Abstract

A new concept for a highway switch, which can be used to connect different optical wavelength division multiplexing data highways for data exchange, is proposed and the system relevant properties are outlined. For the required add–drop filter elements we used ring resonators. Typical characteristics of channel bandwidth, channel spacing, free spectral range, amplification, and cross-talk behavior of a highway switch with double-cavity ring resonators are basically examined and to some extent compared with solutions that were obtained with standard single-ring resonators. A signal flow chart transformation for evaluating filter transfer functions is presented.

© 1996 Optical Society of America

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References

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  1. K. Sasayama, M. Okuno, K. Habara, “Photonic FDM highway switch using coherent optical transversal filter,” in Technical Digest of the International Switching Symposium (Institute of Electronics, Information, and Communication Engineers, Yokohama, Japan, 1992), pp. 347–351.
  2. K. Sasayama, K. Habara, “Photonic FDM highway switch using PLC ring resonators,” in Proceedings of the European Conference on Optical Communication (Montreux, 1993), pp. 545–548.
  3. P. Urquhart, “Compound optical-fiber-based resonators,” J. Opt. Soc. Am. A 5, 803–812 (1988).
    [CrossRef]
  4. S. Suzuki, K. Shuto, Y. Hibino, “Integrated-optic ring resonators with two stacked layers of silica waveguide on Si,” IEEE Photon. Technol. Lett. 4, 1256–1258 (1992).
    [CrossRef]
  5. J. Capmany, M. A. Muriel, “Double-cavity fiber structures as all optical timing extraction circuits for gigabit networks,” Fiber Integ. Opt. 12, 247–255 (1993).
    [CrossRef]
  6. K. Oda, N. Takato, H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
    [CrossRef]
  7. H. Kogelnik, R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
    [CrossRef]
  8. Y. Silberberg, P. Perlmutter, J. E. Baran, “Digital optical switch,” Appl. Phys. Lett. 51, 1230–1232 (1987).
    [CrossRef]
  9. T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, Berlin, 1988).
    [CrossRef]
  10. P. Yeh, H. F. Taylor, “Contradirectional frequency-selective couplers for guided-wave optics,” Appl. Opt. 19, 2848–2855 (1980).
    [CrossRef] [PubMed]
  11. J. Capmany, J. Martí, S. Sales, D. Pastor, J. Cascón, “Theory of integrated ring resonators using electro-optical couplers,” Fiber Integ. Opt. 14, 245–263 (1995).
    [CrossRef]
  12. T. Kominato, Y. Hibino, K. Onose, “Silica-based finesse-variable ring resonator,” in Proceedings of Lasers and Electro-Optic Society (IEEE, Boston, Mass., 1992), pp. 680–681.
  13. J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” J. Lightwave Technol. 8, 1904–1919 (1990).
    [CrossRef]
  14. S. Suzuki, K. Oda, Y. Hibino, “Integrated-optic doublering resonators with a wide free spectral range of 100 GHz,” J. Lightwave Technol. 13, 1766–1771 (1995).
    [CrossRef]
  15. Y. Weissman, Optical Network Theory (Artech House, Boston, 1992).
  16. Y. Fang, S. Tao, P. Ye, “Analysis of compound cross-coupling fiber resonator by means of signal flow graphs,” Opt. Commun. 93, 87–91 (1992).
    [CrossRef]

1995

J. Capmany, J. Martí, S. Sales, D. Pastor, J. Cascón, “Theory of integrated ring resonators using electro-optical couplers,” Fiber Integ. Opt. 14, 245–263 (1995).
[CrossRef]

S. Suzuki, K. Oda, Y. Hibino, “Integrated-optic doublering resonators with a wide free spectral range of 100 GHz,” J. Lightwave Technol. 13, 1766–1771 (1995).
[CrossRef]

1993

J. Capmany, M. A. Muriel, “Double-cavity fiber structures as all optical timing extraction circuits for gigabit networks,” Fiber Integ. Opt. 12, 247–255 (1993).
[CrossRef]

1992

S. Suzuki, K. Shuto, Y. Hibino, “Integrated-optic ring resonators with two stacked layers of silica waveguide on Si,” IEEE Photon. Technol. Lett. 4, 1256–1258 (1992).
[CrossRef]

Y. Fang, S. Tao, P. Ye, “Analysis of compound cross-coupling fiber resonator by means of signal flow graphs,” Opt. Commun. 93, 87–91 (1992).
[CrossRef]

1991

K. Oda, N. Takato, H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[CrossRef]

1990

J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” J. Lightwave Technol. 8, 1904–1919 (1990).
[CrossRef]

1988

1987

Y. Silberberg, P. Perlmutter, J. E. Baran, “Digital optical switch,” Appl. Phys. Lett. 51, 1230–1232 (1987).
[CrossRef]

1980

1976

H. Kogelnik, R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[CrossRef]

Baran, J. E.

Y. Silberberg, P. Perlmutter, J. E. Baran, “Digital optical switch,” Appl. Phys. Lett. 51, 1230–1232 (1987).
[CrossRef]

Capmany, J.

J. Capmany, J. Martí, S. Sales, D. Pastor, J. Cascón, “Theory of integrated ring resonators using electro-optical couplers,” Fiber Integ. Opt. 14, 245–263 (1995).
[CrossRef]

J. Capmany, M. A. Muriel, “Double-cavity fiber structures as all optical timing extraction circuits for gigabit networks,” Fiber Integ. Opt. 12, 247–255 (1993).
[CrossRef]

J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” J. Lightwave Technol. 8, 1904–1919 (1990).
[CrossRef]

Cascón, J.

J. Capmany, J. Martí, S. Sales, D. Pastor, J. Cascón, “Theory of integrated ring resonators using electro-optical couplers,” Fiber Integ. Opt. 14, 245–263 (1995).
[CrossRef]

Fang, Y.

Y. Fang, S. Tao, P. Ye, “Analysis of compound cross-coupling fiber resonator by means of signal flow graphs,” Opt. Commun. 93, 87–91 (1992).
[CrossRef]

Habara, K.

K. Sasayama, M. Okuno, K. Habara, “Photonic FDM highway switch using coherent optical transversal filter,” in Technical Digest of the International Switching Symposium (Institute of Electronics, Information, and Communication Engineers, Yokohama, Japan, 1992), pp. 347–351.

K. Sasayama, K. Habara, “Photonic FDM highway switch using PLC ring resonators,” in Proceedings of the European Conference on Optical Communication (Montreux, 1993), pp. 545–548.

Hibino, Y.

S. Suzuki, K. Oda, Y. Hibino, “Integrated-optic doublering resonators with a wide free spectral range of 100 GHz,” J. Lightwave Technol. 13, 1766–1771 (1995).
[CrossRef]

S. Suzuki, K. Shuto, Y. Hibino, “Integrated-optic ring resonators with two stacked layers of silica waveguide on Si,” IEEE Photon. Technol. Lett. 4, 1256–1258 (1992).
[CrossRef]

T. Kominato, Y. Hibino, K. Onose, “Silica-based finesse-variable ring resonator,” in Proceedings of Lasers and Electro-Optic Society (IEEE, Boston, Mass., 1992), pp. 680–681.

Kogelnik, H.

H. Kogelnik, R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[CrossRef]

Kominato, T.

T. Kominato, Y. Hibino, K. Onose, “Silica-based finesse-variable ring resonator,” in Proceedings of Lasers and Electro-Optic Society (IEEE, Boston, Mass., 1992), pp. 680–681.

Martí, J.

J. Capmany, J. Martí, S. Sales, D. Pastor, J. Cascón, “Theory of integrated ring resonators using electro-optical couplers,” Fiber Integ. Opt. 14, 245–263 (1995).
[CrossRef]

Muriel, M. A.

J. Capmany, M. A. Muriel, “Double-cavity fiber structures as all optical timing extraction circuits for gigabit networks,” Fiber Integ. Opt. 12, 247–255 (1993).
[CrossRef]

J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” J. Lightwave Technol. 8, 1904–1919 (1990).
[CrossRef]

Oda, K.

S. Suzuki, K. Oda, Y. Hibino, “Integrated-optic doublering resonators with a wide free spectral range of 100 GHz,” J. Lightwave Technol. 13, 1766–1771 (1995).
[CrossRef]

K. Oda, N. Takato, H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[CrossRef]

Okuno, M.

K. Sasayama, M. Okuno, K. Habara, “Photonic FDM highway switch using coherent optical transversal filter,” in Technical Digest of the International Switching Symposium (Institute of Electronics, Information, and Communication Engineers, Yokohama, Japan, 1992), pp. 347–351.

Onose, K.

T. Kominato, Y. Hibino, K. Onose, “Silica-based finesse-variable ring resonator,” in Proceedings of Lasers and Electro-Optic Society (IEEE, Boston, Mass., 1992), pp. 680–681.

Pastor, D.

J. Capmany, J. Martí, S. Sales, D. Pastor, J. Cascón, “Theory of integrated ring resonators using electro-optical couplers,” Fiber Integ. Opt. 14, 245–263 (1995).
[CrossRef]

Perlmutter, P.

Y. Silberberg, P. Perlmutter, J. E. Baran, “Digital optical switch,” Appl. Phys. Lett. 51, 1230–1232 (1987).
[CrossRef]

Sales, S.

J. Capmany, J. Martí, S. Sales, D. Pastor, J. Cascón, “Theory of integrated ring resonators using electro-optical couplers,” Fiber Integ. Opt. 14, 245–263 (1995).
[CrossRef]

Sasayama, K.

K. Sasayama, M. Okuno, K. Habara, “Photonic FDM highway switch using coherent optical transversal filter,” in Technical Digest of the International Switching Symposium (Institute of Electronics, Information, and Communication Engineers, Yokohama, Japan, 1992), pp. 347–351.

K. Sasayama, K. Habara, “Photonic FDM highway switch using PLC ring resonators,” in Proceedings of the European Conference on Optical Communication (Montreux, 1993), pp. 545–548.

Schmidt, R. V.

H. Kogelnik, R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[CrossRef]

Shuto, K.

S. Suzuki, K. Shuto, Y. Hibino, “Integrated-optic ring resonators with two stacked layers of silica waveguide on Si,” IEEE Photon. Technol. Lett. 4, 1256–1258 (1992).
[CrossRef]

Silberberg, Y.

Y. Silberberg, P. Perlmutter, J. E. Baran, “Digital optical switch,” Appl. Phys. Lett. 51, 1230–1232 (1987).
[CrossRef]

Suzuki, S.

S. Suzuki, K. Oda, Y. Hibino, “Integrated-optic doublering resonators with a wide free spectral range of 100 GHz,” J. Lightwave Technol. 13, 1766–1771 (1995).
[CrossRef]

S. Suzuki, K. Shuto, Y. Hibino, “Integrated-optic ring resonators with two stacked layers of silica waveguide on Si,” IEEE Photon. Technol. Lett. 4, 1256–1258 (1992).
[CrossRef]

Takato, N.

K. Oda, N. Takato, H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[CrossRef]

Tamir, T.

T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, Berlin, 1988).
[CrossRef]

Tao, S.

Y. Fang, S. Tao, P. Ye, “Analysis of compound cross-coupling fiber resonator by means of signal flow graphs,” Opt. Commun. 93, 87–91 (1992).
[CrossRef]

Taylor, H. F.

Toba, H.

K. Oda, N. Takato, H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[CrossRef]

Urquhart, P.

Weissman, Y.

Y. Weissman, Optical Network Theory (Artech House, Boston, 1992).

Ye, P.

Y. Fang, S. Tao, P. Ye, “Analysis of compound cross-coupling fiber resonator by means of signal flow graphs,” Opt. Commun. 93, 87–91 (1992).
[CrossRef]

Yeh, P.

Appl. Opt.

Appl. Phys. Lett.

Y. Silberberg, P. Perlmutter, J. E. Baran, “Digital optical switch,” Appl. Phys. Lett. 51, 1230–1232 (1987).
[CrossRef]

Fiber Integ. Opt.

J. Capmany, M. A. Muriel, “Double-cavity fiber structures as all optical timing extraction circuits for gigabit networks,” Fiber Integ. Opt. 12, 247–255 (1993).
[CrossRef]

J. Capmany, J. Martí, S. Sales, D. Pastor, J. Cascón, “Theory of integrated ring resonators using electro-optical couplers,” Fiber Integ. Opt. 14, 245–263 (1995).
[CrossRef]

IEEE J. Quantum Electron.

H. Kogelnik, R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[CrossRef]

IEEE Photon. Technol. Lett.

S. Suzuki, K. Shuto, Y. Hibino, “Integrated-optic ring resonators with two stacked layers of silica waveguide on Si,” IEEE Photon. Technol. Lett. 4, 1256–1258 (1992).
[CrossRef]

J. Lightwave Technol.

K. Oda, N. Takato, H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[CrossRef]

J. Capmany, M. A. Muriel, “A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing,” J. Lightwave Technol. 8, 1904–1919 (1990).
[CrossRef]

S. Suzuki, K. Oda, Y. Hibino, “Integrated-optic doublering resonators with a wide free spectral range of 100 GHz,” J. Lightwave Technol. 13, 1766–1771 (1995).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

Y. Fang, S. Tao, P. Ye, “Analysis of compound cross-coupling fiber resonator by means of signal flow graphs,” Opt. Commun. 93, 87–91 (1992).
[CrossRef]

Other

Y. Weissman, Optical Network Theory (Artech House, Boston, 1992).

T. Kominato, Y. Hibino, K. Onose, “Silica-based finesse-variable ring resonator,” in Proceedings of Lasers and Electro-Optic Society (IEEE, Boston, Mass., 1992), pp. 680–681.

K. Sasayama, M. Okuno, K. Habara, “Photonic FDM highway switch using coherent optical transversal filter,” in Technical Digest of the International Switching Symposium (Institute of Electronics, Information, and Communication Engineers, Yokohama, Japan, 1992), pp. 347–351.

K. Sasayama, K. Habara, “Photonic FDM highway switch using PLC ring resonators,” in Proceedings of the European Conference on Optical Communication (Montreux, 1993), pp. 545–548.

T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, Berlin, 1988).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Conventional WDM highway switching network.2 Example with three WDM channels and two optical data highways linked by switchable single-ring resonators.

Fig. 2
Fig. 2

New WDM highway switching network with spatial separation of filter and switch. Example with two optical data highways, linked by three WFS elements for three different WDM channels.

Fig. 3
Fig. 3

(a) Asymmetrical grating coupler used as a filter element that couples over signals only in its passband and (b) a WFS element for highway switching networks, which is based on asymmetrical grating couplers employed as WDM filter elements.

Fig. 4
Fig. 4

Filters as (a) a SCRR with two directional couplers (amplitude coupling ratios k1 and k3), (b) a DCRR with three couplers (k1, k2, and k3), (c) a WFS based on DCRR’s and a MZRS.

Fig. 5
Fig. 5

Amplitude responses of the WFS shown in Fig. 4(c) |H1| (dotted curves) and |H2| (solid curves) corresponding to Eq. (A6) with four equal DCRR’s: ring diameters d1 = d2 = 1 mm, neff = 3.2, k1 = k3 = 0.436, k2 = 0.105. The rings are assumed to be lossless or loss compensated.

Fig. 6
Fig. 6

Amplitude responses |H1| (dotted curve) and |H2| (solid curve) of the WFS discussed in Fig. 5 but with enlarged coupling ratios of k1 = k3 = 0.77 and k2 = 0.43.

Fig. 7
Fig. 7

Amplitude responses (a) |H2| N and (b) |H1| N of a series of N WFS elements in order to simulate the transfer behavior of a multihighway switching network. N is the number of highway transfers. The DCRR’s have ring diameters of d1 = d2 = 400 μm (other parameters are the same as in Fig. 5).

Fig. 8
Fig. 8

Effective −1-dB bandwidth B−1eff of a whole series of WFS elements (parameters from Fig. 7) dependent on the number of highway transfers N. As filters DCRR’s were used with a ripple-free filter passband (solid curve), with a maximum ripple ratio (dashed curve) of |RR| = 1 dB (exactly achieved for N = 70, decreasing with decreasing N) or SCRR’s (dotted curve) with comparable parameters (same ring diameters and input/output coupling ratios k1 and k3).

Fig. 9
Fig. 9

Effective channel spacing of a whole series of WFS elements (parameters from Fig. 7). As filters DCRR’s (solid curve) or SCRR’s (dotted curve) with comparable parameters were used.

Fig. 10
Fig. 10

Amplitude responses |H1| (dotted curve) and |H2| (solid curve) of a WFS based on lossless DCRR’s with different ring diameters (d1 = 382 μm, d2 = 318 μm, and other parameters from Fig. 5). The FSR is enhanced by the Vernier effect.

Fig. 11
Fig. 11

Amplitude responses (a) |H1| (dotted curve) and |H2| (solid curve) of a WFS with active loss-compensated DCRR’s (slightly overcompensated: ring round-trip amplification a of +0.1 dB). (b) WFS total power amplification versus ring round-trip amplification with DCRR’s with k1 = k3 = 0.436, k2 = k2opt = 0.105 [optimum for minimum cross talk, corresponding to Eq. (4)], respectively, with a k2 deviation of 5% and 10% from k2opt (to take possible fabrication tolerances into account) or with SCRR’s (dotted curve) with comparable parameters.

Fig. 12
Fig. 12

(a) Channel cross talk between the signals of both highways (MZRS in the cross state) dependent on k2, using different definitions: SCCF (curve A) and MSCC (curve B), considering the whole channel bandwidth B−1, plotted by curve C (DCRR’s with a = 1, k1 = k3 = 0.436). (b) MSCC dependent on varying coupling ratios k2 and k3 whereas k1 = 0.436 remains constant (to simulate a deviation from the ideal symmetrical case).

Fig. 13
Fig. 13

Cross talk (SCCF) for different values of the ring round-trip amplification a (attenuation for a < 0 dB) of WFS’s with DCRR’s (solid curves) or SCRR’s (dotted curve) with k1 = k3 = 0.436. Since DCRR’s allow better cross-talk values, if we adapt k2 to the operating point, we used the optimum value k2opt = f(a), but taking into account deviations of 1%, 5%, and 10% for k2 from k2opt.

Fig. 14
Fig. 14

Effective cross talk (MSCCeff) of a whole series of WFS elements versus the bandwidth used for a channel for N = 1, 10, 20, and 50 highway transfer events. The values for the effective − 1-dB bandwidths are emphasized.

Fig. 15
Fig. 15

(a), (b) Equivalent flow chart representation of the DCRR in Fig. 4(b) and (c)–(j) the transformation algorithm for solving the amplitude transfer function H f 31 [Eq. (A3)].

Equations (12)

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ACC ( dB ) = 20 dB × log H 2 ( nc ) ( f = f center H 2 ) H 2 ( f = f center H 2 ) = 20 dB × log H 2 ( f = f center H 2 - CS ) H 2 ( f = f center H 2 ) .
CS = 1 2 ( Δ f 1 { 20 dB × log H 1 - 1 dB } + Δ f 2 { 20 dB × log H 1 - 1 dB } ) .
R R = | 20 dB × log H 2 min H 2 max | ,
SCCF ( dB ) = 20 dB × log H 1 ( f = f center H 2 ) H 2 ( f = f center H 2 ) .
MSCC ( dB ) = 20 dB × log ( H 1 ( f 0 ) H 2 ( f 0 ) ) max for f 0 with f 0 - f center H 2 B - 1 / 2 ,
SC eff ( dB ) = 20 dB × log [ E perturb ( f ) E signal ( f ) ] = 20 dB × log [ H 1 ( f ) × n = 0 N - 1 H 2 ( f ) n H 2 ( f ) N ] = 20 dB × log H 1 ( f ) + 20 dB × log [ n + = 1 N H 2 ( f ) - n ] ,
[ E 1 - E 2 - E 3 - E 4 - ] = [ H f 11 H f 12 H f 13 H f 14 H f 21 H f 22 H f 23 H f 24 H f 31 H f 32 H f 33 H f 34 H f 41 H f 42 H f 43 H f 44 ] × [ E 1 + E 2 + E 3 + E 4 + ] = [ 0 H f 21 H f 31 0 H f 21 0 0 H f 24 H f 31 0 0 H f 34 0 H f 24 H f 34 0 ] × [ E 1 + E 2 + E 3 + E 4 + ] ,
H f 21 = 1 - k 1 2 - [ ( 1 - k 1 2 ) ( 1 - k 2 2 ) ( 1 - k 3 2 ) ] 1 / 2 a 3 a 4 exp [ - i ( β 3 l 3 + β 4 l 4 ) ] - 1 - k 2 2 a 1 a 2 exp [ - i ( β 1 l 1 + β 2 l 2 ) ] + 1 - k 3 2 a 1 a 2 a 3 a 4 exp [ - i ( β 1 l 1 + β 2 l 2 + β 3 l 3 + β 4 l 4 ) ] 1 - [ ( 1 - k 2 2 ) ( 1 - k 3 2 ) ] 1 / 2 a 3 a 4 exp [ - i ( β 3 l 3 + β 4 l 4 ) ] - [ ( 1 - k 1 2 ) ( 1 - k 2 2 ) ] 1 / 2 a 1 a 2 exp [ - i ( β 1 l 1 + β 2 l 2 ) ] + [ ( 1 - k 1 2 ) ( 1 - k 3 2 ) ] 1 / 2 a 1 a 2 a 3 a 4 exp [ - i ( β 1 l 1 + β 2 l 2 + β 3 l 3 + β 4 l 4 ) ] ,
H f 31 = + i k 1 k 2 k 3 a 1 a 4 exp [ - i ( β 1 l 1 + β 4 l 4 ) ] 1 - [ ( 1 - k 2 2 ) ( 1 - k 3 2 ) ] 1 / 2 a 3 a 4 exp [ - i ( β 3 l 3 + β 4 l 4 ) ] - [ ( 1 - k 1 2 ) ( 1 - k 2 2 ) ] 1 / 2 a 1 a 2 exp [ - i ( β 1 l 1 + β 2 l 2 ) ] + [ ( 1 - k 1 2 ) ( 1 - k 3 2 ) ] 1 / 2 a 1 a 2 a 3 a 4 exp [ - i ( β 1 l 1 + β 2 l 2 + β 3 l 3 + β 4 l 4 ) ] ,
E out1 = E out11 + E out12 = H 1 × E in1 + H 2 × E in2 .
E out1 = H f 21 2 + E in1 + H f 31 × H s + H f 24 × E in2 .
H 1 = H f 21 2 ,             H 2 = H f 31 × H s × H f 24 ,

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