Abstract

An optimal strategy for cascading phased-array deflectors is presented that allows for high-resolution random-access beam steering with continuous scan-angle control but requires a minimum number of control lines. The system is analyzed theoretically by use of a Fourier optics approach and then verified experimentally. A pair of 32-channel optical phased arrays fabricated by use of surface electrodes on lanthanum-modified lead zirconate titanate (PLZT) was sandwiched together to form a functional two-stage phased-array cascade. Experimental results from the PLZT-based two-stage deflector are presented that confirm the performance enhancements of the optimized cascading technique. A phase-staggered discrete–offset-bias protocol for controlling the cascaded system is shown to be optimal in terms of maximum diffraction efficiency and minimum number of control lines, while still providing for full analog scan control.

© 1998 Optical Society of America

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References

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  1. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
    [CrossRef]
  2. T. C. Cheston, J. Frank, “Phased array radar antennas,” in Radar Handbook, 2nd ed., M. I. Skolnik, ed. (McGraw-Hill, New York, 1990), Chap. 7, pp. 7.1–7.82.
  3. R. M. Matic, “Blazed phase liquid crystal steering,” in Laser Beam Propagation and Control, H. Weichel, L. F. DeSandre, eds., Proc. SPIE2120, 194–205 (1994).
    [CrossRef]
  4. R. A. Meyer, “Optical beam steering using a multichannel lithium tantalate crystal,” Appl. Opt. 11, 613–616 (1972).
    [CrossRef] [PubMed]
  5. Y. Ninomiya, “Ultrahigh resolving electrooptic prism array light deflectors,” IEEE J. Quantum Electron. QE-9(8), 791–795 (1973).
    [CrossRef]
  6. Y. Ninomiya, “High S/N-ratio electrooptic prism-array light deflectors,” IEEE J. Quantum. Electron. QE-10, 358–362 (1974).
    [CrossRef]
  7. T.-C. Lee, J. D. Zook, “Parallel array light beam deflector with variable phase plate,” U.S. patent no. 3,650,602 (issued 21March1972).
  8. C. H. Bulmer, W. K. Burns, T. G. Giallorenzi, “Performance criteria and limitations of electro-optic waveguide array deflectors,” Appl. Opt. 18, 3282–3295 (1979).
    [CrossRef] [PubMed]
  9. D. R. Wight, J. M. Heaton, B. T. Hughes, J. C. H. Birbeck, K. P. Hilton, D. J. Taylor, “Novel phased array optical scanning device implemented using GaAs/AlGaAs technology,” Appl. Phys. Lett. 59, 899–901 (1991).
    [CrossRef]
  10. F. Vasey, F. K. Reinhart, R. Houdré, J. M. Stauffer, “Spatial optical beam steering with an AlGaAs integrated phased array,” Appl. Opt. 32, 3220–3232 (1993).
    [CrossRef] [PubMed]
  11. T. A. Dorschner, D. P. Resler, “Optical beam steerer having subaperture addressing,” U.S. patent no. 5,093,740 (issued 3March1992).
  12. J. A. Thomas, Y. Fainman, “Programmable diffractive optical element using a multichannel lanthanum-modified lead zirconate titanate phase modulator,” Opt. Lett. 20, 1510–1512 (1995).
    [CrossRef] [PubMed]
  13. P. J. Talbot, Q. W. Song, “Design and simulation of PLZT-based electro-optic phased array scanners,” Opt. Memory Neural Net. 3, 111–117 (1994).
  14. T. Tatebayashi, T. Yamamoto, H. Sato, “Electro-optic variable focal-length lens using PLZT ceramic,” Appl. Opt. 30, 5049–5055 (1991).
    [CrossRef] [PubMed]
  15. N. A. Riza, M. C. DeJule, “Three-terminal adaptive nematic liquid-crystal lens device,” Opt. Lett. 19, 1013–1015 (1994).
    [CrossRef] [PubMed]
  16. J. G. Skinner, “Optimal electrooptic deflection scheme,” Appl. Opt. 7, 1239–1240 (1968).
    [CrossRef] [PubMed]
  17. H. J. Boll, “Cascaded light beam deflector system,” U.S. patent no. 3,544,200 (issued 1December1970).
  18. T. C. Lee, J. D. Zook, “Cascade operation of light beam deflectors by fly’s eye lenses,” Appl. Opt. 10, 1965–1966 (1971).
    [CrossRef] [PubMed]
  19. K. M. Flood, B. Cassarly, C. Sigg, J. M. Finlan, “Continuous wide angle beam steering using translation of binary microlens arrays and a liquid crystal phased array,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1211, 296–304 (1990).
    [CrossRef]
  20. J. A. Thomas, M. E. Lasher, Y. Fainman, P. Soltan, “PLZT-based dynamic diffractive optical element for high-speed random-access beam steering,” in Optical Scanning Systems: Design and Applications, L. Beiser, S. F. Sagan, eds., Proc. SPIE3131, 124–132 (1997).
    [CrossRef]
  21. G. H. Haertling, “PLZT electrooptic materials and applications—a review,” Ferroelectrics 75, 25–55 (1987).
    [CrossRef]
  22. R. Fleischmann, A. Lohmann, “Die Bestimmung einer absoluten Lichtphase durch Intensitätsmessung in der Beugungsfigur eines Gitters,” Z. Physik 137, 362–375 (1954).
    [CrossRef]

1996

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

1995

1994

P. J. Talbot, Q. W. Song, “Design and simulation of PLZT-based electro-optic phased array scanners,” Opt. Memory Neural Net. 3, 111–117 (1994).

N. A. Riza, M. C. DeJule, “Three-terminal adaptive nematic liquid-crystal lens device,” Opt. Lett. 19, 1013–1015 (1994).
[CrossRef] [PubMed]

1993

1991

T. Tatebayashi, T. Yamamoto, H. Sato, “Electro-optic variable focal-length lens using PLZT ceramic,” Appl. Opt. 30, 5049–5055 (1991).
[CrossRef] [PubMed]

D. R. Wight, J. M. Heaton, B. T. Hughes, J. C. H. Birbeck, K. P. Hilton, D. J. Taylor, “Novel phased array optical scanning device implemented using GaAs/AlGaAs technology,” Appl. Phys. Lett. 59, 899–901 (1991).
[CrossRef]

1987

G. H. Haertling, “PLZT electrooptic materials and applications—a review,” Ferroelectrics 75, 25–55 (1987).
[CrossRef]

1979

1974

Y. Ninomiya, “High S/N-ratio electrooptic prism-array light deflectors,” IEEE J. Quantum. Electron. QE-10, 358–362 (1974).
[CrossRef]

1973

Y. Ninomiya, “Ultrahigh resolving electrooptic prism array light deflectors,” IEEE J. Quantum Electron. QE-9(8), 791–795 (1973).
[CrossRef]

1972

1971

1968

1954

R. Fleischmann, A. Lohmann, “Die Bestimmung einer absoluten Lichtphase durch Intensitätsmessung in der Beugungsfigur eines Gitters,” Z. Physik 137, 362–375 (1954).
[CrossRef]

Birbeck, J. C. H.

D. R. Wight, J. M. Heaton, B. T. Hughes, J. C. H. Birbeck, K. P. Hilton, D. J. Taylor, “Novel phased array optical scanning device implemented using GaAs/AlGaAs technology,” Appl. Phys. Lett. 59, 899–901 (1991).
[CrossRef]

Boll, H. J.

H. J. Boll, “Cascaded light beam deflector system,” U.S. patent no. 3,544,200 (issued 1December1970).

Bulmer, C. H.

Burns, W. K.

Cassarly, B.

K. M. Flood, B. Cassarly, C. Sigg, J. M. Finlan, “Continuous wide angle beam steering using translation of binary microlens arrays and a liquid crystal phased array,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1211, 296–304 (1990).
[CrossRef]

Cheston, T. C.

T. C. Cheston, J. Frank, “Phased array radar antennas,” in Radar Handbook, 2nd ed., M. I. Skolnik, ed. (McGraw-Hill, New York, 1990), Chap. 7, pp. 7.1–7.82.

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

DeJule, M. C.

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

T. A. Dorschner, D. P. Resler, “Optical beam steerer having subaperture addressing,” U.S. patent no. 5,093,740 (issued 3March1992).

Fainman, Y.

J. A. Thomas, Y. Fainman, “Programmable diffractive optical element using a multichannel lanthanum-modified lead zirconate titanate phase modulator,” Opt. Lett. 20, 1510–1512 (1995).
[CrossRef] [PubMed]

J. A. Thomas, M. E. Lasher, Y. Fainman, P. Soltan, “PLZT-based dynamic diffractive optical element for high-speed random-access beam steering,” in Optical Scanning Systems: Design and Applications, L. Beiser, S. F. Sagan, eds., Proc. SPIE3131, 124–132 (1997).
[CrossRef]

Finlan, J. M.

K. M. Flood, B. Cassarly, C. Sigg, J. M. Finlan, “Continuous wide angle beam steering using translation of binary microlens arrays and a liquid crystal phased array,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1211, 296–304 (1990).
[CrossRef]

Fleischmann, R.

R. Fleischmann, A. Lohmann, “Die Bestimmung einer absoluten Lichtphase durch Intensitätsmessung in der Beugungsfigur eines Gitters,” Z. Physik 137, 362–375 (1954).
[CrossRef]

Flood, K. M.

K. M. Flood, B. Cassarly, C. Sigg, J. M. Finlan, “Continuous wide angle beam steering using translation of binary microlens arrays and a liquid crystal phased array,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1211, 296–304 (1990).
[CrossRef]

Frank, J.

T. C. Cheston, J. Frank, “Phased array radar antennas,” in Radar Handbook, 2nd ed., M. I. Skolnik, ed. (McGraw-Hill, New York, 1990), Chap. 7, pp. 7.1–7.82.

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Giallorenzi, T. G.

Haertling, G. H.

G. H. Haertling, “PLZT electrooptic materials and applications—a review,” Ferroelectrics 75, 25–55 (1987).
[CrossRef]

Heaton, J. M.

D. R. Wight, J. M. Heaton, B. T. Hughes, J. C. H. Birbeck, K. P. Hilton, D. J. Taylor, “Novel phased array optical scanning device implemented using GaAs/AlGaAs technology,” Appl. Phys. Lett. 59, 899–901 (1991).
[CrossRef]

Hilton, K. P.

D. R. Wight, J. M. Heaton, B. T. Hughes, J. C. H. Birbeck, K. P. Hilton, D. J. Taylor, “Novel phased array optical scanning device implemented using GaAs/AlGaAs technology,” Appl. Phys. Lett. 59, 899–901 (1991).
[CrossRef]

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Holz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Houdré, R.

Hughes, B. T.

D. R. Wight, J. M. Heaton, B. T. Hughes, J. C. H. Birbeck, K. P. Hilton, D. J. Taylor, “Novel phased array optical scanning device implemented using GaAs/AlGaAs technology,” Appl. Phys. Lett. 59, 899–901 (1991).
[CrossRef]

Lasher, M. E.

J. A. Thomas, M. E. Lasher, Y. Fainman, P. Soltan, “PLZT-based dynamic diffractive optical element for high-speed random-access beam steering,” in Optical Scanning Systems: Design and Applications, L. Beiser, S. F. Sagan, eds., Proc. SPIE3131, 124–132 (1997).
[CrossRef]

Lee, T. C.

Lee, T.-C.

T.-C. Lee, J. D. Zook, “Parallel array light beam deflector with variable phase plate,” U.S. patent no. 3,650,602 (issued 21March1972).

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Lohmann, A.

R. Fleischmann, A. Lohmann, “Die Bestimmung einer absoluten Lichtphase durch Intensitätsmessung in der Beugungsfigur eines Gitters,” Z. Physik 137, 362–375 (1954).
[CrossRef]

Matic, R. M.

R. M. Matic, “Blazed phase liquid crystal steering,” in Laser Beam Propagation and Control, H. Weichel, L. F. DeSandre, eds., Proc. SPIE2120, 194–205 (1994).
[CrossRef]

McManamon, P. F.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Meyer, R. A.

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Ninomiya, Y.

Y. Ninomiya, “High S/N-ratio electrooptic prism-array light deflectors,” IEEE J. Quantum. Electron. QE-10, 358–362 (1974).
[CrossRef]

Y. Ninomiya, “Ultrahigh resolving electrooptic prism array light deflectors,” IEEE J. Quantum Electron. QE-9(8), 791–795 (1973).
[CrossRef]

Reinhart, F. K.

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

T. A. Dorschner, D. P. Resler, “Optical beam steerer having subaperture addressing,” U.S. patent no. 5,093,740 (issued 3March1992).

Riza, N. A.

Sato, H.

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Sigg, C.

K. M. Flood, B. Cassarly, C. Sigg, J. M. Finlan, “Continuous wide angle beam steering using translation of binary microlens arrays and a liquid crystal phased array,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1211, 296–304 (1990).
[CrossRef]

Skinner, J. G.

Soltan, P.

J. A. Thomas, M. E. Lasher, Y. Fainman, P. Soltan, “PLZT-based dynamic diffractive optical element for high-speed random-access beam steering,” in Optical Scanning Systems: Design and Applications, L. Beiser, S. F. Sagan, eds., Proc. SPIE3131, 124–132 (1997).
[CrossRef]

Song, Q. W.

P. J. Talbot, Q. W. Song, “Design and simulation of PLZT-based electro-optic phased array scanners,” Opt. Memory Neural Net. 3, 111–117 (1994).

Stauffer, J. M.

Talbot, P. J.

P. J. Talbot, Q. W. Song, “Design and simulation of PLZT-based electro-optic phased array scanners,” Opt. Memory Neural Net. 3, 111–117 (1994).

Tatebayashi, T.

Taylor, D. J.

D. R. Wight, J. M. Heaton, B. T. Hughes, J. C. H. Birbeck, K. P. Hilton, D. J. Taylor, “Novel phased array optical scanning device implemented using GaAs/AlGaAs technology,” Appl. Phys. Lett. 59, 899–901 (1991).
[CrossRef]

Thomas, J. A.

J. A. Thomas, Y. Fainman, “Programmable diffractive optical element using a multichannel lanthanum-modified lead zirconate titanate phase modulator,” Opt. Lett. 20, 1510–1512 (1995).
[CrossRef] [PubMed]

J. A. Thomas, M. E. Lasher, Y. Fainman, P. Soltan, “PLZT-based dynamic diffractive optical element for high-speed random-access beam steering,” in Optical Scanning Systems: Design and Applications, L. Beiser, S. F. Sagan, eds., Proc. SPIE3131, 124–132 (1997).
[CrossRef]

Vasey, F.

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Wight, D. R.

D. R. Wight, J. M. Heaton, B. T. Hughes, J. C. H. Birbeck, K. P. Hilton, D. J. Taylor, “Novel phased array optical scanning device implemented using GaAs/AlGaAs technology,” Appl. Phys. Lett. 59, 899–901 (1991).
[CrossRef]

Yamamoto, T.

Zook, J. D.

T. C. Lee, J. D. Zook, “Cascade operation of light beam deflectors by fly’s eye lenses,” Appl. Opt. 10, 1965–1966 (1971).
[CrossRef] [PubMed]

T.-C. Lee, J. D. Zook, “Parallel array light beam deflector with variable phase plate,” U.S. patent no. 3,650,602 (issued 21March1972).

Appl. Opt.

Appl. Phys. Lett.

D. R. Wight, J. M. Heaton, B. T. Hughes, J. C. H. Birbeck, K. P. Hilton, D. J. Taylor, “Novel phased array optical scanning device implemented using GaAs/AlGaAs technology,” Appl. Phys. Lett. 59, 899–901 (1991).
[CrossRef]

Ferroelectrics

G. H. Haertling, “PLZT electrooptic materials and applications—a review,” Ferroelectrics 75, 25–55 (1987).
[CrossRef]

IEEE J. Quantum Electron.

Y. Ninomiya, “Ultrahigh resolving electrooptic prism array light deflectors,” IEEE J. Quantum Electron. QE-9(8), 791–795 (1973).
[CrossRef]

IEEE J. Quantum. Electron.

Y. Ninomiya, “High S/N-ratio electrooptic prism-array light deflectors,” IEEE J. Quantum. Electron. QE-10, 358–362 (1974).
[CrossRef]

Opt. Lett.

Opt. Memory Neural Net.

P. J. Talbot, Q. W. Song, “Design and simulation of PLZT-based electro-optic phased array scanners,” Opt. Memory Neural Net. 3, 111–117 (1994).

Proc. IEEE

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Z. Physik

R. Fleischmann, A. Lohmann, “Die Bestimmung einer absoluten Lichtphase durch Intensitätsmessung in der Beugungsfigur eines Gitters,” Z. Physik 137, 362–375 (1954).
[CrossRef]

Other

H. J. Boll, “Cascaded light beam deflector system,” U.S. patent no. 3,544,200 (issued 1December1970).

T. C. Cheston, J. Frank, “Phased array radar antennas,” in Radar Handbook, 2nd ed., M. I. Skolnik, ed. (McGraw-Hill, New York, 1990), Chap. 7, pp. 7.1–7.82.

R. M. Matic, “Blazed phase liquid crystal steering,” in Laser Beam Propagation and Control, H. Weichel, L. F. DeSandre, eds., Proc. SPIE2120, 194–205 (1994).
[CrossRef]

T.-C. Lee, J. D. Zook, “Parallel array light beam deflector with variable phase plate,” U.S. patent no. 3,650,602 (issued 21March1972).

K. M. Flood, B. Cassarly, C. Sigg, J. M. Finlan, “Continuous wide angle beam steering using translation of binary microlens arrays and a liquid crystal phased array,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. SPIE1211, 296–304 (1990).
[CrossRef]

J. A. Thomas, M. E. Lasher, Y. Fainman, P. Soltan, “PLZT-based dynamic diffractive optical element for high-speed random-access beam steering,” in Optical Scanning Systems: Design and Applications, L. Beiser, S. F. Sagan, eds., Proc. SPIE3131, 124–132 (1997).
[CrossRef]

T. A. Dorschner, D. P. Resler, “Optical beam steerer having subaperture addressing,” U.S. patent no. 5,093,740 (issued 3March1992).

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Figures (12)

Fig. 1
Fig. 1

Basic concept of a 1-D phased-array deflector: (a) near-field layout and far-field intensity pattern, and (b) equivalent phase profile of the 1-D array (with unfolded phases). Quantization errors are shown as dark notches.

Fig. 2
Fig. 2

Central lobes of the normalized far-field intensity pattern I OUT(θ) of a 1-D echelon grating deflector with M = 32 channels, a fill factor of w/ d = 1/5 [solid envelope curve (EF)], and a deflection angle of θ̅ S = (1/8)(λ/d). The ideal fill-factor envelope (w/ d = 1) is shown as a dashed curve.

Fig. 3
Fig. 3

Basic optical layout of a two-stage phased-array cascade with a reduced number of external connections. Stage 1 is addressed by M 1 control lines and stage 2 by M 2 control lines. By itself, stage 1 can deflect to only discrete output angles (shown as thick tick marks on the output screen).

Fig. 4
Fig. 4

Schematic layout of the unfolded phase distribution of an aligned two-stage phased-array cascade with a minimum control-line configuration.

Fig. 5
Fig. 5

Two basic strategies for programming an aligned two-stage phased-array deflector of the form given in Fig. 4. Equivalent phase profiles for the two stages are shown: (a) Coarse–fine programming; quantization errors occur in both stages. (b) Discrete–offset-bias programming; only stage 1 exhibits quantization errors.

Fig. 6
Fig. 6

Theoretical far-field intensity pattern I OUT from an aligned two-stage phased-array cascade with a minimum control-line configuration. The cascaded arrays are programmed for deflection to θ̅ S = (3/8)(λ/d 1) by use of (a) coarse–fine programming (θ̅ S = θ̅1 + θ̅2) and (b) discrete–offset-bias programming (θ̅ S = θ̅1 = θ̅2). There are M 1 = 4 modulators/subarray in stage 1; the fill factor is w 1/d 1 = 1/5.

Fig. 7
Fig. 7

Packaged 32-channel optical phased array made with PLZT. The active window has dimensions of 12.8 mm × 10.0 mm.

Fig. 8
Fig. 8

Average measured phase-modulation response of the PLZT modulators in the 32-channel phased-array device shown in Fig. 7.

Fig. 9
Fig. 9

One-dimensional beam-steering output by use of two 32-channel PLZT phased arrays in an aligned two-stage cascade with M 1 = 4 and M 2 = 8. The cascaded arrays were programmed for deflection to various angles θ S by use of (a) the coarse–fine protocol and (b) the discrete–offset-bias protocol. Only half of the 32 resolvable scan outputs are shown.

Fig. 10
Fig. 10

Horizontal traces through the CCD data shown in Fig. 9 for a deflection angle of θ S = j/32)(λ/d 1). Strong secondary noise lobes appear in the scan zone under coarse–fine programming.

Fig. 11
Fig. 11

Intensity profiles of the two-stage deflector output for the primary deflection angles of θ S = j/32(λ/d 1), j = -14, … , + 16 (solid curves) and j = +1 (dashed curve) under discrete–offset-bias programming. The data cover the central nonredundant scan zone in the output.

Fig. 12
Fig. 12

Comparison of the DE versus the scan angle of an aligned two-stage phased-array deflector cascade by use of the discrete–offset-bias protocol (upper curve) and the coarse–fine protocol (lower curve). Cascade configuration: M 1 = 4, M 2 = 8, 100% filled apertures; minimum control-line arrangement (Fig. 4).

Tables (2)

Tables Icon

Table 1 Deflection Angles Supported by the Individual Stages of an Aligned Two-Stage Phased-Array Deflectora

Tables Icon

Table 2 Summary of the Phase Programming Formulas for an Aligned Two-Stage Phased-Array Deflector Using Either the Coarse–Fine Protocol or the Discrete–Offset-Bias Protocol (n = integer-valued, r = real-valued, and Q = n + r)

Equations (18)

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

T 0 x = W x   *   m = 0 M - 1   δ x - md exp im Δ φ ,
I OUT θ ¯ = C   EF θ ¯ AF θ ¯ - θ ¯ S ,
EF θ ¯ | W x | 2 ,
AF θ ¯ - θ ¯ S = sin M π d λ θ ¯ - θ ¯ S M   sin π d λ θ ¯ - θ ¯ S 2 ,
θ ¯ sin θ = λ ν ,
θ ¯ sin θ S = Δ φ 2 π λ d .
EF θ ¯ = w d sinc θ ¯ Δ θ ¯ ENV 2 ,
W 2 x g x = W 1 x   *   m = 0 M 1 - 1   δ x - md 1 exp im Δ φ 1 ,
EF 2 θ ¯ = C EF 1 θ ¯ AF 1 θ ¯ - θ ¯ 1 ,
EF 1 θ ¯ = w 1 d 1 2 sinc 2 w 1 λ θ ¯ ,
AF 1 θ ¯ - θ ¯ 1 = sin M 1 π d 1 λ θ ¯ - θ ¯ 1 M 1 sin π d 1 λ θ ¯ - θ ¯ 1 2 ,
I 2 OUT θ ¯ = C   EF 1 θ ¯ AF 1 θ ¯ - θ ¯ 1 AF 2 θ ¯ - θ ¯ 2 ,
AF 2 θ ¯ - θ ¯ 2 = sin M 2 π d 2 λ θ ¯ - θ ¯ 2 M 2 sin π d 2 λ θ ¯ - θ ¯ 2 2 .
Δ φ = 2 π λ d sin θ S ,
φ ˆ m φ m mod   2 π = m Δ φ + φ AVE mod   2 π ,     m = 0 , ,   M - 1 .
θ ¯ S = Q λ d 2 = n + r λ d 2 ,
η TOT C F = η coarse η fine = w 1 d 1 2 sinc 2 w 1 d 1 Δ φ 1 2 π × w 2 d 2 2 sinc 2 w 2 d 2 Δ φ 2 2 π ,
η TOT D OB = w 1 d 2 2 sinc 2 w 1 d 1 Δ φ 1 2 π .

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