Abstract

A compound fiber ring resonator is made with a Fabry–Perot étalon built inside a fiber ring that is fed through a 2 × 2 directional single-mode fiber coupler. It is theoretically analyzed by an unfolded equivalent model and a transfer-matrix method. The output intensities are presented, and four cases are discussed. The results may be useful in applications such as fiber spectrum analyzers, sensors, and lasers.

© 1994 Optical Society of America

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  1. I. D. Miller, D. B. Mortimore, P. Urquhart, B. J. Ainslie, S. P. Craig, C. A. Millar, D. B. Payne, “A Nd3+-doped cw laser using all-fiber reflectors,” Appl. Opt. 26, 2197–2201 (1987).
    [Crossref] [PubMed]
  2. G. J. Cowle, D. N. Payne, “Single-frequency travelling-wave erbium-doped fiber loop laser,” Electron. Lett. 27, 229–230 (1991).
    [Crossref]
  3. K. Iwatsuki, H. Okamura, M. Saruwatari, “Wavelength-tunable single-frequency and single polarization Er-doped fiber ring-laser with 1.4 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
    [Crossref]
  4. Y. Ohishi, T. Kanamori, “Ring laser operation at 1.3 μm of Pr3+-doped fluoride single mode fiber,” Electron. Lett. 28, 162–164 (1992).
    [Crossref]
  5. H. Okamura, K. Iwatsuki, “A finesse-enhanced Er-doped-fiber ring resonator,” IEEE J. Lightwave Technol. 9, 1554–1560 (1991).
    [Crossref]
  6. H. Okamura, K. Iwatsuki, “Ultrahigh-finesse, bidirectional Er-doped fiber ring resonator,” Electron. Lett. 28, 326–327 (1992).
    [Crossref]
  7. L. H. Jae, M. Oh, Y. Kim, “Two-mode fiber-optic resonant ring interferometer as a sensor,” Opt. Lett. 15, 198–200 (1990).
    [Crossref] [PubMed]
  8. R. I. Macdonald, R. Nychka, “Differential measurement technique for optical fiber sensors,” Electron. Lett. 27, 2194–2196 (1991).
    [Crossref]
  9. L. F. Stokes, M. Chodorow, H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7, 288–290 (1982).
    [Crossref] [PubMed]
  10. F. Zhang, J. W. Y. Lit, “Direct-coupling single-mode fiber ring resonator,” J. Opt. Soc. Am. A 5, 1347–1355 (1988).
    [Crossref]
  11. Y. H. Ja, “Generalized theory of optical fiber loop and ring resonators with multiple couplers. 2: General characteristics,” Appl. Opt. 29, 3524–3529 (1990).
    [Crossref] [PubMed]
  12. Y. H. Ja, “Optical fiber filter comprising a single-coupler fiber ring (or loop) and a double-coupler fiber mirror,” IEEEJ. Lightwave Technol. 9, 964–974 (1991).
    [Crossref]
  13. G. Abd-el-Hamid, P. A. Davies, “Fiber-optic double ring resonator,” Electron. Lett. 25, 224–225 (1989).
    [Crossref]
  14. P. Urquhart, “Compound optical-fiber-based resonators,” J. Opt. Soc. Am. A 5, 803–812 (1988).
    [Crossref]
  15. J. Capmany, M. A. Muriel, “Investigation on spectral behaviour of novel direct coupling compound fiber ring resonator,” Electron. Lett. 26, 772–773 (1990).
    [Crossref]
  16. D. B. Mortimore, “Fiber loop reflectors,” IEEE J. Lightwave Technol. 6, 1217–1224 (1988).
    [Crossref]
  17. R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All-fiber narrowband reflection gratings at 1550 nm,” Electron. Lett. 26, 730–732 (1990).
    [Crossref]
  18. P. Urquhart, “Transversely coupled fiber Fabry–Perot resonator: theory,” Appl. Opt. 26, 456–463 (1987).
    [Crossref] [PubMed]
  19. M. W. Maeda, J. S. Patel, D. A. Smith, Lin Chinlon, M. A. Saifi, A. Von Lehman, “An electronically tunable fiber laser with a liquid-crystal étalon filter as the wavelength-tuning element,” IEEE Photon. Technol. Lett. 2, 787–789 (1990).
    [Crossref]
  20. J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
    [Crossref]
  21. H. Schmuck, T. H. Pfeiffer, G. Veith, “Widely tunable narrow linewidth erbium doped fiber ring laser,” Electron. Lett. 27, 2117–2119 (1991).
    [Crossref]
  22. G. T. Harvey, L. F. Mollenauer, “Harmonically mode-locked fiber ring laser with an internal Fabry–Perot stabilizer for soliton transmission,” Opt. Lett. 18, 107–109 (1993).
    [Crossref] [PubMed]
  23. J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” IEEE J. Lightwave Technol. 8, 1904–1919 (1990).
    [Crossref]
  24. A. Yariv, Optical Electronics (Saunders, Philadelphia, 1991).
  25. P. R. Morkel, G. J. Cowle, D. N. Payne, “Travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
    [Crossref]

1993 (1)

1992 (2)

Y. Ohishi, T. Kanamori, “Ring laser operation at 1.3 μm of Pr3+-doped fluoride single mode fiber,” Electron. Lett. 28, 162–164 (1992).
[Crossref]

H. Okamura, K. Iwatsuki, “Ultrahigh-finesse, bidirectional Er-doped fiber ring resonator,” Electron. Lett. 28, 326–327 (1992).
[Crossref]

1991 (6)

R. I. Macdonald, R. Nychka, “Differential measurement technique for optical fiber sensors,” Electron. Lett. 27, 2194–2196 (1991).
[Crossref]

H. Okamura, K. Iwatsuki, “A finesse-enhanced Er-doped-fiber ring resonator,” IEEE J. Lightwave Technol. 9, 1554–1560 (1991).
[Crossref]

G. J. Cowle, D. N. Payne, “Single-frequency travelling-wave erbium-doped fiber loop laser,” Electron. Lett. 27, 229–230 (1991).
[Crossref]

Y. H. Ja, “Optical fiber filter comprising a single-coupler fiber ring (or loop) and a double-coupler fiber mirror,” IEEEJ. Lightwave Technol. 9, 964–974 (1991).
[Crossref]

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

H. Schmuck, T. H. Pfeiffer, G. Veith, “Widely tunable narrow linewidth erbium doped fiber ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[Crossref]

1990 (8)

Y. H. Ja, “Generalized theory of optical fiber loop and ring resonators with multiple couplers. 2: General characteristics,” Appl. Opt. 29, 3524–3529 (1990).
[Crossref] [PubMed]

M. W. Maeda, J. S. Patel, D. A. Smith, Lin Chinlon, M. A. Saifi, A. Von Lehman, “An electronically tunable fiber laser with a liquid-crystal étalon filter as the wavelength-tuning element,” IEEE Photon. Technol. Lett. 2, 787–789 (1990).
[Crossref]

J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” IEEE J. Lightwave Technol. 8, 1904–1919 (1990).
[Crossref]

P. R. Morkel, G. J. Cowle, D. N. Payne, “Travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[Crossref]

J. Capmany, M. A. Muriel, “Investigation on spectral behaviour of novel direct coupling compound fiber ring resonator,” Electron. Lett. 26, 772–773 (1990).
[Crossref]

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All-fiber narrowband reflection gratings at 1550 nm,” Electron. Lett. 26, 730–732 (1990).
[Crossref]

K. Iwatsuki, H. Okamura, M. Saruwatari, “Wavelength-tunable single-frequency and single polarization Er-doped fiber ring-laser with 1.4 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[Crossref]

L. H. Jae, M. Oh, Y. Kim, “Two-mode fiber-optic resonant ring interferometer as a sensor,” Opt. Lett. 15, 198–200 (1990).
[Crossref] [PubMed]

1989 (1)

G. Abd-el-Hamid, P. A. Davies, “Fiber-optic double ring resonator,” Electron. Lett. 25, 224–225 (1989).
[Crossref]

1988 (3)

1987 (2)

1982 (1)

Abd-el-Hamid, G.

G. Abd-el-Hamid, P. A. Davies, “Fiber-optic double ring resonator,” Electron. Lett. 25, 224–225 (1989).
[Crossref]

Ainslie, B. J.

Armitage, J. R.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All-fiber narrowband reflection gratings at 1550 nm,” Electron. Lett. 26, 730–732 (1990).
[Crossref]

Capmany, J.

J. Capmany, M. A. Muriel, “Investigation on spectral behaviour of novel direct coupling compound fiber ring resonator,” Electron. Lett. 26, 772–773 (1990).
[Crossref]

J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” IEEE J. Lightwave Technol. 8, 1904–1919 (1990).
[Crossref]

Chinlon, Lin

M. W. Maeda, J. S. Patel, D. A. Smith, Lin Chinlon, M. A. Saifi, A. Von Lehman, “An electronically tunable fiber laser with a liquid-crystal étalon filter as the wavelength-tuning element,” IEEE Photon. Technol. Lett. 2, 787–789 (1990).
[Crossref]

Chodorow, M.

Cowle, G. J.

G. J. Cowle, D. N. Payne, “Single-frequency travelling-wave erbium-doped fiber loop laser,” Electron. Lett. 27, 229–230 (1991).
[Crossref]

P. R. Morkel, G. J. Cowle, D. N. Payne, “Travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[Crossref]

Craig, S. P.

Davey, S. T.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All-fiber narrowband reflection gratings at 1550 nm,” Electron. Lett. 26, 730–732 (1990).
[Crossref]

Davies, P. A.

G. Abd-el-Hamid, P. A. Davies, “Fiber-optic double ring resonator,” Electron. Lett. 25, 224–225 (1989).
[Crossref]

Digiovanni, D. J.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

Harvey, G. T.

Iwatsuki, K.

H. Okamura, K. Iwatsuki, “Ultrahigh-finesse, bidirectional Er-doped fiber ring resonator,” Electron. Lett. 28, 326–327 (1992).
[Crossref]

H. Okamura, K. Iwatsuki, “A finesse-enhanced Er-doped-fiber ring resonator,” IEEE J. Lightwave Technol. 9, 1554–1560 (1991).
[Crossref]

K. Iwatsuki, H. Okamura, M. Saruwatari, “Wavelength-tunable single-frequency and single polarization Er-doped fiber ring-laser with 1.4 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[Crossref]

Ja, Y. H.

Y. H. Ja, “Optical fiber filter comprising a single-coupler fiber ring (or loop) and a double-coupler fiber mirror,” IEEEJ. Lightwave Technol. 9, 964–974 (1991).
[Crossref]

Y. H. Ja, “Generalized theory of optical fiber loop and ring resonators with multiple couplers. 2: General characteristics,” Appl. Opt. 29, 3524–3529 (1990).
[Crossref] [PubMed]

Jae, L. H.

Kanamori, T.

Y. Ohishi, T. Kanamori, “Ring laser operation at 1.3 μm of Pr3+-doped fluoride single mode fiber,” Electron. Lett. 28, 162–164 (1992).
[Crossref]

Kashyap, R.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All-fiber narrowband reflection gratings at 1550 nm,” Electron. Lett. 26, 730–732 (1990).
[Crossref]

Kim, Y.

Lit, J. W. Y.

Macdonald, R. I.

R. I. Macdonald, R. Nychka, “Differential measurement technique for optical fiber sensors,” Electron. Lett. 27, 2194–2196 (1991).
[Crossref]

Maeda, M. W.

M. W. Maeda, J. S. Patel, D. A. Smith, Lin Chinlon, M. A. Saifi, A. Von Lehman, “An electronically tunable fiber laser with a liquid-crystal étalon filter as the wavelength-tuning element,” IEEE Photon. Technol. Lett. 2, 787–789 (1990).
[Crossref]

Millar, C. A.

Miller, I. D.

Mollenauer, L. F.

Morkel, P. R.

P. R. Morkel, G. J. Cowle, D. N. Payne, “Travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[Crossref]

Mortimore, D. B.

Muriel, M. A.

J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” IEEE J. Lightwave Technol. 8, 1904–1919 (1990).
[Crossref]

J. Capmany, M. A. Muriel, “Investigation on spectral behaviour of novel direct coupling compound fiber ring resonator,” Electron. Lett. 26, 772–773 (1990).
[Crossref]

Nychka, R.

R. I. Macdonald, R. Nychka, “Differential measurement technique for optical fiber sensors,” Electron. Lett. 27, 2194–2196 (1991).
[Crossref]

Oh, M.

Ohishi, Y.

Y. Ohishi, T. Kanamori, “Ring laser operation at 1.3 μm of Pr3+-doped fluoride single mode fiber,” Electron. Lett. 28, 162–164 (1992).
[Crossref]

Okamura, H.

H. Okamura, K. Iwatsuki, “Ultrahigh-finesse, bidirectional Er-doped fiber ring resonator,” Electron. Lett. 28, 326–327 (1992).
[Crossref]

H. Okamura, K. Iwatsuki, “A finesse-enhanced Er-doped-fiber ring resonator,” IEEE J. Lightwave Technol. 9, 1554–1560 (1991).
[Crossref]

K. Iwatsuki, H. Okamura, M. Saruwatari, “Wavelength-tunable single-frequency and single polarization Er-doped fiber ring-laser with 1.4 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[Crossref]

Patel, J. S.

M. W. Maeda, J. S. Patel, D. A. Smith, Lin Chinlon, M. A. Saifi, A. Von Lehman, “An electronically tunable fiber laser with a liquid-crystal étalon filter as the wavelength-tuning element,” IEEE Photon. Technol. Lett. 2, 787–789 (1990).
[Crossref]

Payne, D. B.

Payne, D. N.

G. J. Cowle, D. N. Payne, “Single-frequency travelling-wave erbium-doped fiber loop laser,” Electron. Lett. 27, 229–230 (1991).
[Crossref]

P. R. Morkel, G. J. Cowle, D. N. Payne, “Travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[Crossref]

Pfeiffer, T. H.

H. Schmuck, T. H. Pfeiffer, G. Veith, “Widely tunable narrow linewidth erbium doped fiber ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[Crossref]

Piccirili, A.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

Pramagon, P. E.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

Presby, H. M.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

Saifi, M. A.

M. W. Maeda, J. S. Patel, D. A. Smith, Lin Chinlon, M. A. Saifi, A. Von Lehman, “An electronically tunable fiber laser with a liquid-crystal étalon filter as the wavelength-tuning element,” IEEE Photon. Technol. Lett. 2, 787–789 (1990).
[Crossref]

Saruwatari, M.

K. Iwatsuki, H. Okamura, M. Saruwatari, “Wavelength-tunable single-frequency and single polarization Er-doped fiber ring-laser with 1.4 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[Crossref]

Schmuck, H.

H. Schmuck, T. H. Pfeiffer, G. Veith, “Widely tunable narrow linewidth erbium doped fiber ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[Crossref]

Shaw, H. J.

Smith, D. A.

M. W. Maeda, J. S. Patel, D. A. Smith, Lin Chinlon, M. A. Saifi, A. Von Lehman, “An electronically tunable fiber laser with a liquid-crystal étalon filter as the wavelength-tuning element,” IEEE Photon. Technol. Lett. 2, 787–789 (1990).
[Crossref]

Stokes, L. F.

Stone, J.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

Stulz, L. W.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

Sulhoff, J. W.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

Urquhart, P.

Veith, G.

H. Schmuck, T. H. Pfeiffer, G. Veith, “Widely tunable narrow linewidth erbium doped fiber ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[Crossref]

Von Lehman, A.

M. W. Maeda, J. S. Patel, D. A. Smith, Lin Chinlon, M. A. Saifi, A. Von Lehman, “An electronically tunable fiber laser with a liquid-crystal étalon filter as the wavelength-tuning element,” IEEE Photon. Technol. Lett. 2, 787–789 (1990).
[Crossref]

Williams, D. L.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All-fiber narrowband reflection gratings at 1550 nm,” Electron. Lett. 26, 730–732 (1990).
[Crossref]

Wyatt, R.

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All-fiber narrowband reflection gratings at 1550 nm,” Electron. Lett. 26, 730–732 (1990).
[Crossref]

Yariv, A.

A. Yariv, Optical Electronics (Saunders, Philadelphia, 1991).

Zhang, F.

Zyskind, J. L.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

Appl. Opt. (3)

Electron. Lett. (11)

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stulz, H. M. Presby, A. Piccirili, P. E. Pramagon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fiber Fabry–Perot étalon,” Electron. Lett. 27, 1950–1951 (1991).
[Crossref]

H. Schmuck, T. H. Pfeiffer, G. Veith, “Widely tunable narrow linewidth erbium doped fiber ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[Crossref]

P. R. Morkel, G. J. Cowle, D. N. Payne, “Travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[Crossref]

G. Abd-el-Hamid, P. A. Davies, “Fiber-optic double ring resonator,” Electron. Lett. 25, 224–225 (1989).
[Crossref]

J. Capmany, M. A. Muriel, “Investigation on spectral behaviour of novel direct coupling compound fiber ring resonator,” Electron. Lett. 26, 772–773 (1990).
[Crossref]

R. Kashyap, J. R. Armitage, R. Wyatt, S. T. Davey, D. L. Williams, “All-fiber narrowband reflection gratings at 1550 nm,” Electron. Lett. 26, 730–732 (1990).
[Crossref]

G. J. Cowle, D. N. Payne, “Single-frequency travelling-wave erbium-doped fiber loop laser,” Electron. Lett. 27, 229–230 (1991).
[Crossref]

K. Iwatsuki, H. Okamura, M. Saruwatari, “Wavelength-tunable single-frequency and single polarization Er-doped fiber ring-laser with 1.4 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[Crossref]

Y. Ohishi, T. Kanamori, “Ring laser operation at 1.3 μm of Pr3+-doped fluoride single mode fiber,” Electron. Lett. 28, 162–164 (1992).
[Crossref]

H. Okamura, K. Iwatsuki, “Ultrahigh-finesse, bidirectional Er-doped fiber ring resonator,” Electron. Lett. 28, 326–327 (1992).
[Crossref]

R. I. Macdonald, R. Nychka, “Differential measurement technique for optical fiber sensors,” Electron. Lett. 27, 2194–2196 (1991).
[Crossref]

IEEE J. Lightwave Technol. (3)

H. Okamura, K. Iwatsuki, “A finesse-enhanced Er-doped-fiber ring resonator,” IEEE J. Lightwave Technol. 9, 1554–1560 (1991).
[Crossref]

D. B. Mortimore, “Fiber loop reflectors,” IEEE J. Lightwave Technol. 6, 1217–1224 (1988).
[Crossref]

J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” IEEE J. Lightwave Technol. 8, 1904–1919 (1990).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. W. Maeda, J. S. Patel, D. A. Smith, Lin Chinlon, M. A. Saifi, A. Von Lehman, “An electronically tunable fiber laser with a liquid-crystal étalon filter as the wavelength-tuning element,” IEEE Photon. Technol. Lett. 2, 787–789 (1990).
[Crossref]

IEEEJ. Lightwave Technol. (1)

Y. H. Ja, “Optical fiber filter comprising a single-coupler fiber ring (or loop) and a double-coupler fiber mirror,” IEEEJ. Lightwave Technol. 9, 964–974 (1991).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Lett. (3)

Other (1)

A. Yariv, Optical Electronics (Saunders, Philadelphia, 1991).

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Figures (9)

Fig. 1
Fig. 1

Compound ring resonator with a FP étalon. Ei is the input, Er, is the reflected output, Et is the transmitted output, C is the single-mode fiber coupler, M is the mirror, l1 is the length of fiber section, and l2 is the length of the FP cavity.

Fig. 2
Fig. 2

Unfolded equivalent model of the compound ring resonator. The right-hand side of the dashed line is a mirror image of the left-hand side.

Fig. 3
Fig. 3

Transfer-matrix model of the compound ring resonator. C and C′ are couplers, and f and f′ are fiber lines.

Fig. 4
Fig. 4

Separation 2S as a function of phase δ2 for different mirror reflections r. Curve a, r = 0.9; curve b, r = 0.5; curve c, r = 0.1.

Fig. 5
Fig. 5

Normalized transmitted intensity of the resonator as a function of δ1 with (a) r = 0.9 (curve a) and r = 0.1, γ = 0.035 (curve b); (b) γ = 0.001 (curve a) and γ = 0.1, r = 0.5 (curve b). The other parameters are δ2 = π/4, k = 0.071, and α = 1 dB/km.

Fig. 6
Fig. 6

Normalized (a) reflected and (b) transmitted intensities as functions of δ2 with δ1 = π, r = 0.9, k = 0.071, γ = 0.01, and α = 1 dB/km.

Fig. 7
Fig. 7

Spectra responses of the normalized transmission of the resonator with Ra = 1. (a) 0 ≤ δ1 ≤ 4π, k = 0.0355; (b) 0.8πδ1 ≤ 1.2π, k = 0.01 (curve a), k = 0.0355 (curve b), k = 0.1 (curve c). The other parameters are r = 0.9, γ = 0.035, and α = 1 dB/km.

Fig. 8
Fig. 8

Optimum coupling coefficient kr as a function of δ2 with r = 0.1 and 0.9. The other parameters are γ = 0.035 and α = 1 dB/km.

Fig. 9
Fig. 9

Spectra responses of the normalized transmission of a compound traveling-wave ring resonator. (a) Ra = 1, r = 0.9; (b) Ra = 10, r = 0.9; (c) Ra = 15, r = 0.9 (curve a), and r = 0.5 (curve b). The other parameters are k = 0.0355, γ = 0.035, and α = 1 dB/km.

Equations (37)

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[ E 1 + E 1 ] = [ c ] [ E 2 + E 2 ] ,
[ c ] = [ 1 t c r c t c r c t c t c 2 r c 2 t c ] ,
r c = [ ( 1 γ ) ( 1 k ) ] 1 / 2 ,
t c = j [ ( 1 γ ) k ] 1 / 2 .
[ E 2 + E 2 ] = [ f ] [ E 3 + E 3 ] ,
[ f ] = [ exp [ ( α j β 1 ) l a ] 0 0 exp [ ( α j β 1 ) l b ] ] ,
[ E 3 + E 3 ] = [ F P ] [ E 4 + E 4 ] ,
[ FP ] = [ 1 r F t F r F t F r F r F 2 t F 2 r F ] .
r F = F ( sin δ 2 ) exp ( j δ r ) ( 1 + F 2 sin 2 δ 2 ) 1 / 2 ,
t F = exp ( j δ t ) ( 1 + F 2 sin 2 δ 2 ) 1 / 2 ,
δ r = tan 1 [ ( r 2 1 ) cos δ 2 ( 1 + r 2 ) sin δ 2 ] ,
δ t = tan 1 [ ( 1 + r 2 ) sin δ 2 ( 1 r 2 ) cos δ 2 ] ,
F = 2 r 1 r 2 ,
δ 2 = β 2 l 2 = 2 π n 2 λ l 2 ,
[ E 1 + E 1 ] = [ A B C D ] [ E 6 + E 6 ] ,
[ A B C D ] = [ c ] [ f ] [ FP ] [ f ] [ c ] .
E r E i = k ( 1 γ 1 k ) 1 / 2 × { a R exp ( j δ 1 ) [ 1 T exp ( j δ 1 ) ] 2 R 2 exp ( j 2 δ 1 ) } ,
E t E i = ( 1 γ 1 k ) 1 / 2 × { 1 k [ 1 T exp ( j δ 1 ) ] [ 1 T exp ( j δ 1 ) ] 2 R 2 exp ( j 2 δ 1 ) } ,
a = exp [ ( α + j β 1 ) ( l a l b ) ] ,
δ 1 = β 1 l 1 ,
R = r c r F exp ( α l 1 ) ,
T = r c t F exp ( α l 1 ) ,
I r = | E r E i | 2 = k 2 1 γ 1 k | a R | 2 I d ,
I t = | E t E i | 2 = 1 I d [ ( 1 k ) 2 + ( 2 k ) 2 | T | 2 + P 2 2 | T | × ( 2 k ) ( 1 k + P ) cos ϕ + 2 ( 1 k ) P cos ( 2 ϕ ) ] ,
I d = 1 + 4 | T | 2 + P 2 4 | T | ( 1 + P ) cos ϕ + 2 P cos ( 2 ϕ ) ,
P = | R | 2 + | T | 2 ,
ϕ = δ 1 + δ t ,
sin ( δ 1 + δ t ) [ cos ( δ 1 + δ t ) Γ ] = 0 ,
Γ = exp ( α l 1 ) + r c 2 exp ( α l 1 ) 2 r c | t F | .
Γ | t F | = 1 ( 1 + F 2 sin 2 δ 2 ) 1 / 2 .
δ 1 + δ t 2 p π ± S ( p = 0 , 1 , 2 , ) ,
S = cos 1 ( | t F | ) .
E t E i = ( 1 γ 1 k ) 1 / 2 [ 1 k 1 T exp ( j δ 1 ) ] .
δ 1 + δ t = 2 p π ( p = 0 , 1 , 2 , ) .
k r = 1 ( 1 γ ) exp ( 2 α l 1 ) 1 + F 2 sin 2 δ 2 .
n = m R a .
m ( R a + 1 ) = 2 p ( p = 0 , 1 , 2 , ) .

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