Abstract

A wavelength-multiplexed optical scanning scheme is proposed for deflecting a free-space optical beam by selection of the wavelength of the light incident on a wavelength-dispersive optical element. With fast tunable lasers or optical filters, this scanner features microsecond domain scan setting speeds and large- diameter apertures of several centimeters or more for subdegree angular scans. Analysis performed indicates an optimum scan range for a given diffraction order and grating period. Limitations include beam-spreading effects based on the varying scanner aperture sizes and the instantaneous information bandwidth of the data-carrying laser beam.

© 2001 Optical Society of America

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References

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  1. M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Marcel Dekker, New York, 1983).
  2. W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
    [CrossRef]
  3. F. Kubick, “Electro-optic beam scanner,” U.S. patent4,706,094 (10November1987).
  4. P. J. Talbot, “PLZT based electro-optic phased array optical scanner,” U.S. patent5,668,657 (16September1997).
  5. M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
    [CrossRef]
  6. W. Goltsos, M. Holtz, “Agile beam steering using binary optics microlens array,” Opt. Eng. 29, 1392–1397 (1990).
    [CrossRef]
  7. N. A. Riza, “MOST: multiplexed optical scanner technology,” in Lasers and Electro-Optics Society 13th Annual Conference Proceedings, A. Weiner, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), Vol. 2, pp. 828–829.
  8. N. A. Riza, Y. Huang, “High speed optical scanner for multi-dimensional beam pointing and acquisition,” in Lasers and Electro-Optics Society 12th Annual Conference Proceedings, L. Goldberg, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 184–185.
  9. N. A. Riza, Z. Yaqoob, “High speed fiber-optic probe for dynamic blood analysis measurements,” in Optical Techniques and Instrumentation for the Measurement of Blood Composition, Structure, and Dynamics, A. V. Priezzhev, P. A. Oberg, eds., Proc. SPIE4163, 18–23 (2000).
    [CrossRef]
  10. N. A. Riza, Z. Yaqoob, “Ultra high speed scanner for optical data handling,” in Lasers and Electro-Optics Society 13th Annual Conference Proceedings, A. Weiner, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), Vol. 2, pp. 822–823.
  11. F. Delorme, G. Alibert, C. Ougier, S. Slempkes, H. Nakajima, “Sampled-grating DBR lasers with 181 wavelengths over 44 nm and optimized power variation for WDM applications,” in Optical Fiber Communication Conference, Vol. 1 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 379–381.
  12. Product NYW-50-001 (ADC Altitun, P.O. Box 911, SE, 175 29 Järfälla, Stockholm, Sweden, May2000).
  13. Product MTX-TEML (Multiplex Inc., Corporate Headquarters, 115 Corporate Blvd., South Plainfield, N.J. 07080, November2000).
  14. I. C. Chang, “Progress of acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 2, 819–825 (1996).
  15. I. C. Chang, J. Xu, D. Wo, “Bandpass response of collinear beam acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 1, 745–748 (1997).
  16. E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).
  17. E. G. Loewen, M. Nevière, D. Maystre, “Grating efficiency theory as it applies to blazed and holographic gratings,” Appl. Opt. 16, 2711–2721 (1977).
    [CrossRef] [PubMed]
  18. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]
  19. R. S. Chu, J. A. Kong, “Modal theory of spatially periodic media,” IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).
  20. A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984).
  21. N. A. Riza, “Reconfigurable optical wireless,” in Lasers and Electro-Optics Society 12th Annual Conference Proceedings, D. Psaltis, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), Vol. 1, pp. 70–71.
  22. S. Gorshe, Z. Papir, “Topics in broadband: last mile solutions,” IEEE Commun. Mag. 38, 166 (2000).
    [CrossRef]
  23. Y. Koike, “Plastic fibers,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest (Optical Society of America, Washington, D.C., 1997), p. 325.

2000 (1)

S. Gorshe, Z. Papir, “Topics in broadband: last mile solutions,” IEEE Commun. Mag. 38, 166 (2000).
[CrossRef]

1997 (3)

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

I. C. Chang, J. Xu, D. Wo, “Bandpass response of collinear beam acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 1, 745–748 (1997).

1996 (1)

I. C. Chang, “Progress of acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 2, 819–825 (1996).

1990 (1)

W. Goltsos, M. Holtz, “Agile beam steering using binary optics microlens array,” Opt. Eng. 29, 1392–1397 (1990).
[CrossRef]

1981 (1)

1977 (2)

E. G. Loewen, M. Nevière, D. Maystre, “Grating efficiency theory as it applies to blazed and holographic gratings,” Appl. Opt. 16, 2711–2721 (1977).
[CrossRef] [PubMed]

R. S. Chu, J. A. Kong, “Modal theory of spatially periodic media,” IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).

Alibert, G.

F. Delorme, G. Alibert, C. Ougier, S. Slempkes, H. Nakajima, “Sampled-grating DBR lasers with 181 wavelengths over 44 nm and optimized power variation for WDM applications,” in Optical Fiber Communication Conference, Vol. 1 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 379–381.

Andrews, A. P.

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

Chang, I. C.

I. C. Chang, J. Xu, D. Wo, “Bandpass response of collinear beam acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 1, 745–748 (1997).

I. C. Chang, “Progress of acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 2, 819–825 (1996).

Chiou, A. E.

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

Chu, R. S.

R. S. Chu, J. A. Kong, “Modal theory of spatially periodic media,” IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).

Dadkhah, M. S.

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

Delorme, F.

F. Delorme, G. Alibert, C. Ougier, S. Slempkes, H. Nakajima, “Sampled-grating DBR lasers with 181 wavelengths over 44 nm and optimized power variation for WDM applications,” in Optical Fiber Communication Conference, Vol. 1 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 379–381.

Gaylord, T. K.

Goltsos, W.

W. Goltsos, M. Holtz, “Agile beam steering using binary optics microlens array,” Opt. Eng. 29, 1392–1397 (1990).
[CrossRef]

Gorshe, S.

S. Gorshe, Z. Papir, “Topics in broadband: last mile solutions,” IEEE Commun. Mag. 38, 166 (2000).
[CrossRef]

Gottlieb, M.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Marcel Dekker, New York, 1983).

Holtz, M.

W. Goltsos, M. Holtz, “Agile beam steering using binary optics microlens array,” Opt. Eng. 29, 1392–1397 (1990).
[CrossRef]

Huang, Y.

N. A. Riza, Y. Huang, “High speed optical scanner for multi-dimensional beam pointing and acquisition,” in Lasers and Electro-Optics Society 12th Annual Conference Proceedings, L. Goldberg, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 184–185.

Ide, M.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Ireland, C. L. M.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Marcel Dekker, New York, 1983).

Kamiya, T.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Khoshnevisan, M.

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

Klaus, W.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Koike, Y.

Y. Koike, “Plastic fibers,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest (Optical Society of America, Washington, D.C., 1997), p. 325.

Kong, J. A.

R. S. Chu, J. A. Kong, “Modal theory of spatially periodic media,” IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).

Kubick, F.

F. Kubick, “Electro-optic beam scanner,” U.S. patent4,706,094 (10November1987).

Ley, J. M.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Marcel Dekker, New York, 1983).

Loewen, E. G.

Marcy, H. O.

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

Maystre, D.

Moharam, M. G.

Morokawa, S.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Motamedi, M. E.

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

Nakajima, H.

F. Delorme, G. Alibert, C. Ougier, S. Slempkes, H. Nakajima, “Sampled-grating DBR lasers with 181 wavelengths over 44 nm and optimized power variation for WDM applications,” in Optical Fiber Communication Conference, Vol. 1 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 379–381.

Nevière, M.

Ougier, C.

F. Delorme, G. Alibert, C. Ougier, S. Slempkes, H. Nakajima, “Sampled-grating DBR lasers with 181 wavelengths over 44 nm and optimized power variation for WDM applications,” in Optical Fiber Communication Conference, Vol. 1 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 379–381.

Papir, Z.

S. Gorshe, Z. Papir, “Topics in broadband: last mile solutions,” IEEE Commun. Mag. 38, 166 (2000).
[CrossRef]

Park, S.

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

Popov, E.

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Riza, N. A.

N. A. Riza, “Reconfigurable optical wireless,” in Lasers and Electro-Optics Society 12th Annual Conference Proceedings, D. Psaltis, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), Vol. 1, pp. 70–71.

N. A. Riza, “MOST: multiplexed optical scanner technology,” in Lasers and Electro-Optics Society 13th Annual Conference Proceedings, A. Weiner, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), Vol. 2, pp. 828–829.

N. A. Riza, Y. Huang, “High speed optical scanner for multi-dimensional beam pointing and acquisition,” in Lasers and Electro-Optics Society 12th Annual Conference Proceedings, L. Goldberg, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 184–185.

N. A. Riza, Z. Yaqoob, “High speed fiber-optic probe for dynamic blood analysis measurements,” in Optical Techniques and Instrumentation for the Measurement of Blood Composition, Structure, and Dynamics, A. V. Priezzhev, P. A. Oberg, eds., Proc. SPIE4163, 18–23 (2000).
[CrossRef]

N. A. Riza, Z. Yaqoob, “Ultra high speed scanner for optical data handling,” in Lasers and Electro-Optics Society 13th Annual Conference Proceedings, A. Weiner, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), Vol. 2, pp. 822–823.

Slempkes, S.

F. Delorme, G. Alibert, C. Ougier, S. Slempkes, H. Nakajima, “Sampled-grating DBR lasers with 181 wavelengths over 44 nm and optimized power variation for WDM applications,” in Optical Fiber Communication Conference, Vol. 1 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 379–381.

Talbot, P. J.

P. J. Talbot, “PLZT based electro-optic phased array optical scanner,” U.S. patent5,668,657 (16September1997).

Tsuchiya, M.

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Wang, A.

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

Wo, D.

I. C. Chang, J. Xu, D. Wo, “Bandpass response of collinear beam acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 1, 745–748 (1997).

Xu, J.

I. C. Chang, J. Xu, D. Wo, “Bandpass response of collinear beam acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 1, 745–748 (1997).

Yaqoob, Z.

N. A. Riza, Z. Yaqoob, “Ultra high speed scanner for optical data handling,” in Lasers and Electro-Optics Society 13th Annual Conference Proceedings, A. Weiner, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), Vol. 2, pp. 822–823.

N. A. Riza, Z. Yaqoob, “High speed fiber-optic probe for dynamic blood analysis measurements,” in Optical Techniques and Instrumentation for the Measurement of Blood Composition, Structure, and Dynamics, A. V. Priezzhev, P. A. Oberg, eds., Proc. SPIE4163, 18–23 (2000).
[CrossRef]

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984).

Appl. Opt. (1)

IEEE Commun. Mag. (1)

S. Gorshe, Z. Papir, “Topics in broadband: last mile solutions,” IEEE Commun. Mag. 38, 166 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

R. S. Chu, J. A. Kong, “Modal theory of spatially periodic media,” IEEE Trans. Microwave Theory Tech. MTT-25, 18–24 (1977).

IEEE Ultrason. Symp. Proc. (2)

I. C. Chang, “Progress of acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 2, 819–825 (1996).

I. C. Chang, J. Xu, D. Wo, “Bandpass response of collinear beam acousto-optic tunable filters,” IEEE Ultrason. Symp. Proc. 1, 745–748 (1997).

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

W. Klaus, M. Ide, S. Morokawa, M. Tsuchiya, T. Kamiya, “Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes,” Opt. Commun. 138, 151–157 (1997).
[CrossRef]

Opt. Eng. (2)

M. E. Motamedi, S. Park, A. Wang, M. S. Dadkhah, A. P. Andrews, H. O. Marcy, M. Khoshnevisan, A. E. Chiou, “Development of a micro-electro-mechanical optical scanner,” Opt. Eng. 36, 1346–1353 (1997).
[CrossRef]

W. Goltsos, M. Holtz, “Agile beam steering using binary optics microlens array,” Opt. Eng. 29, 1392–1397 (1990).
[CrossRef]

Other (14)

N. A. Riza, “MOST: multiplexed optical scanner technology,” in Lasers and Electro-Optics Society 13th Annual Conference Proceedings, A. Weiner, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), Vol. 2, pp. 828–829.

N. A. Riza, Y. Huang, “High speed optical scanner for multi-dimensional beam pointing and acquisition,” in Lasers and Electro-Optics Society 12th Annual Conference Proceedings, L. Goldberg, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 184–185.

N. A. Riza, Z. Yaqoob, “High speed fiber-optic probe for dynamic blood analysis measurements,” in Optical Techniques and Instrumentation for the Measurement of Blood Composition, Structure, and Dynamics, A. V. Priezzhev, P. A. Oberg, eds., Proc. SPIE4163, 18–23 (2000).
[CrossRef]

N. A. Riza, Z. Yaqoob, “Ultra high speed scanner for optical data handling,” in Lasers and Electro-Optics Society 13th Annual Conference Proceedings, A. Weiner, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), Vol. 2, pp. 822–823.

F. Delorme, G. Alibert, C. Ougier, S. Slempkes, H. Nakajima, “Sampled-grating DBR lasers with 181 wavelengths over 44 nm and optimized power variation for WDM applications,” in Optical Fiber Communication Conference, Vol. 1 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 379–381.

Product NYW-50-001 (ADC Altitun, P.O. Box 911, SE, 175 29 Järfälla, Stockholm, Sweden, May2000).

Product MTX-TEML (Multiplex Inc., Corporate Headquarters, 115 Corporate Blvd., South Plainfield, N.J. 07080, November2000).

F. Kubick, “Electro-optic beam scanner,” U.S. patent4,706,094 (10November1987).

P. J. Talbot, “PLZT based electro-optic phased array optical scanner,” U.S. patent5,668,657 (16September1997).

E. G. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York, 1984).

N. A. Riza, “Reconfigurable optical wireless,” in Lasers and Electro-Optics Society 12th Annual Conference Proceedings, D. Psaltis, ed. (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), Vol. 1, pp. 70–71.

Y. Koike, “Plastic fibers,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest (Optical Society of America, Washington, D.C., 1997), p. 325.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Marcel Dekker, New York, 1983).

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Figures (12)

Fig. 1
Fig. 1

Free-space version of the W-MOS for implementing no moving parts, high-speed one-dimensional scans with (a) a tunable laser and (b) a tunable optical filter cascaded with a broadband source.

Fig. 2
Fig. 2

Angular scan range of W-MOS for the (a) +1 diffraction order when the laser beam is incident at θinc = 2.2° and (b) +2 diffraction order when the laser beam is incident at θinc = -67°.

Fig. 3
Fig. 3

Absolute upper bound on the maximum achievable angular deflection from a W-MOS for the +1 diffraction order when the laser beam is incident at (a) θinc = 0°, L = 1.6 µm; (b) θinc = -30°, L = 1.067 µm; and (c) θinc = -60°, L = 0.857 µm.

Fig. 4
Fig. 4

Scanning TEM00 Gaussian beams in space.

Fig. 5
Fig. 5

Spreading of a propagating TEM00 Gaussian beam.

Fig. 6
Fig. 6

Incident and deflected Gaussian beams showing that the W-MOS aperture size changes with the deflection angle. θinc, angle of incidence; θ(m), deflection angle; w inc, incident Gaussian beam waist; w eff, deflected scanning Gaussian beam waist.

Fig. 7
Fig. 7

(a) Collimation distance z 0 and (b) beam divergence angle θdiv versus the wavelength of the tunable source for +1 and +2 diffraction orders. For +1 diffraction order the angle of incidence θinc = 2.2°, whereas for +2 diffraction order θinc = -67°.

Fig. 8
Fig. 8

(a) Free-space W-MOS when a nonideal source is used with finite spectral width Δλ showing beam-spread jitter δθ. (b) Intensity-modulated deflected beam exiting a W-MOS displays an additional beam spread ΔS in space that is due to the jitter δΘ in the deflection angle. w eff, effective Gaussian beam waist at the W-MOS; R, distance between W-MOS and the optical detector; w(R), Gaussian beam waist at the detector when there is no jitter in the deflection angle; ΔS, beam spread that is due to the bandwidth of the information signal.

Fig. 9
Fig. 9

Focusing of a Gaussian beam at the detector for improved resolution in a W-MOS-based laser communication system. w eff, effective Gaussian beam radius at the W-MOS; r 0, distance between the W-MOS and the focusing lens of focal length f; R, distance between the W-MOS and the optical detector; W L (r 0), overall Gaussian beam radius at the front surface of the focusing lens; d rec, Gaussian beam-spot size at the receiver.

Fig. 10
Fig. 10

Minimum aperture of each focusing lens versus the wavelength of the tunable laser source.

Fig. 11
Fig. 11

Focal length of the individual focusing lens versus the wavelength of the tunable laser source, each placed at 30 cm from the respective optical detector.

Fig. 12
Fig. 12

Minimum size of the optical receiver versus the wavelength of the tunable laser source.

Equations (71)

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

θm=sin-1mλL+sin θinc,
α=λminL,
β=λmaxL,
γ=sin θinc.
θminm+1=sin-1m+1α+γsin-1mβ+γ=θmaxm.
βα=λmaxλminm+1m.
DL=sin-1mλmaxL+γ-sin-1mλminL+γ.
m λmaxL+γ1,
u=mλmax,
v=mλmin.
DL=sin-1uL+γ-sin-1vL+γ.
DL=11-u/L+γ21/2-uL2-11-v/L+γ21/2-vL2=0.
L=2uvγ1-γ2u+v=2mλmaxλmin sin θincλmax+λmincos2 θinc=L0.
DL<0,  if L>L0,
DL>0,  if L<L0.
-1+γu<1L<1-γu,
-1+γv<1L<1-γv.
-1+γv<-1+γu<1L<1-γu<1-γv.
L>u1-γ>v1-γ.
Lmin=u1-γ=mλmax1-sin θinc.
L0Lmin=2λminλmax+λminsin θinc1+sin θinc.
Dmax=DLmin=π2-sin-1λminλmax+sin θinc1-λminλmax.
supDmax=π2-sin-11+sin θinc2.
R=λΔλ=|m|M=|m| WL,
Δλ=λL|m|W.
z0=πw02λ,
θdiv=2λπw0.
dg=2winccos θinc.
deff=dg cos θm=2winccos θinccos θm,
z0=πweff2λ=πwinc2λ cos2 θinccos2 θm.
θdiv=2λπweff=2λ cos θincπwinc cos θm.
dθmdλ=mL cos θm.
Δλ=L cos θmm Δθ=L cos θmm θdiv.
Δλ=2Lλ cos θincmπwinc.
δθ=mL cos θm δλ,
Bideal=δfmodf=2Δfrff,
Bidealdfmodf=-dλmodλ.
Δθ=mBidealcos θmλL,
Bideal=δλmodλ.
δλmod=cδfmodf2=2Δfrfcf2.
Δfmod=δν+2Δfrf.
Bprac=Δfmodf=δν+2Δfrff,
δΘ=mBpraccos θmλL,
Bprac=Δλmodλ.
Δλmod=cΔfmodf2=δν+2Δfrfcf2.
ΔΘ=θdiv+δΘ,
SR=2wR+ΔS/2.
wR=weff1+R2z021/2,
ΔSR=RδΘ=R mBpraccos θmλL.
WLr0=wLr0+ΔSr02,
wLr0=weff1+r02z021/2.
ΔSr02=r0mBpraccos θmλ2L.
WLr0=weff1+r02zL21/2.
zL=r0weffWL2r0-weff21/2.
RLr0=r01+zL2r02.
1q1=1RLr0-j λπWL2r0.
z1=πWL2r0λ,
1q1=1RLr0-j 1z1.
1q2=C+D/q1A+B/q1,
ABCD=10-1/f1.
1q2=1RLr0-1f-j 1z1.
1q3=C+D/q2A+B/q2,
ABCD=1r-r001.
1q3=1/q21+r-r0/q2=1RLr0-1f-j 1z11+1RLr0-1fr-r0-j r-r0z1=1R3-j 1z3,
1R3=1RLr0-1f1+1RLr0-1fr-r0+r-r0z121+1RLr0-1fr-r02+r-r0z12,
z3=1+1RLr0-1fr-r02+r-r0z121z11+1RLr0-1fr-r0-r-r0z11RLr0-1f.
1R3=0.
f=1RLr0+12r-r01+1-4r-r02z121/2-1,
w3=λπ1+1RLr0-1fr-r02+r-r0z121z11+1RLr0-1fr-r0-r-r0z11RLr0-1f1/2.
drec=4λπ1+1RLr0-1fr-r02+r-r0z121z11+1RLr0-1fr-r0-r-r0z11RLr0-1f1/2.
1f=1r0+1r-r0,

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