Abstract

Intelligent fiber-optic value-added modules (VAMs) are proposed using what we believe to be a novel spatially multiplexed processing technique implemented with both reconfigurable and nonreconfigurable predesigned pixels per impinging beam that enables desired optical power split states needed for realizing a two state reconfigurable VAM. The preferred design uses broadband micromirrors such as ones fabricated via optical microelectromechanical systems technology. The basic VAM design uses two broadband micromirror pixels, where each pixel has its specific location and area and only one of these pixels is electrically driven to adjust its small tilt angle. The areas of the pixels are chosen to obtain the desired tap power. A proof-of-concept VAM with 100% digital repeatability is demonstrated using a Texas Instruments Digital Micromirror Device (DMD) where several micromirrors per beam are used to produce the dual-pixel effect. Example tap ratios experimentally implemented at 1550  nm include 10:90, 20:80, 66 .66:33 .33, 50:50, 30:70, and 25:75. DMD multipixel diffraction limits output port optical losses to 3.2 and 3 .6   dB. The proposed VAM can have an impact in both digital electronic and analog RF optically implemented systems.

© 2007 Optical Society of America

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References

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  1. T. Duberstein, "Look both ways before crossing the network," Lightwave Magazine (October 2000), pp. 80-83.
  2. Y. L. Barberio, D. W. Dahringer, J. W. Engelberth, and A. E. Neeves, "Method for making an evanescent field coupler," U.S. patent 5,623,567 (22 April 1997).
  3. J. A. Dobrowolski, "Numerical methods for optical thin films," Optics and Photonics News 8, 25-33 (1997).
    [CrossRef]
  4. M. Cambell-Miller, B. S. Kawasaki, Y. Cheng, N. Galai, and G. Pomerant, "Lensed cascaded optical filter," U.S. patent 6,055,112 (25 April 2000).
  5. J. Li and N. Teitelbaum, "Multi-pass optical filter," U.S. patent 6,055,347 (25 April 2000).
  6. M. Takahashi, "Four polarization maintaining optical fiber ferrule and optical coupler using same," U.S. patent 5,692,081 (25 November 1997).
  7. G. M. Garriss, "Fiber optic coupler/connector with GRIN lens," U.S. patent 5,163,107 (10 November 1992).
  8. S. Kawasaki, K. O. Hill, and R. G. Lamont, "Biconical-taper single-mode fiber coupler," Opt. Lett. 6, 327-328 (1981).
    [CrossRef] [PubMed]
  9. B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A single-mode-fiber coupler with a variable coupling ratio," J. Lightwave Technol. LT-1, 176-178 (1983).
    [CrossRef]
  10. M. Kagami, Y. Sakai, and H. Okada, "Variable-ratio tap for plastic optical fiber," Appl. Opt. 30, 645-649 (1991).
    [CrossRef] [PubMed]
  11. H. Kim, J. Kim, U. C. Paek, B. H. Lee, and K. T. Kim, "Tunable photonic crystal fiber coupler based on a single-polishing technique," Opt. Lett. 29, 1194-1196 (2004).
    [CrossRef] [PubMed]
  12. K. Lizuka, Engineering Optics, 2nd ed. (Springer-Verlag, 1985), Vol. 35.
  13. Z. Yun, L. Wen, C. Long, L. Yong, and X. Qingming, "A 1 × 2 variable optical power splitter development," J. Lightwave Technol. 24, 1566-1570 (2006).
    [CrossRef]
  14. R. Zheng, Z. Wang, K. E. Alameh, and W. A. Crossland, "An opto-VLSI reconfigurable broad-band optical splitter," IEEE Photon. Technol. Lett. 17, 339-341 (2005).
    [CrossRef]
  15. S. Sumriddetchkajorn and K. Chaitavon, "Wavelength sensitive thin-film filter based variable optical attenuator with an embedded monitoring port," IEEE Photon. Technol. Lett. 16, 1507-1509 (2004).
    [CrossRef]
  16. N. A. Riza, "Fault-tolerant fiber-optical beam control modules," U.S. patent 6,222,954 (24 April 2001).
  17. N. A. Riza, "High resolution fault-tolerant fiber-optical beam control modules," U.S. patent 6,563,974 (13 May 2003).
  18. N. A. Riza and S. Sumriddetchkajorn, "Fault-tolerant dense multiwavelength add-drop filter with a two-dimensional digital micromirror device," Appl. Opt. 37, 6355-6361 (1998).
    [CrossRef]
  19. N. A. Riza and S. Sumriddetchkajorn, "Small tilt micromirror device-based multiwavelength three-dimensional 2 × 2 fiber-optic switch structures," Opt. Eng. 39, 379-386 (2000).
    [CrossRef]
  20. N. A. Riza and F. N. Ghauri, "Hybrid analog-digital MEMS fiber-optic variable attenuator," IEEE Photon. Technol. Lett. 17, 124-126 (2005).
    [CrossRef]
  21. N. A. Riza and Y. Huang, "Digital fault-tolerant variable fiber optic attenuator using liquid crystals," Proc. SPIE , 4096, 101-106 (2000).
    [CrossRef]
  22. N. A. Riza, "Liquid crystal agile photonics--From fiber to the free-space domain," in Proceedings of the Conference on Liquid Crystals Optics and Applications LCOA/COO-2005, T. Wolinski, ed., Proc. SPIE 5947, 0J-1-0J-8 (2005).
  23. S. Sumriddetchkajorn and N. A. Riza, "Micro-electro-mechanical system-based digitally controlled optical beam profiler," Appl. Opt. 41, 3506-3510 (2002).
    [CrossRef] [PubMed]
  24. N. A. Riza and M. J. Mughal, "Optical power independent optical beam profiler," Opt. Eng. 43, 793-797 (2004).
    [CrossRef]
  25. N. A. Riza and M. J. Mughal, "Broadband optical equalizer using fault tolerant digital micromirrors," Opt. Express 11, 1559-1565 (2003).
    [CrossRef] [PubMed]
  26. M. van Buren and N. A. Riza, "Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism," Appl. Opt. 42, 550-565 (2003).
    [CrossRef] [PubMed]
  27. N. A. Riza and F. N. Ghauri, "Super-resolution variable fiber-optic attenuation instrument using digital micromirror device (DMD)," Rev. Sci. Instrum. 76, (2005).
    [CrossRef]

2006 (1)

2005 (4)

R. Zheng, Z. Wang, K. E. Alameh, and W. A. Crossland, "An opto-VLSI reconfigurable broad-band optical splitter," IEEE Photon. Technol. Lett. 17, 339-341 (2005).
[CrossRef]

N. A. Riza and F. N. Ghauri, "Hybrid analog-digital MEMS fiber-optic variable attenuator," IEEE Photon. Technol. Lett. 17, 124-126 (2005).
[CrossRef]

N. A. Riza, "Liquid crystal agile photonics--From fiber to the free-space domain," in Proceedings of the Conference on Liquid Crystals Optics and Applications LCOA/COO-2005, T. Wolinski, ed., Proc. SPIE 5947, 0J-1-0J-8 (2005).

N. A. Riza and F. N. Ghauri, "Super-resolution variable fiber-optic attenuation instrument using digital micromirror device (DMD)," Rev. Sci. Instrum. 76, (2005).
[CrossRef]

2004 (3)

N. A. Riza and M. J. Mughal, "Optical power independent optical beam profiler," Opt. Eng. 43, 793-797 (2004).
[CrossRef]

H. Kim, J. Kim, U. C. Paek, B. H. Lee, and K. T. Kim, "Tunable photonic crystal fiber coupler based on a single-polishing technique," Opt. Lett. 29, 1194-1196 (2004).
[CrossRef] [PubMed]

S. Sumriddetchkajorn and K. Chaitavon, "Wavelength sensitive thin-film filter based variable optical attenuator with an embedded monitoring port," IEEE Photon. Technol. Lett. 16, 1507-1509 (2004).
[CrossRef]

2003 (2)

2002 (1)

2000 (2)

N. A. Riza and S. Sumriddetchkajorn, "Small tilt micromirror device-based multiwavelength three-dimensional 2 × 2 fiber-optic switch structures," Opt. Eng. 39, 379-386 (2000).
[CrossRef]

N. A. Riza and Y. Huang, "Digital fault-tolerant variable fiber optic attenuator using liquid crystals," Proc. SPIE , 4096, 101-106 (2000).
[CrossRef]

1998 (1)

1997 (1)

J. A. Dobrowolski, "Numerical methods for optical thin films," Optics and Photonics News 8, 25-33 (1997).
[CrossRef]

1991 (1)

1983 (1)

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A single-mode-fiber coupler with a variable coupling ratio," J. Lightwave Technol. LT-1, 176-178 (1983).
[CrossRef]

1981 (1)

Alameh, K. E.

R. Zheng, Z. Wang, K. E. Alameh, and W. A. Crossland, "An opto-VLSI reconfigurable broad-band optical splitter," IEEE Photon. Technol. Lett. 17, 339-341 (2005).
[CrossRef]

Barberio, Y. L.

Y. L. Barberio, D. W. Dahringer, J. W. Engelberth, and A. E. Neeves, "Method for making an evanescent field coupler," U.S. patent 5,623,567 (22 April 1997).

Cambell-Miller, M.

M. Cambell-Miller, B. S. Kawasaki, Y. Cheng, N. Galai, and G. Pomerant, "Lensed cascaded optical filter," U.S. patent 6,055,112 (25 April 2000).

Chaitavon, K.

S. Sumriddetchkajorn and K. Chaitavon, "Wavelength sensitive thin-film filter based variable optical attenuator with an embedded monitoring port," IEEE Photon. Technol. Lett. 16, 1507-1509 (2004).
[CrossRef]

Cheng, Y.

M. Cambell-Miller, B. S. Kawasaki, Y. Cheng, N. Galai, and G. Pomerant, "Lensed cascaded optical filter," U.S. patent 6,055,112 (25 April 2000).

Crossland, W. A.

R. Zheng, Z. Wang, K. E. Alameh, and W. A. Crossland, "An opto-VLSI reconfigurable broad-band optical splitter," IEEE Photon. Technol. Lett. 17, 339-341 (2005).
[CrossRef]

Dahringer, D. W.

Y. L. Barberio, D. W. Dahringer, J. W. Engelberth, and A. E. Neeves, "Method for making an evanescent field coupler," U.S. patent 5,623,567 (22 April 1997).

Dobrowolski, J. A.

J. A. Dobrowolski, "Numerical methods for optical thin films," Optics and Photonics News 8, 25-33 (1997).
[CrossRef]

Duberstein, T.

T. Duberstein, "Look both ways before crossing the network," Lightwave Magazine (October 2000), pp. 80-83.

Engelberth, J. W.

Y. L. Barberio, D. W. Dahringer, J. W. Engelberth, and A. E. Neeves, "Method for making an evanescent field coupler," U.S. patent 5,623,567 (22 April 1997).

Galai, N.

M. Cambell-Miller, B. S. Kawasaki, Y. Cheng, N. Galai, and G. Pomerant, "Lensed cascaded optical filter," U.S. patent 6,055,112 (25 April 2000).

Garriss, G. M.

G. M. Garriss, "Fiber optic coupler/connector with GRIN lens," U.S. patent 5,163,107 (10 November 1992).

Ghauri, F. N.

N. A. Riza and F. N. Ghauri, "Hybrid analog-digital MEMS fiber-optic variable attenuator," IEEE Photon. Technol. Lett. 17, 124-126 (2005).
[CrossRef]

N. A. Riza and F. N. Ghauri, "Super-resolution variable fiber-optic attenuation instrument using digital micromirror device (DMD)," Rev. Sci. Instrum. 76, (2005).
[CrossRef]

Hill, K. O.

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A single-mode-fiber coupler with a variable coupling ratio," J. Lightwave Technol. LT-1, 176-178 (1983).
[CrossRef]

S. Kawasaki, K. O. Hill, and R. G. Lamont, "Biconical-taper single-mode fiber coupler," Opt. Lett. 6, 327-328 (1981).
[CrossRef] [PubMed]

Huang, Y.

N. A. Riza and Y. Huang, "Digital fault-tolerant variable fiber optic attenuator using liquid crystals," Proc. SPIE , 4096, 101-106 (2000).
[CrossRef]

Johnson, D. C.

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A single-mode-fiber coupler with a variable coupling ratio," J. Lightwave Technol. LT-1, 176-178 (1983).
[CrossRef]

Kagami, M.

Kawachi, M.

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A single-mode-fiber coupler with a variable coupling ratio," J. Lightwave Technol. LT-1, 176-178 (1983).
[CrossRef]

Kawasaki, B. S.

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A single-mode-fiber coupler with a variable coupling ratio," J. Lightwave Technol. LT-1, 176-178 (1983).
[CrossRef]

M. Cambell-Miller, B. S. Kawasaki, Y. Cheng, N. Galai, and G. Pomerant, "Lensed cascaded optical filter," U.S. patent 6,055,112 (25 April 2000).

Kawasaki, S.

Kim, H.

Kim, J.

Kim, K. T.

Lamont, R. G.

Lee, B. H.

Li, J.

J. Li and N. Teitelbaum, "Multi-pass optical filter," U.S. patent 6,055,347 (25 April 2000).

Lizuka, K.

K. Lizuka, Engineering Optics, 2nd ed. (Springer-Verlag, 1985), Vol. 35.

Long, C.

Mughal, M. J.

Neeves, A. E.

Y. L. Barberio, D. W. Dahringer, J. W. Engelberth, and A. E. Neeves, "Method for making an evanescent field coupler," U.S. patent 5,623,567 (22 April 1997).

Okada, H.

Paek, U. C.

Pomerant, G.

M. Cambell-Miller, B. S. Kawasaki, Y. Cheng, N. Galai, and G. Pomerant, "Lensed cascaded optical filter," U.S. patent 6,055,112 (25 April 2000).

Qingming, X.

Riza, N. A.

N. A. Riza, "Liquid crystal agile photonics--From fiber to the free-space domain," in Proceedings of the Conference on Liquid Crystals Optics and Applications LCOA/COO-2005, T. Wolinski, ed., Proc. SPIE 5947, 0J-1-0J-8 (2005).

N. A. Riza and F. N. Ghauri, "Hybrid analog-digital MEMS fiber-optic variable attenuator," IEEE Photon. Technol. Lett. 17, 124-126 (2005).
[CrossRef]

N. A. Riza and F. N. Ghauri, "Super-resolution variable fiber-optic attenuation instrument using digital micromirror device (DMD)," Rev. Sci. Instrum. 76, (2005).
[CrossRef]

N. A. Riza and M. J. Mughal, "Optical power independent optical beam profiler," Opt. Eng. 43, 793-797 (2004).
[CrossRef]

N. A. Riza and M. J. Mughal, "Broadband optical equalizer using fault tolerant digital micromirrors," Opt. Express 11, 1559-1565 (2003).
[CrossRef] [PubMed]

M. van Buren and N. A. Riza, "Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism," Appl. Opt. 42, 550-565 (2003).
[CrossRef] [PubMed]

S. Sumriddetchkajorn and N. A. Riza, "Micro-electro-mechanical system-based digitally controlled optical beam profiler," Appl. Opt. 41, 3506-3510 (2002).
[CrossRef] [PubMed]

N. A. Riza and S. Sumriddetchkajorn, "Small tilt micromirror device-based multiwavelength three-dimensional 2 × 2 fiber-optic switch structures," Opt. Eng. 39, 379-386 (2000).
[CrossRef]

N. A. Riza and Y. Huang, "Digital fault-tolerant variable fiber optic attenuator using liquid crystals," Proc. SPIE , 4096, 101-106 (2000).
[CrossRef]

N. A. Riza and S. Sumriddetchkajorn, "Fault-tolerant dense multiwavelength add-drop filter with a two-dimensional digital micromirror device," Appl. Opt. 37, 6355-6361 (1998).
[CrossRef]

N. A. Riza, "Fault-tolerant fiber-optical beam control modules," U.S. patent 6,222,954 (24 April 2001).

N. A. Riza, "High resolution fault-tolerant fiber-optical beam control modules," U.S. patent 6,563,974 (13 May 2003).

Sakai, Y.

Sumriddetchkajorn, S.

S. Sumriddetchkajorn and K. Chaitavon, "Wavelength sensitive thin-film filter based variable optical attenuator with an embedded monitoring port," IEEE Photon. Technol. Lett. 16, 1507-1509 (2004).
[CrossRef]

S. Sumriddetchkajorn and N. A. Riza, "Micro-electro-mechanical system-based digitally controlled optical beam profiler," Appl. Opt. 41, 3506-3510 (2002).
[CrossRef] [PubMed]

N. A. Riza and S. Sumriddetchkajorn, "Small tilt micromirror device-based multiwavelength three-dimensional 2 × 2 fiber-optic switch structures," Opt. Eng. 39, 379-386 (2000).
[CrossRef]

N. A. Riza and S. Sumriddetchkajorn, "Fault-tolerant dense multiwavelength add-drop filter with a two-dimensional digital micromirror device," Appl. Opt. 37, 6355-6361 (1998).
[CrossRef]

Takahashi, M.

M. Takahashi, "Four polarization maintaining optical fiber ferrule and optical coupler using same," U.S. patent 5,692,081 (25 November 1997).

Teitelbaum, N.

J. Li and N. Teitelbaum, "Multi-pass optical filter," U.S. patent 6,055,347 (25 April 2000).

van Buren, M.

Wang, Z.

R. Zheng, Z. Wang, K. E. Alameh, and W. A. Crossland, "An opto-VLSI reconfigurable broad-band optical splitter," IEEE Photon. Technol. Lett. 17, 339-341 (2005).
[CrossRef]

Wen, L.

Yong, L.

Yun, Z.

Zheng, R.

R. Zheng, Z. Wang, K. E. Alameh, and W. A. Crossland, "An opto-VLSI reconfigurable broad-band optical splitter," IEEE Photon. Technol. Lett. 17, 339-341 (2005).
[CrossRef]

Appl. Opt. (4)

IEEE Photon. Technol. Lett. (3)

N. A. Riza and F. N. Ghauri, "Hybrid analog-digital MEMS fiber-optic variable attenuator," IEEE Photon. Technol. Lett. 17, 124-126 (2005).
[CrossRef]

R. Zheng, Z. Wang, K. E. Alameh, and W. A. Crossland, "An opto-VLSI reconfigurable broad-band optical splitter," IEEE Photon. Technol. Lett. 17, 339-341 (2005).
[CrossRef]

S. Sumriddetchkajorn and K. Chaitavon, "Wavelength sensitive thin-film filter based variable optical attenuator with an embedded monitoring port," IEEE Photon. Technol. Lett. 16, 1507-1509 (2004).
[CrossRef]

J. Lightwave Technol. (2)

B. S. Kawasaki, M. Kawachi, K. O. Hill, and D. C. Johnson, "A single-mode-fiber coupler with a variable coupling ratio," J. Lightwave Technol. LT-1, 176-178 (1983).
[CrossRef]

Z. Yun, L. Wen, C. Long, L. Yong, and X. Qingming, "A 1 × 2 variable optical power splitter development," J. Lightwave Technol. 24, 1566-1570 (2006).
[CrossRef]

Lightwave Magazine (1)

T. Duberstein, "Look both ways before crossing the network," Lightwave Magazine (October 2000), pp. 80-83.

Opt. Eng. (2)

N. A. Riza and S. Sumriddetchkajorn, "Small tilt micromirror device-based multiwavelength three-dimensional 2 × 2 fiber-optic switch structures," Opt. Eng. 39, 379-386 (2000).
[CrossRef]

N. A. Riza and M. J. Mughal, "Optical power independent optical beam profiler," Opt. Eng. 43, 793-797 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Optics and Photonics News (1)

J. A. Dobrowolski, "Numerical methods for optical thin films," Optics and Photonics News 8, 25-33 (1997).
[CrossRef]

Proc. SPIE (2)

N. A. Riza and Y. Huang, "Digital fault-tolerant variable fiber optic attenuator using liquid crystals," Proc. SPIE , 4096, 101-106 (2000).
[CrossRef]

N. A. Riza, "Liquid crystal agile photonics--From fiber to the free-space domain," in Proceedings of the Conference on Liquid Crystals Optics and Applications LCOA/COO-2005, T. Wolinski, ed., Proc. SPIE 5947, 0J-1-0J-8 (2005).

Rev. Sci. Instrum. (1)

N. A. Riza and F. N. Ghauri, "Super-resolution variable fiber-optic attenuation instrument using digital micromirror device (DMD)," Rev. Sci. Instrum. 76, (2005).
[CrossRef]

Other (8)

M. Cambell-Miller, B. S. Kawasaki, Y. Cheng, N. Galai, and G. Pomerant, "Lensed cascaded optical filter," U.S. patent 6,055,112 (25 April 2000).

J. Li and N. Teitelbaum, "Multi-pass optical filter," U.S. patent 6,055,347 (25 April 2000).

M. Takahashi, "Four polarization maintaining optical fiber ferrule and optical coupler using same," U.S. patent 5,692,081 (25 November 1997).

G. M. Garriss, "Fiber optic coupler/connector with GRIN lens," U.S. patent 5,163,107 (10 November 1992).

Y. L. Barberio, D. W. Dahringer, J. W. Engelberth, and A. E. Neeves, "Method for making an evanescent field coupler," U.S. patent 5,623,567 (22 April 1997).

K. Lizuka, Engineering Optics, 2nd ed. (Springer-Verlag, 1985), Vol. 35.

N. A. Riza, "Fault-tolerant fiber-optical beam control modules," U.S. patent 6,222,954 (24 April 2001).

N. A. Riza, "High resolution fault-tolerant fiber-optical beam control modules," U.S. patent 6,563,974 (13 May 2003).

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Figures (7)

Fig. 1
Fig. 1

(a) Present day VAM, (b) use of VAMs in today's collection network scenario, (c) use of VAMs in distributed network scenarios.

Fig. 2
Fig. 2

Proposed smart VAM and its (a) bypass mode and its (b) test or tap mode. As an example, the smart VAM uses a 90 / 10 split ratio.

Fig. 3
Fig. 3

Proposed 90 / 10 smart splitter modules used to used to form the proposed smart VAMs. (a) Bypass mode and (b) test mode of the smart splitter modules used to operate the smart VAM modes.

Fig. 4
Fig. 4

Alternate implementation of the 90 / 10 smart splitter module used to form the proposed smart VAM. Here, polarization optics is used in a transmissive module design to control beam routing and tap level. Each smart splitter module consists of an input fiber-lens port and two output fiber-lens ports, within which are three BDPs and two macro-pixel-based polarization rotation devices.

Fig. 5
Fig. 5

Demonstrated smart VAM design using a DMD chip. C, Circulator; FL1 and FL2, fiber lens 1 and fiber lens 2.

Fig. 6
Fig. 6

DMD-based smart VAM utilization and experimental characterization in a dual-user RF communication FO link. L, laser; IOM, integrated optic modulator; IOC, integrated optic combiner; PD, photodetector; A, RF amplifier; RF SA, RF spectrum analyzer.

Fig. 7
Fig. 7

Measured RF 1 ( 45   MHz ) and RF 2 (50 MHz) spectrum. Analyzer power traces for smart VAM optical power split ratios of (a) 50:50, (b) 10:90, (c) 20:80, (d) 66.66:33.33, (e) 30:70, and (f) 25:75.

Tables (3)

Tables Icon

Table 1 Relationship Between Smart VAM Optical Power Ratios and Measured RF Signal Power Ratios for Typical Smart VAM Optical Power Split Values

Tables Icon

Table 2 Measured Smart VAM Performance Versus RF and Optical Power Ratio Design Values

Tables Icon

Table 3 Smart VAM Optical Power Ratio Setting Versus Experimental Mirror Count Used to Enable the Desired Power Split Ratios Between the Two Output Ports

Equations (3)

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

P RF   1 P R F 2 = i 1 2 i 2 2 = P 1 2 P 2 2 .
RFPR   ( dB ) = 10 log P RF   1 P RF   2 = 10 log i 1 2 i 2 2 = 20 log P 1 P 2 .
RFPR   ( dB ) = 2 × OPR   ( dB ) .

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