Abstract

A novel interferometric polarimeter capable of mapping a spatiotemporal change in the state of polarization (SOP) of light is described. The polarimeter has a reference beam of light with two orthogonal linearly polarized components that interfere with the counterpart components of an elliptically polarized signal beam. The resultant interference pattern is recorded by a computer by the use of a wideband metal-oxide semiconductor video camera. The interference pattern reduces to the ellipticity and azimuth of the ellipse at an instant of time, by which the spatiotemporal change in the SOP is mapped. No optical elements are used for the control of polarization in the polarimeter, and this allows for the mapping of a rapid change in the SOP. Successful experiments are demonstrated by generating an elliptically polarized beam whose SOP varies in space and time.

© 1994 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1988).
  2. J. F. S. Gomes, “Photoelasticity,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987), pp. 677–723.
  3. G. E. Jellison, “Four-channel polarimeter for time-resolved ellipsometry,” Opt. Lett. 12, 766–768 (1987).
    [CrossRef] [PubMed]
  4. K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization,” J. Mod. Opt. 38, 1567–1580 (1991).
    [CrossRef]
  5. K. Oka, Y. Ohtsuka, “Polarimetry for spatiotemporal photoelastic analysis,” Exp. Mech. 33, 44–48 (1993).
    [CrossRef]
  6. J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).
  7. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]

1993 (1)

K. Oka, Y. Ohtsuka, “Polarimetry for spatiotemporal photoelastic analysis,” Exp. Mech. 33, 44–48 (1993).
[CrossRef]

1991 (1)

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

1989 (1)

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).

1987 (1)

1982 (1)

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1988).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1988).

Field, J. E.

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).

Gomes, J. F. S.

J. F. S. Gomes, “Photoelasticity,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987), pp. 677–723.

Huntley, J. M.

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).

Ina, H.

Jellison, G. E.

Kobayashi, S.

Ohtsuka, Y.

K. Oka, Y. Ohtsuka, “Polarimetry for spatiotemporal photoelastic analysis,” Exp. Mech. 33, 44–48 (1993).
[CrossRef]

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

Oka, K.

K. Oka, Y. Ohtsuka, “Polarimetry for spatiotemporal photoelastic analysis,” Exp. Mech. 33, 44–48 (1993).
[CrossRef]

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

Takeda, M.

Takeda, T.

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

Exp. Mech. (1)

K. Oka, Y. Ohtsuka, “Polarimetry for spatiotemporal photoelastic analysis,” Exp. Mech. 33, 44–48 (1993).
[CrossRef]

J. Mod. Opt. (1)

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

J. M. Huntley, J. E. Field, “High resolution moiré photography: application to dynamic stress analysis,” Opt. Eng. 28, 926–933 (1989).

Opt. Lett. (1)

Other (2)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1988).

J. F. S. Gomes, “Photoelasticity,” in Optical Metrology, O. D. D. Soares, ed. (Nijhoff, Dordrecht, The Netherlands, 1987), pp. 677–723.

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Figures (4)

Fig. 1
Fig. 1

Mach–Zehnder interferometric polarimeter. The assembled optical elements, PBS, QWP1, QWP2, M1, and M2, produce a reference beam of light with orthogonal linearly polarized two components.

Fig. 2
Fig. 2

Illustrative schematic of elliptically polarized light. The Cartesian field components |Ex| and |Ey| and azimuth χ are denoted. The major and minor axes of the ellipse are denoted by a and b, respectively.

Fig. 3
Fig. 3

Example of a distorted, meshlike interference pattern.

Fig. 4
Fig. 4

Mapping of the SOP at distinct instants of time. In (A) and (B) the upper part shows the visualized SOP, and the lower part shows the contour mapping of the ellipticity ∊(x, y; t) and azimuth χ(x, y, t).

Equations (8)

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E r ( x , y ) = e x a x exp [ i ( 2 π u 1 x + 2 π υ 1 y ) ] + e y a y exp [ i ( 2 π u 2 x + 2 π υ 2 y ) ] ,
E s ( x , y ; t ) = e x E x ( x , y ; t ) + e y E y ( x , y ; t ) .
I ( x , y ; t ) = | E r ( x , y ) + E s ( x , y ; t ) | 2 = | a x | 2 + | a y | 2 + | E x | 2 + | E y | 2 + E x ( x , y ; t ) a x * exp [ 2 π i ( u 1 x + υ 1 y ) ] + c . c . + E y ( x , y ; t ) a y * exp [ 2 π i ( u 2 x + υ 2 y ) ] + c . c . ,
D x ( f x , f y ; t ) = [ E x ( x , y ; t ) a x * ] D y ( f x , f y ; t ) = [ E y ( x , y ; t ) a y * ] } ,
E x ( x , y ; t ) = 1 [ D x ( f x , f y ; t ) ] / a x * , E y ( x , y ; t ) = 1 [ D y ( f x , f y ; t ) ] / a y * .
( x , y ; t ) = 1 2 tan 1 { S 3 ( x , y ; t ) [ S 1 2 ( x , y ; t ) + S 2 2 ( x , y ; t ) ] 1 / 2 } = ± tan 1 ( b / a ) ,
χ ( x , y ; t ) = 1 2 tan 1 [ S 2 ( x , y ; t ) S 1 ( x , y ; t ) ] ,
S 1 = | E x | 2 | E y | 2 S 2 = E x E y * + E x * E y S 3 = i ( E x * E y E x E y * ) } .

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