Abstract

We predict dramatically reduced switching thresholds for nonlinear optical devices incorporating fiber ring resonators. The circulating power in such a resonator is much larger than the incident power; also, the phase of the transmitted light varies rapidly with the single-pass phase shift. The combined action of these effects leads to a finesse-squared reduction in the switching threshold, allowing for photonic switching devices that operate at milliwatt power levels in ordinary optical fibers.

© 1999 Optical Society of America

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References

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  1. M. N. Islam, Ultrafast Fiber Switching Devices (Cambridge U. Press, Cambridge, 1992), pp. 31, 39.
  2. L. F. Stokes, M. Chodorow, and H. J. Shaw, Opt. Lett. 7, 288 (1982).
    [CrossRef] [PubMed]
  3. C. K. Madsen and G. Lenz, IEEE Photon. Technol. Lett. 10, 994 (1998).
    [CrossRef]
  4. J. Capmany, F. J. Fraille-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
    [CrossRef]
  5. B. Crosignani, B. Daino, P. Di Porto, and S. Wabnitz, Opt. Commun. 59, 309 (1986).
    [CrossRef]
  6. Here the finesse is defined as the free spectral range divided by the full width at half-depth of the resonance peak. Applying this definition to the intensity magnification [Eq.??(3)], we calculate the finesse asF=FSRFWHD ra??1? ?21+ra?1-ra?.Here, a is the single-pass amplitude transmission and ? is the degree of coherence between fields delayed by the ring transit time (see Refs.??14 and 15, below).
  7. A finesse-squared enhancement has been observed in the context of fiber-optic squeezed light generation in a fiber ring resonator. See, for instance, R. M. Shelby, M. D. Levenson, D. F. Walls, and A. Aspect, Phys. Rev. A 33, 4008 (1986)R. M. Shelby, M. D. Levenson, and S. H. Perlmutter, J. Opt. Soc. Am. B 5, 347 (1988).
    [CrossRef] [PubMed]
  8. B. Crosignani, A. Yariv, and P. Di Porto, Opt. Lett. 4, 251 (1986).
    [CrossRef]
  9. G. S. Pandian and F. E. Seraji, Proc. IEE Part J 138, 235 (1991).
  10. F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and Th. J. A. Popma, Appl. Phys. Lett. 71, 747 (1997).
    [CrossRef]
  11. B. E. Little, S. T. Chu, and H. A. Haus, Opt. Lett. 23, 894 (1998).
    [CrossRef]
  12. J. Popp, M. H. Fields, and R. K. Chang, Opt. Lett. 22, 1296 (1997).
    [CrossRef]
  13. N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, Opt. Lett. 20, 813 (1995).
    [CrossRef] [PubMed]
  14. Y. Ohtsuka, J. Lightwave Technol. LT-3, 378 (1985).
    [CrossRef]
  15. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), pp. 52–59.

1998

C. K. Madsen and G. Lenz, IEEE Photon. Technol. Lett. 10, 994 (1998).
[CrossRef]

B. E. Little, S. T. Chu, and H. A. Haus, Opt. Lett. 23, 894 (1998).
[CrossRef]

1997

J. Popp, M. H. Fields, and R. K. Chang, Opt. Lett. 22, 1296 (1997).
[CrossRef]

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and Th. J. A. Popma, Appl. Phys. Lett. 71, 747 (1997).
[CrossRef]

1995

1994

J. Capmany, F. J. Fraille-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

1991

G. S. Pandian and F. E. Seraji, Proc. IEE Part J 138, 235 (1991).

1986

B. Crosignani, B. Daino, P. Di Porto, and S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

A finesse-squared enhancement has been observed in the context of fiber-optic squeezed light generation in a fiber ring resonator. See, for instance, R. M. Shelby, M. D. Levenson, D. F. Walls, and A. Aspect, Phys. Rev. A 33, 4008 (1986)R. M. Shelby, M. D. Levenson, and S. H. Perlmutter, J. Opt. Soc. Am. B 5, 347 (1988).
[CrossRef] [PubMed]

B. Crosignani, A. Yariv, and P. Di Porto, Opt. Lett. 4, 251 (1986).
[CrossRef]

1985

Y. Ohtsuka, J. Lightwave Technol. LT-3, 378 (1985).
[CrossRef]

1982

Aspect, A.

A finesse-squared enhancement has been observed in the context of fiber-optic squeezed light generation in a fiber ring resonator. See, for instance, R. M. Shelby, M. D. Levenson, D. F. Walls, and A. Aspect, Phys. Rev. A 33, 4008 (1986)R. M. Shelby, M. D. Levenson, and S. H. Perlmutter, J. Opt. Soc. Am. B 5, 347 (1988).
[CrossRef] [PubMed]

Blom, F. C.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and Th. J. A. Popma, Appl. Phys. Lett. 71, 747 (1997).
[CrossRef]

Capmany, J.

J. Capmany, F. J. Fraille-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

Chang, R. K.

Chodorow, M.

Chu, S. T.

Crosignani, B.

B. Crosignani, A. Yariv, and P. Di Porto, Opt. Lett. 4, 251 (1986).
[CrossRef]

B. Crosignani, B. Daino, P. Di Porto, and S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

Daino, B.

B. Crosignani, B. Daino, P. Di Porto, and S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

Di Porto, P.

B. Crosignani, B. Daino, P. Di Porto, and S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

B. Crosignani, A. Yariv, and P. Di Porto, Opt. Lett. 4, 251 (1986).
[CrossRef]

Driessen, A.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and Th. J. A. Popma, Appl. Phys. Lett. 71, 747 (1997).
[CrossRef]

Dubreuil, N.

Fields, M. H.

Fraille-Pelaez, F. J.

J. Capmany, F. J. Fraille-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

Hare, J.

Haus, H. A.

Hoekstra, H. J.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and Th. J. A. Popma, Appl. Phys. Lett. 71, 747 (1997).
[CrossRef]

Islam, M. N.

M. N. Islam, Ultrafast Fiber Switching Devices (Cambridge U. Press, Cambridge, 1992), pp. 31, 39.

Knight, J. C.

Lefevre, V.

Lenz, G.

C. K. Madsen and G. Lenz, IEEE Photon. Technol. Lett. 10, 994 (1998).
[CrossRef]

Levenson, M. D.

A finesse-squared enhancement has been observed in the context of fiber-optic squeezed light generation in a fiber ring resonator. See, for instance, R. M. Shelby, M. D. Levenson, D. F. Walls, and A. Aspect, Phys. Rev. A 33, 4008 (1986)R. M. Shelby, M. D. Levenson, and S. H. Perlmutter, J. Opt. Soc. Am. B 5, 347 (1988).
[CrossRef] [PubMed]

Leventhal, D. K.

Little, B. E.

Madsen, C. K.

C. K. Madsen and G. Lenz, IEEE Photon. Technol. Lett. 10, 994 (1998).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), pp. 52–59.

Muriel, M. A.

J. Capmany, F. J. Fraille-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

Ohtsuka, Y.

Y. Ohtsuka, J. Lightwave Technol. LT-3, 378 (1985).
[CrossRef]

Pandian, G. S.

G. S. Pandian and F. E. Seraji, Proc. IEE Part J 138, 235 (1991).

Popma, Th. J. A.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and Th. J. A. Popma, Appl. Phys. Lett. 71, 747 (1997).
[CrossRef]

Popp, J.

Sandoghdar, V.

Seraji, F. E.

G. S. Pandian and F. E. Seraji, Proc. IEE Part J 138, 235 (1991).

Shaw, H. J.

Shelby, R. M.

A finesse-squared enhancement has been observed in the context of fiber-optic squeezed light generation in a fiber ring resonator. See, for instance, R. M. Shelby, M. D. Levenson, D. F. Walls, and A. Aspect, Phys. Rev. A 33, 4008 (1986)R. M. Shelby, M. D. Levenson, and S. H. Perlmutter, J. Opt. Soc. Am. B 5, 347 (1988).
[CrossRef] [PubMed]

Stokes, L. F.

van Dijk, D. R.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and Th. J. A. Popma, Appl. Phys. Lett. 71, 747 (1997).
[CrossRef]

Wabnitz, S.

B. Crosignani, B. Daino, P. Di Porto, and S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

Walls, D. F.

A finesse-squared enhancement has been observed in the context of fiber-optic squeezed light generation in a fiber ring resonator. See, for instance, R. M. Shelby, M. D. Levenson, D. F. Walls, and A. Aspect, Phys. Rev. A 33, 4008 (1986)R. M. Shelby, M. D. Levenson, and S. H. Perlmutter, J. Opt. Soc. Am. B 5, 347 (1988).
[CrossRef] [PubMed]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), pp. 52–59.

Yariv, A.

B. Crosignani, A. Yariv, and P. Di Porto, Opt. Lett. 4, 251 (1986).
[CrossRef]

Appl. Phys. Lett.

F. C. Blom, D. R. van Dijk, H. J. Hoekstra, A. Driessen, and Th. J. A. Popma, Appl. Phys. Lett. 71, 747 (1997).
[CrossRef]

IEEE J. Quantum Electron.

J. Capmany, F. J. Fraille-Pelaez, and M. A. Muriel, IEEE J. Quantum Electron. 30, 2578 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

C. K. Madsen and G. Lenz, IEEE Photon. Technol. Lett. 10, 994 (1998).
[CrossRef]

J. Lightwave Technol.

Y. Ohtsuka, J. Lightwave Technol. LT-3, 378 (1985).
[CrossRef]

Opt. Commun.

B. Crosignani, B. Daino, P. Di Porto, and S. Wabnitz, Opt. Commun. 59, 309 (1986).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A finesse-squared enhancement has been observed in the context of fiber-optic squeezed light generation in a fiber ring resonator. See, for instance, R. M. Shelby, M. D. Levenson, D. F. Walls, and A. Aspect, Phys. Rev. A 33, 4008 (1986)R. M. Shelby, M. D. Levenson, and S. H. Perlmutter, J. Opt. Soc. Am. B 5, 347 (1988).
[CrossRef] [PubMed]

Proc. IEE Part J

G. S. Pandian and F. E. Seraji, Proc. IEE Part J 138, 235 (1991).

Other

M. N. Islam, Ultrafast Fiber Switching Devices (Cambridge U. Press, Cambridge, 1992), pp. 31, 39.

Here the finesse is defined as the free spectral range divided by the full width at half-depth of the resonance peak. Applying this definition to the intensity magnification [Eq.??(3)], we calculate the finesse asF=FSRFWHD ra??1? ?21+ra?1-ra?.Here, a is the single-pass amplitude transmission and ? is the degree of coherence between fields delayed by the ring transit time (see Refs.??14 and 15, below).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995), pp. 52–59.

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Figures (4)

Fig. 1
Fig. 1

(a) Nonlinear fiber ring resonator. The circulating power exceeds the incident power by the factor 1+r/1-r, which is very large for r close to unity. (b) Switching threshold of a nonlinear Mach–Zehnder interferometer can be dramatically reduced by introduction of a nonlinear fiber ring resonator into one arm of the interferometer.

Fig. 2
Fig. 2

Effective phase shift ϕeff=argE3/E1 versus the ring single-pass phase shift ϕ for the fiber ring resonator of Fig.  1(a) for several values of R=r2. For values of R close to unity, the phase sensitivity dϕeff/dϕ can be made extremely large.

Fig. 3
Fig. 3

Transmission characteristics of (a) a standard nonlinear Mach–Zehnder interferometer and (b) the REMZ interferometer of Fig.  1(b). Note that the switching threshold of the REMZ device is lowered by 4 orders of magnitude.

Fig. 4
Fig. 4

Ring resonator dynamic transmission characteristics for a 1-ns FWHM Gaussian pulse that is incident upon two distinct fiber ring lengths (2 and 5  cm), corresponding to resonator lifetimes of 1 and 2.5  ns for a resonator of finesse equal to 10.

Equations (10)

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

E3=rE1+itE2,
E4=itE1+rE2.
E2=exp-α2LexpiβLE4aexpiϕE4.
E2E1=itaexp+iϕ1-raexp+iϕ.
M=I2I1=1-r2a21-2racosϕ+r2a2 ϕ=0,a=1 1+r1-r,
E3E1=exp+iπ+ϕa-rexp-iϕ1-raexp+iϕ.
ϕeff a=1 π+ϕ+2 arctanrsinϕ1-rcosϕ.
dϕeffdϕ=1-r2a21-2racosϕ+r2a2 ϕ=0,a=1 1+r1-r,
dϕeffdP1=dϕeffdϕdϕdP2dP2dP1 ϕ=0,a=1 2πLn2λAeff1+r1-r28Ln2πλAeffF2,
F=FSRFWHD raδ1 π21+raδ1-raδ.

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