Abstract

The theory of optical fiber loop and ring resonators with multiple couplers is generalized. In Part 1 of the paper, general expressions for the circulating (resonant) and output fields and intensities of various configurations of such fiber loop and ring resonators are derived and tabulated. Computed results are presented as graphs. Special characteristics and possible applications of these loop and ring resonators are discussed. For example, they can be used as frequency selective beam splitters. Performance parameters of these loops and rings such as finesses, peak transmission, and contrast, etc. are treated in Part 2 of the paper.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. F. Stokes, M. Chodorow, H. J. Shaw, “All-Single–Mode Fiber Resonator,” Opt. Lett. 7, 288–290 (1982).
    [Crossref] [PubMed]
  2. J. E. Bowers, S. A. Newton, W. V. Sorin, H. J. Shaw, “Filter Resonance of Single-Mode Fibre Recirculating Delay Lines,” Electron. Lett. 18, 110–111 (1982).
    [Crossref]
  3. I. D. Miller, D. B. Mortimore, P. Urquhart, B. J. Ainslie, S. P. Craig, C. A. Millar, D. B. Payne, “A Nd3+-Doped cw Fiber Laser Using All-Fiber Reflectors,” Appl. Opt. 26, 2197–2201 (1987).
    [Crossref] [PubMed]
  4. P. Urquhart, “Compound Optical-Fiber-Based Resonators,” J. Opt. Soc. Am. A 5, 803–812 (1988).
    [Crossref]
  5. C. A. Millar, D. Harvey, P. Urquhart, “Fiber Reflection Mach-Zehnder Interferometer,” Opt. Commun. 70, 304–308 (1989).
    [Crossref]
  6. Y. H. Ja, “Optical Fibre Loop Resonators with Double Couplers,” Opt. Commun. 75, 239–245 (1990).
    [Crossref]
  7. T. C. Starkey, “High-Performance Bend-Resistant Fiber,” Photonics Spectra 23, 119–121 (1989).

1990 (1)

Y. H. Ja, “Optical Fibre Loop Resonators with Double Couplers,” Opt. Commun. 75, 239–245 (1990).
[Crossref]

1989 (2)

T. C. Starkey, “High-Performance Bend-Resistant Fiber,” Photonics Spectra 23, 119–121 (1989).

C. A. Millar, D. Harvey, P. Urquhart, “Fiber Reflection Mach-Zehnder Interferometer,” Opt. Commun. 70, 304–308 (1989).
[Crossref]

1988 (1)

1987 (1)

1982 (2)

L. F. Stokes, M. Chodorow, H. J. Shaw, “All-Single–Mode Fiber Resonator,” Opt. Lett. 7, 288–290 (1982).
[Crossref] [PubMed]

J. E. Bowers, S. A. Newton, W. V. Sorin, H. J. Shaw, “Filter Resonance of Single-Mode Fibre Recirculating Delay Lines,” Electron. Lett. 18, 110–111 (1982).
[Crossref]

Ainslie, B. J.

Bowers, J. E.

J. E. Bowers, S. A. Newton, W. V. Sorin, H. J. Shaw, “Filter Resonance of Single-Mode Fibre Recirculating Delay Lines,” Electron. Lett. 18, 110–111 (1982).
[Crossref]

Chodorow, M.

Craig, S. P.

Harvey, D.

C. A. Millar, D. Harvey, P. Urquhart, “Fiber Reflection Mach-Zehnder Interferometer,” Opt. Commun. 70, 304–308 (1989).
[Crossref]

Ja, Y. H.

Y. H. Ja, “Optical Fibre Loop Resonators with Double Couplers,” Opt. Commun. 75, 239–245 (1990).
[Crossref]

Millar, C. A.

Miller, I. D.

Mortimore, D. B.

Newton, S. A.

J. E. Bowers, S. A. Newton, W. V. Sorin, H. J. Shaw, “Filter Resonance of Single-Mode Fibre Recirculating Delay Lines,” Electron. Lett. 18, 110–111 (1982).
[Crossref]

Payne, D. B.

Shaw, H. J.

L. F. Stokes, M. Chodorow, H. J. Shaw, “All-Single–Mode Fiber Resonator,” Opt. Lett. 7, 288–290 (1982).
[Crossref] [PubMed]

J. E. Bowers, S. A. Newton, W. V. Sorin, H. J. Shaw, “Filter Resonance of Single-Mode Fibre Recirculating Delay Lines,” Electron. Lett. 18, 110–111 (1982).
[Crossref]

Sorin, W. V.

J. E. Bowers, S. A. Newton, W. V. Sorin, H. J. Shaw, “Filter Resonance of Single-Mode Fibre Recirculating Delay Lines,” Electron. Lett. 18, 110–111 (1982).
[Crossref]

Starkey, T. C.

T. C. Starkey, “High-Performance Bend-Resistant Fiber,” Photonics Spectra 23, 119–121 (1989).

Stokes, L. F.

Urquhart, P.

Appl. Opt. (1)

Electron. Lett. (1)

J. E. Bowers, S. A. Newton, W. V. Sorin, H. J. Shaw, “Filter Resonance of Single-Mode Fibre Recirculating Delay Lines,” Electron. Lett. 18, 110–111 (1982).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

C. A. Millar, D. Harvey, P. Urquhart, “Fiber Reflection Mach-Zehnder Interferometer,” Opt. Commun. 70, 304–308 (1989).
[Crossref]

Y. H. Ja, “Optical Fibre Loop Resonators with Double Couplers,” Opt. Commun. 75, 239–245 (1990).
[Crossref]

Opt. Lett. (1)

Photonics Spectra (1)

T. C. Starkey, “High-Performance Bend-Resistant Fiber,” Photonics Spectra 23, 119–121 (1989).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Type II single fiber loop with triple couplers.

Fig. 2
Fig. 2

Computed dependence of (a) (relative) circulating intensity Ic/I1 and (b)–(d) output intensities I01/I1, I02/I1, and I03/I1 of the type II DCFL, as functions of the fiber loop parameter βl = β(l1 + l2 + l3) with K2, the intensity coupling coefficient of coupler 2 as a parameter, and a1 = a2 = a3 = 0.98, t1 = t2 = 0.995, and t = 0.99.

Tables (3)

Tables Icon

Table I Schematic of a Single Fiber Loop and Ring with (a) One and (b) Two Couplers and Formulas for the (Relative) Circulating and Output Fields and Intensities

Tables Icon

Table II Schematic of a Single Fiber Loop and Ring with Three (N = 3) Couplers and Formulas for the (Relative) Circulating and Output Fields and Intensities

Tables Icon

Table III Generalized Formulas for Resonant Conditions, (Relative) Circulating and Output Fields, and Intensities of a Single Fiber Loop and Ring with N Couplers

Equations (34)

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

E 3 = a 1 [ ( 1 - K 1 ) 1 / 2 E 1 + j K 1 1 / 2 E 2 ] ,
E 4 = a 1 [ j K 1 1 / 2 E 1 + ( 1 - K 1 ) 1 / 2 E 2 ] ,
E 7 = a 2 [ ( 1 - K 2 ) 1 / 2 E 5 + j K 2 1 / 2 E 6 ] ,
E 8 = a 2 [ j K 2 1 / 2 E 5 + ( 1 - K 2 ) 1 / 2 E 6 ] ,
E 11 = a 3 [ ( 1 - K 3 ) 1 / 2 E 9 + j K 3 1 / 2 E 10 ] ,
E 12 = a 3 [ j K 3 1 / 2 E 9 + ( 1 - K 3 ) 1 / 2 E 10 ] .
E 1 = E in ,
E 5 = E 3 exp [ ( - α + j β ) l 1 ] = E 3 L 1 ,
E 9 = E 8 exp [ ( - α + j β ) l 2 ] = E 8 L 2 ,
E 2 = E 11 exp [ ( - α + j β ) l 3 ] = E 11 L 3 ,
E 6 = 0 ,
E 10 = 0.
E 7 = a 2 ( 1 - K 2 ) 1 / 2 L 1 E 3 ,
E 8 = a 2 j K 2 1 / 2 L 1 E 3 ,
E 11 = a 3 ( 1 - K 3 ) 1 / 2 L 2 E 8 ,
E 12 = a 3 j K 3 1 / 2 L 2 E 8 .
E 3 = a 1 ( 1 - K 1 ) 1 / 2 E 1 E d .
E d = 1 + A [ K 1 K 2 ( 1 - K 3 ) ] 1 / 2 L ,
A = a 1 a 2 a 3 = i = 1 N a i ,
L = L 1 L 2 L 3 = i = 1 N L i ,             N = 3.
E 7 = a 1 a 2 [ ( 1 - K 1 ) ( 1 - K 2 ) ] 1 / 2 L 1 E 1 E d .
E 12 = - A [ ( 1 - K 1 ) K 2 K 3 ] 1 / 2 L 1 L 2 E 1 E d .
E 4 = j K 1 1 / 2 + j A [ K 2 ( 1 - K 3 ) ] 1 / 2 L E d · a 1 E 1 .
I 3 I 1 = | E 3 E 1 | 2 = a 1 2 ( 1 - K 1 ) I d ,
I d = 1 + A 2 K 1 K 2 ( 1 - K 3 ) t 2 + 2 A [ K 1 K 2 ( 1 - K 3 ) ] 1 / 2 t cos β l ,
t = exp - α l 1 · exp - α l 2 · exp - α l 3 = t 1 t 2 t 3 ( = i = 1 N t i ) ,
l = l 1 + l 2 + l 3 ( = i = 1 N l i )
I 01 I 1 = I 4 I 1 = | E 4 E 1 | 2 = a 1 2 · K 1 + 2 A [ K 1 K 2 ( 1 - K 3 ) ] 1 / 2 t · cos β l + A 2 K 2 ( 1 - K 3 ) t 2 I d ,
I 02 I 1 = I 7 I 1 = | E 7 E 1 | 2 = a 1 2 a 2 2 t 1 2 ( 1 - K 1 ) ( 1 - K 2 ) I d ,
I 03 I 1 = I 12 I 1 = | E 12 E 1 | 2 = A 2 ( 1 - K 1 ) K 2 K 3 t 1 2 t 2 2 I d .
i = n i = m K i = 1 if m < n .
K 3 = 1 - K 2 K 2 t 2 2 a 3 2 .
1 - K n = 1 - K n - 1 K n - 1 t n - 1 2 a n 2             for N > n 3 ,
K N = 1 - K N - 1 K N - 1 t N - 1 2 a N 2 .

Metrics