Abstract

We describe the properties of a surface-corrugated long-period-grating fiber taper fabricated using contact optical lithography and wet etching techniques. The preservation of cylindrical symmetry in this device facilitates investigation of the modal behavior. Comparison of the measured and calculated transmission spectra reveals that the widely used coupled-mode theory is not applicable. Instead, a mode-projection model, in which modal propagation and coupling are treated separately within the grating, explains the experiments very well.

© 2008 Optical Society of America

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Corrections

W. Ding, S. R. Andrews, and S. A. Maier, "Modal coupling in surface-corrugated long-period-grating fiber tapers: erratum," Opt. Lett. 33, 1007-1007 (2008)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-33-9-1007

References

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  1. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
    [CrossRef]
  2. S. W. James and R. P. Tatam, Meas. Sci. Technol. 14, R49 (2003).
    [CrossRef]
  3. T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
    [CrossRef]
  4. J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986).
    [CrossRef]
  5. W. Ding, S. R. Andrews, T. A. Birks, and S. A. Maier, Opt. Lett. 31, 2556 (2006).
    [CrossRef]
  6. W. Ding, S. R. Andrews, and S. A. Maier, Opt. Lett. 32, 2499 (2007).
    [CrossRef]
  7. J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J. 138, 343 (1991).
  8. A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
    [CrossRef]
  9. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  10. T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, J. Lightwave Technol. 14, 2519 (1996).
    [CrossRef]
  11. G. Kakarantzas, T. A. Birks, and P. St. J. Russell, Opt. Lett. 27, 1013 (2002).
    [CrossRef]

2007 (1)

2006 (1)

2003 (1)

S. W. James and R. P. Tatam, Meas. Sci. Technol. 14, R49 (2003).
[CrossRef]

2002 (1)

1996 (2)

T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, J. Lightwave Technol. 14, 2519 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

1992 (1)

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[CrossRef]

1991 (1)

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J. 138, 343 (1991).

1986 (1)

J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986).
[CrossRef]

1983 (1)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

1973 (1)

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Andrews, S. R.

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Birks, T. A.

W. Ding, S. R. Andrews, T. A. Birks, and S. A. Maier, Opt. Lett. 31, 2556 (2006).
[CrossRef]

G. Kakarantzas, T. A. Birks, and P. St. J. Russell, Opt. Lett. 27, 1013 (2002).
[CrossRef]

T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, J. Lightwave Technol. 14, 2519 (1996).
[CrossRef]

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[CrossRef]

Black, R. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J. 138, 343 (1991).

Culverhouse, D. O.

T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, J. Lightwave Technol. 14, 2519 (1996).
[CrossRef]

Ding, W.

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Gonthier, F.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J. 138, 343 (1991).

Henry, W. M.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J. 138, 343 (1991).

J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986).
[CrossRef]

James, S. W.

S. W. James and R. P. Tatam, Meas. Sci. Technol. 14, R49 (2003).
[CrossRef]

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Kakarantzas, G.

Lacroix, S.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J. 138, 343 (1991).

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Li, Y. W.

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[CrossRef]

Love, J. D.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J. 138, 343 (1991).

J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986).
[CrossRef]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Maier, S. A.

Russell, P. St. J.

G. Kakarantzas, T. A. Birks, and P. St. J. Russell, Opt. Lett. 27, 1013 (2002).
[CrossRef]

T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, J. Lightwave Technol. 14, 2519 (1996).
[CrossRef]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Stewart, W. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J. 138, 343 (1991).

Tatam, R. P.

S. W. James and R. P. Tatam, Meas. Sci. Technol. 14, R49 (2003).
[CrossRef]

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Yariv, A.

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Electron. Lett. (1)

J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986).
[CrossRef]

IEE Proc. J. (1)

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J. 138, 343 (1991).

IEEE J. Quantum Electron. (1)

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

J. Lightwave Technol. (3)

T. A. Birks, P. St. J. Russell, and D. O. Culverhouse, J. Lightwave Technol. 14, 2519 (1996).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[CrossRef]

Meas. Sci. Technol. (1)

S. W. James and R. P. Tatam, Meas. Sci. Technol. 14, R49 (2003).
[CrossRef]

Opt. Lett. (3)

Other (1)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

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Figures (4)

Fig. 1
Fig. 1

Schematic showing the modal coupling in a surface-corrugated LPG fiber taper.

Fig. 2
Fig. 2

(a) Calculated transmission spectra of surface-corrugated LPG fiber taper according to coupled-mode theory (gray curve) and mode-projection theory (black curve). (b) Profiles of transverse electric fields.

Fig. 3
Fig. 3

(a) Optical micrograph of the LPG fiber taper. (b) Measured (open circles) and calculated (curves) transmission spectra of the sample. The black curve takes into account the influence of the Ge-doped core, whereas the gray one does not. The right-hand attenuation dips of the calculated curves are marked with arrows for clarity.

Fig. 4
Fig. 4

Resonant wavelengths as function of taper diameter and grating period. The filled circles show the experimentally measured values, and the curves show the predictions of mode-projection theory.

Equations (9)

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d A j ( z ) d z = l C j l ( z ) A l ( z ) exp [ i ( β l β j ) z ] ( uncorrugated ) ,
C j l ( z ) = { 0 A i k 0 2 Δ ε r 4 β j [ e ̂ l × h ̂ j * ] a ̂ z d A ( corrugated ) , }
[ E 1 ( T , S ) ( z + Δ z ) E 2 ( T , S ) ( z + Δ z ) E 3 ( T , S ) ( z + Δ z ) ] = [ δ j l exp ( i β j ( T , S ) Δ z ) ] [ E 1 ( T , S ) ( z ) E 2 ( T , S ) ( z ) E 3 ( T , S ) ( z ) ] ,
[ E 1 ( S , T ) ( z n ) E 2 ( S , T ) ( z n ) E 3 ( S , T ) ( z n ) ] = [ p j l ( S T , T S ) ] [ E 1 ( T , S ) ( z n ) E 2 ( T , S ) ( z n ) E 3 ( T , S ) ( z n ) ] ,
p j l ( S T , T S ) = 2 1 A ( e ̂ l ( T , S ) × h ̂ j ( S , T ) * ) a ̂ z d A .
M = [ M ( T ) M ( T S ) M ( S ) M ( S T ) ] N ,
M ( S T , T S ) = [ p j l ( S T , T S ) ] ,
M ( T , S ) = [ δ j l exp ( i β j ( T , S ) Λ 2 ) ] ,
{ λ R = [ n j ( T ) n l ( T ) ] Λ ( coupled mode ) λ R = [ n j ( T ) n l ( T ) + n j ( S ) n l ( S ) ] Λ 2 ( mode projection ) , }

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