Abstract

In a 1 × N wavelength division (de)multiplexer, N receiving (Rx-) gradient-index-rod lenses (GRIN’s) are connected to a common transmitting (Tx-) GRIN. All GRIN’s are a little longer (ΔZ 0 for the Tx- and ΔZ i with i = 1, 2, … , N for the Rx-GRIN’s) than the quarter-pitch. To reduce the average coupling loss and the deviations, ΔZ 0 and ΔZ i are optimized independently (unequally) or equally by computer programming for small N, such as N = 4 and 8. For a larger N (e.g., 16), a relay GRIN is required, which is a little (ΔZ r) longer than the half-pitch. The best position of the relay GRIN is located between the seventh and the eighth Rx-GRIN’s. Other parameters including ΔZ 0, ΔZ i, and ΔZ r are all optimized. As a result the (de)multiplexer has lower losses.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Fujiwara, M. S. Goodman, M. J. O’Mahony, O. K. Tonguz, A. E. Willner, “Guest editorial - Multiwavelength optical technology and networks,” J. Lightwave Technol. 14, 932–935 (1996).
    [CrossRef]
  2. S. Okamoto, A. Watanabe, K-I. Sato, “Optical path cross-connect node architectures for photonic transport network,” J. Lightwave Technol. 14, 1410–1422 (1996).
    [CrossRef]
  3. C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–899 (1991).
    [CrossRef]
  4. K. Okamoto, K. Takiguchi, Y. Ohimori, “16-channel optical add–drop multiplexer using silica-based arrayed-waveguide gratings,” Electron. Lett. 31, 723–724 (1995).
    [CrossRef]
  5. B. Glance, I. P. Kaminow, R. W. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
    [CrossRef]
  6. K. Okamoto, K. Hattori, Y. Ohmori, “Fabrication of multiwavelength simultaneous monitoring device using arrayed-waveguide grating,” Electron. Lett. 32, 569–570 (1996).
    [CrossRef]
  7. Y. Inoue, A. Himeno, K. Moriwaki, M. Kawachi, “Silica-based arrayed-waveguide grating circuit as optical splitter/router,” Electron. Lett. 31, 726–727 (1995).
    [CrossRef]
  8. J. P. Laude, J. Flamand, J. C. Gautherin, D. Lepere, P. Gacoin, F. Bos, J. Lerner, “Stimax, a grating multiplexer for monomode or multimode fibers,” in ECOC’83—Ninth European Conference on Optical Communication, 23–26 October 1983, Geneva (1983), pp. 417–420.
  9. D. R. Wisely, “32 channel WDM multiplexer with 1-nm channel spacing and 0.7-nm bandwidth,” Electron. Lett. 27, 520–521 (1991).
    [CrossRef]
  10. G. R. Chamberlin, A. M. Hill, “Designs for high channel density single-mode wavelength-division-multiplexers,” in Components for Fiber Optics Applications II, Proc. SPIE893, 60–66 (1987).
  11. M. A. Scobey, D. E. Spock, “Passive DWDM components using microplasma optical interference filters,” in Optical Fiber Communication Conference, Vol. 2 of 1996 Technical Digest Series (Optical Society of America, Washington, D.C., 1996, pp. 242–243.
  12. A. Zoller, R. Gotzelmann, K. Matl, D. Cushing, “Temperature-stable bandpass filters deposited with plasma ion-assisted deposition,” Appl. Opt. 35, 5609–5612 (1996).
    [CrossRef] [PubMed]
  13. Lightwave, Buyer’s Guide Issue113–115 (March1997).
  14. R. W. Gilsdorf, J. C. Palais, “Single-mode fiber coupling efficiency with graded-index rod lenses,” Appl. Opt. 33, 3440–3445 (1994).
    [CrossRef] [PubMed]
  15. T. Sakamoto, “Coupling characteristic analysis of single-mode and multimode optical-fiber connectors using gradient-index-rod lenses,” Appl. Opt. 31, 5184–5190 (1992).
    [CrossRef] [PubMed]
  16. Selfoc Product Guide (NSG America, Inc., Somerset, N.J., 1992).
  17. A. Gerrand, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975), Chaps. 2 and 3.
  18. H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Proceedings of the Symposium on Quasi-Optics, Microwave Research Institute Symposium Series, Vol. 14 (Polytechnic, Brooklyn, 1964), pp. 333–347.

1996 (4)

M. Fujiwara, M. S. Goodman, M. J. O’Mahony, O. K. Tonguz, A. E. Willner, “Guest editorial - Multiwavelength optical technology and networks,” J. Lightwave Technol. 14, 932–935 (1996).
[CrossRef]

S. Okamoto, A. Watanabe, K-I. Sato, “Optical path cross-connect node architectures for photonic transport network,” J. Lightwave Technol. 14, 1410–1422 (1996).
[CrossRef]

K. Okamoto, K. Hattori, Y. Ohmori, “Fabrication of multiwavelength simultaneous monitoring device using arrayed-waveguide grating,” Electron. Lett. 32, 569–570 (1996).
[CrossRef]

A. Zoller, R. Gotzelmann, K. Matl, D. Cushing, “Temperature-stable bandpass filters deposited with plasma ion-assisted deposition,” Appl. Opt. 35, 5609–5612 (1996).
[CrossRef] [PubMed]

1995 (2)

Y. Inoue, A. Himeno, K. Moriwaki, M. Kawachi, “Silica-based arrayed-waveguide grating circuit as optical splitter/router,” Electron. Lett. 31, 726–727 (1995).
[CrossRef]

K. Okamoto, K. Takiguchi, Y. Ohimori, “16-channel optical add–drop multiplexer using silica-based arrayed-waveguide gratings,” Electron. Lett. 31, 723–724 (1995).
[CrossRef]

1994 (2)

B. Glance, I. P. Kaminow, R. W. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

R. W. Gilsdorf, J. C. Palais, “Single-mode fiber coupling efficiency with graded-index rod lenses,” Appl. Opt. 33, 3440–3445 (1994).
[CrossRef] [PubMed]

1992 (1)

1991 (2)

D. R. Wisely, “32 channel WDM multiplexer with 1-nm channel spacing and 0.7-nm bandwidth,” Electron. Lett. 27, 520–521 (1991).
[CrossRef]

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

Bos, F.

J. P. Laude, J. Flamand, J. C. Gautherin, D. Lepere, P. Gacoin, F. Bos, J. Lerner, “Stimax, a grating multiplexer for monomode or multimode fibers,” in ECOC’83—Ninth European Conference on Optical Communication, 23–26 October 1983, Geneva (1983), pp. 417–420.

Burch, J. M.

A. Gerrand, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975), Chaps. 2 and 3.

Chamberlin, G. R.

G. R. Chamberlin, A. M. Hill, “Designs for high channel density single-mode wavelength-division-multiplexers,” in Components for Fiber Optics Applications II, Proc. SPIE893, 60–66 (1987).

Cushing, D.

Dragone, C.

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

Edwards, C. A.

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

Flamand, J.

J. P. Laude, J. Flamand, J. C. Gautherin, D. Lepere, P. Gacoin, F. Bos, J. Lerner, “Stimax, a grating multiplexer for monomode or multimode fibers,” in ECOC’83—Ninth European Conference on Optical Communication, 23–26 October 1983, Geneva (1983), pp. 417–420.

Fujiwara, M.

M. Fujiwara, M. S. Goodman, M. J. O’Mahony, O. K. Tonguz, A. E. Willner, “Guest editorial - Multiwavelength optical technology and networks,” J. Lightwave Technol. 14, 932–935 (1996).
[CrossRef]

Gacoin, P.

J. P. Laude, J. Flamand, J. C. Gautherin, D. Lepere, P. Gacoin, F. Bos, J. Lerner, “Stimax, a grating multiplexer for monomode or multimode fibers,” in ECOC’83—Ninth European Conference on Optical Communication, 23–26 October 1983, Geneva (1983), pp. 417–420.

Gautherin, J. C.

J. P. Laude, J. Flamand, J. C. Gautherin, D. Lepere, P. Gacoin, F. Bos, J. Lerner, “Stimax, a grating multiplexer for monomode or multimode fibers,” in ECOC’83—Ninth European Conference on Optical Communication, 23–26 October 1983, Geneva (1983), pp. 417–420.

Gerrand, A.

A. Gerrand, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975), Chaps. 2 and 3.

Gilsdorf, R. W.

Glance, B.

B. Glance, I. P. Kaminow, R. W. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

Goodman, M. S.

M. Fujiwara, M. S. Goodman, M. J. O’Mahony, O. K. Tonguz, A. E. Willner, “Guest editorial - Multiwavelength optical technology and networks,” J. Lightwave Technol. 14, 932–935 (1996).
[CrossRef]

Gotzelmann, R.

Hattori, K.

K. Okamoto, K. Hattori, Y. Ohmori, “Fabrication of multiwavelength simultaneous monitoring device using arrayed-waveguide grating,” Electron. Lett. 32, 569–570 (1996).
[CrossRef]

Hill, A. M.

G. R. Chamberlin, A. M. Hill, “Designs for high channel density single-mode wavelength-division-multiplexers,” in Components for Fiber Optics Applications II, Proc. SPIE893, 60–66 (1987).

Himeno, A.

Y. Inoue, A. Himeno, K. Moriwaki, M. Kawachi, “Silica-based arrayed-waveguide grating circuit as optical splitter/router,” Electron. Lett. 31, 726–727 (1995).
[CrossRef]

Inoue, Y.

Y. Inoue, A. Himeno, K. Moriwaki, M. Kawachi, “Silica-based arrayed-waveguide grating circuit as optical splitter/router,” Electron. Lett. 31, 726–727 (1995).
[CrossRef]

Kaminow, I. P.

B. Glance, I. P. Kaminow, R. W. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

Kawachi, M.

Y. Inoue, A. Himeno, K. Moriwaki, M. Kawachi, “Silica-based arrayed-waveguide grating circuit as optical splitter/router,” Electron. Lett. 31, 726–727 (1995).
[CrossRef]

Kistler, R. C.

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Proceedings of the Symposium on Quasi-Optics, Microwave Research Institute Symposium Series, Vol. 14 (Polytechnic, Brooklyn, 1964), pp. 333–347.

Laude, J. P.

J. P. Laude, J. Flamand, J. C. Gautherin, D. Lepere, P. Gacoin, F. Bos, J. Lerner, “Stimax, a grating multiplexer for monomode or multimode fibers,” in ECOC’83—Ninth European Conference on Optical Communication, 23–26 October 1983, Geneva (1983), pp. 417–420.

Lepere, D.

J. P. Laude, J. Flamand, J. C. Gautherin, D. Lepere, P. Gacoin, F. Bos, J. Lerner, “Stimax, a grating multiplexer for monomode or multimode fibers,” in ECOC’83—Ninth European Conference on Optical Communication, 23–26 October 1983, Geneva (1983), pp. 417–420.

Lerner, J.

J. P. Laude, J. Flamand, J. C. Gautherin, D. Lepere, P. Gacoin, F. Bos, J. Lerner, “Stimax, a grating multiplexer for monomode or multimode fibers,” in ECOC’83—Ninth European Conference on Optical Communication, 23–26 October 1983, Geneva (1983), pp. 417–420.

Matl, K.

Moriwaki, K.

Y. Inoue, A. Himeno, K. Moriwaki, M. Kawachi, “Silica-based arrayed-waveguide grating circuit as optical splitter/router,” Electron. Lett. 31, 726–727 (1995).
[CrossRef]

O’Mahony, M. J.

M. Fujiwara, M. S. Goodman, M. J. O’Mahony, O. K. Tonguz, A. E. Willner, “Guest editorial - Multiwavelength optical technology and networks,” J. Lightwave Technol. 14, 932–935 (1996).
[CrossRef]

Ohimori, Y.

K. Okamoto, K. Takiguchi, Y. Ohimori, “16-channel optical add–drop multiplexer using silica-based arrayed-waveguide gratings,” Electron. Lett. 31, 723–724 (1995).
[CrossRef]

Ohmori, Y.

K. Okamoto, K. Hattori, Y. Ohmori, “Fabrication of multiwavelength simultaneous monitoring device using arrayed-waveguide grating,” Electron. Lett. 32, 569–570 (1996).
[CrossRef]

Okamoto, K.

K. Okamoto, K. Hattori, Y. Ohmori, “Fabrication of multiwavelength simultaneous monitoring device using arrayed-waveguide grating,” Electron. Lett. 32, 569–570 (1996).
[CrossRef]

K. Okamoto, K. Takiguchi, Y. Ohimori, “16-channel optical add–drop multiplexer using silica-based arrayed-waveguide gratings,” Electron. Lett. 31, 723–724 (1995).
[CrossRef]

Okamoto, S.

S. Okamoto, A. Watanabe, K-I. Sato, “Optical path cross-connect node architectures for photonic transport network,” J. Lightwave Technol. 14, 1410–1422 (1996).
[CrossRef]

Palais, J. C.

Sakamoto, T.

Sato, K-I.

S. Okamoto, A. Watanabe, K-I. Sato, “Optical path cross-connect node architectures for photonic transport network,” J. Lightwave Technol. 14, 1410–1422 (1996).
[CrossRef]

Scobey, M. A.

M. A. Scobey, D. E. Spock, “Passive DWDM components using microplasma optical interference filters,” in Optical Fiber Communication Conference, Vol. 2 of 1996 Technical Digest Series (Optical Society of America, Washington, D.C., 1996, pp. 242–243.

Spock, D. E.

M. A. Scobey, D. E. Spock, “Passive DWDM components using microplasma optical interference filters,” in Optical Fiber Communication Conference, Vol. 2 of 1996 Technical Digest Series (Optical Society of America, Washington, D.C., 1996, pp. 242–243.

Takiguchi, K.

K. Okamoto, K. Takiguchi, Y. Ohimori, “16-channel optical add–drop multiplexer using silica-based arrayed-waveguide gratings,” Electron. Lett. 31, 723–724 (1995).
[CrossRef]

Tonguz, O. K.

M. Fujiwara, M. S. Goodman, M. J. O’Mahony, O. K. Tonguz, A. E. Willner, “Guest editorial - Multiwavelength optical technology and networks,” J. Lightwave Technol. 14, 932–935 (1996).
[CrossRef]

Watanabe, A.

S. Okamoto, A. Watanabe, K-I. Sato, “Optical path cross-connect node architectures for photonic transport network,” J. Lightwave Technol. 14, 1410–1422 (1996).
[CrossRef]

Willner, A. E.

M. Fujiwara, M. S. Goodman, M. J. O’Mahony, O. K. Tonguz, A. E. Willner, “Guest editorial - Multiwavelength optical technology and networks,” J. Lightwave Technol. 14, 932–935 (1996).
[CrossRef]

Wilson, R. W.

B. Glance, I. P. Kaminow, R. W. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

Wisely, D. R.

D. R. Wisely, “32 channel WDM multiplexer with 1-nm channel spacing and 0.7-nm bandwidth,” Electron. Lett. 27, 520–521 (1991).
[CrossRef]

Zoller, A.

Appl. Opt. (3)

Electron. Lett. (4)

K. Okamoto, K. Takiguchi, Y. Ohimori, “16-channel optical add–drop multiplexer using silica-based arrayed-waveguide gratings,” Electron. Lett. 31, 723–724 (1995).
[CrossRef]

K. Okamoto, K. Hattori, Y. Ohmori, “Fabrication of multiwavelength simultaneous monitoring device using arrayed-waveguide grating,” Electron. Lett. 32, 569–570 (1996).
[CrossRef]

Y. Inoue, A. Himeno, K. Moriwaki, M. Kawachi, “Silica-based arrayed-waveguide grating circuit as optical splitter/router,” Electron. Lett. 31, 726–727 (1995).
[CrossRef]

D. R. Wisely, “32 channel WDM multiplexer with 1-nm channel spacing and 0.7-nm bandwidth,” Electron. Lett. 27, 520–521 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. Dragone, C. A. Edwards, R. C. Kistler, “Integrated optics N × N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–899 (1991).
[CrossRef]

J. Lightwave Technol. (3)

B. Glance, I. P. Kaminow, R. W. Wilson, “Applications of the integrated waveguide grating router,” J. Lightwave Technol. 12, 957–962 (1994).
[CrossRef]

M. Fujiwara, M. S. Goodman, M. J. O’Mahony, O. K. Tonguz, A. E. Willner, “Guest editorial - Multiwavelength optical technology and networks,” J. Lightwave Technol. 14, 932–935 (1996).
[CrossRef]

S. Okamoto, A. Watanabe, K-I. Sato, “Optical path cross-connect node architectures for photonic transport network,” J. Lightwave Technol. 14, 1410–1422 (1996).
[CrossRef]

Other (7)

G. R. Chamberlin, A. M. Hill, “Designs for high channel density single-mode wavelength-division-multiplexers,” in Components for Fiber Optics Applications II, Proc. SPIE893, 60–66 (1987).

M. A. Scobey, D. E. Spock, “Passive DWDM components using microplasma optical interference filters,” in Optical Fiber Communication Conference, Vol. 2 of 1996 Technical Digest Series (Optical Society of America, Washington, D.C., 1996, pp. 242–243.

J. P. Laude, J. Flamand, J. C. Gautherin, D. Lepere, P. Gacoin, F. Bos, J. Lerner, “Stimax, a grating multiplexer for monomode or multimode fibers,” in ECOC’83—Ninth European Conference on Optical Communication, 23–26 October 1983, Geneva (1983), pp. 417–420.

Lightwave, Buyer’s Guide Issue113–115 (March1997).

Selfoc Product Guide (NSG America, Inc., Somerset, N.J., 1992).

A. Gerrand, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975), Chaps. 2 and 3.

H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Proceedings of the Symposium on Quasi-Optics, Microwave Research Institute Symposium Series, Vol. 14 (Polytechnic, Brooklyn, 1964), pp. 333–347.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

(a) Schematic of a wavelength division demultiplexer using a set of interference film filters. The light beam is coupled through Tx- and Rx- GRIN’s. (b) Optical equivalence of the demultiplexer. The separation d i between the GRIN pair increases step-by-step. RP, reference plane.

Fig. 2
Fig. 2

Schematic of a 1 × 16 wavelength division demultiplexer on the basis of interference film filters. The light beams are coupled through Tx-, relay, and 16 Rx-GRIN’s. The Rx-GRIN’s are arranged in two groups separated by the relay GRIN.

Fig. 3
Fig. 3

Schematic of two kinds of fundamental collimating units in the (de)multiplexers. A light beam is coupled through a Tx-, a (optional) relay, and an ith Rx-GRIN. RP, reference plane.

Fig. 4
Fig. 4

In a 1 × 4 demultiplexer, the Tx- and the Rx-GRIN’s have the same length (ΔZ 0) exceeding the quarter-pitch (equal-ΔZ scheme). (a) The average loss 〈L〉 and the deviation bounds ΔL i versus ΔZ 0. (b) The respective losses L i at favorably ΔZ 0 = 10 μm.

Fig. 5
Fig. 5

In a 1 × 4 demultiplexer, the Tx- and Rx-GRIN’s are ΔZ 0 and ΔZ i longer, respectively, than the quarter-pitch (unequal-ΔZ scheme). (a) The average loss 〈L〉 and the deviation bounds ΔL i versus ΔZ 0. (b) Independently optimized ΔZ i and (c) respective losses L i at three favorable ΔZ 0 values.

Fig. 6
Fig. 6

In a 1 × 8 demultiplexer the Tx- and the Rx-GRIN’s have the same length (ΔZ 0) exceeding the quarter-pitch (equal-ΔZ scheme). (a) The average loss 〈L〉 and the deviation bounds ΔL i versus ΔZ 0. (b) The respective losses L i at two favorable ΔZ 0 values.

Fig. 7
Fig. 7

In a 1 × 8 demultiplexer the Tx- and Rx-GRIN’s are ΔZ 0 and ΔZ i longer, respectively, than the quarter-pitch (unequal-ΔZ scheme). (a) The average loss 〈L〉 and the deviation bounds ΔL i versus ΔZ 0. (b) Independently optimized ΔZ i , and (c) respective losses L i at three favorable ΔZ 0 values.

Fig. 8
Fig. 8

Optimized parameters in a 1 × 16 demultiplexer without a relay GRIN. (a) Optimized ΔZ i and (b) respective losses L i with i = 1, 2, … , 16. The large losses associated with the last several ports are unacceptable.

Fig. 9
Fig. 9

Optimized length of the Rx-GRIN’s (ΔZ i ) in a 1 × 16 demultiplexer with a relay GRIN in five cases: I (N r = 6), II (N r = 7 with the lowest average loss), III (N r = 7 with the lowest maximum respective loss), IV (N r = 8), and V (N r = 9).

Fig. 10
Fig. 10

Respective loss distribution (L i ) in a 1 × 16 demultiplexer with a relay GRIN: (a) Case I (N r = 6), (b) Case II (N r = 7 with the lowest average loss), (c) Case III (N r = 7 with the lowest maximum respective loss), (d) Case IV (N r = 8), and (e) Case V (N r = 9).

Tables (1)

Tables Icon

Table 1 Optimized Parameters of 1 × 16 (De)multiplexer

Equations (15)

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

L Δ Z 0 ,   Δ Z i = 1 N i = 1 N   L i Δ Z 0 ,   Δ Z i ,
Δ L i Δ Z 0 ,   Δ Z i = L i Δ Z 0 ,   Δ Z i - L Δ Z 0 ,   Δ Z i .
L Δ Z 0 ,   Δ Z r ,   N r ,   Δ Z i = 1 16 i = 1 16   L i Δ Z 0 ,   Δ Z r ,   N r ,   Δ Z i ,
n r = n 0 1 - 1 2 Ar 2 ,
G i = - sin   A Δ Z i cos   A Δ Z i / n 0 A - n 0 A   cos A Δ Z i - sin A Δ Z i = A i B i C i D i ,
T = 1 d i 0 1
M i = A i B i C i D i = A 0 A i + B i C 0 + A i C 0 d i A i B 0 + B i D 0 + A i D 0 d i A 0 C i + C 0 D i + C 0 C i d i B 0 C i + D 0 D i + C i D 0 d i
1 q i = 1 R i + j λ π w i 2 ,
q i = A i q 0 + B i C i q 0 + D i .
w i = w 0 A i 2 + B i 2 λ / π w 0 2 2 1 / 2 ,
1 R i = A i C i + B i D i λ / π w 0 2 2 A i 2 + B i 2 λ / π w 0 2 2
1 κ i = w i / w 0 + w 0 / w i 2 + π w 0 w i / λ 2 1 / R i 2 4 .
L i dB = 4.343   ln 1 / κ i .
M r = - cos   A Δ Z r - 1 n 0 A   sin   A Δ Z r n 0 A   sin   A Δ Z r - cos   A Δ Z r .
M = M i T i M r T r M 0 ,

Metrics