Abstract

Fourier analysis of multibeam interference shows that the total electric field and relative time delay of the beams form a Fourier-transform pair. Fourier-analysis-based multibeam interference analysis and device design is discussed in detail. The principle of the proposed segment-deformable-mirror-based adaptive spectrum attenuator is illustrated.

© 2005 Optical Society of America

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  1. C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.
  2. N. A. Riza, “Fault-tolerant fiber-optical beam control modules,” U.S. patent6,222,954 (24April2001).
  3. A. Vladimir, B. Bradley, D. Bishop, G. Clinton, S. Lawrence, R. Rene, “Optical attenuator,” U.S. patent6,173,105 (9January2001).
  4. E. E. Bergmann, D. Bishop, “Micro-mechanical variable optical attenuator,” U.S. patent6,163,643 (19December2000).
  5. R. R. Abbott, G. W. Berkstresser, C. D. Brandle, V. J. Fratello, S. J. Licht, “Article comprising a variable optical attenuator,” U.S. patent5,978,135 (2November1999).
  6. S. H. Huang, X. Y. Zhou, S. M. Hwang, A. E. Willner, Z. Bao, D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5 Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8, 1243–1245 (1996).
    [CrossRef]
  7. H. S. Kim, S. H. Yun, H. K. Kim, N. Park, B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35 nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
    [CrossRef]
  8. K. Inoue, T. Kominato, H. Toba, “Tunable gain equalization using a Mach–Zehnder optical filter in multistage fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 718–720 (1991).
    [CrossRef]
  9. M. Zirngibl, C. H. Joyner, B. Glance, “Digitally tunable channel dropping filter/equalizer based on waveguide grating router and optical amplifier integration,” IEEE Photonics Technol. Lett. 6, 513–515 (1994).
    [CrossRef]
  10. C. R. Doerr, C. H. Joyner, L. W. Stulz, “Integrated WDM dynamic power equalizer with potentially low insertion loss,” IEEE Photonics Technol. Lett. 10, 1443–1445 (1998).
    [CrossRef]
  11. M. C. Parker, A. D. Cohen, R. J. Mears, “Dynamic holographic spectral equalization for WDM,” IEEE Photonics Technol. Lett. 9, 529–531 (1997).
    [CrossRef]

1998 (2)

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35 nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[CrossRef]

C. R. Doerr, C. H. Joyner, L. W. Stulz, “Integrated WDM dynamic power equalizer with potentially low insertion loss,” IEEE Photonics Technol. Lett. 10, 1443–1445 (1998).
[CrossRef]

1997 (1)

M. C. Parker, A. D. Cohen, R. J. Mears, “Dynamic holographic spectral equalization for WDM,” IEEE Photonics Technol. Lett. 9, 529–531 (1997).
[CrossRef]

1996 (1)

S. H. Huang, X. Y. Zhou, S. M. Hwang, A. E. Willner, Z. Bao, D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5 Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8, 1243–1245 (1996).
[CrossRef]

1994 (1)

M. Zirngibl, C. H. Joyner, B. Glance, “Digitally tunable channel dropping filter/equalizer based on waveguide grating router and optical amplifier integration,” IEEE Photonics Technol. Lett. 6, 513–515 (1994).
[CrossRef]

1991 (1)

K. Inoue, T. Kominato, H. Toba, “Tunable gain equalization using a Mach–Zehnder optical filter in multistage fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 718–720 (1991).
[CrossRef]

Abbott, R. R.

R. R. Abbott, G. W. Berkstresser, C. D. Brandle, V. J. Fratello, S. J. Licht, “Article comprising a variable optical attenuator,” U.S. patent5,978,135 (2November1999).

Bao, Z.

S. H. Huang, X. Y. Zhou, S. M. Hwang, A. E. Willner, Z. Bao, D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5 Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8, 1243–1245 (1996).
[CrossRef]

Bergmann, E. E.

E. E. Bergmann, D. Bishop, “Micro-mechanical variable optical attenuator,” U.S. patent6,163,643 (19December2000).

Berkstresser, G. W.

R. R. Abbott, G. W. Berkstresser, C. D. Brandle, V. J. Fratello, S. J. Licht, “Article comprising a variable optical attenuator,” U.S. patent5,978,135 (2November1999).

Bishop, D.

E. E. Bergmann, D. Bishop, “Micro-mechanical variable optical attenuator,” U.S. patent6,163,643 (19December2000).

A. Vladimir, B. Bradley, D. Bishop, G. Clinton, S. Lawrence, R. Rene, “Optical attenuator,” U.S. patent6,173,105 (9January2001).

Bradley, B.

A. Vladimir, B. Bradley, D. Bishop, G. Clinton, S. Lawrence, R. Rene, “Optical attenuator,” U.S. patent6,173,105 (9January2001).

Brandle, C. D.

R. R. Abbott, G. W. Berkstresser, C. D. Brandle, V. J. Fratello, S. J. Licht, “Article comprising a variable optical attenuator,” U.S. patent5,978,135 (2November1999).

Cappuzzo, M.

C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.

Clinton, G.

A. Vladimir, B. Bradley, D. Bishop, G. Clinton, S. Lawrence, R. Rene, “Optical attenuator,” U.S. patent6,173,105 (9January2001).

Cohen, A. D.

M. C. Parker, A. D. Cohen, R. J. Mears, “Dynamic holographic spectral equalization for WDM,” IEEE Photonics Technol. Lett. 9, 529–531 (1997).
[CrossRef]

Doerr, C. R.

C. R. Doerr, C. H. Joyner, L. W. Stulz, “Integrated WDM dynamic power equalizer with potentially low insertion loss,” IEEE Photonics Technol. Lett. 10, 1443–1445 (1998).
[CrossRef]

C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.

Fratello, V. J.

R. R. Abbott, G. W. Berkstresser, C. D. Brandle, V. J. Fratello, S. J. Licht, “Article comprising a variable optical attenuator,” U.S. patent5,978,135 (2November1999).

Gates, J.

C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.

Glance, B.

M. Zirngibl, C. H. Joyner, B. Glance, “Digitally tunable channel dropping filter/equalizer based on waveguide grating router and optical amplifier integration,” IEEE Photonics Technol. Lett. 6, 513–515 (1994).
[CrossRef]

Gomez, L.

C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.

Huang, S. H.

S. H. Huang, X. Y. Zhou, S. M. Hwang, A. E. Willner, Z. Bao, D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5 Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8, 1243–1245 (1996).
[CrossRef]

Hwang, S. M.

S. H. Huang, X. Y. Zhou, S. M. Hwang, A. E. Willner, Z. Bao, D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5 Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8, 1243–1245 (1996).
[CrossRef]

Inoue, K.

K. Inoue, T. Kominato, H. Toba, “Tunable gain equalization using a Mach–Zehnder optical filter in multistage fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 718–720 (1991).
[CrossRef]

Joyner, C. H.

C. R. Doerr, C. H. Joyner, L. W. Stulz, “Integrated WDM dynamic power equalizer with potentially low insertion loss,” IEEE Photonics Technol. Lett. 10, 1443–1445 (1998).
[CrossRef]

M. Zirngibl, C. H. Joyner, B. Glance, “Digitally tunable channel dropping filter/equalizer based on waveguide grating router and optical amplifier integration,” IEEE Photonics Technol. Lett. 6, 513–515 (1994).
[CrossRef]

Kim, B. Y.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35 nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[CrossRef]

Kim, H. K.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35 nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[CrossRef]

Kim, H. S.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35 nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[CrossRef]

Kominato, T.

K. Inoue, T. Kominato, H. Toba, “Tunable gain equalization using a Mach–Zehnder optical filter in multistage fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 718–720 (1991).
[CrossRef]

Laskowski, E.

C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.

Lawrence, S.

A. Vladimir, B. Bradley, D. Bishop, G. Clinton, S. Lawrence, R. Rene, “Optical attenuator,” U.S. patent6,173,105 (9January2001).

Licht, S. J.

R. R. Abbott, G. W. Berkstresser, C. D. Brandle, V. J. Fratello, S. J. Licht, “Article comprising a variable optical attenuator,” U.S. patent5,978,135 (2November1999).

Mears, R. J.

M. C. Parker, A. D. Cohen, R. J. Mears, “Dynamic holographic spectral equalization for WDM,” IEEE Photonics Technol. Lett. 9, 529–531 (1997).
[CrossRef]

Park, N.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35 nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[CrossRef]

Parker, M. C.

M. C. Parker, A. D. Cohen, R. J. Mears, “Dynamic holographic spectral equalization for WDM,” IEEE Photonics Technol. Lett. 9, 529–531 (1997).
[CrossRef]

Paunescu, A.

C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.

Rene, R.

A. Vladimir, B. Bradley, D. Bishop, G. Clinton, S. Lawrence, R. Rene, “Optical attenuator,” U.S. patent6,173,105 (9January2001).

Riza, N. A.

N. A. Riza, “Fault-tolerant fiber-optical beam control modules,” U.S. patent6,222,954 (24April2001).

Schiffer, P.

C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.

Smith, D. A.

S. H. Huang, X. Y. Zhou, S. M. Hwang, A. E. Willner, Z. Bao, D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5 Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8, 1243–1245 (1996).
[CrossRef]

Stulz, L. W.

C. R. Doerr, C. H. Joyner, L. W. Stulz, “Integrated WDM dynamic power equalizer with potentially low insertion loss,” IEEE Photonics Technol. Lett. 10, 1443–1445 (1998).
[CrossRef]

C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.

Toba, H.

K. Inoue, T. Kominato, H. Toba, “Tunable gain equalization using a Mach–Zehnder optical filter in multistage fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 718–720 (1991).
[CrossRef]

Vladimir, A.

A. Vladimir, B. Bradley, D. Bishop, G. Clinton, S. Lawrence, R. Rene, “Optical attenuator,” U.S. patent6,173,105 (9January2001).

Willner, A. E.

S. H. Huang, X. Y. Zhou, S. M. Hwang, A. E. Willner, Z. Bao, D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5 Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8, 1243–1245 (1996).
[CrossRef]

Yun, S. H.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35 nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[CrossRef]

Zhou, X. Y.

S. H. Huang, X. Y. Zhou, S. M. Hwang, A. E. Willner, Z. Bao, D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5 Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8, 1243–1245 (1996).
[CrossRef]

Zirngibl, M.

M. Zirngibl, C. H. Joyner, B. Glance, “Digitally tunable channel dropping filter/equalizer based on waveguide grating router and optical amplifier integration,” IEEE Photonics Technol. Lett. 6, 513–515 (1994).
[CrossRef]

IEEE Photonics Technol. Lett. (6)

S. H. Huang, X. Y. Zhou, S. M. Hwang, A. E. Willner, Z. Bao, D. A. Smith, “Experimental demonstration of dynamic network equalization of three 2.5 Gb/s WDM channels over 1000 km using acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 8, 1243–1245 (1996).
[CrossRef]

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35 nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[CrossRef]

K. Inoue, T. Kominato, H. Toba, “Tunable gain equalization using a Mach–Zehnder optical filter in multistage fiber amplifiers,” IEEE Photonics Technol. Lett. 3, 718–720 (1991).
[CrossRef]

M. Zirngibl, C. H. Joyner, B. Glance, “Digitally tunable channel dropping filter/equalizer based on waveguide grating router and optical amplifier integration,” IEEE Photonics Technol. Lett. 6, 513–515 (1994).
[CrossRef]

C. R. Doerr, C. H. Joyner, L. W. Stulz, “Integrated WDM dynamic power equalizer with potentially low insertion loss,” IEEE Photonics Technol. Lett. 10, 1443–1445 (1998).
[CrossRef]

M. C. Parker, A. D. Cohen, R. J. Mears, “Dynamic holographic spectral equalization for WDM,” IEEE Photonics Technol. Lett. 9, 529–531 (1997).
[CrossRef]

Other (5)

C. R. Doerr, P. Schiffer, L. W. Stulz, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, J. Gates, “Compact integrated dynamic wavelength equalizer,” in Optical Fiber Communication Conference, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), paper PD30 Suppl.

N. A. Riza, “Fault-tolerant fiber-optical beam control modules,” U.S. patent6,222,954 (24April2001).

A. Vladimir, B. Bradley, D. Bishop, G. Clinton, S. Lawrence, R. Rene, “Optical attenuator,” U.S. patent6,173,105 (9January2001).

E. E. Bergmann, D. Bishop, “Micro-mechanical variable optical attenuator,” U.S. patent6,163,643 (19December2000).

R. R. Abbott, G. W. Berkstresser, C. D. Brandle, V. J. Fratello, S. J. Licht, “Article comprising a variable optical attenuator,” U.S. patent5,978,135 (2November1999).

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Figures (12)

Fig. 1
Fig. 1

Fabry–Perot cavity interference model.

Fig. 2
Fig. 2

(a) RTD spectrum A(T) versus different reflectivity for n = 1, h = 20 μm FP. (b) Reflected spectrum versus different reflectivity for n = 1, h = 20 μm FP.

Fig. 3
Fig. 3

Basic unit of SDM.

Fig. 4
Fig. 4

(a) SDM generated multibeam interference. (b) SDM RTD assignment. (c) SDM RTD magnitude assignment.

Fig. 5
Fig. 5

SDM symmetric distribution.

Fig. 6
Fig. 6

SDM moving direction.

Fig. 7
Fig. 7

Idea of the proposed system.

Fig. 8
Fig. 8

Comparison of target spectrum and SDM spectrum.

Fig. 9
Fig. 9

Comparison of target RTD spectrum and SDM RTD spectrum.

Fig. 10
Fig. 10

(a) Spectrum versus mirror number (L = 10 μm, b = 103. (b) A(T) distortion versus number of mirrors M.

Fig. 11
Fig. 11

Spectrum versus dynamic range (b = 10, M = 3200).

Fig. 12
Fig. 12

Spectrum versus number of bits (L = 10 μm, M = 3200).

Equations (13)

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F ( ω ) = FT { f ( t ) } = - + f ( t ) exp ( - j ω t ) d t , f ( t ) = IFT { F ( ω ) } = 1 2 π - + F ( ω ) exp ( j ω t ) d ω ,
E ( t ) ( ω ) = p = 0 a p exp ( - j T p ω ) ,
A ( T ) = - + E ( ω ) exp ( - j T ω ) d ω , E ( ω ) = 1 2 π - + A ( T ) exp ( j T ω ) d T .
I ( ω ) = E ( ω ) E * ( ω ) = E ( ω ) exp [ - j φ ( ω ) ] E ( ω ) exp [ j φ ( ω ) ] = E ( ω ) 2 .
E even ( - ω ) = E even ( ω ) = I even ( ω ) = I ( ω ) , ω 0.
Δ ω / 2 ω c = ɛ 1.
T π = π / ω c .
A ( T i ) exp [ - j ω ( T i + T π ) ] = - A ( T i ) exp ( - j T i ω ) × exp ( - j ω - ω c ω c π ) = A ( T i ) exp ( - j T i ω ) × [ cos ( ω - ω c ω c π ) + j sin ( ω - ω c ω c π ) ] A ( T i ) exp ( - j T i ω ) .
cos ( Δ λ / 2 λ c - Δ λ / 2 π ) + j sin ( Δ λ / 2 λ c - Δ λ / 2 π ) = 0.9995 + j 0.0307 1.
cos ( ω c ± Δ ω / 2 ω c π ) = cos ( π ) + co s ( π ) 1 ! ( ± ɛ π ) + co s ( π ) 2 ! ( ± ɛ π ) 2 + 1 , sin ( ω c ± Δ ω / 2 ω c π ) = sin ( π ) + si n ( π ) 1 ! ( ± ɛ π ) + co s ( π ) 2 ! ( ± ɛ π ) 2 + 0.
A n ( T i ) = A ( T i ) A ( T i ) .
A n ( T i ) = M ( T i ) M ,
M ( T i ) = [ A n ( T i ) × M ] .

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