Abstract

This paper reports the realization of integrated acousto-optic (AO) device modules that combine a wideband AO Bragg cell, an ion-milled Bragg diffraction grating, and a titanium-indiffused proton-exchanged waveguide lens in a Y-cut LiNbO3 substrate, 1 × 8 × 16 mm3 in size, to perform optical heterodyning, and their application to rf signal processing. These integrated AO heterodyne modules have demonstrated the capabilities for channelized detection of the amplitude, the frequency, and the phase of wideband rf signals and thus the capability to perform interferometric rf spectral analysis with significantly improved performances over the conventional AO Bragg cells. The single-unit (basic) modules have provided single-tone simultaneous and two-tone third-order spurious-free dynamic ranges of 51 and 40 dB, respectively, and a bandwidth of 205 MHz centered at 350 MHz at the optical wavelength of 0.6328 μm, the optical power of 1.0 mW, and the drive power of 50 mW/rf signal input. Furthermore the dual-unit modules that consist of a pair of identical basic heterodyne devices in the same LiNbO3 waveguide substrate, also 1 × 8 × 16 mm3 in size, have been constructed and used to measure the angle of arrival of the rf signals.

© 1992 Optical Society of America

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References

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  1. R. Adler, “Interaction between light and sound,” IEEE Spectrum 4(5), 42–54 (1967).
    [Crossref]
  2. A. VanderLugt, “Interferometric spectrum analyzer,” Appl. Opt. 20, 2770–2779 (1981).
    [Crossref]
  3. A. Korpel, R. L. Whitman, “Visualization of a coherent light field by heterodyning with a scanning laser beam,” Appl. Opt. 8, 1577–1580 (1969).
    [Crossref] [PubMed]
  4. M. King, W. R. Bennett, M. Aerm, “Real-time electrooptical signal processors with coherent detection,” Appl. Opt. 6, 1367–1375 (1967).
    [Crossref] [PubMed]
  5. E. H. Young, B. A. Morris, R. V. Balfatto, “Acousto-optic interferometrical spectrum analyzer with direct rf frequency output,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 140–144 (1986).
  6. I. C. Chang, R. Lu, L. S. Lee, “High dynamic range acousto-optic receiver,” in Optical Technology for Microwave Applications II, S. Yao, ed, Proc. Soc. Photo-Opt. Instrum. Eng.545, 95–101 (1985).
  7. M. D. Koonyz, “Miniature interferometric spectrum analyzer,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 126–130 (1986).
  8. G. D. Xu, C. S. Tsai, “A novel integrated acoustooptic and electrooptic heterodyning device in a LiNbO3 waveguide,” Appl. Phys. Lett. 58, 28–30 (1991).
    [Crossref]
  9. D. Y. Zang, C. S. Tsai, “Single mode waveguide microlenses and microlens array fabrication in LiNbO3 using TIPE technique,” Appl. Phys. Lett. 40, 703–705 (1985); “Titanium-indiffused proton-exchanged waveguide lenses in LiNbO3 for optical information processing,” Appl. Opt. 25, 2264–2272 (1986).
    [Crossref] [PubMed]
  10. A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).
  11. C. C. Lee, K. Y. Liao, C. L. Chang, C. S. Tsai, “Wide-band guided-wave acoustooptic Bragg deflector using a tilted-finger chirp transducer,” IEEE J. Quantum Electron. QE-15, 1166–1170 (1979).
  12. C. S. Tsai, “Guided-wave acoustooptic Bragg modulators for wide-band integrated optic communications and signal processing,” IEEE Trans. Circuits Syst. CAS-26, 1072–1098 (1979), and the many references cited in Guided-Wave Acousto-Optics, C.S. Tsai, ed., Vol. 23 of Springer-Verlag Series on Electronics and Photonics (Springer-Verlag, Berlin, 1990).
    [Crossref]
  13. G. I. Harakoshi, S. I. Tanaka, “Grating lenses for integrated optics,” Opt. Lett. 2, 142–144 (1978).
    [Crossref]
  14. G. D. Xu, G. S. Tsai, “Integrated acoustooptic modules for interferometric RF spectrum analyzers,” IEEE Photon. Technol. Lett. 3, 153–155 (1991).
    [Crossref]
  15. S. K. Yao, D. E. Thompson, “Chirp-grating lens for guided-wave optics,” Appl. Phys. Lett. 33, 635–637 (1978).
    [Crossref]
  16. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
    [Crossref]
  17. T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
    [Crossref]
  18. T. Tamir, ed, Integrated Optics (Springer-Verlag, Berlin, 1975).
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    [Crossref]
  20. A. M. Glass, I. P. Kaminow, A. A. Ballman, D. H. Olsson, “Absorption loss and photorefractive-index changes in Ti:LiNbO3 substrates and waveguides,” Appl. Opt. 19, 276–281 (1980).
    [Crossref] [PubMed]
  21. J. Jackel, C. E. Rice, J. J. Veselka, “Proton exchange for high index waveguides in LiNbO3,” Appl. Phys. Lett. 41, 607–608 (1982).
    [Crossref]
  22. M. Goodwin, C. Stewart, “Proton-exchanged optical waveguides in Y-cut lithum niobate,” Electron. Lett. 19, 223–225 (1983).
    [Crossref]
  23. T. Q. Vu, J. A. Norris, C. S. Tsai, “Formation of negative index-change waveguide lenses in LiNbO3 using ion milling,” Opt. Lett. 13, 1141–1143 (1988).
    [Crossref] [PubMed]
  24. H. I. Smith, F. J. Bachner, N. Efremow, “A high-yield photolithographic technique for surface wave devices,” J. Electrochem. Soc. 118, 821–825 (1971).
    [Crossref]
  25. D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7–18 (1977).
    [Crossref]

1991 (2)

G. D. Xu, C. S. Tsai, “A novel integrated acoustooptic and electrooptic heterodyning device in a LiNbO3 waveguide,” Appl. Phys. Lett. 58, 28–30 (1991).
[Crossref]

G. D. Xu, G. S. Tsai, “Integrated acoustooptic modules for interferometric RF spectrum analyzers,” IEEE Photon. Technol. Lett. 3, 153–155 (1991).
[Crossref]

1988 (1)

1986 (1)

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[Crossref]

1985 (1)

D. Y. Zang, C. S. Tsai, “Single mode waveguide microlenses and microlens array fabrication in LiNbO3 using TIPE technique,” Appl. Phys. Lett. 40, 703–705 (1985); “Titanium-indiffused proton-exchanged waveguide lenses in LiNbO3 for optical information processing,” Appl. Opt. 25, 2264–2272 (1986).
[Crossref] [PubMed]

1983 (1)

M. Goodwin, C. Stewart, “Proton-exchanged optical waveguides in Y-cut lithum niobate,” Electron. Lett. 19, 223–225 (1983).
[Crossref]

1982 (1)

J. Jackel, C. E. Rice, J. J. Veselka, “Proton exchange for high index waveguides in LiNbO3,” Appl. Phys. Lett. 41, 607–608 (1982).
[Crossref]

1981 (1)

1980 (1)

1979 (2)

C. C. Lee, K. Y. Liao, C. L. Chang, C. S. Tsai, “Wide-band guided-wave acoustooptic Bragg deflector using a tilted-finger chirp transducer,” IEEE J. Quantum Electron. QE-15, 1166–1170 (1979).

C. S. Tsai, “Guided-wave acoustooptic Bragg modulators for wide-band integrated optic communications and signal processing,” IEEE Trans. Circuits Syst. CAS-26, 1072–1098 (1979), and the many references cited in Guided-Wave Acousto-Optics, C.S. Tsai, ed., Vol. 23 of Springer-Verlag Series on Electronics and Photonics (Springer-Verlag, Berlin, 1990).
[Crossref]

1978 (3)

G. I. Harakoshi, S. I. Tanaka, “Grating lenses for integrated optics,” Opt. Lett. 2, 142–144 (1978).
[Crossref]

S. K. Yao, D. E. Thompson, “Chirp-grating lens for guided-wave optics,” Appl. Phys. Lett. 33, 635–637 (1978).
[Crossref]

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).

1977 (1)

D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7–18 (1977).
[Crossref]

1974 (1)

R. V. Schmidt, I. P. Kaminow, “Metal diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[Crossref]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[Crossref]

1971 (1)

H. I. Smith, F. J. Bachner, N. Efremow, “A high-yield photolithographic technique for surface wave devices,” J. Electrochem. Soc. 118, 821–825 (1971).
[Crossref]

1969 (1)

1967 (2)

Adler, R.

R. Adler, “Interaction between light and sound,” IEEE Spectrum 4(5), 42–54 (1967).
[Crossref]

Aerm, M.

Bachner, F. J.

H. I. Smith, F. J. Bachner, N. Efremow, “A high-yield photolithographic technique for surface wave devices,” J. Electrochem. Soc. 118, 821–825 (1971).
[Crossref]

Balfatto, R. V.

E. H. Young, B. A. Morris, R. V. Balfatto, “Acousto-optic interferometrical spectrum analyzer with direct rf frequency output,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 140–144 (1986).

Ballman, A. A.

Bennett, W. R.

Chang, C. L.

C. C. Lee, K. Y. Liao, C. L. Chang, C. S. Tsai, “Wide-band guided-wave acoustooptic Bragg deflector using a tilted-finger chirp transducer,” IEEE J. Quantum Electron. QE-15, 1166–1170 (1979).

Chang, I. C.

I. C. Chang, R. Lu, L. S. Lee, “High dynamic range acousto-optic receiver,” in Optical Technology for Microwave Applications II, S. Yao, ed, Proc. Soc. Photo-Opt. Instrum. Eng.545, 95–101 (1985).

Efremow, N.

H. I. Smith, F. J. Bachner, N. Efremow, “A high-yield photolithographic technique for surface wave devices,” J. Electrochem. Soc. 118, 821–825 (1971).
[Crossref]

Glass, A. M.

Goodwin, M.

M. Goodwin, C. Stewart, “Proton-exchanged optical waveguides in Y-cut lithum niobate,” Electron. Lett. 19, 223–225 (1983).
[Crossref]

Harakoshi, G. I.

Hecht, D. L.

D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7–18 (1977).
[Crossref]

Jackel, J.

J. Jackel, C. E. Rice, J. J. Veselka, “Proton exchange for high index waveguides in LiNbO3,” Appl. Phys. Lett. 41, 607–608 (1982).
[Crossref]

Kaminow, I. P.

King, M.

Koonyz, M. D.

M. D. Koonyz, “Miniature interferometric spectrum analyzer,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 126–130 (1986).

Korpel, A.

Lee, C. C.

C. C. Lee, K. Y. Liao, C. L. Chang, C. S. Tsai, “Wide-band guided-wave acoustooptic Bragg deflector using a tilted-finger chirp transducer,” IEEE J. Quantum Electron. QE-15, 1166–1170 (1979).

Lee, L. S.

I. C. Chang, R. Lu, L. S. Lee, “High dynamic range acousto-optic receiver,” in Optical Technology for Microwave Applications II, S. Yao, ed, Proc. Soc. Photo-Opt. Instrum. Eng.545, 95–101 (1985).

Liao, K. Y.

C. C. Lee, K. Y. Liao, C. L. Chang, C. S. Tsai, “Wide-band guided-wave acoustooptic Bragg deflector using a tilted-finger chirp transducer,” IEEE J. Quantum Electron. QE-15, 1166–1170 (1979).

Lu, R.

I. C. Chang, R. Lu, L. S. Lee, “High dynamic range acousto-optic receiver,” in Optical Technology for Microwave Applications II, S. Yao, ed, Proc. Soc. Photo-Opt. Instrum. Eng.545, 95–101 (1985).

Morris, B. A.

E. H. Young, B. A. Morris, R. V. Balfatto, “Acousto-optic interferometrical spectrum analyzer with direct rf frequency output,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 140–144 (1986).

Nishihara, H.

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[Crossref]

Norris, J. A.

Olsson, D. H.

Rice, C. E.

J. Jackel, C. E. Rice, J. J. Veselka, “Proton exchange for high index waveguides in LiNbO3,” Appl. Phys. Lett. 41, 607–608 (1982).
[Crossref]

Schmidt, R. V.

R. V. Schmidt, I. P. Kaminow, “Metal diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[Crossref]

Smith, H. I.

H. I. Smith, F. J. Bachner, N. Efremow, “A high-yield photolithographic technique for surface wave devices,” J. Electrochem. Soc. 118, 821–825 (1971).
[Crossref]

Stewart, C.

M. Goodwin, C. Stewart, “Proton-exchanged optical waveguides in Y-cut lithum niobate,” Electron. Lett. 19, 223–225 (1983).
[Crossref]

Suhara, T.

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[Crossref]

Tanaka, S. I.

Thompson, D. E.

S. K. Yao, D. E. Thompson, “Chirp-grating lens for guided-wave optics,” Appl. Phys. Lett. 33, 635–637 (1978).
[Crossref]

Tsai, C. S.

G. D. Xu, C. S. Tsai, “A novel integrated acoustooptic and electrooptic heterodyning device in a LiNbO3 waveguide,” Appl. Phys. Lett. 58, 28–30 (1991).
[Crossref]

T. Q. Vu, J. A. Norris, C. S. Tsai, “Formation of negative index-change waveguide lenses in LiNbO3 using ion milling,” Opt. Lett. 13, 1141–1143 (1988).
[Crossref] [PubMed]

D. Y. Zang, C. S. Tsai, “Single mode waveguide microlenses and microlens array fabrication in LiNbO3 using TIPE technique,” Appl. Phys. Lett. 40, 703–705 (1985); “Titanium-indiffused proton-exchanged waveguide lenses in LiNbO3 for optical information processing,” Appl. Opt. 25, 2264–2272 (1986).
[Crossref] [PubMed]

C. C. Lee, K. Y. Liao, C. L. Chang, C. S. Tsai, “Wide-band guided-wave acoustooptic Bragg deflector using a tilted-finger chirp transducer,” IEEE J. Quantum Electron. QE-15, 1166–1170 (1979).

C. S. Tsai, “Guided-wave acoustooptic Bragg modulators for wide-band integrated optic communications and signal processing,” IEEE Trans. Circuits Syst. CAS-26, 1072–1098 (1979), and the many references cited in Guided-Wave Acousto-Optics, C.S. Tsai, ed., Vol. 23 of Springer-Verlag Series on Electronics and Photonics (Springer-Verlag, Berlin, 1990).
[Crossref]

Tsai, G. S.

G. D. Xu, G. S. Tsai, “Integrated acoustooptic modules for interferometric RF spectrum analyzers,” IEEE Photon. Technol. Lett. 3, 153–155 (1991).
[Crossref]

VanderLugt, A.

Veselka, J. J.

J. Jackel, C. E. Rice, J. J. Veselka, “Proton exchange for high index waveguides in LiNbO3,” Appl. Phys. Lett. 41, 607–608 (1982).
[Crossref]

Vu, T. Q.

Whitman, R. L.

Xu, G. D.

G. D. Xu, G. S. Tsai, “Integrated acoustooptic modules for interferometric RF spectrum analyzers,” IEEE Photon. Technol. Lett. 3, 153–155 (1991).
[Crossref]

G. D. Xu, C. S. Tsai, “A novel integrated acoustooptic and electrooptic heterodyning device in a LiNbO3 waveguide,” Appl. Phys. Lett. 58, 28–30 (1991).
[Crossref]

Yao, S. K.

S. K. Yao, D. E. Thompson, “Chirp-grating lens for guided-wave optics,” Appl. Phys. Lett. 33, 635–637 (1978).
[Crossref]

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[Crossref]

Young, E. H.

E. H. Young, B. A. Morris, R. V. Balfatto, “Acousto-optic interferometrical spectrum analyzer with direct rf frequency output,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 140–144 (1986).

Zang, D. Y.

D. Y. Zang, C. S. Tsai, “Single mode waveguide microlenses and microlens array fabrication in LiNbO3 using TIPE technique,” Appl. Phys. Lett. 40, 703–705 (1985); “Titanium-indiffused proton-exchanged waveguide lenses in LiNbO3 for optical information processing,” Appl. Opt. 25, 2264–2272 (1986).
[Crossref] [PubMed]

Appl. Opt. (4)

Appl. Phys. Lett. (5)

J. Jackel, C. E. Rice, J. J. Veselka, “Proton exchange for high index waveguides in LiNbO3,” Appl. Phys. Lett. 41, 607–608 (1982).
[Crossref]

S. K. Yao, D. E. Thompson, “Chirp-grating lens for guided-wave optics,” Appl. Phys. Lett. 33, 635–637 (1978).
[Crossref]

G. D. Xu, C. S. Tsai, “A novel integrated acoustooptic and electrooptic heterodyning device in a LiNbO3 waveguide,” Appl. Phys. Lett. 58, 28–30 (1991).
[Crossref]

D. Y. Zang, C. S. Tsai, “Single mode waveguide microlenses and microlens array fabrication in LiNbO3 using TIPE technique,” Appl. Phys. Lett. 40, 703–705 (1985); “Titanium-indiffused proton-exchanged waveguide lenses in LiNbO3 for optical information processing,” Appl. Opt. 25, 2264–2272 (1986).
[Crossref] [PubMed]

R. V. Schmidt, I. P. Kaminow, “Metal diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[Crossref]

Electron. Lett. (1)

M. Goodwin, C. Stewart, “Proton-exchanged optical waveguides in Y-cut lithum niobate,” Electron. Lett. 19, 223–225 (1983).
[Crossref]

IEEE J. Quantum Electron. (3)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[Crossref]

T. Suhara, H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. QE-22, 845–867 (1986).
[Crossref]

C. C. Lee, K. Y. Liao, C. L. Chang, C. S. Tsai, “Wide-band guided-wave acoustooptic Bragg deflector using a tilted-finger chirp transducer,” IEEE J. Quantum Electron. QE-15, 1166–1170 (1979).

IEEE Photon. Technol. Lett. (1)

G. D. Xu, G. S. Tsai, “Integrated acoustooptic modules for interferometric RF spectrum analyzers,” IEEE Photon. Technol. Lett. 3, 153–155 (1991).
[Crossref]

IEEE Spectrum (1)

R. Adler, “Interaction between light and sound,” IEEE Spectrum 4(5), 42–54 (1967).
[Crossref]

IEEE Trans. Circuits Syst. (1)

C. S. Tsai, “Guided-wave acoustooptic Bragg modulators for wide-band integrated optic communications and signal processing,” IEEE Trans. Circuits Syst. CAS-26, 1072–1098 (1979), and the many references cited in Guided-Wave Acousto-Optics, C.S. Tsai, ed., Vol. 23 of Springer-Verlag Series on Electronics and Photonics (Springer-Verlag, Berlin, 1990).
[Crossref]

IEEE Trans. Sonics Ultrason. (1)

D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7–18 (1977).
[Crossref]

J. Electrochem. Soc. (1)

H. I. Smith, F. J. Bachner, N. Efremow, “A high-yield photolithographic technique for surface wave devices,” J. Electrochem. Soc. 118, 821–825 (1971).
[Crossref]

Opt. Eng. (1)

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).

Opt. Lett. (2)

Other (4)

T. Tamir, ed, Integrated Optics (Springer-Verlag, Berlin, 1975).

E. H. Young, B. A. Morris, R. V. Balfatto, “Acousto-optic interferometrical spectrum analyzer with direct rf frequency output,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 140–144 (1986).

I. C. Chang, R. Lu, L. S. Lee, “High dynamic range acousto-optic receiver,” in Optical Technology for Microwave Applications II, S. Yao, ed, Proc. Soc. Photo-Opt. Instrum. Eng.545, 95–101 (1985).

M. D. Koonyz, “Miniature interferometric spectrum analyzer,” in Optical Information Processing II, D. R. Pape, ed., Proc. Soc. Photo-Opt. Instrum. Eng.639, 126–130 (1986).

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Figures (11)

Fig. 1
Fig. 1

Guided-wave AO heterodyning detection using a Mach–Zehnder interferometer configuration.

Fig. 2
Fig. 2

Integrated AO heterodyne device module using active and passive Bragg diffractions in cascade.

Fig. 3
Fig. 3

Dual-unit integrated AO heterodyne device module and the block diagram for measurement of the angle of arrival of rf signals.

Fig. 4
Fig. 4

Dual-unit integrated AO heterodyne device module in a Y-cut LiNbO3 planar waveguide.

Fig. 5
Fig. 5

Block diagram for performance measurement of a single-unit integrated AO heterodyne device module.

Fig. 6
Fig. 6

Output light beams from a single-unit integrated AO heterodyne device module.

Fig. 7
Fig. 7

Measured frequency response of an integrated AO heterodyne device module.

Fig. 8
Fig. 8

Measured dynamic ranges of rf signals of a single-unit integrated AO heterodyne device module: (a) the single-tone instantaneous dynamic range (50 dB; f = 325 MHz; rf drive power = 50 mW); (b) the two-tone third-order spurious-free dynamic range (40 dB; f1 = 325 MHz, f2 = 350 MHz; rf drive power = 50 mW/input).

Fig. 9
Fig. 9

Block diagram for differential phase measurement using integrated AO heterodyne device module.

Fig. 10
Fig. 10

Wave-form comparison showing the differential phase detection of an integrated AO heterodyne device module: upper wave forms, reference signal; bottom wave forms, heterodyned signals (f = 320 MHz) obtained by inserting phase shifts at the input: (a) 0 deg, (b) 54 deg, (c) 93 deg, and (d) 192 deg.

Fig. 11
Fig. 11

Plot of the measured phase difference versus the inserted phase difference.

Tables (4)

Tables Icon

Table 1 Design Parameters for the Tilted-Finger Chirp SAW Transducer

Tables Icon

Table 2 Design Parameters of Ion-Milled Concave Grating Lens

Tables Icon

Table 3 Fabrication Conditions for Ion-Milled Concave Grating Lens

Tables Icon

Table 4 Measured Performance Figures of Single-Unit Integrated AO Heterodyne Device Module

Equations (10)

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

I h ( ξ , t ) = I r + C 1 S 2 ( ξ , t ) I s + C 2 ( I r I s ) 1 / 2 × S ( ξ , t ) [ 2 π f s t - ϕ ( x , t ) + θ r ] ,
Δ ϕ 1 = ( 2 π f 1 / c ) d sin θ 1 ,             Δ ϕ 2 = ( 2 π f 2 / c ) d sin θ 2 ,
θ = sin - 1 ( Δ ϕ c / 2 π f d ) .
I b I 0 [ η s 2 ( 1 - η s ) 2 η a ] 1 / 2 = C 1 ( η a ) 1 / 2 ,
I i I 0 [ η g ( 1 - η g ) η a ( 1 - η a ) ] 1 / 2 = C 2 [ η a ( 1 - η a ) ] 1 / 2 ,
x m = [ ( 2 m π / k 0 n e ) 2 + 4 m π f / k 0 n e ]             m = 1 , 2 , ,
θ m = x m / [ ( x m 2 + f 2 ) 1 / 2 + f ]             m = 1 , 2 , ,
Δ n e = n e 1 - n e 2 = λ [ arcsin ( η 1 / 2 ) + m π ] / 2 d ,             m = 1 , 2 , ,
V i . f . = 2 R g 1 μ 1 cos ( Δ ϕ + π ) = A cos ( Δ ϕ + π ) ,
θ = sin - 1 ( Δ ϕ c / 2 π f d ) .

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