Abstract

Continuous-wave laser oscillation with a long optical-fiber resonator has been observed. The fiber resonators that were examined were 1.65, 11.3, and 101 m long, and longitudinal self-beat spectra of laser oscillations were confirmed with a 1.15-μm He–Ne laser; the observed frequencies were in good agreement with the calculated ones. By using a spectrum analyzer, the spectral amplitude was found to be modulated, which is attributable to the fact that a complex Fabry–Perot resonator was formed by reflections on a lens and an input portion of the optical fiber.

© 1982 Optical Society of America

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References

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  1. N. Niizeki, “Recent progress in glass fibers for optical communication,” Jpn. J. Appl. Phys. 20, 1347–1360 (1980).
    [Crossref]
  2. T. Yoshino, “Fiber Fabry–Perot interferometers,” presented at the third International Conference on Integrated Optics and Optical Fiber Communication, San Francisco, California,April 1981.
  3. S. J. Petuchowski, T. G. Giallorenzi, and S. K. Sheem, “A sensitive fiber-optic Fabry–Perot interferometer,” IEEE J. Quantum Electron. QE-17, 2168–2170 (1981).
    [Crossref]
  4. C. J. Koester and E. Snitzer, “Amplification in a fiber laser,” Appl. Opt. 3, 1182–1186 (1964).
    [Crossref]
  5. C. J. Koester, “Laser action by enhanced total internal reflection,” IEEE J. Quantum Electron. QE-2, 580–584 (1966).
    [Crossref]
  6. A. C. Beck, “An experimental gas lens optical transmission line,” IEEE J. Microwave Theory Tech. MTT-15, 433–434 (1967).
    [Crossref]
  7. K. Shimoda, “Theory of masers for higher frequency,” Sci. Pap. Inst. Phys. Chem. Res. Jpn. 55, 1–6 (1961).
  8. K. Shimoda, T. Yajima, Y. Ueda, T. Shimizu, and T. Kasuya, Quantum Electronics, 2nd ed. (Syokabo, Tokyo, 1972), Chaps. 1 and 2.
  9. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chaps. 7–9.
  10. H. Takuma, Introduction to Quantum Electronics, 2nd ed. (Baifukan, Tokyo, 1972), Chaps.2–4.
  11. A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
    [Crossref]
  12. G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
    [Crossref]
  13. P. W. Smith, “Stabilized, single-frequency output from a long laser cavity,” IEEE J. Quantum Electron. QE-1, 343–348 (1965).
    [Crossref]
  14. D. Gloge, E. L. Chinnock, and D. H. Ring, “Direct measurement of the (baseband) frequency response of multimode fibers,” Appl. Opt. 11, 1534–1538 (1972).
    [Crossref] [PubMed]

1981 (1)

S. J. Petuchowski, T. G. Giallorenzi, and S. K. Sheem, “A sensitive fiber-optic Fabry–Perot interferometer,” IEEE J. Quantum Electron. QE-17, 2168–2170 (1981).
[Crossref]

1980 (1)

N. Niizeki, “Recent progress in glass fibers for optical communication,” Jpn. J. Appl. Phys. 20, 1347–1360 (1980).
[Crossref]

1972 (1)

1967 (1)

A. C. Beck, “An experimental gas lens optical transmission line,” IEEE J. Microwave Theory Tech. MTT-15, 433–434 (1967).
[Crossref]

1966 (1)

C. J. Koester, “Laser action by enhanced total internal reflection,” IEEE J. Quantum Electron. QE-2, 580–584 (1966).
[Crossref]

1965 (1)

P. W. Smith, “Stabilized, single-frequency output from a long laser cavity,” IEEE J. Quantum Electron. QE-1, 343–348 (1965).
[Crossref]

1964 (1)

1961 (3)

K. Shimoda, “Theory of masers for higher frequency,” Sci. Pap. Inst. Phys. Chem. Res. Jpn. 55, 1–6 (1961).

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
[Crossref]

Beck, A. C.

A. C. Beck, “An experimental gas lens optical transmission line,” IEEE J. Microwave Theory Tech. MTT-15, 433–434 (1967).
[Crossref]

Boyd, G. D.

G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
[Crossref]

Chinnock, E. L.

Fox, A. G.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

Giallorenzi, T. G.

S. J. Petuchowski, T. G. Giallorenzi, and S. K. Sheem, “A sensitive fiber-optic Fabry–Perot interferometer,” IEEE J. Quantum Electron. QE-17, 2168–2170 (1981).
[Crossref]

Gloge, D.

Gordon, J. P.

G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
[Crossref]

Kasuya, T.

K. Shimoda, T. Yajima, Y. Ueda, T. Shimizu, and T. Kasuya, Quantum Electronics, 2nd ed. (Syokabo, Tokyo, 1972), Chaps. 1 and 2.

Koester, C. J.

C. J. Koester, “Laser action by enhanced total internal reflection,” IEEE J. Quantum Electron. QE-2, 580–584 (1966).
[Crossref]

C. J. Koester and E. Snitzer, “Amplification in a fiber laser,” Appl. Opt. 3, 1182–1186 (1964).
[Crossref]

Li, T.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

Niizeki, N.

N. Niizeki, “Recent progress in glass fibers for optical communication,” Jpn. J. Appl. Phys. 20, 1347–1360 (1980).
[Crossref]

Petuchowski, S. J.

S. J. Petuchowski, T. G. Giallorenzi, and S. K. Sheem, “A sensitive fiber-optic Fabry–Perot interferometer,” IEEE J. Quantum Electron. QE-17, 2168–2170 (1981).
[Crossref]

Ring, D. H.

Sheem, S. K.

S. J. Petuchowski, T. G. Giallorenzi, and S. K. Sheem, “A sensitive fiber-optic Fabry–Perot interferometer,” IEEE J. Quantum Electron. QE-17, 2168–2170 (1981).
[Crossref]

Shimizu, T.

K. Shimoda, T. Yajima, Y. Ueda, T. Shimizu, and T. Kasuya, Quantum Electronics, 2nd ed. (Syokabo, Tokyo, 1972), Chaps. 1 and 2.

Shimoda, K.

K. Shimoda, “Theory of masers for higher frequency,” Sci. Pap. Inst. Phys. Chem. Res. Jpn. 55, 1–6 (1961).

K. Shimoda, T. Yajima, Y. Ueda, T. Shimizu, and T. Kasuya, Quantum Electronics, 2nd ed. (Syokabo, Tokyo, 1972), Chaps. 1 and 2.

Smith, P. W.

P. W. Smith, “Stabilized, single-frequency output from a long laser cavity,” IEEE J. Quantum Electron. QE-1, 343–348 (1965).
[Crossref]

Snitzer, E.

Takuma, H.

H. Takuma, Introduction to Quantum Electronics, 2nd ed. (Baifukan, Tokyo, 1972), Chaps.2–4.

Ueda, Y.

K. Shimoda, T. Yajima, Y. Ueda, T. Shimizu, and T. Kasuya, Quantum Electronics, 2nd ed. (Syokabo, Tokyo, 1972), Chaps. 1 and 2.

Yajima, T.

K. Shimoda, T. Yajima, Y. Ueda, T. Shimizu, and T. Kasuya, Quantum Electronics, 2nd ed. (Syokabo, Tokyo, 1972), Chaps. 1 and 2.

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chaps. 7–9.

Yoshino, T.

T. Yoshino, “Fiber Fabry–Perot interferometers,” presented at the third International Conference on Integrated Optics and Optical Fiber Communication, San Francisco, California,April 1981.

Appl. Opt. (2)

Bell Syst. Tech. J. (2)

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
[Crossref]

IEEE J. Microwave Theory Tech. (1)

A. C. Beck, “An experimental gas lens optical transmission line,” IEEE J. Microwave Theory Tech. MTT-15, 433–434 (1967).
[Crossref]

IEEE J. Quantum Electron. (3)

C. J. Koester, “Laser action by enhanced total internal reflection,” IEEE J. Quantum Electron. QE-2, 580–584 (1966).
[Crossref]

P. W. Smith, “Stabilized, single-frequency output from a long laser cavity,” IEEE J. Quantum Electron. QE-1, 343–348 (1965).
[Crossref]

S. J. Petuchowski, T. G. Giallorenzi, and S. K. Sheem, “A sensitive fiber-optic Fabry–Perot interferometer,” IEEE J. Quantum Electron. QE-17, 2168–2170 (1981).
[Crossref]

Jpn. J. Appl. Phys. (1)

N. Niizeki, “Recent progress in glass fibers for optical communication,” Jpn. J. Appl. Phys. 20, 1347–1360 (1980).
[Crossref]

Sci. Pap. Inst. Phys. Chem. Res. Jpn. (1)

K. Shimoda, “Theory of masers for higher frequency,” Sci. Pap. Inst. Phys. Chem. Res. Jpn. 55, 1–6 (1961).

Other (4)

K. Shimoda, T. Yajima, Y. Ueda, T. Shimizu, and T. Kasuya, Quantum Electronics, 2nd ed. (Syokabo, Tokyo, 1972), Chaps. 1 and 2.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), Chaps. 7–9.

H. Takuma, Introduction to Quantum Electronics, 2nd ed. (Baifukan, Tokyo, 1972), Chaps.2–4.

T. Yoshino, “Fiber Fabry–Perot interferometers,” presented at the third International Conference on Integrated Optics and Optical Fiber Communication, San Francisco, California,April 1981.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for laser oscillation with an ultralong optical-fiber cavity.

Fig. 2
Fig. 2

Relations between (a) Lf(max) and r1r2R2 and (b) Lf(max) and 2α, for variations of a laser medium length La.

Fig. 3
Fig. 3

Self-beat spectrum of laser oscillation without a fiber cavity. Trace (a) is expanded in trace (b), where Δf is equal to 88.0 MHz.

Fig. 4
Fig. 4

Self-beat spectrum of the laser oscillation with a 1.65-m fiber cavity. The spectrum in trace (a) is expanded in trace (b), where Δf is equal to 34.0 MHz.

Fig. 5
Fig. 5

Self-beat spectrum of the oscillation with a 11.3-m fiber cavity. The spectrum shown in trace (a) is expanded in traces (b) and (c), where Δf is equal to 8.2 MHz.

Fig. 6
Fig. 6

Self-beat spectrum of the laser oscillation with a 101-m fiber cavity. The spectrum shown in trace (a) is expanded in traces (b) and (c), which are further resolved in traces (d) and (e), where Δf is equal to 1.0 MHz.

Fig. 7
Fig. 7

Resonant modes of a complex laser cavity. Optical spectrum (4) is a superposition of three spectrum components (1)–(3). (a), naLa + LgnfLf; (b), naLa + LgnfLf, (c), naLa + LgnfLf.

Tables (1)

Tables Icon

Table 1 Comparisons between Fiber Lengths and Calculated Ones Using the Observed Δf

Equations (22)

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( r 1 r 2 ) 1 / 2 R exp { 2 i k 0 [ n a ( ω ) L a + L g + n f ( ω ) L f ] } × exp { 2 [ g f ( ω ) L a α ( ω ) L f ] } = 1 ,
n a ( ω ) n ( 1 + χ ( ω ) 2 n 2 )
g f ( ω ) k 0 χ ( ω ) 2 n = n π | μ | 2 ω 0 Δ N 2 c g ( ω ω 0 ) ,
N F = a 2 / d λ ,
Q = 2 ( n a L a + L g + n f L f ) ω c [ 4 α L f + ln ( 1 / r 1 r 2 R 2 ) ] .
Δ P c = ω Q ( U a V a + U f V f ) ,
Δ P e = Δ N π | μ | 2 ω Δ ω eff U a V a ,
Δ N th = Δ ω eff π | μ | 2 Q ( 1 + U f V f U a V a ) .
Δ N th c Δ ω eff π | μ | 2 ω [ 4 α L f + ln ( 1 / r 1 r 2 R 2 ) ] 2 n a L a .
Δ N 0 = c Δ ω eff π | μ | 2 ω ln ( 1 / r 01 r 02 ) 2 n a L a ,
( r 01 r 02 ) 1 / 2 exp [ 2 g 0 ( ω ) L a ] = 1 ,
η = Δ N th Δ N 0 = 4 α L f + ln ( 1 / r 1 r 2 R 2 ) ln ( 1 / r 01 r 02 ) .
L f ( max ) = g f ( ω ) α ( ω ) L a + 1 2 α ( ω ) ln [ ( r 1 r 2 ) 1 / 2 R ] .
g f ( ω ) = n π | μ | 2 ω 0 Δ N th 2 c Δ ω eff = Δ N th Δ N 0 ln (1 / r 01 r 02 ) 4 L a ,
η = 1 ,
L f ( max ) = 1 4 α ln ( r 1 r 2 R 2 r 01 r 02 ) .
k 0 { n [ 1 + χ ( ω ) 2 n 2 ] L a + L g + n f L f } = q π ,
Q n 2 χ ( ω ) ( 1 + n f L f n a L a )
ω ω c ( ω ω 0 ) Δ ω c / Δ ω ,
ω c = q π c / ( n a L a + L g + n f L f ) ,
Δ ω c = ω c 2 Q ω 2 Q .
Δ f = c / 2 ( n a L a + L g + n f L f ) c / 2 n f L f , for L a L f .