Abstract

A novel wavelength-insensitive differential laser Doppler velocimeter (LDV) without a grating has been proposed. The proposed LDV utilizes a position shift of the beam at the input plane according to wavelength change induced by Mach-Zehnder interferometers (MZIs). The gradual shift in the incident angle of the beam to the object is brought about with the combination of MZIs, lenses and apertures. The characteristics of the proposed structure are simulated using paraxial approximation of a lens system with an aperture. The simulation results indicate that almost wavelength-insensitive operation can be obtained by using the proposed structure without any grating element.

©2009 Optical Society of America

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References

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  1. A. LeDuff, G. Plantier, J.-C. Valiere, and T. Bosch,“Analog sensor design proposal for laser Doppler velocimetry,” IEEE Sens. J. 4(2), 257–261 (2004).
    [Crossref]
  2. M. Haruna, K. Kasazumi, and H. Nishihara, “Integrated-optic differential laser Doppler velocimeter with a micro Fresnel lens array,” in Proceedings of Conf. Integ. & Guided-Wave Opt. (IGWO ’89), MBB6.
  3. T. Ito, R. Sawada, and E. Higurashi, “Integrated microlaser Doppler velocimeter,” J. Lightwave Technol. 17(1), 30–34 (1999).
    [Crossref]
  4. J. Foremen, E. George, J. Jetton, R. Lewis, J. Thornton, and H. Watson,“8C2-fluid flow measurements with a laser Doppler velocimeter,” J. Quantum Electron. 2(8), 260–266 (1966).
    [Crossref]
  5. J. Schmidt, R. Völkel, W. Stork, J. T. Sheridan, J. Schwider, N. Streibl, and F. Durst,“Diffractive beam splitter for laser Doppler velocimetry,” Opt. Lett. 17(17), 1240–1242 (1992).
    [Crossref] [PubMed]
  6. R. Sawada, K. Hane, and E. Higurashi, Optical micro electro mechanical systems (Ohmsha, Tokyo, 2002), Section 5.2. (in Japanese)
  7. H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer – Verlag Berlin Heidelberg, 2003), Section 7.2.2.
  8. K. Maru and Y. Fujii, “Integrated wavelength-insensitive differential laser Doppler velocimeter using planar lightwave circuit,” J. Lightwave Technol.in press.
  9. H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer – Verlag Berlin Heidelberg, 2003), Section 2.1.
  10. C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
    [Crossref]
  11. I. Kaminow, and T. Li, Optical Fiber Telecommunications IVA (Academic Press, San Diego, 2002), pp. 424–427.
  12. K. Maru, T. Mizumoto, and H. Uetsuka, “Modeling of multi-input arrayed waveguide grating and its application to design of flat-passband response using cascaded Mach-Zehnder interferometers,” J. Lightwave Technol. 25(2), 544–555 (2007).
    [Crossref]
  13. J. W. Goodman, Introduction to Fourier optics (McGraw-Hill, San Francisco, 1968), Chap. 4–5.
  14. C. K. Madsen, and J. H. Zhao, Optical filter design and analysis (John Willey & Sons, New York, 1999), Chap. 3.
  15. J. W. Goodman, Introduction to Fourier optics. (McGraw-Hill, San Francisco, 1968), p. 94.
  16. D. Botez and M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-heterojunction lasers,” J. Quantum Electron. 14(11), 827–830 (1978).
    [Crossref]

2007 (1)

2004 (1)

A. LeDuff, G. Plantier, J.-C. Valiere, and T. Bosch,“Analog sensor design proposal for laser Doppler velocimetry,” IEEE Sens. J. 4(2), 257–261 (2004).
[Crossref]

1999 (2)

T. Ito, R. Sawada, and E. Higurashi, “Integrated microlaser Doppler velocimeter,” J. Lightwave Technol. 17(1), 30–34 (1999).
[Crossref]

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
[Crossref]

1992 (1)

1978 (1)

D. Botez and M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-heterojunction lasers,” J. Quantum Electron. 14(11), 827–830 (1978).
[Crossref]

1966 (1)

J. Foremen, E. George, J. Jetton, R. Lewis, J. Thornton, and H. Watson,“8C2-fluid flow measurements with a laser Doppler velocimeter,” J. Quantum Electron. 2(8), 260–266 (1966).
[Crossref]

Bosch, T.

A. LeDuff, G. Plantier, J.-C. Valiere, and T. Bosch,“Analog sensor design proposal for laser Doppler velocimetry,” IEEE Sens. J. 4(2), 257–261 (2004).
[Crossref]

Botez, D.

D. Botez and M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-heterojunction lasers,” J. Quantum Electron. 14(11), 827–830 (1978).
[Crossref]

Cappuzzo, M.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
[Crossref]

Doerr, C. R.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
[Crossref]

Durst, F.

Ettenberg, M.

D. Botez and M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-heterojunction lasers,” J. Quantum Electron. 14(11), 827–830 (1978).
[Crossref]

Foremen, J.

J. Foremen, E. George, J. Jetton, R. Lewis, J. Thornton, and H. Watson,“8C2-fluid flow measurements with a laser Doppler velocimeter,” J. Quantum Electron. 2(8), 260–266 (1966).
[Crossref]

Fujii, Y.

K. Maru and Y. Fujii, “Integrated wavelength-insensitive differential laser Doppler velocimeter using planar lightwave circuit,” J. Lightwave Technol.in press.

Gates, J.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
[Crossref]

George, E.

J. Foremen, E. George, J. Jetton, R. Lewis, J. Thornton, and H. Watson,“8C2-fluid flow measurements with a laser Doppler velocimeter,” J. Quantum Electron. 2(8), 260–266 (1966).
[Crossref]

Gomez, L.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
[Crossref]

Higurashi, E.

Ito, T.

Jetton, J.

J. Foremen, E. George, J. Jetton, R. Lewis, J. Thornton, and H. Watson,“8C2-fluid flow measurements with a laser Doppler velocimeter,” J. Quantum Electron. 2(8), 260–266 (1966).
[Crossref]

Laskowski, E.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
[Crossref]

LeDuff, A.

A. LeDuff, G. Plantier, J.-C. Valiere, and T. Bosch,“Analog sensor design proposal for laser Doppler velocimetry,” IEEE Sens. J. 4(2), 257–261 (2004).
[Crossref]

Lewis, R.

J. Foremen, E. George, J. Jetton, R. Lewis, J. Thornton, and H. Watson,“8C2-fluid flow measurements with a laser Doppler velocimeter,” J. Quantum Electron. 2(8), 260–266 (1966).
[Crossref]

Maru, K.

Mizumoto, T.

Paunescu, A.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
[Crossref]

Plantier, G.

A. LeDuff, G. Plantier, J.-C. Valiere, and T. Bosch,“Analog sensor design proposal for laser Doppler velocimetry,” IEEE Sens. J. 4(2), 257–261 (2004).
[Crossref]

Sawada, R.

Schmidt, J.

Schwider, J.

Sheridan, J. T.

Stork, W.

Streibl, N.

Stulz, L. W.

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
[Crossref]

Thornton, J.

J. Foremen, E. George, J. Jetton, R. Lewis, J. Thornton, and H. Watson,“8C2-fluid flow measurements with a laser Doppler velocimeter,” J. Quantum Electron. 2(8), 260–266 (1966).
[Crossref]

Uetsuka, H.

Valiere, J.-C.

A. LeDuff, G. Plantier, J.-C. Valiere, and T. Bosch,“Analog sensor design proposal for laser Doppler velocimetry,” IEEE Sens. J. 4(2), 257–261 (2004).
[Crossref]

Völkel, R.

Watson, H.

J. Foremen, E. George, J. Jetton, R. Lewis, J. Thornton, and H. Watson,“8C2-fluid flow measurements with a laser Doppler velocimeter,” J. Quantum Electron. 2(8), 260–266 (1966).
[Crossref]

IEEE Photon. Technol. Lett. (1)

C. R. Doerr, M. Cappuzzo, E. Laskowski, A. Paunescu, L. Gomez, L. W. Stulz, and J. Gates, “Dynamic wavelength equalizer in silica using the single-filtered-arm interferometer,” IEEE Photon. Technol. Lett. 11(5), 581–583 (1999).
[Crossref]

IEEE Sens. J. (1)

A. LeDuff, G. Plantier, J.-C. Valiere, and T. Bosch,“Analog sensor design proposal for laser Doppler velocimetry,” IEEE Sens. J. 4(2), 257–261 (2004).
[Crossref]

J. Lightwave Technol. (3)

J. Quantum Electron. (2)

D. Botez and M. Ettenberg, “Beamwidth approximations for the fundamental mode in symmetric double-heterojunction lasers,” J. Quantum Electron. 14(11), 827–830 (1978).
[Crossref]

J. Foremen, E. George, J. Jetton, R. Lewis, J. Thornton, and H. Watson,“8C2-fluid flow measurements with a laser Doppler velocimeter,” J. Quantum Electron. 2(8), 260–266 (1966).
[Crossref]

Opt. Lett. (1)

Other (8)

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer – Verlag Berlin Heidelberg, 2003), Section 2.1.

R. Sawada, K. Hane, and E. Higurashi, Optical micro electro mechanical systems (Ohmsha, Tokyo, 2002), Section 5.2. (in Japanese)

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer – Verlag Berlin Heidelberg, 2003), Section 7.2.2.

M. Haruna, K. Kasazumi, and H. Nishihara, “Integrated-optic differential laser Doppler velocimeter with a micro Fresnel lens array,” in Proceedings of Conf. Integ. & Guided-Wave Opt. (IGWO ’89), MBB6.

I. Kaminow, and T. Li, Optical Fiber Telecommunications IVA (Academic Press, San Diego, 2002), pp. 424–427.

J. W. Goodman, Introduction to Fourier optics (McGraw-Hill, San Francisco, 1968), Chap. 4–5.

C. K. Madsen, and J. H. Zhao, Optical filter design and analysis (John Willey & Sons, New York, 1999), Chap. 3.

J. W. Goodman, Introduction to Fourier optics. (McGraw-Hill, San Francisco, 1968), p. 94.

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Figures (7)

Fig. 1
Fig. 1 Optical system of proposed wavelength-insensitive LDV. (a) whole system and (b) one set of components.
Fig. 2
Fig. 2 Contour plot of calculated power distribution of beam at output plane for various Δλ/ΔλFSR . f = 2 mm and L 1 = L 2 = 4 mm.
Fig. 3
Fig. 3 Beam transition around output plane of L 2 = 4 mm. f = 2 mm and L 1 = 4 mm. (a) Δλ/ΔλFSR = –0.25 and (b) Δλ/ΔλFSR = –0.125.
Fig. 4
Fig. 4 Propagation angle at output plane as function of Δλ/ΔλFSR . f = 2 mm and L 1 = L 2 = 4 mm.
Fig. 5
Fig. 5 ΔλFSR (dψ/dλ) value at λ = λ 0 as function of L 2 for various L 2 /f under condition Eq. (16).
Fig. 6
Fig. 6 Deviation in FD/v as function of Δλ. ΔλFSR = 48.6 nm, ψ 0 = 30°, f = 2 mm, and L 1 = L 2 = 4 mm. The deviation for conventional LDV without MZIs is also plotted in this figure.
Fig. 7
Fig. 7 Deviation in FD/v as function of Δλ for various ΔλFSR . ψ 0 = 30°, f = 2 mm, and L 1 = L 2 = 4 mm. The deviation for conventional LDV without MZIs is also plotted in this figure.

Tables (1)

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Table 1 Design parameters for simulation.

Equations (19)

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FD=2vsinψλ,
dψdλ|λ=λ0=tanψ0λ0,
(h1(λ)h2(λ))=(cosθjsinθjsinθcosθ)(ej(πλ0ΔλΔλFSR+φ)00e+j(πλ0ΔλΔλFSR+φ))(cosθjsinθjsinθcosθ),
(h1(λ)h2(λ))=(sin(πλ0ΔλΔλFSR+φ)cos(πλ0ΔλΔλFSR+φ)).
u2(x)=jλL1ejkL1u1(x0)ejk(xx0)22L1dx0,
F(x)=f(x0)ejkxx0L1dx0,
U2(x)=jλL1ejkL1G1(x)U1(x),
G1(x)=λL1jejkx22L1.
p(x)={1(|x|a)0(|x|>a).
a=L1λ2d.
U2(x)=k2πL1P(x)*U2(x),
u3(x)=u2(x)ejkx22f.
u4(x)=jλL2ejkL2u3(x0)ejk(xx0)22L2dx0.
u4(x)=jλ3L12L1L2ejk(L1+L2)ejkx22L2P(L1L2x)*G2(L1L2x)*[G1(L1L2x)U1(L1L2x)],
G2(x)=λj(1L21f)ejkx22L12(1L21f).
1f=1L1+1L2.
u0(x)=2πwin24e(xwin)2,
U1(x)=2πwin24(h1(λ)ejkdx2L1+h1(λ)ejkdx2L1)e(kwinx2L1)2.
win=Wcore(0.31+2.1D3/2+4D6), for 1.8<D<6.

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