Abstract

The spherical beam volume hologram, recorded by a plane wave and a spherical beam, is investigated for spectroscopic applications in detail. It is shown that both the diffracted and the transmitted beam can be used for spectroscopy when the hologram is read with a collimated beam. A new method is introduced and used for analysis of the spherical beam volume hologram that can be extended for analysis of arbitrary holograms. Experimental results are consistent with the theoretical study. It is shown that the spherical beam volume hologram can be used in a compact spectroscopic configuration when the transmitted beam is monitored. Also, on the basis of the properties of the spherical beam hologram, the response of a hologram recorded by a plane wave and an arbitrary pattern is predicted. The information can be used to optimize holographic spectrometer design.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Z. Xu, Z. Wang, M. E. Sullivan, D. J. Brady, S. H. Foulger, A. Adibi, “Multimodal multiplex spectroscopy using photonic crystals,” Opt. Express 11, 2126–2133 (2003), www.opticsexpress.org .
    [CrossRef] [PubMed]
  2. D. J. Brady, “Multiplex sensors and the constant radiance theorem,” Opt. Lett. 27, 16–18 (2002).
    [CrossRef]
  3. A. Karbaschi, C. Hsieh, O. Momtahan, A. Adibi, M. E. Sullivan, D. J. Brady, “Qualitative demonstration of spectral diversity filtering using spherical beam volume holograms,” Opt. Express 12, 3018–3024 (2004), www.opticsexpress.org .
    [CrossRef] [PubMed]
  4. C. Hsieh, O. Momtahan, A. Karbaschi, A. Adibi, M. E. Sullivan, D. J. Brady, “Role of recording geometry in the performance of spectral diversity filters using spherical beam volume holograms,” Opt. Lett. (to be published).
  5. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (IEEE Press, Piscataway, N.J., 1996).
  6. E. Chuang, D. Psaltis, “Storage of 1000 holograms with use of a dual-wavelength method,” Appl. Opt. 36, 8445–8454 (1997).
    [CrossRef]
  7. G. Barbastathis, D. Psaltis, “Volume holographic multiplexing methods,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, G. T. Sincerbox, eds. (Springer, New York, 2000), pp. 21–59.
    [CrossRef]
  8. F. Gori, “Why is the Fresnel transform so little known?” in Current Trends in Optics, J. C. Dainty, ed. (Academic, New York, 1994), pp. 139–148.
  9. G. Barbastathis, M. Levene, D. Psaltis, “Shift multiplexing with spherical reference waves,” Appl. Opt. 35, 2403–2417 (1996).
    [CrossRef] [PubMed]
  10. R. T. Ingwall, D. Waldman, “Photopolymer systems,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, G. T. Sincerbox, eds. (Springer, New York, 2000), pp. 171–197, see also, www.aprilisinc.com .
    [CrossRef]
  11. For example, J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 2, p. 16.
  12. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef] [PubMed]
  13. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), pp. 418–422.

2004

2003

2002

1997

1996

1983

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Adibi, A.

Barbastathis, G.

G. Barbastathis, M. Levene, D. Psaltis, “Shift multiplexing with spherical reference waves,” Appl. Opt. 35, 2403–2417 (1996).
[CrossRef] [PubMed]

G. Barbastathis, D. Psaltis, “Volume holographic multiplexing methods,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, G. T. Sincerbox, eds. (Springer, New York, 2000), pp. 21–59.
[CrossRef]

Brady, D. J.

Chuang, E.

Clemmow, P. C.

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (IEEE Press, Piscataway, N.J., 1996).

Foulger, S. H.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Goodman, J. W.

For example, J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 2, p. 16.

Gori, F.

F. Gori, “Why is the Fresnel transform so little known?” in Current Trends in Optics, J. C. Dainty, ed. (Academic, New York, 1994), pp. 139–148.

Hsieh, C.

A. Karbaschi, C. Hsieh, O. Momtahan, A. Adibi, M. E. Sullivan, D. J. Brady, “Qualitative demonstration of spectral diversity filtering using spherical beam volume holograms,” Opt. Express 12, 3018–3024 (2004), www.opticsexpress.org .
[CrossRef] [PubMed]

C. Hsieh, O. Momtahan, A. Karbaschi, A. Adibi, M. E. Sullivan, D. J. Brady, “Role of recording geometry in the performance of spectral diversity filters using spherical beam volume holograms,” Opt. Lett. (to be published).

Ingwall, R. T.

R. T. Ingwall, D. Waldman, “Photopolymer systems,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, G. T. Sincerbox, eds. (Springer, New York, 2000), pp. 171–197, see also, www.aprilisinc.com .
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), pp. 418–422.

Karbaschi, A.

A. Karbaschi, C. Hsieh, O. Momtahan, A. Adibi, M. E. Sullivan, D. J. Brady, “Qualitative demonstration of spectral diversity filtering using spherical beam volume holograms,” Opt. Express 12, 3018–3024 (2004), www.opticsexpress.org .
[CrossRef] [PubMed]

C. Hsieh, O. Momtahan, A. Karbaschi, A. Adibi, M. E. Sullivan, D. J. Brady, “Role of recording geometry in the performance of spectral diversity filters using spherical beam volume holograms,” Opt. Lett. (to be published).

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Levene, M.

Momtahan, O.

A. Karbaschi, C. Hsieh, O. Momtahan, A. Adibi, M. E. Sullivan, D. J. Brady, “Qualitative demonstration of spectral diversity filtering using spherical beam volume holograms,” Opt. Express 12, 3018–3024 (2004), www.opticsexpress.org .
[CrossRef] [PubMed]

C. Hsieh, O. Momtahan, A. Karbaschi, A. Adibi, M. E. Sullivan, D. J. Brady, “Role of recording geometry in the performance of spectral diversity filters using spherical beam volume holograms,” Opt. Lett. (to be published).

Psaltis, D.

Sullivan, M. E.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Waldman, D.

R. T. Ingwall, D. Waldman, “Photopolymer systems,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, G. T. Sincerbox, eds. (Springer, New York, 2000), pp. 171–197, see also, www.aprilisinc.com .
[CrossRef]

Wang, Z.

Xu, Z.

Appl. Opt.

Opt. Express

Opt. Lett.

Science

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Other

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), pp. 418–422.

G. Barbastathis, D. Psaltis, “Volume holographic multiplexing methods,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, G. T. Sincerbox, eds. (Springer, New York, 2000), pp. 21–59.
[CrossRef]

F. Gori, “Why is the Fresnel transform so little known?” in Current Trends in Optics, J. C. Dainty, ed. (Academic, New York, 1994), pp. 139–148.

C. Hsieh, O. Momtahan, A. Karbaschi, A. Adibi, M. E. Sullivan, D. J. Brady, “Role of recording geometry in the performance of spectral diversity filters using spherical beam volume holograms,” Opt. Lett. (to be published).

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (IEEE Press, Piscataway, N.J., 1996).

R. T. Ingwall, D. Waldman, “Photopolymer systems,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, G. T. Sincerbox, eds. (Springer, New York, 2000), pp. 171–197, see also, www.aprilisinc.com .
[CrossRef]

For example, J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 2, p. 16.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

(a) Recording geometry for a SBVH. The point source is at distance d from the center of the crystal. The reference beam incident angle is θ r . A line from the coordinate origin to the point source makes an angle θ s with the z axis. (b) Reading configuration. A collimated beam reads the hologram with a θ′ s incident angle. Note that the direction of the reading beam corresponds to the direction of the signal beam in the recording configuration. The diffracted beam propagates in a direction that makes an angle θ′ r with the z axis. The thickness of the holographic material is L in both cases.

Fig. 2
Fig. 2

(a) Recording configuration represented in the k domain. The major angular extent of the spherical beam is indicated by Δθ in the k domain. (b) Reading configuration in the k domain. In general, the reading wavelength is different from the recording one. Δk z ′ is a measure of a partial Bragg-matched condition. All other parameters are the same as those in Fig. 1.

Fig. 3
Fig. 3

(a) Theoretical calculations of the pattern of the diffracted beam of a SBVH recorded with the setup shown in Fig. 1(a) with d = 1.6 cm and λ = 532 nm. The angles θ r and θ s are chosen to be 45° and 0°, respectively. The holographic material is assumed to have a refractive index of 1.5 and a thickness of 100 μm. For these calculations, we assumed the dimensions of the holograms in the x and y directions to be 1.5 and 1.5 cm, respectively. The hologram is read by a beam with normal incidence (i.e., propagation along the z axis) at a wavelength of 700 nm. The origin of the coordinate system is shown by O. (b) The diffracted beam pattern of the same SBVH as in (a) but with lateral dimensions of 3.5 mm × 3.5 mm. The corresponding hologram is shown by the dashed box in (a).

Fig. 4
Fig. 4

Different crescents for reading with different wavelengths of 532, 630, and 700 nm. All other parameters are the same as those described in the caption of Fig. 3(b).

Fig. 5
Fig. 5

(a) Diffracted beam from a SBVH illuminated by an approximately collimated white-light beam from the direction of the spherical recording beam. The white light is from a regular 60-W lamp. The white screen is approximately 20 mm from the hologram. The hologram is recorded with the setup shown in Fig. 1(a) with d = 1.6 cm and λ = 532 nm. The holographic material is Aprilis photopolymer with a refractive index of 1.5 and a thickness of 100 μm. The angles θ s and θ r in the recording setup are -9.6° and 44°, respectively. (b) The transmitted beam through the SBVH when illuminated by a collimated beam at λ = 700 nm at a normal incident angle (θ′ s = 0°). The reading light is obtained when a white-light beam is passed through a monochromator with an output aperture size of 0.45 mm. The full width at half-maximum of the output spectrum of the monochromator at a 700-nm wavelength is approximately 3 nm. The output of the monochromator is collimated with a collimating lens. The dark crescent in the transmitted beam can be clearly seen. The dots in the figure correspond to the imperfection in the material.

Fig. 6
Fig. 6

Transmitted beam through the SBVH when read by an approximately collimated white-light beam from the direction of the spherical recording beam. The hologram is the same as that described in the caption of Fig. 5(a).

Fig. 7
Fig. 7

(a) Variation of the crescent width with the distance between the point source and the recording material during recording [i.e., d in Fig. 1(a)]. Five different holograms are recorded at λ = 532 nm, each with a different value of d. All other recording parameters are the same as those described in the caption of Fig. 5(a). The hologram is read at both λ′ = 532 nm and λ′ = 830 nm. (b) Experimental and theoretical variation of the crescent width with a hologram thickness for 100-, 200-, and 300-μm-thick samples. The recording point source is at a distance of d = 1.6 cm from the hologram for all cases. All other recording parameters are the same as those described in the caption of Fig. 5(a). In both plots, squares and diamonds with the error bars show the experimental results for the reading at 532- and 830-nm wavelengths, respectively. The solid curves show the corresponding theoretical results based on the model described in this paper. In both (a) and (b) the error bars represent the range of crescent widths measured at different heights of each crescent (i.e., different values of y in Fig. 4) close to the crescent center (y = 0).

Fig. 8
Fig. 8

Theoretical and experimental shape of the dark crescent in the transmitted beam when the SBVH is read at (a) λ′ = 532 nm and (b) λ′ = 830 nm. All parameters are the same as those described in the caption of Fig. 5(a).

Equations (29)

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

1r-r0 expjkr-r0= j2π 1kz×expjkzz+d×expjkxaexpjkxx+kyydkxdky,
aˆp= kxkxˆ+kykyˆ+k2-kx2-ky21/2kzˆ,
Akx,ky= j2πk2-kx2-ky21/2 expjkxaexpjkzd.
εr=ε0+Δεkx, kyexpjKg · r+c.c.,
Kg= krx-kxxˆ+-kyyˆ+krz-kzzˆ.
1λ sinθr+θs2=1λ sinθr+θs2,
θr-θs=θr-θs.
E˜dkx, ky, z=jΔεk2L2ε0kdz expjKgx+ksxx×expjKgy+ksyyexpjkdzz×sincL2πKgz+ksz-kdz,
kdz=k2- Kgx+ksx2- Kgy+ksy21/2.
kdz=k2-krx+ksx-kx2-ksy-ky21/2.
Edx, y, z=E˜dkx, ky, zdkxdky.
E˜dkx, ky, z=4π2E˜dkx, ky, zexpjkxx+kyyexp-jkrx+ksxxexp-jksyy=j2π2Δεk2Lε0kdz expjkdzz×sincL2πKgz+ksz-kdz.
Edx, y, z=expjkrx+ksxxexpjksyy4π2×E˜d kx, ky, zexp-jkxx+kyy×dkxdky,
Edx, y, z=expj krx+ksxxexpjksyy×F-1Edkx, ky, zx-xy-y,
Edx, y, z=C1F-1expjkxaexp-j2k× kx2+kx2dsincKgz+ksz-kdzL2πx-xy-y,
Edx, y, z=C2exp-j kd2kxk- x-ad2+ kyk- yd2×sincKgz+k-kdzL2πdkxkdkyk,
Edx, y, zC3 sincfx-ad, ydL2π,
fu, ν=kz+k-k1-u2-ν21/2-kk2k2 -krxk -u2-ν21/2.
fu, ν k21+ 1cosθru- sinθr1+cosθr2+ν2-sinθr1+cosθr2.
fx-ad, yd=m 2πL,
w=2dλL cotθr.
wa=2d- L21- 1nλaL cotθr,inside,
x=ad+ 2krk-krz-k+krkk+kr+ krx2 k+kr 2 1/2.
Et=Es-Ed.
Edr=14πVexpjkr-rr-r×× Δεrε0Eprdv,
Δεr=ε1ErrEs*r+c.c.,
Esr=kx,ky Akx, ky, zexpjkxx+kyydkxdky,
Edr=kx kyVε1 expjkr-r4πε0r-r×× A* kx, ky, zexp-j kxx+kyy×ErrEprdvdkxdky,
Edr=kxkyE˜kx, ky, zdkxdky.

Metrics