (d) partial, conventional mode spectrum; (e) single set of three cavity-like waveguide beams; (f), (g), (h), (i), and (j) transition to counter-rotating set of three cavity-like waveguide beams; (k) as (g) but with counter-rotating cavity-like waveguide beams; (l) full sets of cavity-like waveguide beams and conventional-fiber modes. The fiber length was 40 m in all cases except for part (a) which was 2 m. The divergence angle for the bright circular region shown in part (b) is about 12°.

Fig. 5
Fig. 5

Transition from near-field to far-field radiation pattern. Side of triangular core is 85 μm. (a) Near field, (b) 80 μm above end, (c) 170 μm above, (d) 250 μm above, (e) 380 μm above, and (f) 600 μm above. Divergence angle of three beams is about 15°.

Fig. 6
Fig. 6

Near-field mode patterns observed with arrangement shown in Fig. 3. Side of triangular core measures 85 μm. (a), (b), and (c) Fiber excited with white light, fiber length is 40 m; (d) laser excitation in length of 2 m and a 3-mm-diam opaque mask as in Fig. 3 used to eliminate low-order modes from field of view. Orientation of fiber core can be inferred from Figs. 5 and 7.

Fig. 7
Fig. 7

Sketches of near-field mode patterns. (a) Path near vertices. Six reflections per transit. (b) Path near center. Six reflections per transit. (c) Path at middle of side. Three reflections per transit. External lines of (c) show transition to far field, (d) Full set of near-field modes. Note similarity to part (a) of Fig. 6.

Fig. 8
Fig. 8

(a), (b), and (c) 45° off-axis near-field mode patterns, (d) Far-field observed parallel to fiber axis. Fiber length is 2 m. Divergence angle of the two beams is about 15°.

Fig. 9
Fig. 9

Far-field mode patterns with laser (0.633 μm) excitation. (a) and (b) Far-field patterns. Divergence angle of three beams is about 15°. (c) Near field showing bright slit-like source on side of output end of fiber core.

Fig. 10
Fig. 10

Far-field mode patterns (a) 400 μm above and (b) 400 μm below end of fiber. Side of triangular core is 85 μm. Divergence angles of three beams is about 15°.

Fig. 11
Fig. 11

Laser configurations, (a) Laser with mirrors directly on laser-core rod. Laser mirrors M1 and M2, lens L, end-pumping sources S, laser output O, with only one output beam shown for simplicity. Side-pumping source not shown (b) Laser mirrors M1 and M2. High reflectance coating over only shaded region so that end pumping can be through center, clear aperture (c) Laser with external mirror M2′ that has center removed to permit end-pumping, beam-limiting aperture A, beam-control device C, lens L, end-pumping source S, amplifiers Amp, and laser-output beam O, with only one shown, for simplicity.

Fig. 12
Fig. 12

Near-field and far-field mode patterns for equilateral-triangular-cored fiber. Two additional ray paths are not shown, for clarity.

Fig. 13
Fig. 13

Scalene-triangular-cored fiber. Small interior triangle represents near-field mode pattern and outer triangle represents the fiber core cross section.

Fig. 14
Fig. 14

Near-field and far-field mode patterns of a square-cored fiber. (a) Mode requiring two reflections per transit, (b) modes requiring four reflections per transit, and (c) modes requiring six reflections per transit. Counter-rotating rays not shown, for clarity.