## Out-of-phase mixed holographic gratings : a quantative analysis

Optics Express, Vol. 16, Issue 9, pp. 6528-6536 (2008)

http://dx.doi.org/10.1364/OE.16.006528

Acrobat PDF (207 KB)

### Abstract

We show, that by performing a simultaneous analysis of the angular dependencies of the ± first and the zeroth diffraction orders of mixed holographic gratings, each of the relevant parameters can be obtained: the strength of the phase grating and the amplitude grating, respectively, as well as a potential phase between them. Experiments on a pure lithium niobate crystal are used to demonstrate the applicability of the analysis.

© 2008 Optical Society of America

## 1. Introduction

1. L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya, and A. Beléndez, “Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect,” Opt. Lett. **26**, 786–788 (2001). [CrossRef]

2. C. Neipp, C. Pascual, and A. Beléndez, “Mixed phase-amplitude holographic gratings recorded in bleached silver halide materials,” J. Phys. D Appl. Phys. **35**, 957–967 (2002). [CrossRef]

3. C. Neipp, I. Pascual, and A. Beléndez, “Experimental evidence of mixed gratings with a phase difference between the phase and amplitude grating in volume holograms,” Opt. Express **10**, 1374–1383 (2002). [PubMed]

4. M. A. Ellabban, M. Fally, R. A. Rupp, and L. Kovács, “Light-induced phase and amplitude gratings in centrosymmetric Gadolinium Gallium garnet doped with Calcium,” Opt. Express **14**, 593–602 (2006). [CrossRef] [PubMed]

5. A. S. Shcheulin, A. V. Veniaminov, Y. L. Korzinin, A. E. Angervaks, and A. I. Ryskin, “A Highly Stable Holographic Medium Based on CaF2 :Na Crystals with Colloidal Color Centers: III. Properties of Holograms,” Opt. Spectrosc.-USSR **103**, 655–659 (2007). [CrossRef]

*in phase*. Later Guibelalde generalized the equations to be valid for

*out-of-phase*gratings [7

7. E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. **16**, 173–178 (1984). [CrossRef]

*η*

_{1}, defined as the ratio of powers between the diffracted beam and the incoming beam. For the case of high diffraction efficiencies (above 50%) or even for overmodulated gratings [8

8. C. Neipp, I. Pascual, and A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsions,” J. Opt. A-Pure Appl. Op. **3**, 504–513 (2001). [CrossRef]

3. C. Neipp, I. Pascual, and A. Beléndez, “Experimental evidence of mixed gratings with a phase difference between the phase and amplitude grating in volume holograms,” Opt. Express **10**, 1374–1383 (2002). [PubMed]

9. S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Overmodulation effects in volume holograms recorded on photopolymers,” Opt. Commun. **215**, 263–269 (2003). [CrossRef]

*η*

_{0}, i.e., more correctly termed as zero order diffraction efficiency, was also employed for characterization of the grating parameters. It was suggested, that by measuring the diffraction and transmission efficiency it is possible to evaluate the refractive-index modulation

*n*

_{1}and the absorption constant modulation

*α*

_{1}if one assumes in-phase gratings [1

1. L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya, and A. Beléndez, “Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect,” Opt. Lett. **26**, 786–788 (2001). [CrossRef]

*n*

_{1},

*α*

_{1}and the phase

*φ*between them. We generalize the formulae given in Ref. [1

1. L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya, and A. Beléndez, “Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect,” Opt. Lett. **26**, 786–788 (2001). [CrossRef]

## 2. Diffraction efficiencies of zero and ± first order

7. E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. **16**, 173–178 (1984). [CrossRef]

*n*(

*x*)=

*n*

_{0}+

*n*

_{1}cos(

*Kx*) and imaginary part

*α*(

*x*)=

*α*

_{0}+

*α*

_{1}cos(

*Kx*+

*φ*), yields outgoing complex electric field amplitudes for the (zero order) forward diffracted

*R*̂

_{0}and (first order) diffracted

*R*̂

_{±1}waves. These depend characteristically on the following parameters: the mean absorption constant

*α*

_{0}, the thickness

*d*of the grating, the dephasing

*ϑ*due to the deviation from Bragg’s law and the complex coupling constant

*κ*

^{±}=

*n*

_{1}

*π*/

*λ*-

*iα*

_{1}/2

*e*

^{±iφ}=

*κ*

_{1}-

*iκ*

_{2}

*e*

^{±iφ}. Further,

*K*denotes the spatial frequency of the grating,

*n*

_{0}the mean refractive index of the medium, and

*φ*a possible phase shift between the refractive-index and absorption grating. The goal of an experiment is to extract the grating parameters

*n*

_{1},

*α*

_{1},

*φ*by varying the dephasing, e.g., through measuring the angular response of

*η*

_{0}=

*R̂*

_{0}

*R̂*

^{*}

_{0}/

*I*and

*η*

_{±1}=

*R̂*

_{±1}

*R̂*

^{*}

_{±1}/

*I*where

^{*}denotes the complex conjugate and

*I*the incident intensity. For simplicity in calculations and as the most often used experimental setup we assume a symmetrical geometry, i.e., that the grating vector and the surface normal are mutually perpendicular. A schematic of the setup is shown in Fig. 1.

**26**, 786–788 (2001). [CrossRef]

*A*(

*θ*)=exp{-2

*α*

_{0}

*D*},

*D*=

*d*/cos

*θ*and

*θ*denotes the Bragg angle (inside the medium). Eq. (1) and Eq. (2) are valid for

_{B}*θ*≥0; for

*θ*≤0 the angles and phase-shifts are replaced by their negative values, i.e.,

*η*

_{±1}(-

*θ*)=

*η*

_{∓1}(

*θ*) and

*η*

_{±1}(

*-φ*)=

*η*

_{∓1}(

*φ*). Note, that Eq. (1) is identical to Eq. (11) from Ref. [7

7. E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. **16**, 173–178 (1984). [CrossRef]

*α*

_{0}

*d*=1 and

*κ*

_{2}=

*α*

_{0}/2, i.e., maximal grating strength for the amplitude contribution [6]. We vary the strength of the phase grating between

*κ*

_{1}=

*κ*

_{2}/4,

*κ*

_{2},4

*κ*

_{2}with different phase angles

*φ*=0,

*π*/4,

*π*/2,3

*π*/4 between the grating types. The angular dependencies of the zero order and ± first order diffraction efficiencies are depicted in Fig. 1(a)-(d).

*φ*=

*π*/4 to obtain a qualitative understanding of the curve shapes and their dependency on the ratio of

*κ*

_{1}/

*κ*

_{2}:

- Zero order diffraction efficiency
*η*_{0}(*θ*)- The curves are symmetric with respect to normal incidence, i.e.,
*θ*=0. - Neither the minima nor the maxima of the curve are located at the Bragg angle, except for
*κ*_{1}=0 or*κ*_{2}=0 or*φ*=*π*/2. In general the position and the height of the minima or maxima depend in a complex way on*κ*_{1},*κ*_{2},*φ*and even the mean absorption constant*α*_{0}(see discussion for*α*_{0}*d*≫1). - Note, that for |
*θ*|≪*θ*the curve resides below the mean absorption curve, for |_{B}*θ*|≫*θ*above_{B}

- Diffraction efficiency
- The maximum value of the diffraction efficiency differs for
*η*_{-1}(*θ*) and_{B}*η*_{+1}(*θ*); in our case_{B}*η*_{-1}(*θ*)<_{B}*η*_{+1}(*θ*)._{B} - The curves are symmetric with respect to
*θ*, i.e.,_{B}*η*_{1}(*θ*+_{B}*x*)=*η*_{1}(*θ*-_{B}*x*) except for their different mean absorption*A*(*θ*±_{B}*x*). - Note, that despite
*κ*_{1}<*κ*_{2}the diffraction efficiency*η*_{-1}(*θ*,_{B}*κ*_{2}/4)>*η*_{-1}(*θ*,_{B}*κ*) for the minus first diffraction order, whereas it is vice versa for the plus first diffraction order, i.e.,_{2}*η*_{+1}(*θ*,_{B}*κ*/4)<_{2}*η*_{+1}(*θ*,_{B}*κ*)_{2}

*φ*values. Figure 2(c) shows a unique case which is most instructive. For

*φ*=

*π*/2 the coupling constant

*κ*=

*κ*

_{1}±

*κ*

_{2},∈ℝ. Thus a maximum difference between η

_{-1}and η

_{+1}is obtained, culminating in the full depletion of

*η*

_{-1}if

*κ*

_{1}=

*κ*

_{2}(see appendix). Finally, we want to draw the attention to the case of

*φ*=3

*π*/4>

*π*/2. Then

*η*

_{±1}gives identical results as for

*φ*-

*π*/2. The zero order diffraction efficiency

*η*

_{0}, however, approaches the mean absorption curve for |

*θ*|≫

*θ*from above in the case of

_{B}*φ*<

*π*/2 and contrary from below for

*φ*>

*π*/2. Considering these arguments it is obvious, that only a simultaneous fit of all diffraction data, i.e., zero and ± first order diffracted intensities, allows to extract the decisive parameters

*κ*

_{1},

*κ*

_{2},

*φ*. On the other hand these curves are therefore fingerprints of the relation between the parameters. The following recipe can help in judging about the general situation (for

*α*

_{0}

*d*≈1):

- Check
*η*_{±1}: if their magnitudes differ, this is a fingerprint that mixed gratings exist that are out of phase (*φ*≠0). The ratio*η*_{+1}/*η*_{-1}at the Bragg position obtains a maximum value for*φ*=*π*/2 and for*κ*_{1}=*κ*_{2}[4].4. M. A. Ellabban, M. Fally, R. A. Rupp, and L. Kovács, “Light-induced phase and amplitude gratings in centrosymmetric Gadolinium Gallium garnet doped with Calcium,” Opt. Express

**14**, 593–602 (2006). [CrossRef] [PubMed] - Check
*η*_{0}: if*η*_{0}(*θ*=0)<*A*(0) then |*φ*|<*π*/2 and else vice versa - If
*η*^{max}_{0}+*η*^{min}_{0}>2*A*(*θ*), the absorptive component is dominating and else vice versa._{B} - For overmodulated phase gratings another feature of the diffraction efficiencies becomes prominent: the side minima near the Bragg peak are lifted to nonzero values (for
*φ*≠*π*/2). This striking feature can already be understood in the case*φ*=0 where we simply add up the pure absorptive and the pure phase grating. The positions of the sth side minima are then given by*ϑ*^{(1)}=2[(_{s}*sπ*/*D*)^{2}-*κ*^{2}_{1}]^{1/2}(phase grating) and*ϑ*^{(2)}_{s}=2[(*sπ*/*D*)^{2}+*κ*^{2}_{2}]^{1/2}(absorption grating). Thus, their minima considerably deviate from each other for*κ*_{1,2}≈*sπ*/*D*. Recalling, that*κ*_{2}=*α*_{1}/2≤*α*_{0}/2 such a situation will practically occur if*κ*_{1}≫*π*/*D*, i.e., for*s*>1 (overmodulated phase gratings exist). This is realized in various systems (see e.g., [2, 82. C. Neipp, C. Pascual, and A. Beléndez, “Mixed phase-amplitude holographic gratings recorded in bleached silver halide materials,” J. Phys. D Appl. Phys.

**35**, 957–967 (2002). [CrossRef], 108. C. Neipp, I. Pascual, and A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsions,” J. Opt. A-Pure Appl. Op.

**3**, 504–513 (2001). [CrossRef]] but did not deserve proper attention.10. I. Drevenšek-Olenik, M. Fally, and M. Ellabban, “Optical anisotropy of holographic polymer-dispersed liquid crystal transmission gratings,” Phys. Rev. E

**74**, 021707 (2006). [CrossRef]

*φ*→

*φ*+

*π*the complex coupling parameters

*κ*

^{±}→

*κ*

^{∓}are interchanged and thus the

*η*

_{±1}→

*η*

_{∓1}. For

*η*

_{0}the term in the second line of Eq. 2 changes sign because of cos

*φ*→cos(

*φ*+

*π*)=-cos

*φ*.

## 3. Experimental and discussion

*λ*=351 nm. Two plane waves with equal intensities and parallel polarization states (s-polarization) were employed as recording beams under a crossing angle of 2Θ

_{p}*=20.21° (outside the medium) corresponding to a grating period of 1000 nm where the polar*

_{B}*c*-axis is lying in the plane of incidence. The total intensity of the writing beams was 9 mW/cm

^{2}. HPDLC samples were fabricated from a UV curable mixture prepared from commercially available constituents as previously reported in literature [10

10. I. Drevenšek-Olenik, M. Fally, and M. Ellabban, “Optical anisotropy of holographic polymer-dispersed liquid crystal transmission gratings,” Phys. Rev. E **74**, 021707 (2006). [CrossRef]

*µ*m [11

11. M. Fally, I. Drevenšek-Olenik, M. A. Ellabban, K. P. Pranzas, and J. Vollbrandt, “Colossal light-induced refractive-index modulation for neutrons in holographic polymer-dispersed liquid crystals,” Phys. Rev. Lett. **97**, 167803 (2006). [CrossRef] [PubMed]

_{3}we used a single considerably reduced readout beam at

*λ*=

_{r}*λ*=351 nm and s-polarization, whereas for the HPDLC a He-Ne laser beam at a readout wavelength of

_{p}*λ*=543 nm and p-polarization state was employed. Figure 3 shows the experimental curves for the 0.,±1. diffraction orders from a grating recorded in nominally pure congruently melted LiNbO

_{r}_{3}. According to the recipe given above we immediately can diagnose

*mixed out-of-phase*refractive-index and amplitude gratings, because the

*η*

_{+1}>

*η*

_{-1}. Further by inspecting the zero order diffraction we come to know that the phase 0<

*φ*<

*π*/2. The effects in the zero order are not so prominent for two reasons: the overall diffraction efficiency is very small and the phase grating is dominant because the zero order diffraction curve extends mostly to values below the mean absorption curve (dash-dot line in Fig. 3). A simultaneous fit of Eq. 1 and Eq. 2 to the measured data yielded the following parameters:

*n*

_{1}=(3.01±0.04)×10

^{-6},

*α*

_{1}=8.18±0.48m

^{-1},

*φ*=1.027±0.059,

*α*

_{0}=118±1.7m

^{-1}with a reduced chi-square value of 1.89×10

^{-7}. From this value and Fig. 3 it is obvious that the equations excellently fit the data.

14. M. A. Ellabban, M. Bichler, M. Fally, and I. Drevenšek Olenik, “Role of optical extinction in holographic polymer-dispersed liquid crystals,” in *Liquid Crystals and Applications in Optics*, M. Glogarova, P. Palffy-Muhoray, and M. Copic, eds., vol. 6587, p. 65871J (SPIE Proc., 2007). [CrossRef]

**74**, 021707 (2006). [CrossRef]

14. M. A. Ellabban, M. Bichler, M. Fally, and I. Drevenšek Olenik, “Role of optical extinction in holographic polymer-dispersed liquid crystals,” in *Liquid Crystals and Applications in Optics*, M. Glogarova, P. Palffy-Muhoray, and M. Copic, eds., vol. 6587, p. 65871J (SPIE Proc., 2007). [CrossRef]

12. G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E **55**, 1035–1047 (1997). [CrossRef]

15. L. De Sio, R. Caputo, A. De Luca, A. Veltri, C. Umeton, and A. V. Sukhov, “In situ optical control and stabilization of the curing process of holographic gratings with a nematic film-polymer-slice sequence structure,” Appl. Optics **45**, 3721–3727 (2006). [CrossRef]

16. N. Uchida, “Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am. **63**, 280–287 (1973). [CrossRef]

**74**, 021707 (2006). [CrossRef]

## 4. Remarks and conclusion

*α*

_{0}

*d*≈1,

*κ*

_{1}≈

*κ*

_{2}and

*η*

_{1}(

*θ*)/

_{B}*η*

_{0}(

*θ*)≿0.01, so that with the chosen example of LiNbO

_{B}_{3}above we are already at the limit. If one grating type is dominant the analysis still remains valid, however, the resulting values for

*φ*and the smaller component result in quite large errors.

_{0}≪1 the absorptive grating strength is considerably limited, so that in general the zero order diffraction will not feel the Bragg diffraction. On the other hand, for

*α*

_{0}

*d*≫1, the forward diffracted beam will exhibit a maximum near the Bragg position, a fact which is well known in x-ray optics (anomalous transmission), see e.g. [17

17. B. W. Batterman and H. Cole, “Dynamical Diffraction of X Rays by Perfect Crystals,” Rev. Mod. Phys. **36**, 681–717 (1964). [CrossRef]

**14**, 593–602 (2006). [CrossRef] [PubMed]

18. K. Sutter and P. Günter, “Photorefractive gratings in the organic crystal 2-cyclooctylamino-5-nitropyridine doped with 7,7,8,8-tetracyanoquinodimethane,” J. Opt. Soc. Am. B **7**, 2274–2278 (1990). [CrossRef]

19. F. Kahmann, “Separate and simultaneous investigation of absorption gratings and refractive-index gratings by beam-coupling analysis,” J. Opt. Soc. Am. A **10**, 1562–1569 (1993). [CrossRef]

20. M. Fally, “Separate and simultaneous investigation of absorption gratings and refractive-index gratings by beamcoupling analysis: comment,” J. Opt. Soc. Am. A **23**, 2662–2663 (2006). [CrossRef]

12. G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E **55**, 1035–1047 (1997). [CrossRef]

*α*

_{1}≤

*α*

_{0}(for violation of this condition see [5

5. A. S. Shcheulin, A. V. Veniaminov, Y. L. Korzinin, A. E. Angervaks, and A. I. Ryskin, “A Highly Stable Holographic Medium Based on CaF2 :Na Crystals with Colloidal Color Centers: III. Properties of Holograms,” Opt. Spectrosc.-USSR **103**, 655–659 (2007). [CrossRef]

13. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. **71**, 811–818 (1981). [CrossRef]

## Appendix

*φ*=

*π*/2 the diffraction efficiencies read:

*κ*

^{2}

_{1}-

*κ*

^{2}

_{2}]

^{1/2}. The amplitude of the diffracted beams, however, is enhanced or diminished by a multiplication with or division by

*r*=(

*κ*

_{1}−

*κ*

_{2})/(

*κ*

_{1}+

*κ*

_{2}), respectively. Therefore, it’s easy to see that for

*κ*

_{1}=

*κ*

_{2}the curves shown in Fig. 2 (c) arise.

## Acknowledgment

_{3}sample. Financially supported by the Austrian Science Fund (P-18988) and the ÖAD in the frame of the STC program Slovenia-Austria (SI-A4/0708). We acknowledge continuous support by E. Tillmanns by making one of his labs available to us.

## References and links

1. | L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya, and A. Beléndez, “Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect,” Opt. Lett. |

2. | C. Neipp, C. Pascual, and A. Beléndez, “Mixed phase-amplitude holographic gratings recorded in bleached silver halide materials,” J. Phys. D Appl. Phys. |

3. | C. Neipp, I. Pascual, and A. Beléndez, “Experimental evidence of mixed gratings with a phase difference between the phase and amplitude grating in volume holograms,” Opt. Express |

4. | M. A. Ellabban, M. Fally, R. A. Rupp, and L. Kovács, “Light-induced phase and amplitude gratings in centrosymmetric Gadolinium Gallium garnet doped with Calcium,” Opt. Express |

5. | A. S. Shcheulin, A. V. Veniaminov, Y. L. Korzinin, A. E. Angervaks, and A. I. Ryskin, “A Highly Stable Holographic Medium Based on CaF2 :Na Crystals with Colloidal Color Centers: III. Properties of Holograms,” Opt. Spectrosc.-USSR |

6. | H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” AT&T Tech. J. |

7. | E. Guibelalde, “Coupled wave analysis for out-of-phase mixed thick hologram gratings,” Opt. Quantum Electron. |

8. | C. Neipp, I. Pascual, and A. Beléndez, “Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsions,” J. Opt. A-Pure Appl. Op. |

9. | S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, “Overmodulation effects in volume holograms recorded on photopolymers,” Opt. Commun. |

10. | I. Drevenšek-Olenik, M. Fally, and M. Ellabban, “Optical anisotropy of holographic polymer-dispersed liquid crystal transmission gratings,” Phys. Rev. E |

11. | M. Fally, I. Drevenšek-Olenik, M. A. Ellabban, K. P. Pranzas, and J. Vollbrandt, “Colossal light-induced refractive-index modulation for neutrons in holographic polymer-dispersed liquid crystals,” Phys. Rev. Lett. |

12. | G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E |

13. | M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. |

14. | M. A. Ellabban, M. Bichler, M. Fally, and I. Drevenšek Olenik, “Role of optical extinction in holographic polymer-dispersed liquid crystals,” in |

15. | L. De Sio, R. Caputo, A. De Luca, A. Veltri, C. Umeton, and A. V. Sukhov, “In situ optical control and stabilization of the curing process of holographic gratings with a nematic film-polymer-slice sequence structure,” Appl. Optics |

16. | N. Uchida, “Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector,” J. Opt. Soc. Am. |

17. | B. W. Batterman and H. Cole, “Dynamical Diffraction of X Rays by Perfect Crystals,” Rev. Mod. Phys. |

18. | K. Sutter and P. Günter, “Photorefractive gratings in the organic crystal 2-cyclooctylamino-5-nitropyridine doped with 7,7,8,8-tetracyanoquinodimethane,” J. Opt. Soc. Am. B |

19. | F. Kahmann, “Separate and simultaneous investigation of absorption gratings and refractive-index gratings by beam-coupling analysis,” J. Opt. Soc. Am. A |

20. | M. Fally, “Separate and simultaneous investigation of absorption gratings and refractive-index gratings by beamcoupling analysis: comment,” J. Opt. Soc. Am. A |

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(050.7330) Diffraction and gratings : Volume gratings

(090.0090) Holography : Holography

(090.2900) Holography : Optical storage materials

(090.7330) Holography : Volume gratings

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: March 11, 2008

Revised Manuscript: April 17, 2008

Manuscript Accepted: April 20, 2008

Published: April 23, 2008

**Citation**

Martin Fally, Mostafa Ellabban, and Irena Drevensek-Olenik, "Out-of-phase mixed holographic gratings : a quantative analysis," Opt. Express **16**, 6528-6536 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6528

Sort: Year | Journal | Reset

### References

- L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya, and A. Beléndez, "Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect," Opt. Lett. 26, 786-788 (2001). [CrossRef]
- C. Neipp, C. Pascual, and A. Beléndez, "Mixed phase-amplitude holographic gratings recorded in bleached silver halide materials," J. Phys. D Appl. Phys. 35, 957-967 (2002). [CrossRef]
- C. Neipp, I. Pascual, and A. Beléndez, "Experimental evidence of mixed gratings with a phase difference between the phase and amplitude grating in volume holograms," Opt. Express 10, 1374-1383 (2002). [PubMed]
- M. A. Ellabban, M. Fally, R. A. Rupp, and L. Kovács, "Light-induced phase and amplitude gratings in centrosymmetric Gadolinium Gallium garnet doped with Calcium," Opt. Express 14, 593-602 (2006). [CrossRef] [PubMed]
- A. S. Shcheulin, A. V. Veniaminov, Y. L. Korzinin, A. E. Angervaks, and A. I. Ryskin, "A Highly Stable Holographic Medium Based on CaF2 :Na Crystals with Colloidal Color Centers: III. Properties of Holograms," Opt. Spectrosc. (USSR) 103, 655-659 (2007). [CrossRef]
- H. Kogelnik, "Coupled Wave Theory for Thick Hologram Gratings," AT&T Tech. J. 48, 2909-2947 (1969).
- E. Guibelalde, "Coupled wave analysis for out-of-phase mixed thick hologram gratings," Opt. Quantum Electron. 16, 173-178 (1984). [CrossRef]
- C. Neipp, I. Pascual, and A. Beléndez, "Theoretical and experimental analysis of overmodulation effects in volume holograms recorded on BB-640 emulsions," J. Opt. A-Pure Appl. Opt. 3, 504-513 (2001). [CrossRef]
- S. Gallego, M. Ortuño, C. Neipp, C. García, A. Beléndez, and I. Pascual, "Overmodulation effects in volume holograms recorded on photopolymers," Opt. Commun. 215, 263-269 (2003). [CrossRef]
- I. Drevensek-Olenik, M. Fally, and M. Ellabban, "Optical anisotropy of holographic polymer-dispersed liquid crystal transmission gratings," Phys. Rev. E 74, 021707 (2006). [CrossRef]
- M. Fally, I. Drevensek-Olenik, M. A. Ellabban, K. P. Pranzas, and J. Vollbrandt, "Colossal light-induced refractive-index modulation for neutrons in holographic polymer-dispersed liquid crystals," Phys. Rev. Lett. 97, 167803 (2006). [CrossRef] [PubMed]
- G. Montemezzani and M. Zgonik, "Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries," Phys. Rev. E 55, 1035-1047 (1997). [CrossRef]
- M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981). [CrossRef]
- M. A. Ellabban, M. Bichler, M. Fally, and I. Drevensek Olenik, "Role of optical extinction in holographic polymer-dispersed liquid crystals," in Liquid Crystals and Applications in Optics, M. Glogarova, P. Palffy-Muhoray, and M. Copic, eds., Proc. SPIE 6587, 65871J (2007). [CrossRef]
- L. De Sio, R. Caputo, A. De Luca, A. Veltri, C. Umeton, and A. V. Sukhov, "In situ optical control and stabilization of the curing process of holographic gratings with a nematic film-polymer-slice sequence structure," Appl. Opt. 45, 3721-3727 (2006). [CrossRef]
- N. Uchida, "Calculation of diffraction efficiency in hologram gratings attenuated along the direction perpendicular to the grating vector," J. Opt. Soc. Am. 63, 280-287 (1973). [CrossRef]
- B. W. Batterman and H. Cole, "Dynamical Diffraction of X Rays by Perfect Crystals," Rev. Mod. Phys. 36, 681-717 (1964). [CrossRef]
- K. Sutter and P. Günter, "Photorefractive gratings in the organic crystal 2-cyclooctylamino-5-nitropyridine doped with 7,7,8,8-tetracyanoquinodimethane," J. Opt. Soc. Am. B 7, 2274-2278 (1990). [CrossRef]
- F. Kahmann, "Separate and simultaneous investigation of absorption gratings and refractive-index gratings by beam-coupling analysis," J. Opt. Soc. Am. A 10, 1562-1569 (1993). [CrossRef]
- M. Fally, "Separate and simultaneous investigation of absorption gratings and refractive-index gratings by beamcoupling analysis: comment," J. Opt. Soc. Am. A 23, 2662-2663 (2006). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.