Abstract

We have proposed and experimentally demonstrated a new radio-over-fiber system technique generating optical millimeter-waves with central carriers suppressed by simply tuning the modulation index of an optical phase modulator without requiring any complicated bias control circuits or narrowband optical filters. Error-free transmission of the generated 40-GHz optical mm-wave with 2.5-Gb/s data over 10-km single mode fiber (SMF-28) and 3-m air distance was achieved. The experimental results were analyzed and compared with the traditional method that requires a specific carrier suppression optical filter. The power penalty caused by the crosstalk between wavelength division multiplexed (WDM) channels was experimentally measured and studied and was about 4 dB at a bit error rate (BER) of 109. The filter bandwidth requirement, achievable carrier suppression ratio, and harmonics fluctuation due to fiber dispersion were also theoretically analyzed.

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  1. A. Koonen and L. Garcia, "Radio-over-MMF techniques—Part II: Microwave to millimeter-wave systems," J. Lightwave Technol. 26(15), 2396‒2408 (2008).
    [CrossRef]
  2. M. Bakaul, A. Nirmalathas, C. Lim, D. Novak, and R. Waterhouse, "Simultaneous multiplexing and demultiplexing of wavelength-interleaved channels in DWDM millimeter-wave fiber-radio networks," J. Lightwave Technol. 24(9), 3341‒3352 (2006).
    [CrossRef]
  3. M. Weiß, M. Huchard, A. Stöhr, B. Charbonnier, S. Fedderwitz, and D. S. Jäger, "60-GHz photonic millimeter-wave link for short- to medium-range wireless transmission up to 12.5 Gb/s," J. Lightwave Technol. 26(15), 2424‒2429 (2008).
    [CrossRef]
  4. Z. Jia, J. Yu, G. Ellinas, and G.-K. Chang, "Key enabling technologies for optical-wireless networks: optical millimeter-wave generation, wavelength reuse, and architecture," J. Lightwave Technol. 25(11), 3452‒3471 (2007).
    [CrossRef]
  5. G.-K. Chang, A. Chowdhury, Z. Ji, H.-C. Chien, M.-F. Huang, J. Yu, and G. Ellinas, "Key technologies of WDM-PON for future converged optical broadband access networks [invited]," J. Opt. Commun. Netw. 1(4), C35‒C50 (2009).
    [CrossRef]
  6. A. Chowdhury, H.-C. Chien, Y.-T. Hsueh, and G.-K. Chang, "Advanced system technologies and field demonstration for in-building optical-wireless network with integrated broadband services," J. Lightwave Technol. 27(12), 1920‒1927 (2009).
    [CrossRef]
  7. S.-H. Fan, H.-C. Chien, Y.-T. Hsueh, A. Chowdhury, J. Yu, and G.-K. Chang, "Simultaneous transmission of wireless and wireline services using a single 60-GHz radio-over-fiber channel by coherent subcarrier modulation," IEEE Photon. Technol. Lett. 21(16), 1127‒1129 (2009).
    [CrossRef]
  8. H. Yang, F. Q. Wang, X. Huang, R. Liang, and Y. Wu, "An improved full-duplex radio-over-fiber system using optical carrier suppressed double sideband modulation at 60 GHz," Micro Opt. Technol. Lett. 51(6), 1473‒1476 (2009).
    [CrossRef]
  9. P. Shen, A. Nkansah, J. James, and N. J. Gomes, "Multilevel modulated signal transmission for millimeter-wave radio over fiber system," MWP/APMP, 2008, pp. 27‒30.
  10. J. Yu, Z. Jia, L. Xu, L. Chen, T. Wang, and G. K. Chang, "DWDM optical millimeter-wave generation for radio-over-fiber using an optical phase modulator and an optical interleaver," IEEE Photon. Technol. Lett. 18(13), 1734‒1736 (2006).
  11. G. Qi, J. Yao, J. Seregelyi, S. Paquet, and C. Bélisle, "Optical generation and distribution of continuously tunable millimeter-wave signals using an optical phase modulator," J. Lightwave Technol. 23(9), 2687‒2695 (2005).
    [CrossRef]
  12. C. Lim, A. Nirmalathas, K.-L. Lee, D. Novak, and R. Waterhouse, "Intermodulation distortion improvement for fiber-radio applications incorporating OSSB+C modulation in an optical integrated-access environment," J. Lightwave Technol. 25(6), 1602‒1612 (2007).
    [CrossRef]
  13. J. Olmos, T. Kuri, and K. Kitayama, "Dynamic reconfigurable WDM 60-GHz millimeter-waveband radio-over-fiber access network: architectural considerations and experiment," J. Lightwave Technol. 25(11), 3374‒3380 (2007).
    [CrossRef]
  14. J. Ma, X. Xin, J. Yu, C. Yu, K. Wang, H. Huang, and L. Rao, "Optical millimeter wave generated by octupling the frequency of the local oscillator," J. Opt. Netw. 7(10), 837‒845 (2008).
    [CrossRef]
  15. Y. Le Guennec, G. Maury, J. P. Yao, and B. Cabon, "New optical microwave up-conversion solution in radio-over-fiber networks for 60 GHz wireless applications," J. Lightwave Technol. 24(3), 1277‒1282 (2006).
    [CrossRef]
  16. F. Zeng and J. Yao, "Investigation of phase-modulator-based all-optical bandpass microwave filter," J. Lightwave Technol. 23(4), 1721‒1727 (2005).
    [CrossRef]
  17. H. T. Friis, "A note on a simple transmission formula," Proc. IRE, Vol. 34, 1946, p. 254.
  18. Y.-T. Hsueh, H.-C. Chien, A. Chowdhury, and G.-K. Chang, "Multiband signals generation and transmission over fiber and air by a novel frequency-doubled, radio-over-fiber architecture without expensive carrier suppression filters," OFC/NFOEC, 2010, JThA35.

2009 (4)

S.-H. Fan, H.-C. Chien, Y.-T. Hsueh, A. Chowdhury, J. Yu, and G.-K. Chang, "Simultaneous transmission of wireless and wireline services using a single 60-GHz radio-over-fiber channel by coherent subcarrier modulation," IEEE Photon. Technol. Lett. 21(16), 1127‒1129 (2009).
[CrossRef]

H. Yang, F. Q. Wang, X. Huang, R. Liang, and Y. Wu, "An improved full-duplex radio-over-fiber system using optical carrier suppressed double sideband modulation at 60 GHz," Micro Opt. Technol. Lett. 51(6), 1473‒1476 (2009).
[CrossRef]

A. Chowdhury, H.-C. Chien, Y.-T. Hsueh, and G.-K. Chang, "Advanced system technologies and field demonstration for in-building optical-wireless network with integrated broadband services," J. Lightwave Technol. 27(12), 1920‒1927 (2009).
[CrossRef]

G.-K. Chang, A. Chowdhury, Z. Ji, H.-C. Chien, M.-F. Huang, J. Yu, and G. Ellinas, "Key technologies of WDM-PON for future converged optical broadband access networks [invited]," J. Opt. Commun. Netw. 1(4), C35‒C50 (2009).
[CrossRef]

2008 (3)

2007 (3)

2006 (3)

2005 (2)

Bakaul, M.

Bélisle, C.

Cabon, B.

Chang, G. K.

J. Yu, Z. Jia, L. Xu, L. Chen, T. Wang, and G. K. Chang, "DWDM optical millimeter-wave generation for radio-over-fiber using an optical phase modulator and an optical interleaver," IEEE Photon. Technol. Lett. 18(13), 1734‒1736 (2006).

Chang, G.-K.

S.-H. Fan, H.-C. Chien, Y.-T. Hsueh, A. Chowdhury, J. Yu, and G.-K. Chang, "Simultaneous transmission of wireless and wireline services using a single 60-GHz radio-over-fiber channel by coherent subcarrier modulation," IEEE Photon. Technol. Lett. 21(16), 1127‒1129 (2009).
[CrossRef]

A. Chowdhury, H.-C. Chien, Y.-T. Hsueh, and G.-K. Chang, "Advanced system technologies and field demonstration for in-building optical-wireless network with integrated broadband services," J. Lightwave Technol. 27(12), 1920‒1927 (2009).
[CrossRef]

G.-K. Chang, A. Chowdhury, Z. Ji, H.-C. Chien, M.-F. Huang, J. Yu, and G. Ellinas, "Key technologies of WDM-PON for future converged optical broadband access networks [invited]," J. Opt. Commun. Netw. 1(4), C35‒C50 (2009).
[CrossRef]

Z. Jia, J. Yu, G. Ellinas, and G.-K. Chang, "Key enabling technologies for optical-wireless networks: optical millimeter-wave generation, wavelength reuse, and architecture," J. Lightwave Technol. 25(11), 3452‒3471 (2007).
[CrossRef]

Y.-T. Hsueh, H.-C. Chien, A. Chowdhury, and G.-K. Chang, "Multiband signals generation and transmission over fiber and air by a novel frequency-doubled, radio-over-fiber architecture without expensive carrier suppression filters," OFC/NFOEC, 2010, JThA35.

Charbonnier, B.

Chen, L.

J. Yu, Z. Jia, L. Xu, L. Chen, T. Wang, and G. K. Chang, "DWDM optical millimeter-wave generation for radio-over-fiber using an optical phase modulator and an optical interleaver," IEEE Photon. Technol. Lett. 18(13), 1734‒1736 (2006).

Chien, H.-C.

S.-H. Fan, H.-C. Chien, Y.-T. Hsueh, A. Chowdhury, J. Yu, and G.-K. Chang, "Simultaneous transmission of wireless and wireline services using a single 60-GHz radio-over-fiber channel by coherent subcarrier modulation," IEEE Photon. Technol. Lett. 21(16), 1127‒1129 (2009).
[CrossRef]

A. Chowdhury, H.-C. Chien, Y.-T. Hsueh, and G.-K. Chang, "Advanced system technologies and field demonstration for in-building optical-wireless network with integrated broadband services," J. Lightwave Technol. 27(12), 1920‒1927 (2009).
[CrossRef]

G.-K. Chang, A. Chowdhury, Z. Ji, H.-C. Chien, M.-F. Huang, J. Yu, and G. Ellinas, "Key technologies of WDM-PON for future converged optical broadband access networks [invited]," J. Opt. Commun. Netw. 1(4), C35‒C50 (2009).
[CrossRef]

Y.-T. Hsueh, H.-C. Chien, A. Chowdhury, and G.-K. Chang, "Multiband signals generation and transmission over fiber and air by a novel frequency-doubled, radio-over-fiber architecture without expensive carrier suppression filters," OFC/NFOEC, 2010, JThA35.

Chowdhury, A.

S.-H. Fan, H.-C. Chien, Y.-T. Hsueh, A. Chowdhury, J. Yu, and G.-K. Chang, "Simultaneous transmission of wireless and wireline services using a single 60-GHz radio-over-fiber channel by coherent subcarrier modulation," IEEE Photon. Technol. Lett. 21(16), 1127‒1129 (2009).
[CrossRef]

G.-K. Chang, A. Chowdhury, Z. Ji, H.-C. Chien, M.-F. Huang, J. Yu, and G. Ellinas, "Key technologies of WDM-PON for future converged optical broadband access networks [invited]," J. Opt. Commun. Netw. 1(4), C35‒C50 (2009).
[CrossRef]

A. Chowdhury, H.-C. Chien, Y.-T. Hsueh, and G.-K. Chang, "Advanced system technologies and field demonstration for in-building optical-wireless network with integrated broadband services," J. Lightwave Technol. 27(12), 1920‒1927 (2009).
[CrossRef]

Y.-T. Hsueh, H.-C. Chien, A. Chowdhury, and G.-K. Chang, "Multiband signals generation and transmission over fiber and air by a novel frequency-doubled, radio-over-fiber architecture without expensive carrier suppression filters," OFC/NFOEC, 2010, JThA35.

Ellinas, G.

Fan, S.-H.

S.-H. Fan, H.-C. Chien, Y.-T. Hsueh, A. Chowdhury, J. Yu, and G.-K. Chang, "Simultaneous transmission of wireless and wireline services using a single 60-GHz radio-over-fiber channel by coherent subcarrier modulation," IEEE Photon. Technol. Lett. 21(16), 1127‒1129 (2009).
[CrossRef]

Fedderwitz, S.

Friis, H. T.

H. T. Friis, "A note on a simple transmission formula," Proc. IRE, Vol. 34, 1946, p. 254.

Garcia, L.

Gomes, N. J.

P. Shen, A. Nkansah, J. James, and N. J. Gomes, "Multilevel modulated signal transmission for millimeter-wave radio over fiber system," MWP/APMP, 2008, pp. 27‒30.

Hsueh, Y.-T.

S.-H. Fan, H.-C. Chien, Y.-T. Hsueh, A. Chowdhury, J. Yu, and G.-K. Chang, "Simultaneous transmission of wireless and wireline services using a single 60-GHz radio-over-fiber channel by coherent subcarrier modulation," IEEE Photon. Technol. Lett. 21(16), 1127‒1129 (2009).
[CrossRef]

A. Chowdhury, H.-C. Chien, Y.-T. Hsueh, and G.-K. Chang, "Advanced system technologies and field demonstration for in-building optical-wireless network with integrated broadband services," J. Lightwave Technol. 27(12), 1920‒1927 (2009).
[CrossRef]

Y.-T. Hsueh, H.-C. Chien, A. Chowdhury, and G.-K. Chang, "Multiband signals generation and transmission over fiber and air by a novel frequency-doubled, radio-over-fiber architecture without expensive carrier suppression filters," OFC/NFOEC, 2010, JThA35.

Huang, H.

Huang, M.-F.

Huang, X.

H. Yang, F. Q. Wang, X. Huang, R. Liang, and Y. Wu, "An improved full-duplex radio-over-fiber system using optical carrier suppressed double sideband modulation at 60 GHz," Micro Opt. Technol. Lett. 51(6), 1473‒1476 (2009).
[CrossRef]

Huchard, M.

Jäger, D. S.

James, J.

P. Shen, A. Nkansah, J. James, and N. J. Gomes, "Multilevel modulated signal transmission for millimeter-wave radio over fiber system," MWP/APMP, 2008, pp. 27‒30.

Ji, Z.

Jia, Z.

Z. Jia, J. Yu, G. Ellinas, and G.-K. Chang, "Key enabling technologies for optical-wireless networks: optical millimeter-wave generation, wavelength reuse, and architecture," J. Lightwave Technol. 25(11), 3452‒3471 (2007).
[CrossRef]

J. Yu, Z. Jia, L. Xu, L. Chen, T. Wang, and G. K. Chang, "DWDM optical millimeter-wave generation for radio-over-fiber using an optical phase modulator and an optical interleaver," IEEE Photon. Technol. Lett. 18(13), 1734‒1736 (2006).

Kitayama, K.

Koonen, A.

Kuri, T.

Le Guennec, Y.

Lee, K.-L.

Liang, R.

H. Yang, F. Q. Wang, X. Huang, R. Liang, and Y. Wu, "An improved full-duplex radio-over-fiber system using optical carrier suppressed double sideband modulation at 60 GHz," Micro Opt. Technol. Lett. 51(6), 1473‒1476 (2009).
[CrossRef]

Lim, C.

Ma, J.

Maury, G.

Nirmalathas, A.

Nkansah, A.

P. Shen, A. Nkansah, J. James, and N. J. Gomes, "Multilevel modulated signal transmission for millimeter-wave radio over fiber system," MWP/APMP, 2008, pp. 27‒30.

Novak, D.

Olmos, J.

Paquet, S.

Qi, G.

Rao, L.

Seregelyi, J.

Shen, P.

P. Shen, A. Nkansah, J. James, and N. J. Gomes, "Multilevel modulated signal transmission for millimeter-wave radio over fiber system," MWP/APMP, 2008, pp. 27‒30.

Stöhr, A.

Wang, F. Q.

H. Yang, F. Q. Wang, X. Huang, R. Liang, and Y. Wu, "An improved full-duplex radio-over-fiber system using optical carrier suppressed double sideband modulation at 60 GHz," Micro Opt. Technol. Lett. 51(6), 1473‒1476 (2009).
[CrossRef]

Wang, K.

Wang, T.

J. Yu, Z. Jia, L. Xu, L. Chen, T. Wang, and G. K. Chang, "DWDM optical millimeter-wave generation for radio-over-fiber using an optical phase modulator and an optical interleaver," IEEE Photon. Technol. Lett. 18(13), 1734‒1736 (2006).

Waterhouse, R.

Waterhouse, R.

Weiß, M.

Wu, Y.

H. Yang, F. Q. Wang, X. Huang, R. Liang, and Y. Wu, "An improved full-duplex radio-over-fiber system using optical carrier suppressed double sideband modulation at 60 GHz," Micro Opt. Technol. Lett. 51(6), 1473‒1476 (2009).
[CrossRef]

Xin, X.

Xu, L.

J. Yu, Z. Jia, L. Xu, L. Chen, T. Wang, and G. K. Chang, "DWDM optical millimeter-wave generation for radio-over-fiber using an optical phase modulator and an optical interleaver," IEEE Photon. Technol. Lett. 18(13), 1734‒1736 (2006).

Yang, H.

H. Yang, F. Q. Wang, X. Huang, R. Liang, and Y. Wu, "An improved full-duplex radio-over-fiber system using optical carrier suppressed double sideband modulation at 60 GHz," Micro Opt. Technol. Lett. 51(6), 1473‒1476 (2009).
[CrossRef]

Yao, J.

Yao, J. P.

Yu, C.

Yu, J.

S.-H. Fan, H.-C. Chien, Y.-T. Hsueh, A. Chowdhury, J. Yu, and G.-K. Chang, "Simultaneous transmission of wireless and wireline services using a single 60-GHz radio-over-fiber channel by coherent subcarrier modulation," IEEE Photon. Technol. Lett. 21(16), 1127‒1129 (2009).
[CrossRef]

G.-K. Chang, A. Chowdhury, Z. Ji, H.-C. Chien, M.-F. Huang, J. Yu, and G. Ellinas, "Key technologies of WDM-PON for future converged optical broadband access networks [invited]," J. Opt. Commun. Netw. 1(4), C35‒C50 (2009).
[CrossRef]

J. Ma, X. Xin, J. Yu, C. Yu, K. Wang, H. Huang, and L. Rao, "Optical millimeter wave generated by octupling the frequency of the local oscillator," J. Opt. Netw. 7(10), 837‒845 (2008).
[CrossRef]

Z. Jia, J. Yu, G. Ellinas, and G.-K. Chang, "Key enabling technologies for optical-wireless networks: optical millimeter-wave generation, wavelength reuse, and architecture," J. Lightwave Technol. 25(11), 3452‒3471 (2007).
[CrossRef]

J. Yu, Z. Jia, L. Xu, L. Chen, T. Wang, and G. K. Chang, "DWDM optical millimeter-wave generation for radio-over-fiber using an optical phase modulator and an optical interleaver," IEEE Photon. Technol. Lett. 18(13), 1734‒1736 (2006).

Zeng, F.

IEEE Photon. Technol. Lett. (2)

J. Yu, Z. Jia, L. Xu, L. Chen, T. Wang, and G. K. Chang, "DWDM optical millimeter-wave generation for radio-over-fiber using an optical phase modulator and an optical interleaver," IEEE Photon. Technol. Lett. 18(13), 1734‒1736 (2006).

S.-H. Fan, H.-C. Chien, Y.-T. Hsueh, A. Chowdhury, J. Yu, and G.-K. Chang, "Simultaneous transmission of wireless and wireline services using a single 60-GHz radio-over-fiber channel by coherent subcarrier modulation," IEEE Photon. Technol. Lett. 21(16), 1127‒1129 (2009).
[CrossRef]

J. Lightwave Technol. (10)

A. Chowdhury, H.-C. Chien, Y.-T. Hsueh, and G.-K. Chang, "Advanced system technologies and field demonstration for in-building optical-wireless network with integrated broadband services," J. Lightwave Technol. 27(12), 1920‒1927 (2009).
[CrossRef]

Y. Le Guennec, G. Maury, J. P. Yao, and B. Cabon, "New optical microwave up-conversion solution in radio-over-fiber networks for 60 GHz wireless applications," J. Lightwave Technol. 24(3), 1277‒1282 (2006).
[CrossRef]

F. Zeng and J. Yao, "Investigation of phase-modulator-based all-optical bandpass microwave filter," J. Lightwave Technol. 23(4), 1721‒1727 (2005).
[CrossRef]

G. Qi, J. Yao, J. Seregelyi, S. Paquet, and C. Bélisle, "Optical generation and distribution of continuously tunable millimeter-wave signals using an optical phase modulator," J. Lightwave Technol. 23(9), 2687‒2695 (2005).
[CrossRef]

C. Lim, A. Nirmalathas, K.-L. Lee, D. Novak, and R. Waterhouse, "Intermodulation distortion improvement for fiber-radio applications incorporating OSSB+C modulation in an optical integrated-access environment," J. Lightwave Technol. 25(6), 1602‒1612 (2007).
[CrossRef]

J. Olmos, T. Kuri, and K. Kitayama, "Dynamic reconfigurable WDM 60-GHz millimeter-waveband radio-over-fiber access network: architectural considerations and experiment," J. Lightwave Technol. 25(11), 3374‒3380 (2007).
[CrossRef]

A. Koonen and L. Garcia, "Radio-over-MMF techniques—Part II: Microwave to millimeter-wave systems," J. Lightwave Technol. 26(15), 2396‒2408 (2008).
[CrossRef]

M. Bakaul, A. Nirmalathas, C. Lim, D. Novak, and R. Waterhouse, "Simultaneous multiplexing and demultiplexing of wavelength-interleaved channels in DWDM millimeter-wave fiber-radio networks," J. Lightwave Technol. 24(9), 3341‒3352 (2006).
[CrossRef]

M. Weiß, M. Huchard, A. Stöhr, B. Charbonnier, S. Fedderwitz, and D. S. Jäger, "60-GHz photonic millimeter-wave link for short- to medium-range wireless transmission up to 12.5 Gb/s," J. Lightwave Technol. 26(15), 2424‒2429 (2008).
[CrossRef]

Z. Jia, J. Yu, G. Ellinas, and G.-K. Chang, "Key enabling technologies for optical-wireless networks: optical millimeter-wave generation, wavelength reuse, and architecture," J. Lightwave Technol. 25(11), 3452‒3471 (2007).
[CrossRef]

J. Opt. Commun. Netw. (1)

J. Opt. Netw. (1)

Micro Opt. Technol. Lett. (1)

H. Yang, F. Q. Wang, X. Huang, R. Liang, and Y. Wu, "An improved full-duplex radio-over-fiber system using optical carrier suppressed double sideband modulation at 60 GHz," Micro Opt. Technol. Lett. 51(6), 1473‒1476 (2009).
[CrossRef]

Other (3)

P. Shen, A. Nkansah, J. James, and N. J. Gomes, "Multilevel modulated signal transmission for millimeter-wave radio over fiber system," MWP/APMP, 2008, pp. 27‒30.

H. T. Friis, "A note on a simple transmission formula," Proc. IRE, Vol. 34, 1946, p. 254.

Y.-T. Hsueh, H.-C. Chien, A. Chowdhury, and G.-K. Chang, "Multiband signals generation and transmission over fiber and air by a novel frequency-doubled, radio-over-fiber architecture without expensive carrier suppression filters," OFC/NFOEC, 2010, JThA35.

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Figures (6)

Fig. 1
Fig. 1

(Color online) (a) Conceptual diagram and (b) schematic structure of the proposed optical mm-wave generation with the suppressed carrier using a MIE-PM.

Fig. 2
Fig. 2

(Color online) Simulation analyses of (a) carrier suppression ratio versus MI for the proposed MIE-PM scheme, (b) power levels of the optical carrier, the first and second sidebands versus MI for the proposed MIE-PM scheme, (c) CSR versus relative bias voltage detuning for the carrier suppression scheme using a minimum-point biased MZM, and (d) RF power of the first and second harmonics versus the 3-dB filter bandwidth for the proposed MIE-PM scheme.

Fig. 3
Fig. 3

(Color online) Experimental setup of the proposed 40-GHz RoF system for (a) single channel and (b) WDM transmission (PC: polarization controller; PM: phase modulator; IL: interleaver; PA: power amplifier; LNA: low noise amplifier; 4f: 1:4 frequency multiplier; PD: photodiode; LPF: low-pass filter.

Fig. 4
Fig. 4

(Color online) BER performance measurements of the single channel case with different wireless distance after 10-km SMF-28 transmission.

Fig. 5
Fig. 5

(Color online) The measured optical spectra of the WDM optical mm-wave generation scheme (a) with and (b) without the MIE-PM.

Fig. 6
Fig. 6

(a) BER performance measurements of the single channel case and WDM case with and without the MIE-PM. (b) Optical eye diagrams with different MIs at 2.5 Gb/s after 10-km SMF-28 transmission (100 ps/div).

Equations (3)

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

E o u t ( t ) = E 0 e j ω 0 t e j β cos ω m = E 0 n = (j) n J n ( β ) e j ( ω 0 + n ω m ) t E 0 { J 0 ( β ) e j ω 0 t + J 1 ( β ) e j ( ω 0 + ω m ) t + π / 2 J 1 ( β ) e j ( ω 0 ω m ) t π / 2 J 2 ( β ) e j ( ω 0 + 2 ω m ) t J 2 ( β ) e j ( ω 0 2 ω m ) t } ,
I ( t ) μ E 0 2 { [ 2 J 1 2 ( β 2 ) + 2 J 2 2 ( β 2 ) ] + [ 2 J 1 2 ( β 2 ) cos ( 2 ω m t ) ] } ,
P r = P t G t G r λ 4 π R 2 ,