Abstract

We demonstrate that grating tilt is an important adjustable parameter that can be utilized in addition to the more familiar parameters of grating length and index change to tune the spectral shapes of fiber phase gratings designed to perform demanding filter applications through guided-mode to radiation-mode coupling loss. A comparison is made between calculated transmission spectra obtained from a coupled-mode-theory analysis and measured spectra obtained from strong gratings written by ultraviolet irradiation of deuterium-sensitized fiber with grating tilt angles ranging from 0° to 15°. We show that good agreement is obtained between the experimental measurements and the theoretical predictions.

© 1995 Optical Society of America

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  1. G. Meltz, W. W. Morey, W. H. Glenn, Opt. Lett. 14, 823 (1989).
    [CrossRef] [PubMed]
  2. V. Mizrahi, J. E. Sipe, J. Lightwave Technol. 11, 1513 (1993).
    [CrossRef]
  3. V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
    [CrossRef]
  4. R. Kashyap, R. Wyatt, R. J. Campbell, Electron. Lett. 29, 154 (1993).
    [CrossRef]
  5. M. C. Farries, C. M. Ragdale, D. C. J. Reid, Electron. Lett. 28, 487 (1992). For phase-grating implementations see M. C. Farries, K. Sugden, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, Electron. Lett. 30, 891 (1994).
    [CrossRef]
  6. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, in Optical Fiber Communication Conference, Vol. 4 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD4.
  7. G. Meltz, W. W. Morey, W. H. Glenn, in Optical Fiber Communication Conference, Vol. 1 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper TUG1.
  8. T. Erdogan, J. E. Sipe, “Tilted fiber phase gratings,” submitted toJ. Opt. Soc. Am. A.
  9. P. J. Lemaire, R. M. Atkins, V. Mizrahi, K. L. Walker, K. S. Kranz, W. A. Reed, Electron. Lett. 29, 1191 (1993).
    [CrossRef]

1994

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

1993

R. Kashyap, R. Wyatt, R. J. Campbell, Electron. Lett. 29, 154 (1993).
[CrossRef]

V. Mizrahi, J. E. Sipe, J. Lightwave Technol. 11, 1513 (1993).
[CrossRef]

P. J. Lemaire, R. M. Atkins, V. Mizrahi, K. L. Walker, K. S. Kranz, W. A. Reed, Electron. Lett. 29, 1191 (1993).
[CrossRef]

1992

M. C. Farries, C. M. Ragdale, D. C. J. Reid, Electron. Lett. 28, 487 (1992). For phase-grating implementations see M. C. Farries, K. Sugden, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, Electron. Lett. 30, 891 (1994).
[CrossRef]

1989

Atkins, R. M.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, K. L. Walker, K. S. Kranz, W. A. Reed, Electron. Lett. 29, 1191 (1993).
[CrossRef]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, in Optical Fiber Communication Conference, Vol. 4 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD4.

Cabot, S.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

Campbell, R. J.

R. Kashyap, R. Wyatt, R. J. Campbell, Electron. Lett. 29, 154 (1993).
[CrossRef]

DiGiovanni, D. J.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

Erdogan, T.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, in Optical Fiber Communication Conference, Vol. 4 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD4.

T. Erdogan, J. E. Sipe, “Tilted fiber phase gratings,” submitted toJ. Opt. Soc. Am. A.

Farries, M. C.

M. C. Farries, C. M. Ragdale, D. C. J. Reid, Electron. Lett. 28, 487 (1992). For phase-grating implementations see M. C. Farries, K. Sugden, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, Electron. Lett. 30, 891 (1994).
[CrossRef]

Glenn, W. H.

G. Meltz, W. W. Morey, W. H. Glenn, Opt. Lett. 14, 823 (1989).
[CrossRef] [PubMed]

G. Meltz, W. W. Morey, W. H. Glenn, in Optical Fiber Communication Conference, Vol. 1 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper TUG1.

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, in Optical Fiber Communication Conference, Vol. 4 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD4.

Kashyap, R.

R. Kashyap, R. Wyatt, R. J. Campbell, Electron. Lett. 29, 154 (1993).
[CrossRef]

Kosinski, S. G.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

Kranz, K. S.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, K. L. Walker, K. S. Kranz, W. A. Reed, Electron. Lett. 29, 1191 (1993).
[CrossRef]

Lemaire, P. J.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

P. J. Lemaire, R. M. Atkins, V. Mizrahi, K. L. Walker, K. S. Kranz, W. A. Reed, Electron. Lett. 29, 1191 (1993).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, in Optical Fiber Communication Conference, Vol. 4 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD4.

MacDonald, W. M.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

Meltz, G.

G. Meltz, W. W. Morey, W. H. Glenn, Opt. Lett. 14, 823 (1989).
[CrossRef] [PubMed]

G. Meltz, W. W. Morey, W. H. Glenn, in Optical Fiber Communication Conference, Vol. 1 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper TUG1.

Mizrahi, V.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

P. J. Lemaire, R. M. Atkins, V. Mizrahi, K. L. Walker, K. S. Kranz, W. A. Reed, Electron. Lett. 29, 1191 (1993).
[CrossRef]

V. Mizrahi, J. E. Sipe, J. Lightwave Technol. 11, 1513 (1993).
[CrossRef]

Morey, W. W.

G. Meltz, W. W. Morey, W. H. Glenn, Opt. Lett. 14, 823 (1989).
[CrossRef] [PubMed]

G. Meltz, W. W. Morey, W. H. Glenn, in Optical Fiber Communication Conference, Vol. 1 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper TUG1.

Ragdale, C. M.

M. C. Farries, C. M. Ragdale, D. C. J. Reid, Electron. Lett. 28, 487 (1992). For phase-grating implementations see M. C. Farries, K. Sugden, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, Electron. Lett. 30, 891 (1994).
[CrossRef]

Reed, W. A.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, K. L. Walker, K. S. Kranz, W. A. Reed, Electron. Lett. 29, 1191 (1993).
[CrossRef]

Reid, D. C. J.

M. C. Farries, C. M. Ragdale, D. C. J. Reid, Electron. Lett. 28, 487 (1992). For phase-grating implementations see M. C. Farries, K. Sugden, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, Electron. Lett. 30, 891 (1994).
[CrossRef]

Sipe, J. E.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

V. Mizrahi, J. E. Sipe, J. Lightwave Technol. 11, 1513 (1993).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, in Optical Fiber Communication Conference, Vol. 4 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD4.

T. Erdogan, J. E. Sipe, “Tilted fiber phase gratings,” submitted toJ. Opt. Soc. Am. A.

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, in Optical Fiber Communication Conference, Vol. 4 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD4.

Walker, K. L.

P. J. Lemaire, R. M. Atkins, V. Mizrahi, K. L. Walker, K. S. Kranz, W. A. Reed, Electron. Lett. 29, 1191 (1993).
[CrossRef]

Wyatt, R.

R. Kashyap, R. Wyatt, R. J. Campbell, Electron. Lett. 29, 154 (1993).
[CrossRef]

Electron. Lett.

V. Mizrahi, T. Erdogan, D. J. DiGiovanni, P. J. Lemaire, W. M. MacDonald, S. G. Kosinski, S. Cabot, J. E. Sipe, Electron. Lett. 30, 780 (1994).
[CrossRef]

R. Kashyap, R. Wyatt, R. J. Campbell, Electron. Lett. 29, 154 (1993).
[CrossRef]

M. C. Farries, C. M. Ragdale, D. C. J. Reid, Electron. Lett. 28, 487 (1992). For phase-grating implementations see M. C. Farries, K. Sugden, D. C. J. Reid, I. Bennion, A. Molony, M. J. Goodwin, Electron. Lett. 30, 891 (1994).
[CrossRef]

P. J. Lemaire, R. M. Atkins, V. Mizrahi, K. L. Walker, K. S. Kranz, W. A. Reed, Electron. Lett. 29, 1191 (1993).
[CrossRef]

J. Lightwave Technol.

V. Mizrahi, J. E. Sipe, J. Lightwave Technol. 11, 1513 (1993).
[CrossRef]

Opt. Lett.

Other

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, in Optical Fiber Communication Conference, Vol. 4 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD4.

G. Meltz, W. W. Morey, W. H. Glenn, in Optical Fiber Communication Conference, Vol. 1 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper TUG1.

T. Erdogan, J. E. Sipe, “Tilted fiber phase gratings,” submitted toJ. Opt. Soc. Am. A.

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Figures (3)

Fig. 1
Fig. 1

Diagram of a step-index optical fiber showing a tilted fiber phase grating. Also shown are the rays representing two UV beams incident upon the fiber during grating writing and their associated angles inside and outside the fiber.

Fig. 2
Fig. 2

(a) Experimentally measured transmission loss spectra versus grating tilt angle for gratings written with tilt angles of 0 to 15° and (b) corresponding calculated transmission loss spectra, where loss that is due to Bragg scattering has been excluded.

Fig. 3
Fig. 3

Measured (circles) and calculated (solid curve) wavelength of minimum transmission versus tilt angle, where loss that is due to Bragg scattering has been excluded.

Equations (5)

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

2 α ext = arcsin [ n cl sin ( α + θ ) ] + arcsin [ n cl sin ( α - θ ) ] , θ ext = 1 2 arcsin [ n cl sin ( α + θ ) ] - 1 2 arcsin [ n cl sin ( α - θ ) ] .
sin α = ( n eff / n cl ) ( λ UV / λ B 0 cos θ ) ,
d a + ( z ) d z = - β ¯ α ¯ ( z ) a + ( z ) ,
α ¯ ( z ) = κ 2 ( z ) q β π ρ β ¯ ν ρ q ; 01 - + 2 .
ν α q ; α q - + = n ¯ c ɛ 0 2 1 P α q P α q core E α q - * ( x , y ) × exp ( - 2 i 2 π Λ x sin θ ) E α q + ( x , y ) d x d y .

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