Abstract

An approach is described for the recovery of images from tightly confined spaces by use of multimode fibers, and an analytical demonstration shows that the concept is sound. The proof of concept draws on earlier studies that concentrated on image recovery after two-way and one-way transmissions through a multimode fiber; both types of transmission used four-wave-mixing techniques. The approach described also uses four-wave mixing but utilizes two fibers to capture the image at some intermediate point that is accessible to the fibers but that is visually inaccessible to the casual viewer.

© 1999 Optical Society of America

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References

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  1. A. Volyar, A. Gnatovskii, N. Kukhtarev, S. Lapaeva, “Image transmission via a multimode fiber assisted by polarization preserving phase conjugation in the photorefractive crystal,” Appl. Phys. B: Photophys. Laser Chem. 52, 400–401 (1991).
    [CrossRef]
  2. G. J. Dunning, R. C. Lind, “Demonstration of image transmission through fibers by optical phase conjugation,” Opt. Lett. 7, 558–560 (1982).
    [CrossRef] [PubMed]
  3. E. G. Paek, C. E. Zah, K. W. Cheung, L. Curtis, “All-optical image transmission through a single-mode fiber,” Opt. Lett. 17, 613–615 (1992).
    [CrossRef] [PubMed]
  4. A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
    [CrossRef]
  5. A. Yariv, “On transmission and recovery of three-dimensional image information in optical waveguides,” J. Opt. Soc. Am. 66, 301–306 (1976).
    [CrossRef]
  6. A. Yariv, “Chapter 19: Phase conjugate optics and photorefractive beam coupling,” in Quantum Electronics (Wiley, New York, 1988), pp. 495–533.
  7. B. Fischer, S. Sternklar, “Image transmission and interferometry with multimode fibers using self-pumped phase conjugation,” Appl. Phys. Lett. 46, 113–114 (1985).
    [CrossRef]
  8. G. L. Christenson, A. T. T. D. Tran, S. A. Miller, D. Haronian, Y. H. Lo, “Surface micromachined interferometer-based optical reading technique,” Appl. Phys. Lett. 69, 3324–3326 (1996).
    [CrossRef]

1996 (1)

G. L. Christenson, A. T. T. D. Tran, S. A. Miller, D. Haronian, Y. H. Lo, “Surface micromachined interferometer-based optical reading technique,” Appl. Phys. Lett. 69, 3324–3326 (1996).
[CrossRef]

1992 (1)

1991 (1)

A. Volyar, A. Gnatovskii, N. Kukhtarev, S. Lapaeva, “Image transmission via a multimode fiber assisted by polarization preserving phase conjugation in the photorefractive crystal,” Appl. Phys. B: Photophys. Laser Chem. 52, 400–401 (1991).
[CrossRef]

1985 (1)

B. Fischer, S. Sternklar, “Image transmission and interferometry with multimode fibers using self-pumped phase conjugation,” Appl. Phys. Lett. 46, 113–114 (1985).
[CrossRef]

1982 (1)

1978 (1)

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
[CrossRef]

1976 (1)

Cheung, K. W.

Christenson, G. L.

G. L. Christenson, A. T. T. D. Tran, S. A. Miller, D. Haronian, Y. H. Lo, “Surface micromachined interferometer-based optical reading technique,” Appl. Phys. Lett. 69, 3324–3326 (1996).
[CrossRef]

Curtis, L.

Dunning, G. J.

Fischer, B.

B. Fischer, S. Sternklar, “Image transmission and interferometry with multimode fibers using self-pumped phase conjugation,” Appl. Phys. Lett. 46, 113–114 (1985).
[CrossRef]

Gnatovskii, A.

A. Volyar, A. Gnatovskii, N. Kukhtarev, S. Lapaeva, “Image transmission via a multimode fiber assisted by polarization preserving phase conjugation in the photorefractive crystal,” Appl. Phys. B: Photophys. Laser Chem. 52, 400–401 (1991).
[CrossRef]

Haronian, D.

G. L. Christenson, A. T. T. D. Tran, S. A. Miller, D. Haronian, Y. H. Lo, “Surface micromachined interferometer-based optical reading technique,” Appl. Phys. Lett. 69, 3324–3326 (1996).
[CrossRef]

Kukhtarev, N.

A. Volyar, A. Gnatovskii, N. Kukhtarev, S. Lapaeva, “Image transmission via a multimode fiber assisted by polarization preserving phase conjugation in the photorefractive crystal,” Appl. Phys. B: Photophys. Laser Chem. 52, 400–401 (1991).
[CrossRef]

Lapaeva, S.

A. Volyar, A. Gnatovskii, N. Kukhtarev, S. Lapaeva, “Image transmission via a multimode fiber assisted by polarization preserving phase conjugation in the photorefractive crystal,” Appl. Phys. B: Photophys. Laser Chem. 52, 400–401 (1991).
[CrossRef]

Lind, R. C.

Lo, Y. H.

G. L. Christenson, A. T. T. D. Tran, S. A. Miller, D. Haronian, Y. H. Lo, “Surface micromachined interferometer-based optical reading technique,” Appl. Phys. Lett. 69, 3324–3326 (1996).
[CrossRef]

Miller, S. A.

G. L. Christenson, A. T. T. D. Tran, S. A. Miller, D. Haronian, Y. H. Lo, “Surface micromachined interferometer-based optical reading technique,” Appl. Phys. Lett. 69, 3324–3326 (1996).
[CrossRef]

Paek, E. G.

Sternklar, S.

B. Fischer, S. Sternklar, “Image transmission and interferometry with multimode fibers using self-pumped phase conjugation,” Appl. Phys. Lett. 46, 113–114 (1985).
[CrossRef]

Tran, A. T. T. D.

G. L. Christenson, A. T. T. D. Tran, S. A. Miller, D. Haronian, Y. H. Lo, “Surface micromachined interferometer-based optical reading technique,” Appl. Phys. Lett. 69, 3324–3326 (1996).
[CrossRef]

Volyar, A.

A. Volyar, A. Gnatovskii, N. Kukhtarev, S. Lapaeva, “Image transmission via a multimode fiber assisted by polarization preserving phase conjugation in the photorefractive crystal,” Appl. Phys. B: Photophys. Laser Chem. 52, 400–401 (1991).
[CrossRef]

Yariv, A.

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
[CrossRef]

A. Yariv, “On transmission and recovery of three-dimensional image information in optical waveguides,” J. Opt. Soc. Am. 66, 301–306 (1976).
[CrossRef]

A. Yariv, “Chapter 19: Phase conjugate optics and photorefractive beam coupling,” in Quantum Electronics (Wiley, New York, 1988), pp. 495–533.

Zah, C. E.

Appl. Phys. B: Photophys. Laser Chem. (1)

A. Volyar, A. Gnatovskii, N. Kukhtarev, S. Lapaeva, “Image transmission via a multimode fiber assisted by polarization preserving phase conjugation in the photorefractive crystal,” Appl. Phys. B: Photophys. Laser Chem. 52, 400–401 (1991).
[CrossRef]

Appl. Phys. Lett. (2)

B. Fischer, S. Sternklar, “Image transmission and interferometry with multimode fibers using self-pumped phase conjugation,” Appl. Phys. Lett. 46, 113–114 (1985).
[CrossRef]

G. L. Christenson, A. T. T. D. Tran, S. A. Miller, D. Haronian, Y. H. Lo, “Surface micromachined interferometer-based optical reading technique,” Appl. Phys. Lett. 69, 3324–3326 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Other (1)

A. Yariv, “Chapter 19: Phase conjugate optics and photorefractive beam coupling,” in Quantum Electronics (Wiley, New York, 1988), pp. 495–533.

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Figures (3)

Fig. 1
Fig. 1

Setup for remote image sampling with fibers.

Fig. 2
Fig. 2

Schematic of the use of phase conjugation to recover an image after transmission through a multimode fiber.

Fig. 3
Fig. 3

Setup for calibrating fiber distortion by writing a hologram.

Equations (30)

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f1(x, y, z=0, t)=m=0Nn=0NAmnEmn(x, y)exp(iωt),
f2(x, y, L, t)=m=0Nn=0NAmnEmn(x, y)×exp[i(ωt-βmnL)],
f2(x, y, L, t)=m=0Nn=0NCmnEmn(x, y)exp(iωt),
f3(x, y, L, t)=m=0Nn=0NCmn*Emn*(x, y)exp(iωt)=m=0Nn=0NAmn*Emn*(x, y)exp[i(ωt+βmnL)]
f4(x, y, 0, t)=m=0Nn=0NAmn*Emn*(x, y)×exp[i(ωt+βmnL-βmnL)]=m=0Nn=0NAmn*Emn*(x, y)exp(iωt),
f1(x, y, z=0, t)=i=0Nj=0NaijFij(x, y)exp(iωt),
f1(x, y, z=L1, t)=i=0Nj=0NaijFij(x, y)×exp[i(ωt-βijL1)].
f2(x, y, z=0, t)=k=0Nl=0NbklFkl(x, y)exp(iωt),
f2(x, y, z=L2, t)=k=0Nl=0NbklFkl(x, y)×exp[i(ωt-βklL2)].
bkl=i=0Nj=0Nhklijaij exp[-i(βijL1)].
f2(x, y, z=L2, t)=k=0Nl=0NbklFkl(x, y)×exp[i(ωt-βklL2)],
fr(x, y, z, t)=k=0Nl=0NrklFkl(x, y)exp[i(ωt-kzz)]
fholo(x, y, z, t)=fr(x, y, z, t)+f2(x, y, z, t),
|fholo(x, y, z)|2=k=0Nl=0Nk=0Nl=0N[rklrkl*+rklbkl* exp[i(βklL2+kzz)]+bklrkl* exp[-i(βklL2+kzz)]+bklbkl*]Fkl(x, y)Fkl*(x, y).
f3(x, y, z=L2, t)=p=0Nq=0Nk=0Nl=0Nk=0Nl=0N×[rklbkl* exp(iβklL2)rpq*]×Fkl(x, y)Fkl*(x, y)Fpq*(x, y)×exp(iωt).
f3(x, y, z=L2, t)=k=0Nl=0Nbkl*Fkl*(x, y)×exp[i(ωt+βklL2)],
f3(x, y, z=0, t)=k=0Nl=0Nbkl*Fkl*(x, y)exp(iωt),
bkl*=bkl*|fr(x, y)|2=bkl*p=0N q=0N k=0N l=0N(rklrpq*)×Fkl(x, y)Fpq*(x, y).
dmn=k=0Nl=0Ngmnklbkl*|fr(x, y)|2,
bkl*=i=0N j=0Nhklijaij* exp[i(βij L1)],and
dmn=k=0Nl=0Ni=0Nj=0Ngmnklhklij*aij*|fr(x, y)|2×exp[i(βijL1)].
gmnkl=hklij-1=Hklmn(mn)det H(mn),
i=0Nj=0Nk=0Nl=0NhklijHklmn(mn)
=det H(mn)ifi=m;j=n0ifim;jn.
f4(x, y, z=L1, t)=m=0Nn=0Ndmn*Fmn*(x, y)×exp[i(ωt+βmnL1)],
f4(x, y, z=L1, t)=m=0Nn=0Namn*|fr(x, y)|2Fmn*(x, y)×exp[i(ωt+βmnL1)],
f4(x, y, z=0, t)=m=0Nn=0Nαmn*|fr(x, y)|2Fmn*(x, y)×exp(iωt).
bkl=i=0Nj=0Nνklhklijaij exp[-i(βijL1)]=i=0Nj=0Nhklijaij exp[-i(βijL1)],
dmn=k=0Nl=0Ni=0Nj=0Nηmngmnklhklij*aij*|fr(x, y)|2 ×exp[i(βijL1)]=k=0Nl=0Ni=0Nj=0Ngmnklhklij*aij*|fr(x, y)|2 ×exp[i(βijL1)],
f4(x, y, z=0, t)=m=0Nn=0Nηmnamn*Fmn*(x, y)exp[i(ωt)],

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