Abstract

The frequency resolution of an active waveguide ring resonator spectrometer is fundamentally limited by spontaneous emission noise produced by the gain medium. A closed-form expression for this resolution is derived, and the result is used to determine the minimum, rms, angular rotation rate, random walk error achievable by an active ring resonator gyroscope. An active waveguide ring resonator is demonstrated in a neodymium-doped glass, and a finesse of 250 at a signal wavelength of 1060 nm is achieved for the 1.6 cm diameter ring under laser diode pumping. This finesse corresponds to an effective propagation loss on the order of 0.013 dB/cm, which is the lowest value reported to date for rings of this size.

© 2007 Optical Society of America

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References

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  1. C.K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” Photon. Technol. Lett. 11, 1623–1625 (1999).
    [CrossRef]
  2. S. T. Chu, B.E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “A second-order filter response from parallel coupled glass microring resonators,” Photon. Technol. Lett. 11, 1426–1428 (1999).
    [CrossRef]
  3. G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behavior in silicon-on-insulator ring resonator structures,” Opt. Express 13, 9623–9628 (2005).
    [CrossRef] [PubMed]
  4. Q. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15, 924–929 (2007).
    [CrossRef] [PubMed]
  5. A. Ksendzov and Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30, 3344–3346 (2005).
    [CrossRef]
  6. P. Mottier and P. Pouteau, “Solid state optical gyrometer integrated on silicon,” Electron. Lett. 33, 1975–1977 (1997).
    [CrossRef]
  7. J. Haavisto and G. A. Pajer, “Resonance effects in low-loss ring waveguides,” Opt. Lett. 5, 510–512 (1980).
    [CrossRef] [PubMed]
  8. R. G. Walker and C. D. W. Wilkinson, “Integrated optical ring resonators made by silver ion-exchange in glass,” Appl. Opt. 22, 1029–1035 (1983).
    [CrossRef] [PubMed]
  9. G. Li, K. A. Winick, H. C. Griffin, and J. Hayden, “Systematic modeling study of channel waveguide fabrication by thermal silver ion exchange,” Appl. Opt. 45, 1743–1755 (2006).
    [CrossRef] [PubMed]
  10. R. Adar, M. R. Serbin, and V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
    [CrossRef]
  11. T. Kitagawa, K. Hattori, Y. Hibino, and Y. Ohmori, “Laser Oscillation in Erbium-Doped Silica-Based Planar Ring Resonators,” in Proceedings of 18th European Conf. on Optical Commun. (ECOC), (1992), Th PD-II.5, pp. 907–910.
  12. W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche, and R. Ricken, “Erbium-doped lithium niobate waveguide lasers,” IEICE Trans. Electron. E88-C, 990–997 (2005).
    [CrossRef]
  13. T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” J. Quantum Electron. QE-16, 1376–1379 (1980).
    [CrossRef]
  14. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7, 288–290 (1982).
    [CrossRef] [PubMed]
  15. S. Ezekiel, S. P. Smith, and F. Zarinetchi “Basic principles of fiber-optic gyroscopes,” in Optical fiber Rotation Sensing, W. K. Burns, ed., (Academic Press, NY, 1994), Chap. 1.
  16. S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
    [CrossRef]
  17. R. E. Meyer, S. Ezekiel, D. W. Stowe, and V. J. Tekippe, “Passive fiber-optic ring resonator for rotation sensing,” Opt. Lett. 8, 644–646 (1983).
    [CrossRef] [PubMed]
  18. K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator microoptic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18, 66–72 (2000).
    [CrossRef]
  19. H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive resonator gyro using phase modulation spectroscopy technique,” Optical Engineering Letters 45, 080506-1–080506-3 (2006).
  20. H. Okamura and K Iwatsuki, “A finesse-enhanced Er-doped-fiber ring resonator,” J. Lightwave Technol. 9, 1554–1560 (1991).
    [CrossRef]
  21. J. T. Kringlebotn, “Amplified fiber ring resonator gyro,” Photon. Technol. Lett. 4, 1180–1183 (1992).
    [CrossRef]
  22. J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne, and R. I. Laming, “Amplified fibre delay line with 27 000 recirculations,” Electron. Lett. 28, 201–202 (1992).
  23. W. T. Silfvast, “Radiation and thermal equilibrium,” in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 6.
  24. W. T. Silfvast, “Conditions for producing a laser,” in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 7.

2007 (1)

2006 (2)

G. Li, K. A. Winick, H. C. Griffin, and J. Hayden, “Systematic modeling study of channel waveguide fabrication by thermal silver ion exchange,” Appl. Opt. 45, 1743–1755 (2006).
[CrossRef] [PubMed]

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive resonator gyro using phase modulation spectroscopy technique,” Optical Engineering Letters 45, 080506-1–080506-3 (2006).

2005 (3)

2000 (1)

1999 (2)

C.K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” Photon. Technol. Lett. 11, 1623–1625 (1999).
[CrossRef]

S. T. Chu, B.E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “A second-order filter response from parallel coupled glass microring resonators,” Photon. Technol. Lett. 11, 1426–1428 (1999).
[CrossRef]

1997 (1)

P. Mottier and P. Pouteau, “Solid state optical gyrometer integrated on silicon,” Electron. Lett. 33, 1975–1977 (1997).
[CrossRef]

1994 (1)

R. Adar, M. R. Serbin, and V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

1992 (2)

J. T. Kringlebotn, “Amplified fiber ring resonator gyro,” Photon. Technol. Lett. 4, 1180–1183 (1992).
[CrossRef]

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne, and R. I. Laming, “Amplified fibre delay line with 27 000 recirculations,” Electron. Lett. 28, 201–202 (1992).

1991 (1)

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

1983 (2)

1982 (1)

1980 (2)

J. Haavisto and G. A. Pajer, “Resonance effects in low-loss ring waveguides,” Opt. Lett. 5, 510–512 (1980).
[CrossRef] [PubMed]

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

1977 (1)

S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Adar, R.

R. Adar, M. R. Serbin, and V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

Baets, R.

Balsamo, S. R.

S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Bogaerts, W.

Bruce, A. J.

C.K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” Photon. Technol. Lett. 11, 1623–1625 (1999).
[CrossRef]

Cappuzzo, M. A.

C.K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” Photon. Technol. Lett. 11, 1623–1625 (1999).
[CrossRef]

Chodorow, M.

Chu, S. T.

S. T. Chu, B.E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “A second-order filter response from parallel coupled glass microring resonators,” Photon. Technol. Lett. 11, 1426–1428 (1999).
[CrossRef]

Das, B. K.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche, and R. Ricken, “Erbium-doped lithium niobate waveguide lasers,” IEICE Trans. Electron. E88-C, 990–997 (2005).
[CrossRef]

Dey, D.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche, and R. Ricken, “Erbium-doped lithium niobate waveguide lasers,” IEICE Trans. Electron. E88-C, 990–997 (2005).
[CrossRef]

Ding, C.

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive resonator gyro using phase modulation spectroscopy technique,” Optical Engineering Letters 45, 080506-1–080506-3 (2006).

Dorschner, T. A.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

Dumon, P.

Ezekiel, S.

R. E. Meyer, S. Ezekiel, D. W. Stowe, and V. J. Tekippe, “Passive fiber-optic ring resonator for rotation sensing,” Opt. Lett. 8, 644–646 (1983).
[CrossRef] [PubMed]

S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

S. Ezekiel, S. P. Smith, and F. Zarinetchi “Basic principles of fiber-optic gyroscopes,” in Optical fiber Rotation Sensing, W. K. Burns, ed., (Academic Press, NY, 1994), Chap. 1.

Gomez, L. T.

C.K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” Photon. Technol. Lett. 11, 1623–1625 (1999).
[CrossRef]

Griffin, H. C.

Haavisto, J.

Hattori, K.

T. Kitagawa, K. Hattori, Y. Hibino, and Y. Ohmori, “Laser Oscillation in Erbium-Doped Silica-Based Planar Ring Resonators,” in Proceedings of 18th European Conf. on Optical Commun. (ECOC), (1992), Th PD-II.5, pp. 907–910.

Haus, H. A.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

Hayden, J.

Hibino, Y.

T. Kitagawa, K. Hattori, Y. Hibino, and Y. Ohmori, “Laser Oscillation in Erbium-Doped Silica-Based Planar Ring Resonators,” in Proceedings of 18th European Conf. on Optical Commun. (ECOC), (1992), Th PD-II.5, pp. 907–910.

Holz, M.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

Hotate, K.

Iwatsuki, K

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

Jin, Z.

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive resonator gyro using phase modulation spectroscopy technique,” Optical Engineering Letters 45, 080506-1–080506-3 (2006).

Kaneko, T.

S. T. Chu, B.E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “A second-order filter response from parallel coupled glass microring resonators,” Photon. Technol. Lett. 11, 1426–1428 (1999).
[CrossRef]

Kitagawa, T.

T. Kitagawa, K. Hattori, Y. Hibino, and Y. Ohmori, “Laser Oscillation in Erbium-Doped Silica-Based Planar Ring Resonators,” in Proceedings of 18th European Conf. on Optical Commun. (ECOC), (1992), Th PD-II.5, pp. 907–910.

Kokubun, Y.

S. T. Chu, B.E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “A second-order filter response from parallel coupled glass microring resonators,” Photon. Technol. Lett. 11, 1426–1428 (1999).
[CrossRef]

Kringlebotn, J. T.

J. T. Kringlebotn, “Amplified fiber ring resonator gyro,” Photon. Technol. Lett. 4, 1180–1183 (1992).
[CrossRef]

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne, and R. I. Laming, “Amplified fibre delay line with 27 000 recirculations,” Electron. Lett. 28, 201–202 (1992).

Ksendzov, A.

Laming, R. I.

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne, and R. I. Laming, “Amplified fibre delay line with 27 000 recirculations,” Electron. Lett. 28, 201–202 (1992).

Lenz, G.

C.K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” Photon. Technol. Lett. 11, 1623–1625 (1999).
[CrossRef]

Li, G.

Lin, Y.

Lipson, M.

Little, B.E.

S. T. Chu, B.E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “A second-order filter response from parallel coupled glass microring resonators,” Photon. Technol. Lett. 11, 1426–1428 (1999).
[CrossRef]

Ma, H.

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive resonator gyro using phase modulation spectroscopy technique,” Optical Engineering Letters 45, 080506-1–080506-3 (2006).

Madsen, C.K.

C.K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” Photon. Technol. Lett. 11, 1623–1625 (1999).
[CrossRef]

Meyer, R. E.

Mizrahi, V.

R. Adar, M. R. Serbin, and V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

Morkel, P. R.

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne, and R. I. Laming, “Amplified fibre delay line with 27 000 recirculations,” Electron. Lett. 28, 201–202 (1992).

Morthier, G.

Mottier, P.

P. Mottier and P. Pouteau, “Solid state optical gyrometer integrated on silicon,” Electron. Lett. 33, 1975–1977 (1997).
[CrossRef]

Ohmori, Y.

T. Kitagawa, K. Hattori, Y. Hibino, and Y. Ohmori, “Laser Oscillation in Erbium-Doped Silica-Based Planar Ring Resonators,” in Proceedings of 18th European Conf. on Optical Commun. (ECOC), (1992), Th PD-II.5, pp. 907–910.

Okamura, H.

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

Pajer, G. A.

Pan, W.

S. T. Chu, B.E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “A second-order filter response from parallel coupled glass microring resonators,” Photon. Technol. Lett. 11, 1426–1428 (1999).
[CrossRef]

Pannell, C. N.

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne, and R. I. Laming, “Amplified fibre delay line with 27 000 recirculations,” Electron. Lett. 28, 201–202 (1992).

Payne, D. N.

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne, and R. I. Laming, “Amplified fibre delay line with 27 000 recirculations,” Electron. Lett. 28, 201–202 (1992).

Pouteau, P.

P. Mottier and P. Pouteau, “Solid state optical gyrometer integrated on silicon,” Electron. Lett. 33, 1975–1977 (1997).
[CrossRef]

Priem, G.

Reza, S.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche, and R. Ricken, “Erbium-doped lithium niobate waveguide lasers,” IEICE Trans. Electron. E88-C, 990–997 (2005).
[CrossRef]

Ricken, R.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche, and R. Ricken, “Erbium-doped lithium niobate waveguide lasers,” IEICE Trans. Electron. E88-C, 990–997 (2005).
[CrossRef]

Scotti, R. E.

C.K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” Photon. Technol. Lett. 11, 1623–1625 (1999).
[CrossRef]

Serbin, M. R.

R. Adar, M. R. Serbin, and V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

Shaw, H. J.

Silfvast, W. T.

W. T. Silfvast, “Radiation and thermal equilibrium,” in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 6.

W. T. Silfvast, “Conditions for producing a laser,” in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 7.

Smith, I. W.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

Smith, S. P.

S. Ezekiel, S. P. Smith, and F. Zarinetchi “Basic principles of fiber-optic gyroscopes,” in Optical fiber Rotation Sensing, W. K. Burns, ed., (Academic Press, NY, 1994), Chap. 1.

Sohler, W.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche, and R. Ricken, “Erbium-doped lithium niobate waveguide lasers,” IEICE Trans. Electron. E88-C, 990–997 (2005).
[CrossRef]

Statz, H.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

Stokes, L. F.

Stowe, D. W.

Suche, H.

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche, and R. Ricken, “Erbium-doped lithium niobate waveguide lasers,” IEICE Trans. Electron. E88-C, 990–997 (2005).
[CrossRef]

Suzuki, K.

Takiguchi, K.

Tekippe, V. J.

Van Thourhout, D.

Walker, R. G.

Wilkinson, C. D. W.

Winick, K. A.

Xu, Q.

Zarinetchi, F.

S. Ezekiel, S. P. Smith, and F. Zarinetchi “Basic principles of fiber-optic gyroscopes,” in Optical fiber Rotation Sensing, W. K. Burns, ed., (Academic Press, NY, 1994), Chap. 1.

Zhang, X.

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive resonator gyro using phase modulation spectroscopy technique,” Optical Engineering Letters 45, 080506-1–080506-3 (2006).

Amplified fibre delay line with 27 000 recirculations (1)

J. T. Kringlebotn, P. R. Morkel, C. N. Pannell, D. N. Payne, and R. I. Laming, “Amplified fibre delay line with 27 000 recirculations,” Electron. Lett. 28, 201–202 (1992).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

S. Ezekiel and S. R. Balsamo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Electron. Lett. (1)

P. Mottier and P. Pouteau, “Solid state optical gyrometer integrated on silicon,” Electron. Lett. 33, 1975–1977 (1997).
[CrossRef]

IEICE Trans. Electron. (1)

W. Sohler, B. K. Das, D. Dey, S. Reza, H. Suche, and R. Ricken, “Erbium-doped lithium niobate waveguide lasers,” IEICE Trans. Electron. E88-C, 990–997 (2005).
[CrossRef]

J. Lightwave Technol. (3)

R. Adar, M. R. Serbin, and V. Mizrahi, “Less than 1 dB per meter propagation loss of silica waveguides measured using a ring resonator,” J. Lightwave Technol. 12, 1369–1372 (1994).
[CrossRef]

K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator microoptic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18, 66–72 (2000).
[CrossRef]

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

J. Quantum Electron. (1)

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Optical Engineering Letters (1)

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive resonator gyro using phase modulation spectroscopy technique,” Optical Engineering Letters 45, 080506-1–080506-3 (2006).

Photon. Technol. Lett. (3)

J. T. Kringlebotn, “Amplified fiber ring resonator gyro,” Photon. Technol. Lett. 4, 1180–1183 (1992).
[CrossRef]

C.K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” Photon. Technol. Lett. 11, 1623–1625 (1999).
[CrossRef]

S. T. Chu, B.E. Little, W. Pan, T. Kaneko, and Y. Kokubun, “A second-order filter response from parallel coupled glass microring resonators,” Photon. Technol. Lett. 11, 1426–1428 (1999).
[CrossRef]

Other (4)

T. Kitagawa, K. Hattori, Y. Hibino, and Y. Ohmori, “Laser Oscillation in Erbium-Doped Silica-Based Planar Ring Resonators,” in Proceedings of 18th European Conf. on Optical Commun. (ECOC), (1992), Th PD-II.5, pp. 907–910.

S. Ezekiel, S. P. Smith, and F. Zarinetchi “Basic principles of fiber-optic gyroscopes,” in Optical fiber Rotation Sensing, W. K. Burns, ed., (Academic Press, NY, 1994), Chap. 1.

W. T. Silfvast, “Radiation and thermal equilibrium,” in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 6.

W. T. Silfvast, “Conditions for producing a laser,” in Laser Fundamentals, (Cambridge University Press, 2004), Chap. 7.

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Figures (7)

Fig. 1.
Fig. 1.

Double arm ring resonator.

Fig. 2.
Fig. 2.

Effect of spontaneous emission on frequency.

Fig. 3.
Fig. 3.

Mask layout for single-arm racetrack active ring resonator with pump coupler. W=1.3 µm, Ds=8.4 µm, Lp=2.915 mm, Dp=7.55 µm

Fig. 4.
Fig. 4.

Spectral response of active ring resonator.

Fig. 5.
Fig. 5.

Spectral response of active ring resonator as a function of pump power at fixed signal power.

Fig. 6.
Fig. 6.

Spectral response of active ring resonator as a function of signal power at fixed pump power.

Fig. 7.
Fig. 7.

Lasing characteristic.

Equations (50)

Equations on this page are rendered with MathJax. Learn more.

A = [ A o 1 K cw j B o K cw ]
B = [ j A o K cw + B o 1 K cw ]
B o = B 1 K ccw exp ( ρ 2 L j β L )
T ( ϕ ) A A o 2 = 1 ( 1 x 2 ) ( 1 y 2 ) ( 1 xy ) 2 + 4 xy sin 2 ( ϕ 2 )
x 1 K ccw exp ( ρ 2 L )
y 1 K cw
ϕ β L = 2 π λ N eff L = ω N eff L c
D T max T min T max = 4 xy ( 1 x 2 ) ( 1 y 2 ) ( 1 xy ) 2 ( x + y ) 2
δ ϕ FWHM = 2 cos 1 [ 2 xy 1 + x 2 y 2 ]
T ( m π ± δ ϕ FWHM 2 ) T min T max T min = 1 2
F 2 π δ ϕ FWHM = 2 π c N eff L δ ω FWHM
F π 1 xy
B A o 2 = 1 y 2 [ 1 xy ] 2
B A o 2 F π
f m = m c N eff L
f m , ccw f m , cw = 4 A λ m L Ω
δ Ω rms ( λ m L 4 A ) [ 2 δ ω FWHM ( 2 π ) [ η D ( P in h f m ) τ int ] 1 2 ]
= ( λ m c 4 A N eff ) [ 2 F c [ η D ( P in h f m ) τ int ] 1 2 ] rad s
δ Ω rms ( λ m c 4 A N eff ) [ 1 F c F a [ ( P in h f m ) τ int ] 1 2 ] rad s
δ θ 1 · cos β < n >
< ( δ θ ) 2 > 1 2 < n >
< [ δ ϕ ( τ int ) ] 2 > M ( τ int ) 2 < n >
M ( τ int ) = τ int τ fl N 2 s
ρ b ( f ) = 8 π λ a 2 n r 3 c
S ( f ) = 1 1 + [ 2 ( f f a ) δ f a ] 2
s = 8 π λ a 2 n r 3 c V δ ω a 4 = 2 π λ a 2 n r 3 V c Δ ω a
τ p = n r L c 1 y 2 x 2
1 τ p δ ω FWHM = 2 π c n r L F c
G = e σ e N 2 L V 1 + σ e N 2 L V
y 2 x 2 G 1
N 2 V σ e L ( 1 x 2 y 2 ) = n r V σ e c 1 τ p
σ e = 1 2 π 1 τ fl λ a 2 n r 2 Δ ω a
< n > = n r P c L 2 h f a c
< [ δ ϕ ( τ int ) ] 2 > = 2 π τ int h f a c 2 F c P c n r 2 L 2
P c 1 π F a P in
< [ δ f cw ] 2 > = < [ δ f ccw ] 2 >
= < [ δ ϕ ( τ int ) ] 2 > ( 2 π τ int ) 2
( δ f cw ) rms = ( δ f ccw ) rms c 2 n r L [ 1 F a F c [ ( P in h f a ) τ int ] 1 2 ]
δ Ω rms = < [ δ Ω ] 2 > 1 2 = λ a L 4 2 π A τ int < [ δ ϕ ( τ int ) ] 2 > 1 2
δ Ω rms ( λ a c 4 A n r ) [ 1 F a F c [ ( P in h f a ) τ int ] 1 2 ]
( λ a c 4 A n r ) [ 1 F c F a F c [ ( P in h f a ) τ int ] 1 2 ] rad s
F c π 1 ( 1 K cw ) e ρ c L 2 2 π ρ c L
F a π K cw
reduction factor = F a F c ρ c L 2 K cw
P c = P in K cw
σ e N 2 ( sat ) ρ c
N 2 ( sat ) N 2 ( unsat ) 1 + 2 P c P sat
P sat h f a σ e τ fl A wg
P p = hc λ p τ fl N 2 ( usat ) A wg L
P p 4 λ a λ p F a F c P in

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