Abstract

We propose three types of narrowband optical filters based on a Fox–Smith resonator. We demonstrate that by choosing the appropriate combination of coating materials on each prism facet, one can design either a high reflectance or a high transmittance optical filter, suitable for low bit rate optical communication applications with International Telecommunication Union-Telecommunication Standardization Sector (ITU-T) standards. We also show the possibility of designing an optical filter having a desirable finite reflectance/transmittance ratio with simultaneous peaks at ITU-T standard wavelengths. Such filters could be suitable for wavelength tuning applications.

© 2008 Optical Society of America

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  1. A. Vengsarkar, J. Pedrazzani, J. Judkins, P. Lemaire, N. Bergano, and C. Davidson, “Long period fiber grating based gain equalizers,” Opt. Lett. 21, 336-338 (1996).
    [CrossRef] [PubMed]
  2. Y. Li, C. Henry, E. Laskowski, C. Mak, and H. Yaffe, “Waveguide EDFA gain equalisation filter,” Electron. Lett. 31, 2005-2006 (1995).
    [CrossRef]
  3. C. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett . 10, 994-996 (1998).
    [CrossRef]
  4. C. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, 1999).
    [CrossRef]
  5. H. Macleod, Thin-Film Optical Filters (McGraw-Hill, 1989).
  6. R. B. Sargent and N. A. O'Brien, “Review of thin films in telecommunications applications,” in Optical Interference Coatings (Optical Society of America, 2001), paper WA2.
  7. S. Golmohammadi, M. K. Moravvej-Farshi, A. Rostami, and A. Zarifkar, “Narrowband DWDM filters based on Fibonacci-class quasi-periodic structures,” Opt. Express 15, 10520-10532 (2007).
    [CrossRef] [PubMed]
  8. L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moiré gratings,” Electron. Lett. 35, 584-585 (1999).
    [CrossRef]
  9. J. Floriot, F. Lemarchand, and M. Lequime, “Cascaded solid-spaced filters for DWDM applications,” Proc. SPIE 5250, 384-392 (2003).
    [CrossRef]
  10. J. Floriot, F. Lemarchand, and M. Lequime, “Solid-spaced filters: an alternative for narrow bandpass applications,” Appl. Opt. 45, 1349-1355 (2006).
    [CrossRef] [PubMed]
  11. E. Koteles, J. He, B. Lamontagne, A. Delage, L. Erickson, G. Champion, and M. Davies, “Recent advances in inp-based waveguide grating demultiplexers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 82-83.
  12. B. Moeyersoon, G. Morthier, R. Bockstaele, and R. Baets, “Improvement of the wavelength switching behavior of semiconductor tunable lasers through optical feedback from a periodic reference filter based on a novel prism-based implementation of a Fox-Smith resonator,” IEEE Photon. Technol. Lett 17, 2032-2034 (2005).
    [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. M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), pp. 323-367.
  15. G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Pre-compensation techniques to suppress the thermally induced wavelength drift in tunable DBR lasers,” IEEE J. Quantum Electron. 44 (2008), to be published.
    [CrossRef]

2008

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Pre-compensation techniques to suppress the thermally induced wavelength drift in tunable DBR lasers,” IEEE J. Quantum Electron. 44 (2008), to be published.
[CrossRef]

2007

2006

2005

B. Moeyersoon, G. Morthier, R. Bockstaele, and R. Baets, “Improvement of the wavelength switching behavior of semiconductor tunable lasers through optical feedback from a periodic reference filter based on a novel prism-based implementation of a Fox-Smith resonator,” IEEE Photon. Technol. Lett 17, 2032-2034 (2005).
[CrossRef]

2003

J. Floriot, F. Lemarchand, and M. Lequime, “Cascaded solid-spaced filters for DWDM applications,” Proc. SPIE 5250, 384-392 (2003).
[CrossRef]

1999

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moiré gratings,” Electron. Lett. 35, 584-585 (1999).
[CrossRef]

1998

C. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett . 10, 994-996 (1998).
[CrossRef]

1996

1995

Y. Li, C. Henry, E. Laskowski, C. Mak, and H. Yaffe, “Waveguide EDFA gain equalisation filter,” Electron. Lett. 31, 2005-2006 (1995).
[CrossRef]

1965

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

Baets, R.

B. Moeyersoon, G. Morthier, R. Bockstaele, and R. Baets, “Improvement of the wavelength switching behavior of semiconductor tunable lasers through optical feedback from a periodic reference filter based on a novel prism-based implementation of a Fox-Smith resonator,” IEEE Photon. Technol. Lett 17, 2032-2034 (2005).
[CrossRef]

Bergano, N.

Bockstaele, R.

B. Moeyersoon, G. Morthier, R. Bockstaele, and R. Baets, “Improvement of the wavelength switching behavior of semiconductor tunable lasers through optical feedback from a periodic reference filter based on a novel prism-based implementation of a Fox-Smith resonator,” IEEE Photon. Technol. Lett 17, 2032-2034 (2005).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), pp. 323-367.

Champion, G.

E. Koteles, J. He, B. Lamontagne, A. Delage, L. Erickson, G. Champion, and M. Davies, “Recent advances in inp-based waveguide grating demultiplexers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 82-83.

Chen, L. R.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moiré gratings,” Electron. Lett. 35, 584-585 (1999).
[CrossRef]

Cooper, D. J. F.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moiré gratings,” Electron. Lett. 35, 584-585 (1999).
[CrossRef]

Darvish, G.

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Pre-compensation techniques to suppress the thermally induced wavelength drift in tunable DBR lasers,” IEEE J. Quantum Electron. 44 (2008), to be published.
[CrossRef]

Davidson, C.

Davies, M.

E. Koteles, J. He, B. Lamontagne, A. Delage, L. Erickson, G. Champion, and M. Davies, “Recent advances in inp-based waveguide grating demultiplexers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 82-83.

Delage, A.

E. Koteles, J. He, B. Lamontagne, A. Delage, L. Erickson, G. Champion, and M. Davies, “Recent advances in inp-based waveguide grating demultiplexers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 82-83.

Erickson, L.

E. Koteles, J. He, B. Lamontagne, A. Delage, L. Erickson, G. Champion, and M. Davies, “Recent advances in inp-based waveguide grating demultiplexers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 82-83.

Floriot, J.

J. Floriot, F. Lemarchand, and M. Lequime, “Solid-spaced filters: an alternative for narrow bandpass applications,” Appl. Opt. 45, 1349-1355 (2006).
[CrossRef] [PubMed]

J. Floriot, F. Lemarchand, and M. Lequime, “Cascaded solid-spaced filters for DWDM applications,” Proc. SPIE 5250, 384-392 (2003).
[CrossRef]

Golmohammadi, S.

Gu, X.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moiré gratings,” Electron. Lett. 35, 584-585 (1999).
[CrossRef]

He, J.

E. Koteles, J. He, B. Lamontagne, A. Delage, L. Erickson, G. Champion, and M. Davies, “Recent advances in inp-based waveguide grating demultiplexers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 82-83.

Henry, C.

Y. Li, C. Henry, E. Laskowski, C. Mak, and H. Yaffe, “Waveguide EDFA gain equalisation filter,” Electron. Lett. 31, 2005-2006 (1995).
[CrossRef]

Judkins, J.

Koteles, E.

E. Koteles, J. He, B. Lamontagne, A. Delage, L. Erickson, G. Champion, and M. Davies, “Recent advances in inp-based waveguide grating demultiplexers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 82-83.

Lamontagne, B.

E. Koteles, J. He, B. Lamontagne, A. Delage, L. Erickson, G. Champion, and M. Davies, “Recent advances in inp-based waveguide grating demultiplexers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 82-83.

Laskowski, E.

Y. Li, C. Henry, E. Laskowski, C. Mak, and H. Yaffe, “Waveguide EDFA gain equalisation filter,” Electron. Lett. 31, 2005-2006 (1995).
[CrossRef]

Lemaire, P.

Lemarchand, F.

J. Floriot, F. Lemarchand, and M. Lequime, “Solid-spaced filters: an alternative for narrow bandpass applications,” Appl. Opt. 45, 1349-1355 (2006).
[CrossRef] [PubMed]

J. Floriot, F. Lemarchand, and M. Lequime, “Cascaded solid-spaced filters for DWDM applications,” Proc. SPIE 5250, 384-392 (2003).
[CrossRef]

Lenz, G.

C. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett . 10, 994-996 (1998).
[CrossRef]

Lequime, M.

J. Floriot, F. Lemarchand, and M. Lequime, “Solid-spaced filters: an alternative for narrow bandpass applications,” Appl. Opt. 45, 1349-1355 (2006).
[CrossRef] [PubMed]

J. Floriot, F. Lemarchand, and M. Lequime, “Cascaded solid-spaced filters for DWDM applications,” Proc. SPIE 5250, 384-392 (2003).
[CrossRef]

Li, Y.

Y. Li, C. Henry, E. Laskowski, C. Mak, and H. Yaffe, “Waveguide EDFA gain equalisation filter,” Electron. Lett. 31, 2005-2006 (1995).
[CrossRef]

Loka, H. S.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moiré gratings,” Electron. Lett. 35, 584-585 (1999).
[CrossRef]

Macleod, H.

H. Macleod, Thin-Film Optical Filters (McGraw-Hill, 1989).

Madsen, C.

C. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett . 10, 994-996 (1998).
[CrossRef]

C. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, 1999).
[CrossRef]

Mak, C.

Y. Li, C. Henry, E. Laskowski, C. Mak, and H. Yaffe, “Waveguide EDFA gain equalisation filter,” Electron. Lett. 31, 2005-2006 (1995).
[CrossRef]

Moeyersoon, B.

B. Moeyersoon, G. Morthier, R. Bockstaele, and R. Baets, “Improvement of the wavelength switching behavior of semiconductor tunable lasers through optical feedback from a periodic reference filter based on a novel prism-based implementation of a Fox-Smith resonator,” IEEE Photon. Technol. Lett 17, 2032-2034 (2005).
[CrossRef]

Moravvej-Farshi, M. K.

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Pre-compensation techniques to suppress the thermally induced wavelength drift in tunable DBR lasers,” IEEE J. Quantum Electron. 44 (2008), to be published.
[CrossRef]

S. Golmohammadi, M. K. Moravvej-Farshi, A. Rostami, and A. Zarifkar, “Narrowband DWDM filters based on Fibonacci-class quasi-periodic structures,” Opt. Express 15, 10520-10532 (2007).
[CrossRef] [PubMed]

Morthier, G.

B. Moeyersoon, G. Morthier, R. Bockstaele, and R. Baets, “Improvement of the wavelength switching behavior of semiconductor tunable lasers through optical feedback from a periodic reference filter based on a novel prism-based implementation of a Fox-Smith resonator,” IEEE Photon. Technol. Lett 17, 2032-2034 (2005).
[CrossRef]

O'Brien, N. A.

R. B. Sargent and N. A. O'Brien, “Review of thin films in telecommunications applications,” in Optical Interference Coatings (Optical Society of America, 2001), paper WA2.

Pedrazzani, J.

Rostami, A.

Saghafi, K.

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Pre-compensation techniques to suppress the thermally induced wavelength drift in tunable DBR lasers,” IEEE J. Quantum Electron. 44 (2008), to be published.
[CrossRef]

Sargent, R. B.

R. B. Sargent and N. A. O'Brien, “Review of thin films in telecommunications applications,” in Optical Interference Coatings (Optical Society of America, 2001), paper WA2.

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]

Smith, P. W. E.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moiré gratings,” Electron. Lett. 35, 584-585 (1999).
[CrossRef]

Tam, R.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moiré gratings,” Electron. Lett. 35, 584-585 (1999).
[CrossRef]

Vengsarkar, A.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), pp. 323-367.

Yaffe, H.

Y. Li, C. Henry, E. Laskowski, C. Mak, and H. Yaffe, “Waveguide EDFA gain equalisation filter,” Electron. Lett. 31, 2005-2006 (1995).
[CrossRef]

Zarifkar, A.

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Pre-compensation techniques to suppress the thermally induced wavelength drift in tunable DBR lasers,” IEEE J. Quantum Electron. 44 (2008), to be published.
[CrossRef]

S. Golmohammadi, M. K. Moravvej-Farshi, A. Rostami, and A. Zarifkar, “Narrowband DWDM filters based on Fibonacci-class quasi-periodic structures,” Opt. Express 15, 10520-10532 (2007).
[CrossRef] [PubMed]

Zhao, J. H.

C. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, 1999).
[CrossRef]

Appl. Opt.

Electron. Lett.

L. R. Chen, H. S. Loka, D. J. F. Cooper, P. W. E. Smith, R. Tam, and X. Gu, “Fabrication of transmission filters with single or multiple flattened passbands based on chirped Moiré gratings,” Electron. Lett. 35, 584-585 (1999).
[CrossRef]

Y. Li, C. Henry, E. Laskowski, C. Mak, and H. Yaffe, “Waveguide EDFA gain equalisation filter,” Electron. Lett. 31, 2005-2006 (1995).
[CrossRef]

IEEE J. Quantum Electron.

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

G. Darvish, M. K. Moravvej-Farshi, A. Zarifkar, and K. Saghafi, “Pre-compensation techniques to suppress the thermally induced wavelength drift in tunable DBR lasers,” IEEE J. Quantum Electron. 44 (2008), to be published.
[CrossRef]

IEEE Photon. Technol. Lett

B. Moeyersoon, G. Morthier, R. Bockstaele, and R. Baets, “Improvement of the wavelength switching behavior of semiconductor tunable lasers through optical feedback from a periodic reference filter based on a novel prism-based implementation of a Fox-Smith resonator,” IEEE Photon. Technol. Lett 17, 2032-2034 (2005).
[CrossRef]

C. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett . 10, 994-996 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

J. Floriot, F. Lemarchand, and M. Lequime, “Cascaded solid-spaced filters for DWDM applications,” Proc. SPIE 5250, 384-392 (2003).
[CrossRef]

Other

C. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, 1999).
[CrossRef]

H. Macleod, Thin-Film Optical Filters (McGraw-Hill, 1989).

R. B. Sargent and N. A. O'Brien, “Review of thin films in telecommunications applications,” in Optical Interference Coatings (Optical Society of America, 2001), paper WA2.

E. Koteles, J. He, B. Lamontagne, A. Delage, L. Erickson, G. Champion, and M. Davies, “Recent advances in inp-based waveguide grating demultiplexers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 82-83.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1999), pp. 323-367.

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Figures (5)

Fig. 1
Fig. 1

Simple schematic diagrams of the proposed filter structure: (a) 3D view, (b) 2D front view showing the optical field path throughout the structure

Fig. 2
Fig. 2

Total reflection spectrum at P 1 (a) and transmission spectrum through P 3 (b) for a high reflectance filter whose individual facets’ coatings and reflectivities are given in Table 1 with L 1 = 1.04 mm , L 2 = 0 , FWHM = 0.1 nm , and FSR = 0.8 nm .

Fig. 3
Fig. 3

Total transmission spectra of the high reflectance filter of Fig. 2, through ports P 2 ( 10 × T B ) , P 4 ( T D ) , and P 6 ( T F ) .

Fig. 4
Fig. 4

Total reflection spectrum at P 1 (a) and transmission spectrum through P 3 (b) for a high transmittance filter whose individual facets’ coatings and reflectivities are given in Table 1 with L 1 = 1.04 mm , L 2 = 0 , FWHM = 0.1 nm , and FSR = 0.8 nm .

Fig. 5
Fig. 5

Total reflection spectrum at P 1 (a) and transmission spectrum through P 3 (b) for a filter with finite reflectance/transmittance ratio whose individual facets’ coatings and reflectivities are given in Table 1 with L 1 = 1.04 mm , L 2 = 0 , FWHM = 0.075 nm , and FSR = 0.8 nm .

Tables (1)

Tables Icon

Table 1 Individual Facets’ Coatings and Reflectivities for Filters with High Reflectance, High Transmittance, and Finite Reflectance/Transmittance Ratio for the Wavelength Range of 1400 1700 nm

Equations (28)

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

R A = | r a + t a ' A ( L 1 / 2 , 0 ) E in | 2 = R ,
T C = | t c C + ( L 1 / 2 , 0 ) E in | 2 = T ,
T B = | t b B + ( 0 , L 1 / 2 ) E in | 2 ,
T E = | t e E + ( L 1 / 2 , ( L 1 + L 2 ) ) E in | 2 ,
T D = | t d D ( 0 , ( L 1 + L 2 ) L 1 / 2 ) E in | 2 ,
T F = | t f F ( L 1 / 2 , ( L 1 + L 2 ) ) E in | 2 = T A ,
r AR = R AR ,
t AR | a ir / BK 7 = i T AR / n BK 7 ,
t AR | BK 7 / air = in BK 7 T AR ,
r D B R = R D B R ,
t DBR = n BK 7 T HR , BK 7 / air .
r s 1 , 2 = ± R s 1 , 2 ,
t s 1 , 2 = T s 1 , 2 .
E ± ( x ) = E 0 exp ( j k x ) ,
A ( 0 ) = t s 1 C ( 0 ) + r s 1 S 2 + exp [ j k ( L 1 + L 2 ) ] ,
B + ( 0 ) = t s 1 S 2 + exp [ j k ( L 1 + L 2 ) ] r s 1 C ( 0 ) ,
C + ( 0 ) = t s 1 A + ( 0 ) r s 1 B ( 0 ) ,
S 1 ( 0 ) = r s 1 A + ( 0 ) + t s 1 B ( 0 ) ,
S 2 + = t s 2 D + + r s 2 F + ,
D = t s 2 S 1 ( 0 ) exp [ j k ( L 1 + L 2 ) ] r s 2 E ,
E + = t s 2 F + r s 2 D + ,
F = r s 2 S 1 ( 0 ) exp [ j k ( L 1 + L 2 ) ] + t s 2 E ,
A + ( 0 ) = r a A ( 0 ) exp ( j k L 1 ) + t a E in exp ( j k L 1 / 2 ) ,
B ( 0 ) = r b B + ( 0 ) exp ( j k L 1 ) ,
C ( 0 ) = r c C + ( 0 ) exp ( j k L 1 ) ,
D + = r d D exp ( j k L 1 ) ,
E = r e E + exp ( j k L 1 ) ,
F + = r f F exp ( j k L 1 ) ,

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