Abstract

Visible Light Communication (VLC) as a new technology for ultrahigh-speed communication is still limited when using slow modulation light-emitting diode (LED). Alternatively, we present a 4-Gbit/s VLC system using coherent blue-laser diode (LD) via 16-quadrature amplitude modulation orthogonal frequency division multiplexing. By changing the composition and the optical-configuration of a remote phosphor-film the generated white light is tuned from cool day to neutral, and the bit error rate is optimized from 1.9 × 10−2 to 2.8 × 10−5 in a blue filter-free link due to enhanced blue light transmission in forward direction. Briefly, blue-LD is an alternative to LED for generating white light and boosting the data rate of VLC.

© 2015 Optical Society of America

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2015 (10)

R. Won, “View from... communication networks beyond the capacity crunch: Is it crunch time?” Nat. Photonics 9(7), 424–426 (2015).
[Crossref]

W. Ding, F. Yang, H. Yang, J. Wang, X. Wang, X. Zhang, and J. Song, “A hybrid power line and visible light communication system for indoor hospital applications,” Comput. Ind. 68, 170–178 (2015).
[Crossref]

H. M. Oubei, J. R. Duran, B. Janjua, H.-Y. Wang, C.-T. Tsai, Y.-C. Chi, T. K. Ng, H.-C. Kuo, J.-H. He, M.-S. Alouini, G.-R. Lin, and B. S. Ooi, “4.8 Gbit/s 16-QAM-OFDM transmission based on compact 450-nm laser for underwater wireless optical communication,” Opt. Express 23(18), 23302–23309 (2015).
[Crossref] [PubMed]

H. M. Oubei, C. Li, K.-H. Park, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “2.3 Gbit/s underwater wireless optical communications using directly modulated 520 nm laser diode,” Opt. Express 23(16), 20743–20748 (2015).
[Crossref] [PubMed]

P. Pust, P. J. Schmidt, and W. Schnick, “A revolution in lighting,” Nat. Mater. 14(5), 454–458 (2015).
[Crossref] [PubMed]

Y.-C. Chi, D.-H. Hsieh, C.-T. Tsai, H.-Y. Chen, H.-C. Kuo, and G.-R. Lin, “450-nm GaN laser diode enables high-speed visible light communication with 9-Gbps QAM-OFDM,” Opt. Express 23(10), 13051–13059 (2015).
[Crossref] [PubMed]

D. Tsonev, S. Videv, and H. Haas, “Towards a 100 Gb/s visible light wireless access network,” Opt. Express 23(2), 1627–1637 (2015).
[Crossref] [PubMed]

B. Janjua, H. M. Oubei, J. R. D. Retamal, T. K. Ng, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, H.-C. Kuo, G.-R. Lin, J.-H. He, and B. S. Ooi, “Going beyond 4 Gbps data rate by employing RGB laser diodes for visible light communication,” Opt. Express 23(14), 18746–18753 (2015).
[Crossref] [PubMed]

A. T. Hussein and J. M. H. Elmirghani, “Mobile multi-gigabit visible light communication system in realistic indoor environment,” J. Lightwave Technol. 33(15), 3293–3307 (2015).
[Crossref]

C. H. Yeh, H. Y. Chen, Y. L. Liu, and C. W. Chow, “Polarization-multiplexed 2×2 phosphor-LED wireless light communication without using analog equalization and optical blue filter,” Opt. Commun. 334, 8–11 (2015).
[Crossref]

2014 (9)

Y. Wang, C. Yang, Y. Wang, and N. Chi, “Gigabit polarization division multiplexing in visible light communication,” Opt. Lett. 39(7), 1823–1826 (2014).
[Crossref] [PubMed]

J.-Y. Sung, C.-W. Chow, and C.-H. Yeh, “Is blue optical filter necessary in high speed phosphor-based white light LED visible light communications?” Opt. Express 22(17), 20646–20651 (2014).
[Crossref] [PubMed]

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, Y. L. Liu, and Y. F. Wu, “High-speed phosphor-LED wireless communication system utilizing no blue filter,” Proc. SPIE 9193, 91931A (2014).
[Crossref]

D. Tsonev, H. Chun, S. Rajbhandari, J. J. D. McKendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC link using a gallium nitride µLED,” IEEE Photonics Technol. Lett. 26(7), 637–640 (2014).
[Crossref]

H. Li, X. Chen, J. Guo, and H. Chen, “A 550 Mbit/s real-time visible light communication system based on phosphorescent white light LED for practical high-speed low-complexity application,” Opt. Express 22(22), 27203–27213 (2014).
[Crossref] [PubMed]

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, and Y. L. Liu, “Adaptive 84.44-190 Mbit/s phosphor-LED wireless communication utilizing no blue filter at practical transmission distance,” Opt. Express 22(8), 9783–9788 (2014).
[Crossref] [PubMed]

C.-Y. Lin, Y.-P. Lin, H.-H. Lu, C.-Y. Chen, T.-W. Jhang, and M.-C. Chen, “Optical free-space wavelength-division-multiplexing transport system,” Opt. Lett. 39(2), 315–318 (2014).
[Crossref] [PubMed]

I. Takai, T. Harada, M. Andoh, K. Yasutomi, K. Kagawa, and S. Kawahito, “Optical vehicle-to-vehicle communication system using LED transmitter and camera receiver,” IEEE Photonics J. 6(5), 1–14 (2014).
[Crossref]

T. Yamazato, I. Takai, H. Okada, T. Fujii, T. Yendo, S. Arai, M. Andoh, T. Harada, K. Yasutomi, K. Kagawa, and S. Kawahito, “Image-sensor-based visible light communication for automotive applications,” IEEE Commun. Mag. 52(7), 88–97 (2014).
[Crossref]

2013 (5)

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and C. Sien, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photonics J. 5(4), 7901507 (2013).
[Crossref]

Y. Pei, S. Zhu, H. Yang, L. Zhao, X. Yi, J. J. Wang, and J. Li, “LED modulation characteristics in a visible-light communication system,” Opt. Photonics J. 3(2), 4 (2013).
[Crossref]

J. J. Wierer, J. Y. Tsao, and D. S. Sizov, “Comparison between blue lasers and light-emitting diodes for future solid-state lighting,” Laser Photonics Rev. 7(6), 963–993 (2013).
[Crossref]

S. Watson, M. Tan, S. P. Najda, P. Perlin, M. Leszczynski, G. Targowski, S. Grzanka, and A. E. Kelly, “Visible light communications using a directly modulated 422 nm GaN laser diode,” Opt. Lett. 38(19), 3792–3794 (2013).
[Crossref] [PubMed]

C.-Y. Chen, P.-Y. Wu, H.-H. Lu, Y.-P. Lin, J.-Y. Wen, and F.-C. Hu, “Bidirectional 16-QAM OFDM in-building network over SMF and free-space VLC transport,” Opt. Lett. 38(13), 2345–2347 (2013).
[Crossref] [PubMed]

2012 (3)

A. M. Khalid, G. Cossu, R. Corsini, P. Choudhury, and E. Ciaramella, “1-Gb/s Transmission over a phosphorescent white LED by using rate-adaptive discrete multitone modulation,” IEEE Photonics J. 4(5), 1465–1473 (2012).
[Crossref]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

M. O’Grady and G. O’Hare, “Computer science. How smart is your city?” Science 335(6076), 1581–1582 (2012).
[Crossref] [PubMed]

2011 (6)

D. D. G. C. Jones, “Semiconductor devices for high-speed optoelectronics, by Giovanni Ghione,” Contemp. Phys. 52(2), 169–170 (2011).
[Crossref]

A. Neumann, J. J. Wierer, W. Davis, Y. Ohno, S. R. J. Brueck, and J. Y. Tsao, “Four-color laser white illuminant demonstrating high color-rendering quality,” Opt. Express 19(S4), A982–A990 (2011).
[Crossref] [PubMed]

H.-C. Kuo, C.-W. Hung, H.-C. Chen, K.-J. Chen, C.-H. Wang, C.-W. Sher, C.-C. Yeh, C.-C. Lin, C.-H. Chen, and Y.-J. Cheng, “Patterned structure of remote phosphor for phosphor-converted white LEDs,” Opt. Express 19(S4), A930–A936 (2011).
[Crossref] [PubMed]

News, “Wireless future drives microwave photonics,” Nat. Photonics 5(12), 724 (2011).
[Crossref]

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

J. Tan, K. Yang, and M. Xia, “Adaptive equalization for high speed optical MIMO wireless communications using white LED,” Front. Optoelectron. China 4(4), 454–461 (2011).
[Crossref]

2010 (1)

A. C. C. Esteves, J. Brokken-Zijp, J. Laven, and G. de With, “Light converter coatings from cross-linked PDMS/particles composite materials,” Prog. Org. Coat. 68(1-2), 12–18 (2010).
[Crossref]

2009 (1)

2008 (1)

D. O’Brien, H. Le Minh, L. Zeng, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “Indoor visible light communications: challenges and prospects,” Proc. SPIE 7091, 709106 (2008).
[Crossref]

2007 (2)

M. Jinno, Y. Miyamoto, and Y. Hibino, “Networks: optical-transport networks in 2015,” Nat. Photonics 1(3), 157–159 (2007).
[Crossref]

G.-y. Hu, C.-y. Chen, and Z. Chen, “Free-space optical communication using visible light,” J. Zhejiang University 8(2), 186–191 (2007).
[Crossref]

Alouini, M.-S.

Andoh, M.

I. Takai, T. Harada, M. Andoh, K. Yasutomi, K. Kagawa, and S. Kawahito, “Optical vehicle-to-vehicle communication system using LED transmitter and camera receiver,” IEEE Photonics J. 6(5), 1–14 (2014).
[Crossref]

T. Yamazato, I. Takai, H. Okada, T. Fujii, T. Yendo, S. Arai, M. Andoh, T. Harada, K. Yasutomi, K. Kagawa, and S. Kawahito, “Image-sensor-based visible light communication for automotive applications,” IEEE Commun. Mag. 52(7), 88–97 (2014).
[Crossref]

Arai, S.

T. Yamazato, I. Takai, H. Okada, T. Fujii, T. Yendo, S. Arai, M. Andoh, T. Harada, K. Yasutomi, K. Kagawa, and S. Kawahito, “Image-sensor-based visible light communication for automotive applications,” IEEE Commun. Mag. 52(7), 88–97 (2014).
[Crossref]

Armstrong, J.

Azurdia-Meza, C.

D. Iturralde, C. Azurdia-Meza, N. Krommenacker, I. Soto, Z. Ghassemlooy, and N. Becerra, “A new location system for an underground mining environment using visible light communications,” in 9th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP, 2014), pp. 1165–1169.
[Crossref]

Becerra, N.

D. Iturralde, C. Azurdia-Meza, N. Krommenacker, I. Soto, Z. Ghassemlooy, and N. Becerra, “A new location system for an underground mining environment using visible light communications,” in 9th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP, 2014), pp. 1165–1169.
[Crossref]

Becker, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Brokken-Zijp, J.

A. C. C. Esteves, J. Brokken-Zijp, J. Laven, and G. de With, “Light converter coatings from cross-linked PDMS/particles composite materials,” Prog. Org. Coat. 68(1-2), 12–18 (2010).
[Crossref]

Brueck, S. R. J.

Chen, C. W.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and C. Sien, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photonics J. 5(4), 7901507 (2013).
[Crossref]

Chen, C.-H.

Chen, C.-Y.

Chen, H.

Chen, H. Y.

C. H. Yeh, H. Y. Chen, Y. L. Liu, and C. W. Chow, “Polarization-multiplexed 2×2 phosphor-LED wireless light communication without using analog equalization and optical blue filter,” Opt. Commun. 334, 8–11 (2015).
[Crossref]

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, Y. L. Liu, and Y. F. Wu, “High-speed phosphor-LED wireless communication system utilizing no blue filter,” Proc. SPIE 9193, 91931A (2014).
[Crossref]

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, and Y. L. Liu, “Adaptive 84.44-190 Mbit/s phosphor-LED wireless communication utilizing no blue filter at practical transmission distance,” Opt. Express 22(8), 9783–9788 (2014).
[Crossref] [PubMed]

Chen, H.-C.

Chen, H.-Y.

Chen, J.

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, and Y. L. Liu, “Adaptive 84.44-190 Mbit/s phosphor-LED wireless communication utilizing no blue filter at practical transmission distance,” Opt. Express 22(8), 9783–9788 (2014).
[Crossref] [PubMed]

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, Y. L. Liu, and Y. F. Wu, “High-speed phosphor-LED wireless communication system utilizing no blue filter,” Proc. SPIE 9193, 91931A (2014).
[Crossref]

Chen, K.-J.

Chen, M.-C.

Chen, X.

Chen, Z.

G.-y. Hu, C.-y. Chen, and Z. Chen, “Free-space optical communication using visible light,” J. Zhejiang University 8(2), 186–191 (2007).
[Crossref]

Chen, Z. Y.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and C. Sien, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photonics J. 5(4), 7901507 (2013).
[Crossref]

Cheng, Y.-J.

Chi, N.

Chi, Y.-C.

Choudhury, P.

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D. Tsonev, H. Chun, S. Rajbhandari, J. J. D. McKendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC link using a gallium nitride µLED,” IEEE Photonics Technol. Lett. 26(7), 637–640 (2014).
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A. M. Khalid, G. Cossu, R. Corsini, P. Choudhury, and E. Ciaramella, “1-Gb/s Transmission over a phosphorescent white LED by using rate-adaptive discrete multitone modulation,” IEEE Photonics J. 4(5), 1465–1473 (2012).
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R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
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A. C. C. Esteves, J. Brokken-Zijp, J. Laven, and G. de With, “Light converter coatings from cross-linked PDMS/particles composite materials,” Prog. Org. Coat. 68(1-2), 12–18 (2010).
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D. O’Brien, H. Le Minh, L. Zeng, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “Indoor visible light communications: challenges and prospects,” Proc. SPIE 7091, 709106 (2008).
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D. O’Brien, H. Le Minh, L. Zeng, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “Indoor visible light communications: challenges and prospects,” Proc. SPIE 7091, 709106 (2008).
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R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
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F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and C. Sien, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photonics J. 5(4), 7901507 (2013).
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C. H. Yeh, H. Y. Chen, Y. L. Liu, and C. W. Chow, “Polarization-multiplexed 2×2 phosphor-LED wireless light communication without using analog equalization and optical blue filter,” Opt. Commun. 334, 8–11 (2015).
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D. Tsonev, H. Chun, S. Rajbhandari, J. J. D. McKendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC link using a gallium nitride µLED,” IEEE Photonics Technol. Lett. 26(7), 637–640 (2014).
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H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
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Nebendahl, B.

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[Crossref]

Rajbhandari, S.

D. Tsonev, H. Chun, S. Rajbhandari, J. J. D. McKendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC link using a gallium nitride µLED,” IEEE Photonics Technol. Lett. 26(7), 637–640 (2014).
[Crossref]

Retamal, J. R. D.

Rufo, J.

R. Perez-Jimenez, J. Rufo, C. Quintana, J. Rabadan, and F. J. Lopez-Hernandez, “Visible light communication systems for passenger in-flight data networking,” in IEEE International Conference on Consumer Electronics (ICCE, 2011), pp. 445–446.
[Crossref]

Schmidt, P. J.

P. Pust, P. J. Schmidt, and W. Schnick, “A revolution in lighting,” Nat. Mater. 14(5), 454–458 (2015).
[Crossref] [PubMed]

Schmogrow, R.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Schnick, W.

P. Pust, P. J. Schmidt, and W. Schnick, “A revolution in lighting,” Nat. Mater. 14(5), 454–458 (2015).
[Crossref] [PubMed]

Shafik, R. A.

R. A. Shafik, S. Rahman, and R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” in International Conference on Electrical and Computer Engineering (ICECE, 2006), pp. 408–411.
[Crossref]

Sher, C.-W.

Shinich, T.

T. Morio, T. Hideki, K. Yoshisada, T. Yoshihisa, K. Hiroo, K. Toshihiro, S. Kenji, Y. Shinich, T. Shinich, T. Hiroyuki, N. Isao, and A. Maki, “Terrestrial free-space optical communications network for future airborne and satellite-based optical communications projects,” in 31st AIAA International Communications Satellite Systems Conference (ICSSC, 2013).

Shinich, Y.

T. Morio, T. Hideki, K. Yoshisada, T. Yoshihisa, K. Hiroo, K. Toshihiro, S. Kenji, Y. Shinich, T. Shinich, T. Hiroyuki, N. Isao, and A. Maki, “Terrestrial free-space optical communications network for future airborne and satellite-based optical communications projects,” in 31st AIAA International Communications Satellite Systems Conference (ICSSC, 2013).

Sien, C.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and C. Sien, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photonics J. 5(4), 7901507 (2013).
[Crossref]

Sizov, D. S.

J. J. Wierer, J. Y. Tsao, and D. S. Sizov, “Comparison between blue lasers and light-emitting diodes for future solid-state lighting,” Laser Photonics Rev. 7(6), 963–993 (2013).
[Crossref]

Song, J.

W. Ding, F. Yang, H. Yang, J. Wang, X. Wang, X. Zhang, and J. Song, “A hybrid power line and visible light communication system for indoor hospital applications,” Comput. Ind. 68, 170–178 (2015).
[Crossref]

Soto, I.

D. Iturralde, C. Azurdia-Meza, N. Krommenacker, I. Soto, Z. Ghassemlooy, and N. Becerra, “A new location system for an underground mining environment using visible light communications,” in 9th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP, 2014), pp. 1165–1169.
[Crossref]

Sung, J.-Y.

Takai, I.

I. Takai, T. Harada, M. Andoh, K. Yasutomi, K. Kagawa, and S. Kawahito, “Optical vehicle-to-vehicle communication system using LED transmitter and camera receiver,” IEEE Photonics J. 6(5), 1–14 (2014).
[Crossref]

T. Yamazato, I. Takai, H. Okada, T. Fujii, T. Yendo, S. Arai, M. Andoh, T. Harada, K. Yasutomi, K. Kagawa, and S. Kawahito, “Image-sensor-based visible light communication for automotive applications,” IEEE Commun. Mag. 52(7), 88–97 (2014).
[Crossref]

Tan, J.

J. Tan, K. Yang, and M. Xia, “Adaptive equalization for high speed optical MIMO wireless communications using white LED,” Front. Optoelectron. China 4(4), 454–461 (2011).
[Crossref]

Tan, M.

Targowski, G.

Toshihiro, K.

T. Morio, T. Hideki, K. Yoshisada, T. Yoshihisa, K. Hiroo, K. Toshihiro, S. Kenji, Y. Shinich, T. Shinich, T. Hiroyuki, N. Isao, and A. Maki, “Terrestrial free-space optical communications network for future airborne and satellite-based optical communications projects,” in 31st AIAA International Communications Satellite Systems Conference (ICSSC, 2013).

Tsai, C.-T.

Tsao, J. Y.

J. J. Wierer, J. Y. Tsao, and D. S. Sizov, “Comparison between blue lasers and light-emitting diodes for future solid-state lighting,” Laser Photonics Rev. 7(6), 963–993 (2013).
[Crossref]

A. Neumann, J. J. Wierer, W. Davis, Y. Ohno, S. R. J. Brueck, and J. Y. Tsao, “Four-color laser white illuminant demonstrating high color-rendering quality,” Opt. Express 19(S4), A982–A990 (2011).
[Crossref] [PubMed]

Tsonev, D.

D. Tsonev, S. Videv, and H. Haas, “Towards a 100 Gb/s visible light wireless access network,” Opt. Express 23(2), 1627–1637 (2015).
[Crossref] [PubMed]

D. Tsonev, H. Chun, S. Rajbhandari, J. J. D. McKendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC link using a gallium nitride µLED,” IEEE Photonics Technol. Lett. 26(7), 637–640 (2014).
[Crossref]

Videv, S.

D. Tsonev, S. Videv, and H. Haas, “Towards a 100 Gb/s visible light wireless access network,” Opt. Express 23(2), 1627–1637 (2015).
[Crossref] [PubMed]

D. Tsonev, H. Chun, S. Rajbhandari, J. J. D. McKendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC link using a gallium nitride µLED,” IEEE Photonics Technol. Lett. 26(7), 637–640 (2014).
[Crossref]

Wang, C.-H.

Wang, H.-Y.

Wang, J.

W. Ding, F. Yang, H. Yang, J. Wang, X. Wang, X. Zhang, and J. Song, “A hybrid power line and visible light communication system for indoor hospital applications,” Comput. Ind. 68, 170–178 (2015).
[Crossref]

Wang, J. J.

Y. Pei, S. Zhu, H. Yang, L. Zhao, X. Yi, J. J. Wang, and J. Li, “LED modulation characteristics in a visible-light communication system,” Opt. Photonics J. 3(2), 4 (2013).
[Crossref]

Wang, X.

W. Ding, F. Yang, H. Yang, J. Wang, X. Wang, X. Zhang, and J. Song, “A hybrid power line and visible light communication system for indoor hospital applications,” Comput. Ind. 68, 170–178 (2015).
[Crossref]

Wang, Y.

Watson, S.

D. Tsonev, H. Chun, S. Rajbhandari, J. J. D. McKendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC link using a gallium nitride µLED,” IEEE Photonics Technol. Lett. 26(7), 637–640 (2014).
[Crossref]

S. Watson, M. Tan, S. P. Najda, P. Perlin, M. Leszczynski, G. Targowski, S. Grzanka, and A. E. Kelly, “Visible light communications using a directly modulated 422 nm GaN laser diode,” Opt. Lett. 38(19), 3792–3794 (2013).
[Crossref] [PubMed]

Wei, C. C.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and C. Sien, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photonics J. 5(4), 7901507 (2013).
[Crossref]

Wen, J.-Y.

Wierer, J. J.

J. J. Wierer, J. Y. Tsao, and D. S. Sizov, “Comparison between blue lasers and light-emitting diodes for future solid-state lighting,” Laser Photonics Rev. 7(6), 963–993 (2013).
[Crossref]

A. Neumann, J. J. Wierer, W. Davis, Y. Ohno, S. R. J. Brueck, and J. Y. Tsao, “Four-color laser white illuminant demonstrating high color-rendering quality,” Opt. Express 19(S4), A982–A990 (2011).
[Crossref] [PubMed]

Winter, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Won, E. T.

D. O’Brien, H. Le Minh, L. Zeng, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “Indoor visible light communications: challenges and prospects,” Proc. SPIE 7091, 709106 (2008).
[Crossref]

Won, R.

R. Won, “View from... communication networks beyond the capacity crunch: Is it crunch time?” Nat. Photonics 9(7), 424–426 (2015).
[Crossref]

Wu, F. M.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and C. Sien, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photonics J. 5(4), 7901507 (2013).
[Crossref]

Wu, P.-Y.

Wu, Y. F.

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, Y. L. Liu, and Y. F. Wu, “High-speed phosphor-LED wireless communication system utilizing no blue filter,” Proc. SPIE 9193, 91931A (2014).
[Crossref]

Xia, M.

J. Tan, K. Yang, and M. Xia, “Adaptive equalization for high speed optical MIMO wireless communications using white LED,” Front. Optoelectron. China 4(4), 454–461 (2011).
[Crossref]

Yamazato, T.

T. Yamazato, I. Takai, H. Okada, T. Fujii, T. Yendo, S. Arai, M. Andoh, T. Harada, K. Yasutomi, K. Kagawa, and S. Kawahito, “Image-sensor-based visible light communication for automotive applications,” IEEE Commun. Mag. 52(7), 88–97 (2014).
[Crossref]

Yang, C.

Yang, F.

W. Ding, F. Yang, H. Yang, J. Wang, X. Wang, X. Zhang, and J. Song, “A hybrid power line and visible light communication system for indoor hospital applications,” Comput. Ind. 68, 170–178 (2015).
[Crossref]

Yang, H.

W. Ding, F. Yang, H. Yang, J. Wang, X. Wang, X. Zhang, and J. Song, “A hybrid power line and visible light communication system for indoor hospital applications,” Comput. Ind. 68, 170–178 (2015).
[Crossref]

Y. Pei, S. Zhu, H. Yang, L. Zhao, X. Yi, J. J. Wang, and J. Li, “LED modulation characteristics in a visible-light communication system,” Opt. Photonics J. 3(2), 4 (2013).
[Crossref]

Yang, K.

J. Tan, K. Yang, and M. Xia, “Adaptive equalization for high speed optical MIMO wireless communications using white LED,” Front. Optoelectron. China 4(4), 454–461 (2011).
[Crossref]

Yasutomi, K.

I. Takai, T. Harada, M. Andoh, K. Yasutomi, K. Kagawa, and S. Kawahito, “Optical vehicle-to-vehicle communication system using LED transmitter and camera receiver,” IEEE Photonics J. 6(5), 1–14 (2014).
[Crossref]

T. Yamazato, I. Takai, H. Okada, T. Fujii, T. Yendo, S. Arai, M. Andoh, T. Harada, K. Yasutomi, K. Kagawa, and S. Kawahito, “Image-sensor-based visible light communication for automotive applications,” IEEE Commun. Mag. 52(7), 88–97 (2014).
[Crossref]

Yeh, C. H.

C. H. Yeh, H. Y. Chen, Y. L. Liu, and C. W. Chow, “Polarization-multiplexed 2×2 phosphor-LED wireless light communication without using analog equalization and optical blue filter,” Opt. Commun. 334, 8–11 (2015).
[Crossref]

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, Y. L. Liu, and Y. F. Wu, “High-speed phosphor-LED wireless communication system utilizing no blue filter,” Proc. SPIE 9193, 91931A (2014).
[Crossref]

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, and Y. L. Liu, “Adaptive 84.44-190 Mbit/s phosphor-LED wireless communication utilizing no blue filter at practical transmission distance,” Opt. Express 22(8), 9783–9788 (2014).
[Crossref] [PubMed]

Yeh, C.-C.

Yeh, C.-H.

Yendo, T.

T. Yamazato, I. Takai, H. Okada, T. Fujii, T. Yendo, S. Arai, M. Andoh, T. Harada, K. Yasutomi, K. Kagawa, and S. Kawahito, “Image-sensor-based visible light communication for automotive applications,” IEEE Commun. Mag. 52(7), 88–97 (2014).
[Crossref]

Yi, X.

Y. Pei, S. Zhu, H. Yang, L. Zhao, X. Yi, J. J. Wang, and J. Li, “LED modulation characteristics in a visible-light communication system,” Opt. Photonics J. 3(2), 4 (2013).
[Crossref]

Yoshihisa, T.

T. Morio, T. Hideki, K. Yoshisada, T. Yoshihisa, K. Hiroo, K. Toshihiro, S. Kenji, Y. Shinich, T. Shinich, T. Hiroyuki, N. Isao, and A. Maki, “Terrestrial free-space optical communications network for future airborne and satellite-based optical communications projects,” in 31st AIAA International Communications Satellite Systems Conference (ICSSC, 2013).

Yoshisada, K.

T. Morio, T. Hideki, K. Yoshisada, T. Yoshihisa, K. Hiroo, K. Toshihiro, S. Kenji, Y. Shinich, T. Shinich, T. Hiroyuki, N. Isao, and A. Maki, “Terrestrial free-space optical communications network for future airborne and satellite-based optical communications projects,” in 31st AIAA International Communications Satellite Systems Conference (ICSSC, 2013).

Zeng, L.

D. O’Brien, H. Le Minh, L. Zeng, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “Indoor visible light communications: challenges and prospects,” Proc. SPIE 7091, 709106 (2008).
[Crossref]

Zhang, X.

W. Ding, F. Yang, H. Yang, J. Wang, X. Wang, X. Zhang, and J. Song, “A hybrid power line and visible light communication system for indoor hospital applications,” Comput. Ind. 68, 170–178 (2015).
[Crossref]

Zhao, L.

Y. Pei, S. Zhu, H. Yang, L. Zhao, X. Yi, J. J. Wang, and J. Li, “LED modulation characteristics in a visible-light communication system,” Opt. Photonics J. 3(2), 4 (2013).
[Crossref]

Zhu, S.

Y. Pei, S. Zhu, H. Yang, L. Zhao, X. Yi, J. J. Wang, and J. Li, “LED modulation characteristics in a visible-light communication system,” Opt. Photonics J. 3(2), 4 (2013).
[Crossref]

Comput. Ind. (1)

W. Ding, F. Yang, H. Yang, J. Wang, X. Wang, X. Zhang, and J. Song, “A hybrid power line and visible light communication system for indoor hospital applications,” Comput. Ind. 68, 170–178 (2015).
[Crossref]

Contemp. Phys. (1)

D. D. G. C. Jones, “Semiconductor devices for high-speed optoelectronics, by Giovanni Ghione,” Contemp. Phys. 52(2), 169–170 (2011).
[Crossref]

Front. Optoelectron. China (1)

J. Tan, K. Yang, and M. Xia, “Adaptive equalization for high speed optical MIMO wireless communications using white LED,” Front. Optoelectron. China 4(4), 454–461 (2011).
[Crossref]

IEEE Commun. Mag. (2)

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

T. Yamazato, I. Takai, H. Okada, T. Fujii, T. Yendo, S. Arai, M. Andoh, T. Harada, K. Yasutomi, K. Kagawa, and S. Kawahito, “Image-sensor-based visible light communication for automotive applications,” IEEE Commun. Mag. 52(7), 88–97 (2014).
[Crossref]

IEEE Photonics J. (3)

A. M. Khalid, G. Cossu, R. Corsini, P. Choudhury, and E. Ciaramella, “1-Gb/s Transmission over a phosphorescent white LED by using rate-adaptive discrete multitone modulation,” IEEE Photonics J. 4(5), 1465–1473 (2012).
[Crossref]

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, H. T. Huang, and C. Sien, “Performance comparison of OFDM signal and CAP signal over high capacity RGB-LED-based WDM visible light communication,” IEEE Photonics J. 5(4), 7901507 (2013).
[Crossref]

I. Takai, T. Harada, M. Andoh, K. Yasutomi, K. Kagawa, and S. Kawahito, “Optical vehicle-to-vehicle communication system using LED transmitter and camera receiver,” IEEE Photonics J. 6(5), 1–14 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (2)

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

D. Tsonev, H. Chun, S. Rajbhandari, J. J. D. McKendry, S. Videv, E. Gu, M. Haji, S. Watson, A. E. Kelly, G. Faulkner, M. D. Dawson, H. Haas, and D. O’Brien, “A 3-Gb/s single-LED OFDM-based wireless VLC link using a gallium nitride µLED,” IEEE Photonics Technol. Lett. 26(7), 637–640 (2014).
[Crossref]

J. Lightwave Technol. (2)

J. Zhejiang University (1)

G.-y. Hu, C.-y. Chen, and Z. Chen, “Free-space optical communication using visible light,” J. Zhejiang University 8(2), 186–191 (2007).
[Crossref]

Laser Photonics Rev. (1)

J. J. Wierer, J. Y. Tsao, and D. S. Sizov, “Comparison between blue lasers and light-emitting diodes for future solid-state lighting,” Laser Photonics Rev. 7(6), 963–993 (2013).
[Crossref]

Nat. Mater. (1)

P. Pust, P. J. Schmidt, and W. Schnick, “A revolution in lighting,” Nat. Mater. 14(5), 454–458 (2015).
[Crossref] [PubMed]

Nat. Photonics (3)

R. Won, “View from... communication networks beyond the capacity crunch: Is it crunch time?” Nat. Photonics 9(7), 424–426 (2015).
[Crossref]

M. Jinno, Y. Miyamoto, and Y. Hibino, “Networks: optical-transport networks in 2015,” Nat. Photonics 1(3), 157–159 (2007).
[Crossref]

News, “Wireless future drives microwave photonics,” Nat. Photonics 5(12), 724 (2011).
[Crossref]

Opt. Commun. (1)

C. H. Yeh, H. Y. Chen, Y. L. Liu, and C. W. Chow, “Polarization-multiplexed 2×2 phosphor-LED wireless light communication without using analog equalization and optical blue filter,” Opt. Commun. 334, 8–11 (2015).
[Crossref]

Opt. Express (10)

H.-C. Kuo, C.-W. Hung, H.-C. Chen, K.-J. Chen, C.-H. Wang, C.-W. Sher, C.-C. Yeh, C.-C. Lin, C.-H. Chen, and Y.-J. Cheng, “Patterned structure of remote phosphor for phosphor-converted white LEDs,” Opt. Express 19(S4), A930–A936 (2011).
[Crossref] [PubMed]

Y.-C. Chi, D.-H. Hsieh, C.-T. Tsai, H.-Y. Chen, H.-C. Kuo, and G.-R. Lin, “450-nm GaN laser diode enables high-speed visible light communication with 9-Gbps QAM-OFDM,” Opt. Express 23(10), 13051–13059 (2015).
[Crossref] [PubMed]

A. Neumann, J. J. Wierer, W. Davis, Y. Ohno, S. R. J. Brueck, and J. Y. Tsao, “Four-color laser white illuminant demonstrating high color-rendering quality,” Opt. Express 19(S4), A982–A990 (2011).
[Crossref] [PubMed]

D. Tsonev, S. Videv, and H. Haas, “Towards a 100 Gb/s visible light wireless access network,” Opt. Express 23(2), 1627–1637 (2015).
[Crossref] [PubMed]

B. Janjua, H. M. Oubei, J. R. D. Retamal, T. K. Ng, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, H.-C. Kuo, G.-R. Lin, J.-H. He, and B. S. Ooi, “Going beyond 4 Gbps data rate by employing RGB laser diodes for visible light communication,” Opt. Express 23(14), 18746–18753 (2015).
[Crossref] [PubMed]

H. Li, X. Chen, J. Guo, and H. Chen, “A 550 Mbit/s real-time visible light communication system based on phosphorescent white light LED for practical high-speed low-complexity application,” Opt. Express 22(22), 27203–27213 (2014).
[Crossref] [PubMed]

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, and Y. L. Liu, “Adaptive 84.44-190 Mbit/s phosphor-LED wireless communication utilizing no blue filter at practical transmission distance,” Opt. Express 22(8), 9783–9788 (2014).
[Crossref] [PubMed]

H. M. Oubei, J. R. Duran, B. Janjua, H.-Y. Wang, C.-T. Tsai, Y.-C. Chi, T. K. Ng, H.-C. Kuo, J.-H. He, M.-S. Alouini, G.-R. Lin, and B. S. Ooi, “4.8 Gbit/s 16-QAM-OFDM transmission based on compact 450-nm laser for underwater wireless optical communication,” Opt. Express 23(18), 23302–23309 (2015).
[Crossref] [PubMed]

H. M. Oubei, C. Li, K.-H. Park, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “2.3 Gbit/s underwater wireless optical communications using directly modulated 520 nm laser diode,” Opt. Express 23(16), 20743–20748 (2015).
[Crossref] [PubMed]

J.-Y. Sung, C.-W. Chow, and C.-H. Yeh, “Is blue optical filter necessary in high speed phosphor-based white light LED visible light communications?” Opt. Express 22(17), 20646–20651 (2014).
[Crossref] [PubMed]

Opt. Lett. (4)

Opt. Photonics J. (1)

Y. Pei, S. Zhu, H. Yang, L. Zhao, X. Yi, J. J. Wang, and J. Li, “LED modulation characteristics in a visible-light communication system,” Opt. Photonics J. 3(2), 4 (2013).
[Crossref]

Proc. SPIE (2)

D. O’Brien, H. Le Minh, L. Zeng, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “Indoor visible light communications: challenges and prospects,” Proc. SPIE 7091, 709106 (2008).
[Crossref]

C. H. Yeh, C. W. Chow, H. Y. Chen, J. Chen, Y. L. Liu, and Y. F. Wu, “High-speed phosphor-LED wireless communication system utilizing no blue filter,” Proc. SPIE 9193, 91931A (2014).
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Prog. Org. Coat. (1)

A. C. C. Esteves, J. Brokken-Zijp, J. Laven, and G. de With, “Light converter coatings from cross-linked PDMS/particles composite materials,” Prog. Org. Coat. 68(1-2), 12–18 (2010).
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Science (1)

M. O’Grady and G. O’Hare, “Computer science. How smart is your city?” Science 335(6076), 1581–1582 (2012).
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Other (6)

T. Morio, T. Hideki, K. Yoshisada, T. Yoshihisa, K. Hiroo, K. Toshihiro, S. Kenji, Y. Shinich, T. Shinich, T. Hiroyuki, N. Isao, and A. Maki, “Terrestrial free-space optical communications network for future airborne and satellite-based optical communications projects,” in 31st AIAA International Communications Satellite Systems Conference (ICSSC, 2013).

D. Iturralde, C. Azurdia-Meza, N. Krommenacker, I. Soto, Z. Ghassemlooy, and N. Becerra, “A new location system for an underground mining environment using visible light communications,” in 9th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP, 2014), pp. 1165–1169.
[Crossref]

R. Perez-Jimenez, J. Rufo, C. Quintana, J. Rabadan, and F. J. Lopez-Hernandez, “Visible light communication systems for passenger in-flight data networking,” in IEEE International Conference on Consumer Electronics (ICCE, 2011), pp. 445–446.
[Crossref]

N. Kumar, N. Lourenco, D. Terra, L. N. Alves, and R. L. Aguiar, “Visible light communications in intelligent transportation systems,” in IEEE Intelligent Vehicles Symposium (IV, 2012), pp. 748–753.
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R. A. Shafik, S. Rahman, and R. Islam, “On the extended relationships among EVM, BER and SNR as performance metrics,” in International Conference on Electrical and Computer Engineering (ICECE, 2006), pp. 408–411.
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T. Deepa and R. Kumar, “Performance of comparison metrics on M-QAM OFDM systems with high power amplifier,” in World Congress on Information and Communication Technologies (WICT, 2012), pp. 909–914.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

(a) Experimental set-up configuration of our proposed phosphor-based blue-LD VLC system. (b) Schematic block diagram of the 16-QAM OFDM transmission (Tx) and reception (Rx) units. The inset is the time-frequency scheme of the 16-QAM OFDM data. TEC, thermoelectric cooler; APD, avalanche photodetector; PRBS, pseudo-random binary sequence; S/P, serial-to-parallel multiplexer; P/S, parallel-to-serial demultiplexer; DAC, digital-to-analog converter; ADC, analog-to-digital converter; FFT, fast Fourier transformation; IFFT, inverse fast Fourier transformation; QAM, quadrature amplitude modulation; OFDM, orthogonal frequency-division multiplexing; TS, training symbol; CP, cyclic prefix; FEC, forward error correction; AWG, arbitrary waveform generator; DSA; digital serial analyzer; BER, bit error rate.

Fig. 2
Fig. 2

(a) Photographs of as-synthesized phosphor-film with varying YAG:Ce concentration on PDMS, spin coating speed, and baking time. Experimental setup of our proposed optics-phosphor-films configurations: (b) standalone and (c) mirror-coated. Experimental setups of four different approaches to evaluate the necessity of the optical blue filter (BF) and the linear polarizer (LP): (d) with linear polarizer and with blue filter (LP/BF), (e) without linear polarizer and with blue filter (wLP/BF), (f) with linear polarizer and without blue filter (LP/wBF), and (g) without linear polarizer and without blue filter (wLP/wBF).

Fig. 3
Fig. 3

(a) L-I-V curve of the blue-LD under continuous wave operation at 25 °C. (b) Emission spectra of the blue-LD. (c) Small-signal frequency response of the blue-LD in free space with injection currents of 50, 60, 70 and 90 mA.

Fig. 4
Fig. 4

(a) Absorption spectra of the three phosphor-films P1, P2, and P3 in standalone configuration. (b) Irradiance spectrum of the white light generated by standalone P1, P2, and P3 and mirror-coated M1, M2, and M3 phosphor-films when illuminated by blue-LD under 70 mA and 16-QAM OFDM signal.

Fig. 5
Fig. 5

(a) CIE 1931 chromaticity diagram with lines of constant CCT, (x,y) coordinates from 2° observer, and CCT value obtained from the irradiance spectrum of measured white light generation with phosphor-films in standalone (P1, P2, and P3) and mirror-coated (M1, M2, and M3) configurations. Photographs of the as-generated white light by (b) standalone phosphor-film P1 and (c) mirror-coated phosphor-film M1.

Fig. 6
Fig. 6

(a) The measured BER of the transmitted 16-QAM OFDM signal emitted from blue-LD and exciting phosphor-films in standalone P1, and P2, and mirror-coated M1, M2, and M3 configurations under four approaches at receiver side: LP/BF, wLP/BF, LP/wBF, and wPL/wBF. Dashed line indicates the BER of FEC Limit: 3.8 × 10−3. Constellation plots and related BER of the transmitted 16-QAM OFDM signal through the wLP/wBF setup approach for phosphor-films in standalone (b) P1, and (c) P2, and mirror-coated (d) M1, (e) M2, and (f) M3 configurations. Schematic of white light generation by blue-LD illumination of phosphor-films in (g) standalone, and (h) mirror-coated configuration.

Equations (2)

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t r [bit/s]= Δf[sample/s] L FFT [sample] N OFDM [symbol] m QAM [bit/symbol]
BER 2( 1 1 L ) log 2 L Q[ [ 3 log 2 L L 2 1 ] 2 EV M RMS 2 log 2 M ]

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