Abstract

A highly efficient optical polarization and phase modulator formed by the placement of a thin transparent piezofilm with indium tin oxide electrodes directly in the path of the output from an optical fiber is presented. Various configurations that differ in the clamping conditions, utilization of epoxy, and optical arrangement are presented. For a film thickness of 63.9 μm, a linear phase-shifting coefficient of 0.131 rad/voltage peak (Vp) at 2 kHz and of 0.508 rad/Vp at 7.4 kHz is demonstrated. An intrinsic birefringence of 0.0328 between the directions along the stretch and its perpendicular in the plane of the film has been measured. The polarization modulation coefficient was determined to be 0.323 rad/Vp at 8.423 kHz, corresponding to a half-wave voltage of 8.353 Vp. Applications of the device involving concurrent spatiotemporal polarization and phase modulation are indicated.

© 1995 Optical Society of America

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References

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  1. R. P. De Paula, E. L. Moore, “Review of all-fiber phase and polarization modulators,” in Fiber Optic and Laser Sensors II, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.478, 3–11 (1984).
  2. V. S. Sudarshanam, K. Srinivasan, “Linear readout of dynamic phase change in a fiber optic homodyne interferometer,” Opt. Lett. 14, 140–142 (1989).
    [CrossRef] [PubMed]
  3. V. S. Sudarshanam, K. Srinivasan, “Phase shift nonlinearity at resonance in a piezofilm based fiber optic phase modulator,” J. Appl. Phys. 68, 1975–1980 (1990).
    [CrossRef]
  4. V. S. Sudarshanam, R. O. Claus, “Frequency response and phase shift nonlinearity of a cylindrical PVDF film based fiber optic phase modulator,” J. Lightwave Technol 11, 595–602 (1993).
    [CrossRef]
  5. T. Sato, Y. Ueda, O. Ikeda, “Transmission type PVDF 2-D optical phase modulator,” Appl. Opt. 20, 343–350 (1981).
    [CrossRef] [PubMed]
  6. “Kynar piezofilm,” Tech. Note (Atochem Sensors, Valley Forge, PA, 1990), p. 13.
  7. V. S. Sudarshanam, R. O. Claus, “Split-cavity cross-coupled extrinsic fiber-optic interferometric sensor,” Opt. Lett. 18, 543–545 (1993).
    [CrossRef] [PubMed]
  8. V. S. Sudarshanam, “Multimode fibre axial strain sensor utilizing end reflection interference,” J. Mod. Opt. 39, 615–624 (1992).
    [CrossRef]
  9. V. S. Sudarshanam, S. V. Pappu, “Holographic optical element based single mode hybrid fiber optic interferometer for realizing zero order fringe,” Fiber Integr. Opt. 11, 71–83 (1992).
    [CrossRef]
  10. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  11. R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium tantalate light modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
    [CrossRef]
  12. D. K. Das-Gupta, K. Doughty, D. B. Shier, “A study of structural and electrical properties of stretched polyvinylidene films,” J. Electrostat. 7, 267–282 (1979).
    [CrossRef]
  13. J. H. McFee, J. G. Bergman, G. R. Crane, “Pyroelectric and nonlinear optical properties of poled polyvinylidene fluoride films,” Ferroelectrics 3, 305–313 (1972).
    [CrossRef]
  14. R. J. Shuford, A. F. Wilde, J. J. Ricca, G. R. Thomas, “Characterization and piezoelectric activity of stretched and poled polyvinylidene fluoride. Part I: Effect of draw ratio and poling conditions,” Polym. Eng. Sci. 16, 25–35 (1976).
    [CrossRef]
  15. “Model 2010 prism coupler,” Applications Note, Metricon Corp., Pennington, N.J., 1990.
  16. H. Ogura, K. Kase, “Evaluation of the Lorentz factor of β-phase polyvinylidene fluoride crystals with the measured refractive index,” Ferroelectrics 110, 145–156 (1990).
    [CrossRef]
  17. Z. K. Ioannidis, I. P. Giles, C. Bowry, “All-fiber optic intensity modulators using liquid crystals,” Appl. Opt. 30, 328–333 (1991).
    [CrossRef] [PubMed]
  18. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E. 9, 1002–1004 (1976).
    [CrossRef]
  19. W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
    [CrossRef]
  20. K. Hane, S. Hattori, “Photothermal bending of a layered sample in plate form,” Appl. Opt. 29, 145–150 (1990).
    [CrossRef] [PubMed]
  21. See, for example, R. O. B. Carpenter, “The electro-optic effect in uniaxial crystals of the dihydrogen phosphate type. III. Measurement of coefficients,” J. Opt. Soc. Am. 40, 225–229 (1950).
    [CrossRef]
  22. D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020–2023 (1980).
    [CrossRef]
  23. D. Gookin, R. Morris, “Electro-optic hysteresis in polyvinylidene fluoride,” Appl. Phys. Lett 45, 603–604 (1984).
    [CrossRef]

1993 (2)

V. S. Sudarshanam, R. O. Claus, “Frequency response and phase shift nonlinearity of a cylindrical PVDF film based fiber optic phase modulator,” J. Lightwave Technol 11, 595–602 (1993).
[CrossRef]

V. S. Sudarshanam, R. O. Claus, “Split-cavity cross-coupled extrinsic fiber-optic interferometric sensor,” Opt. Lett. 18, 543–545 (1993).
[CrossRef] [PubMed]

1992 (2)

V. S. Sudarshanam, “Multimode fibre axial strain sensor utilizing end reflection interference,” J. Mod. Opt. 39, 615–624 (1992).
[CrossRef]

V. S. Sudarshanam, S. V. Pappu, “Holographic optical element based single mode hybrid fiber optic interferometer for realizing zero order fringe,” Fiber Integr. Opt. 11, 71–83 (1992).
[CrossRef]

1991 (1)

1990 (3)

K. Hane, S. Hattori, “Photothermal bending of a layered sample in plate form,” Appl. Opt. 29, 145–150 (1990).
[CrossRef] [PubMed]

H. Ogura, K. Kase, “Evaluation of the Lorentz factor of β-phase polyvinylidene fluoride crystals with the measured refractive index,” Ferroelectrics 110, 145–156 (1990).
[CrossRef]

V. S. Sudarshanam, K. Srinivasan, “Phase shift nonlinearity at resonance in a piezofilm based fiber optic phase modulator,” J. Appl. Phys. 68, 1975–1980 (1990).
[CrossRef]

1989 (1)

1984 (1)

D. Gookin, R. Morris, “Electro-optic hysteresis in polyvinylidene fluoride,” Appl. Phys. Lett 45, 603–604 (1984).
[CrossRef]

1981 (1)

1980 (1)

D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020–2023 (1980).
[CrossRef]

1979 (1)

D. K. Das-Gupta, K. Doughty, D. B. Shier, “A study of structural and electrical properties of stretched polyvinylidene films,” J. Electrostat. 7, 267–282 (1979).
[CrossRef]

1976 (2)

R. J. Shuford, A. F. Wilde, J. J. Ricca, G. R. Thomas, “Characterization and piezoelectric activity of stretched and poled polyvinylidene fluoride. Part I: Effect of draw ratio and poling conditions,” Polym. Eng. Sci. 16, 25–35 (1976).
[CrossRef]

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E. 9, 1002–1004 (1976).
[CrossRef]

1972 (1)

J. H. McFee, J. G. Bergman, G. R. Crane, “Pyroelectric and nonlinear optical properties of poled polyvinylidene fluoride films,” Ferroelectrics 3, 305–313 (1972).
[CrossRef]

1967 (1)

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium tantalate light modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

1964 (1)

W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
[CrossRef]

1950 (1)

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Ballman, A. A.

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium tantalate light modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bergman, J. G.

J. H. McFee, J. G. Bergman, G. R. Crane, “Pyroelectric and nonlinear optical properties of poled polyvinylidene fluoride films,” Ferroelectrics 3, 305–313 (1972).
[CrossRef]

Bowry, C.

Broussoux, D.

D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020–2023 (1980).
[CrossRef]

Carpenter, R. O. B.

Chen, F. S.

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium tantalate light modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

Claus, R. O.

V. S. Sudarshanam, R. O. Claus, “Split-cavity cross-coupled extrinsic fiber-optic interferometric sensor,” Opt. Lett. 18, 543–545 (1993).
[CrossRef] [PubMed]

V. S. Sudarshanam, R. O. Claus, “Frequency response and phase shift nonlinearity of a cylindrical PVDF film based fiber optic phase modulator,” J. Lightwave Technol 11, 595–602 (1993).
[CrossRef]

Conrad, E. E.

W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
[CrossRef]

Crane, G. R.

J. H. McFee, J. G. Bergman, G. R. Crane, “Pyroelectric and nonlinear optical properties of poled polyvinylidene fluoride films,” Ferroelectrics 3, 305–313 (1972).
[CrossRef]

Das-Gupta, D. K.

D. K. Das-Gupta, K. Doughty, D. B. Shier, “A study of structural and electrical properties of stretched polyvinylidene films,” J. Electrostat. 7, 267–282 (1979).
[CrossRef]

De Paula, R. P.

R. P. De Paula, E. L. Moore, “Review of all-fiber phase and polarization modulators,” in Fiber Optic and Laser Sensors II, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.478, 3–11 (1984).

Denton, R. T.

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium tantalate light modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

Doughty, K.

D. K. Das-Gupta, K. Doughty, D. B. Shier, “A study of structural and electrical properties of stretched polyvinylidene films,” J. Electrostat. 7, 267–282 (1979).
[CrossRef]

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E. 9, 1002–1004 (1976).
[CrossRef]

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E. 9, 1002–1004 (1976).
[CrossRef]

Giles, I. P.

Gookin, D.

D. Gookin, R. Morris, “Electro-optic hysteresis in polyvinylidene fluoride,” Appl. Phys. Lett 45, 603–604 (1984).
[CrossRef]

Hane, K.

Hattori, S.

Ikeda, O.

Ioannidis, Z. K.

Kase, K.

H. Ogura, K. Kase, “Evaluation of the Lorentz factor of β-phase polyvinylidene fluoride crystals with the measured refractive index,” Ferroelectrics 110, 145–156 (1990).
[CrossRef]

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E. 9, 1002–1004 (1976).
[CrossRef]

McFee, J. H.

J. H. McFee, J. G. Bergman, G. R. Crane, “Pyroelectric and nonlinear optical properties of poled polyvinylidene fluoride films,” Ferroelectrics 3, 305–313 (1972).
[CrossRef]

Micheron, F.

D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020–2023 (1980).
[CrossRef]

Moore, E. L.

R. P. De Paula, E. L. Moore, “Review of all-fiber phase and polarization modulators,” in Fiber Optic and Laser Sensors II, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.478, 3–11 (1984).

Morris, R.

D. Gookin, R. Morris, “Electro-optic hysteresis in polyvinylidene fluoride,” Appl. Phys. Lett 45, 603–604 (1984).
[CrossRef]

Ogura, H.

H. Ogura, K. Kase, “Evaluation of the Lorentz factor of β-phase polyvinylidene fluoride crystals with the measured refractive index,” Ferroelectrics 110, 145–156 (1990).
[CrossRef]

Pappu, S. V.

V. S. Sudarshanam, S. V. Pappu, “Holographic optical element based single mode hybrid fiber optic interferometer for realizing zero order fringe,” Fiber Integr. Opt. 11, 71–83 (1992).
[CrossRef]

Pliskin, W. A.

W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
[CrossRef]

Ricca, J. J.

R. J. Shuford, A. F. Wilde, J. J. Ricca, G. R. Thomas, “Characterization and piezoelectric activity of stretched and poled polyvinylidene fluoride. Part I: Effect of draw ratio and poling conditions,” Polym. Eng. Sci. 16, 25–35 (1976).
[CrossRef]

Sato, T.

Shier, D. B.

D. K. Das-Gupta, K. Doughty, D. B. Shier, “A study of structural and electrical properties of stretched polyvinylidene films,” J. Electrostat. 7, 267–282 (1979).
[CrossRef]

Shuford, R. J.

R. J. Shuford, A. F. Wilde, J. J. Ricca, G. R. Thomas, “Characterization and piezoelectric activity of stretched and poled polyvinylidene fluoride. Part I: Effect of draw ratio and poling conditions,” Polym. Eng. Sci. 16, 25–35 (1976).
[CrossRef]

Srinivasan, K.

V. S. Sudarshanam, K. Srinivasan, “Phase shift nonlinearity at resonance in a piezofilm based fiber optic phase modulator,” J. Appl. Phys. 68, 1975–1980 (1990).
[CrossRef]

V. S. Sudarshanam, K. Srinivasan, “Linear readout of dynamic phase change in a fiber optic homodyne interferometer,” Opt. Lett. 14, 140–142 (1989).
[CrossRef] [PubMed]

Sudarshanam, V. S.

V. S. Sudarshanam, R. O. Claus, “Frequency response and phase shift nonlinearity of a cylindrical PVDF film based fiber optic phase modulator,” J. Lightwave Technol 11, 595–602 (1993).
[CrossRef]

V. S. Sudarshanam, R. O. Claus, “Split-cavity cross-coupled extrinsic fiber-optic interferometric sensor,” Opt. Lett. 18, 543–545 (1993).
[CrossRef] [PubMed]

V. S. Sudarshanam, “Multimode fibre axial strain sensor utilizing end reflection interference,” J. Mod. Opt. 39, 615–624 (1992).
[CrossRef]

V. S. Sudarshanam, S. V. Pappu, “Holographic optical element based single mode hybrid fiber optic interferometer for realizing zero order fringe,” Fiber Integr. Opt. 11, 71–83 (1992).
[CrossRef]

V. S. Sudarshanam, K. Srinivasan, “Phase shift nonlinearity at resonance in a piezofilm based fiber optic phase modulator,” J. Appl. Phys. 68, 1975–1980 (1990).
[CrossRef]

V. S. Sudarshanam, K. Srinivasan, “Linear readout of dynamic phase change in a fiber optic homodyne interferometer,” Opt. Lett. 14, 140–142 (1989).
[CrossRef] [PubMed]

Thomas, G. R.

R. J. Shuford, A. F. Wilde, J. J. Ricca, G. R. Thomas, “Characterization and piezoelectric activity of stretched and poled polyvinylidene fluoride. Part I: Effect of draw ratio and poling conditions,” Polym. Eng. Sci. 16, 25–35 (1976).
[CrossRef]

Ueda, Y.

Wilde, A. F.

R. J. Shuford, A. F. Wilde, J. J. Ricca, G. R. Thomas, “Characterization and piezoelectric activity of stretched and poled polyvinylidene fluoride. Part I: Effect of draw ratio and poling conditions,” Polym. Eng. Sci. 16, 25–35 (1976).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett (1)

D. Gookin, R. Morris, “Electro-optic hysteresis in polyvinylidene fluoride,” Appl. Phys. Lett 45, 603–604 (1984).
[CrossRef]

Ferroelectrics (2)

J. H. McFee, J. G. Bergman, G. R. Crane, “Pyroelectric and nonlinear optical properties of poled polyvinylidene fluoride films,” Ferroelectrics 3, 305–313 (1972).
[CrossRef]

H. Ogura, K. Kase, “Evaluation of the Lorentz factor of β-phase polyvinylidene fluoride crystals with the measured refractive index,” Ferroelectrics 110, 145–156 (1990).
[CrossRef]

Fiber Integr. Opt. (1)

V. S. Sudarshanam, S. V. Pappu, “Holographic optical element based single mode hybrid fiber optic interferometer for realizing zero order fringe,” Fiber Integr. Opt. 11, 71–83 (1992).
[CrossRef]

IBM J. Res. Dev. (1)

W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
[CrossRef]

J. Appl. Phys. (3)

V. S. Sudarshanam, K. Srinivasan, “Phase shift nonlinearity at resonance in a piezofilm based fiber optic phase modulator,” J. Appl. Phys. 68, 1975–1980 (1990).
[CrossRef]

D. Broussoux, F. Micheron, “Electro-optic and elasto-optic effects in polyvinylidene fluoride,” J. Appl. Phys. 51, 2020–2023 (1980).
[CrossRef]

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium tantalate light modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

J. Electrostat. (1)

D. K. Das-Gupta, K. Doughty, D. B. Shier, “A study of structural and electrical properties of stretched polyvinylidene films,” J. Electrostat. 7, 267–282 (1979).
[CrossRef]

J. Lightwave Technol (1)

V. S. Sudarshanam, R. O. Claus, “Frequency response and phase shift nonlinearity of a cylindrical PVDF film based fiber optic phase modulator,” J. Lightwave Technol 11, 595–602 (1993).
[CrossRef]

J. Mod. Opt. (1)

V. S. Sudarshanam, “Multimode fibre axial strain sensor utilizing end reflection interference,” J. Mod. Opt. 39, 615–624 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. E. (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E. 9, 1002–1004 (1976).
[CrossRef]

Opt. Lett. (2)

Polym. Eng. Sci. (1)

R. J. Shuford, A. F. Wilde, J. J. Ricca, G. R. Thomas, “Characterization and piezoelectric activity of stretched and poled polyvinylidene fluoride. Part I: Effect of draw ratio and poling conditions,” Polym. Eng. Sci. 16, 25–35 (1976).
[CrossRef]

Other (4)

“Model 2010 prism coupler,” Applications Note, Metricon Corp., Pennington, N.J., 1990.

R. P. De Paula, E. L. Moore, “Review of all-fiber phase and polarization modulators,” in Fiber Optic and Laser Sensors II, E. L. Moore, O. G. Ramer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.478, 3–11 (1984).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

“Kynar piezofilm,” Tech. Note (Atochem Sensors, Valley Forge, PA, 1990), p. 13.

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Figures (20)

Fig. 1
Fig. 1

Transmission spectrum of the PVDF film with the ITO electrodes as measured by the ultraviolet–visible–near-infrared scanning spectrophotometer. The vertical axis is marked on the left-hand side in dimensionless units of transmittance, whereas the right-hand side is in terms of corresponding percentage of transmission.

Fig. 2
Fig. 2

Combined MZI–FPI configuration for the measurement of dynamic phase shift.

Fig. 3
Fig. 3

(a) Extrinsic FPI and polarimetric mode of concurrent detection of phase and polarization modulation. (b) The transmission ellipsometric arrangement in the PSCA mode.

Fig. 4
Fig. 4

General mounting arrangement for the elements IPMA, IPMB, and IPMC: (a) cross-sectional view, (b) direct end-face view. (c) Geometry of IPMD.

Fig. 5
Fig. 5

Photograph of the direct end-face view of IPMB with the ST connector epoxied to the piezofilm at the center of the circular washer.

Fig. 6
Fig. 6

Phase shift measured by the J1J4 method as a function of the input voltage applied to IPMA at 2 kHz.

Fig. 7
Fig. 7

Frequency response of IPMA measured in the FPI mode. Note that the curves connecting the data points are only for indication and are not the best-fit curves.

Fig. 8
Fig. 8

FFT of the output of a, the MZI and b, the FPI for phase shift at 2 kHz, and c, the MZI and d, the FPI for phase shift at the resonance frequency of 7.4 kHz. The vertical axis in each of these plots indicates the photovoltage, whereas the horizontal axis indicates the frequency.

Fig. 9
Fig. 9

Variation of the totally reflected intensity seen by the detector in the prism coupler as a function of the angle of incidence of the laser beam. The numbers on the horizontal axis correspond to discrete steps in angle, with 20 steps = 1° and the reference direction of 0° being along the perpendicular to the prism incident face. This plot is for TE incidence along the direction of the stretch marks on the piezofilm.

Fig. 10
Fig. 10

Variation of the surface-reflected intensity seen by the detector in the variable angle monochromatic fringe observation arrangement as a function of the angle of incidence of the laser beam. The numbers on the horizontal axis indicate discrete steps in angle, with 40 steps = 1°.

Fig. 11
Fig. 11

Output of IPMA as seen by the detector when the analyzer is rotated (*) for an arbitrary angle of the half-wave plate, and the angle of the half-wave plate is rotated (×) for an arbitrary angle of the analyzer. Note that the curves connecting the data points are only for indication.

Fig. 12
Fig. 12

Instantaneous output of IPMA when the analyzer is inserted (st) and ×subsequently removed (sp).

Fig. 13
Fig. 13

Frequency response of IPMA (upper curve) and IPMC (lower curve) as measured by the detection of polarization modulation. Note that the curves connecting the data points are only for indication.

Fig. 14
Fig. 14

Linearity of response of IPMA with the input voltage at 8.4 kHz.

Fig. 15
Fig. 15

Linearity of response of IPMB in the FPI mode (*) and the polarimetric mode (○) simultaneously measured with the input voltage at 6 kHz.

Fig. 16
Fig. 16

Frequency response of IPMB in the FPI (*) mode and the polarimetric mode (○) for an input voltage of 10.3 Vp. Note that the curves connecting the data points are only for indication.

Fig. 17
Fig. 17

Output of the FPI and the polarimetric modes for IPMB with the input voltage at 6 kHz as the analyzer is rotated (*) and the half-wave plate is rotated (○).

Fig. 18
Fig. 18

Linearity of response of IPMC at the frequencies, kilohertz of 9.912 (*), 11.914 (○), 12.500 (×), and 17.334 (+). The legend summarizing the least-squares fit to the plots shows the values of the frequency, the nonlinear and linear coefficients, and the intercept.

Fig. 19
Fig. 19

Frequency response of IPMD in the polarimetric mode measured by the J1J4 method.

Fig. 20
Fig. 20

Depth of polarization modulation for IPMD measured by the J1J4 method as a function of the input voltage at 8.423 kHz.

Tables (1)

Tables Icon

Table 1 Clamping Conditions and Optical Arrangement for Testing Different IPM Elements

Equations (5)

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ϕ = ( 2 π L / λ ) ( n e - n o ) + Δ ϕ c + Δ ϕ r + Δ ϕ s ,
I = ( I 0 / 2 ) ( 1 - cos Δ ϕ R [ J 0 ( m ) + 2 n = 1 J 2 n ( m ) cos ( 2 n ω t ) ] + sin Δ ϕ R { 2 n = 1 J 2 n - 1 ( m ) sin [ ( 2 n - 1 ) ω t ] } )
θ c = sin - 1 ( n / n p ) .
d = Δ N λ / [ 2 μ ( cos r 2 - cos r 1 ) ] ,
r i j = r i j + k = 1 6 p i k d k j ,

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