Abstract

In this paper, we present a method for achieving precise evaluation of amplitude of refractive index modulation (RIM) inside the volume Bragg grating (VBG) recorded in photo-thermo-refractive (PTR) glasses. The Gaussian divergence characteristics of the incident beam is theoretically considered when calculating the angular selectivity of VBG, and the profiles of experimental angular selectivity curves are utilized to determine the value of RIM with one step. The effectiveness of our proposed method is experimentally verified. This method is applicable even if the full width at half maximum (FWHM) of VBG’s angular selectivity curve has the same order of magnitude as or is less than the beam divergence.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. A. L. Glebov, O. Mokhun, A. Rapaport, S. Vergnole, V. Smirnov, and L. B. Glebov, “Volume Bragg gratings as ultra-narrow and multiband optical filters,” Proc. SPIE 8428, 84280C (2012).
    [Crossref]
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    [Crossref]
  5. M. Niebuhr, C. Zink, A. Jechow, A. Heuer, L. B. Glebov, and R. Menzel, “Mode stabilization of a laterally structured broad area diode laser using an external volume Bragg grating,” Opt. Express 23(9), 12394–12400 (2015).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  19. I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of phase volume diffractive gratings, part 1: transmitting sinusoidal uniform gratings,” Opt. Eng. 45(1), 015802 (2006).
    [Crossref]

2017 (1)

2016 (2)

2015 (2)

2014 (1)

2013 (2)

2012 (2)

A. L. Glebov, O. Mokhun, A. Rapaport, S. Vergnole, V. Smirnov, and L. B. Glebov, “Volume Bragg gratings as ultra-narrow and multiband optical filters,” Proc. SPIE 8428, 84280C (2012).
[Crossref]

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

2009 (1)

J. Lumeau, L. Glebova, V. Golubkov, E. Zanotto, and L. B. Glebov, “Origin of crystallization-induced refractive index changes in photo-thermo-refractive glass,” Opt. Mater. 32(1), 139–146 (2009).
[Crossref]

2007 (1)

L. Cao, Y. Zhao, Q. He, and G. Jin, “Angle amplifier based on multiplexed volume holographic gratings,” Proc. SPIE 6832, 683216 (2007).
[Crossref]

2006 (1)

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of phase volume diffractive gratings, part 1: transmitting sinusoidal uniform gratings,” Opt. Eng. 45(1), 015802 (2006).
[Crossref]

2004 (2)

2003 (1)

1999 (1)

1981 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Anderson, B.

Arain, M. A.

Ban, V. S.

Beléndez, A.

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

Cao, L.

L. Cao, Y. Zhao, Q. He, and G. Jin, “Angle amplifier based on multiplexed volume holographic gratings,” Proc. SPIE 6832, 683216 (2007).
[Crossref]

Chen, M.

Ciapurin, I. V.

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of phase volume diffractive gratings, part 1: transmitting sinusoidal uniform gratings,” Opt. Eng. 45(1), 015802 (2006).
[Crossref]

Divliansky, I.

Dolgy, S. V.

Downs, E.

Efimov, O. M.

Estepa, L. A.

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

Feng, J.

Francés, J.

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

Gallego, S.

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

Gao, F.

Gaylord, T. K.

Glebov, A. L.

A. L. Glebov, O. Mokhun, A. Rapaport, S. Vergnole, V. Smirnov, and L. B. Glebov, “Volume Bragg gratings as ultra-narrow and multiband optical filters,” Proc. SPIE 8428, 84280C (2012).
[Crossref]

Glebov, L.

Glebov, L. B.

M. Niebuhr, C. Zink, A. Jechow, A. Heuer, L. B. Glebov, and R. Menzel, “Mode stabilization of a laterally structured broad area diode laser using an external volume Bragg grating,” Opt. Express 23(9), 12394–12400 (2015).
[Crossref] [PubMed]

J. Lumeau and L. B. Glebov, “Modeling of the induced refractive index kinetics in photo-thermo-refractive glass,” Opt. Mater. Express 3(1), 95–104 (2013).
[Crossref]

A. L. Glebov, O. Mokhun, A. Rapaport, S. Vergnole, V. Smirnov, and L. B. Glebov, “Volume Bragg gratings as ultra-narrow and multiband optical filters,” Proc. SPIE 8428, 84280C (2012).
[Crossref]

J. Lumeau, L. Glebova, V. Golubkov, E. Zanotto, and L. B. Glebov, “Origin of crystallization-induced refractive index changes in photo-thermo-refractive glass,” Opt. Mater. 32(1), 139–146 (2009).
[Crossref]

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of phase volume diffractive gratings, part 1: transmitting sinusoidal uniform gratings,” Opt. Eng. 45(1), 015802 (2006).
[Crossref]

L. B. Glebov, “Kinetics modeling in photosensitive glass,” Opt. Mater. 25(4), 413–418 (2004).
[Crossref]

O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson, and V. I. Smirnov, “High-efficiency Bragg gratings in photothermorefractive glass,” Appl. Opt. 38(4), 619–627 (1999).
[Crossref] [PubMed]

Glebova, L.

J. Lumeau, L. Glebova, V. Golubkov, E. Zanotto, and L. B. Glebov, “Origin of crystallization-induced refractive index changes in photo-thermo-refractive glass,” Opt. Mater. 32(1), 139–146 (2009).
[Crossref]

Glebova, L. N.

Golubkov, V.

J. Lumeau, L. Glebova, V. Golubkov, E. Zanotto, and L. B. Glebov, “Origin of crystallization-induced refractive index changes in photo-thermo-refractive glass,” Opt. Mater. 32(1), 139–146 (2009).
[Crossref]

He, Q.

L. Cao, Y. Zhao, Q. He, and G. Jin, “Angle amplifier based on multiplexed volume holographic gratings,” Proc. SPIE 6832, 683216 (2007).
[Crossref]

Heuer, A.

Hong, C.

Huang, H.

Jechow, A.

Jin, D.

Jin, G.

L. Cao, Y. Zhao, Q. He, and G. Jin, “Angle amplifier based on multiplexed volume holographic gratings,” Proc. SPIE 6832, 683216 (2007).
[Crossref]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Li, G.

Liu, J.

Liu, X.

Long, M.

Lumeau, J.

J. Lumeau and L. B. Glebov, “Modeling of the induced refractive index kinetics in photo-thermo-refractive glass,” Opt. Mater. Express 3(1), 95–104 (2013).
[Crossref]

J. Lumeau, L. Glebova, V. Golubkov, E. Zanotto, and L. B. Glebov, “Origin of crystallization-induced refractive index changes in photo-thermo-refractive glass,” Opt. Mater. 32(1), 139–146 (2009).
[Crossref]

Márquez, A.

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

Melnik, E. D.

Menzel, R.

Moharam, M. G.

Mokhun, O.

A. L. Glebov, O. Mokhun, A. Rapaport, S. Vergnole, V. Smirnov, and L. B. Glebov, “Volume Bragg gratings as ultra-narrow and multiband optical filters,” Proc. SPIE 8428, 84280C (2012).
[Crossref]

Neipp, C.

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

Niebuhr, M.

Ortuño, M.

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

Ott, D.

Pascual, I.

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

Rapaport, A.

A. L. Glebov, O. Mokhun, A. Rapaport, S. Vergnole, V. Smirnov, and L. B. Glebov, “Volume Bragg gratings as ultra-narrow and multiband optical filters,” Proc. SPIE 8428, 84280C (2012).
[Crossref]

Richardson, K. C.

Riza, N. A.

Shaw, J.

Shen, D.

Smirnov, V.

A. L. Glebov, O. Mokhun, A. Rapaport, S. Vergnole, V. Smirnov, and L. B. Glebov, “Volume Bragg gratings as ultra-narrow and multiband optical filters,” Proc. SPIE 8428, 84280C (2012).
[Crossref]

Smirnov, V. I.

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of phase volume diffractive gratings, part 1: transmitting sinusoidal uniform gratings,” Opt. Eng. 45(1), 015802 (2006).
[Crossref]

O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson, and V. I. Smirnov, “High-efficiency Bragg gratings in photothermorefractive glass,” Appl. Opt. 38(4), 619–627 (1999).
[Crossref] [PubMed]

Sun, R.

Tan, F.

Tang, D.

Venus, G.

Vergnole, S.

A. L. Glebov, O. Mokhun, A. Rapaport, S. Vergnole, V. Smirnov, and L. B. Glebov, “Volume Bragg gratings as ultra-narrow and multiband optical filters,” Proc. SPIE 8428, 84280C (2012).
[Crossref]

Volodin, B. L.

Wang, P.

Wei, S.

Wu, S.

Xu, J.

Yaqoob, Z.

Yuan, X.

Zanotto, E.

J. Lumeau, L. Glebova, V. Golubkov, E. Zanotto, and L. B. Glebov, “Origin of crystallization-induced refractive index changes in photo-thermo-refractive glass,” Opt. Mater. 32(1), 139–146 (2009).
[Crossref]

Zhang, G.

Zhang, J.

Zhang, X.

Zhao, Y.

L. Cao, Y. Zhao, Q. He, and G. Jin, “Angle amplifier based on multiplexed volume holographic gratings,” Proc. SPIE 6832, 683216 (2007).
[Crossref]

Zhu, H.

Zink, C.

Zou, K.

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Chin. Opt. Lett. (3)

J. Opt. Soc. Am. (1)

Materials (Basel) (1)

S. Gallego, C. Neipp, L. A. Estepa, M. Ortuño, A. Márquez, J. Francés, I. Pascual, and A. Beléndez, “Volume holograms in photopolymers: Comparison between analytical and rigorous theories,” Materials (Basel) 5(8), 1373–1388 (2012).
[Crossref]

Opt. Eng. (1)

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of phase volume diffractive gratings, part 1: transmitting sinusoidal uniform gratings,” Opt. Eng. 45(1), 015802 (2006).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Opt. Mater. (2)

L. B. Glebov, “Kinetics modeling in photosensitive glass,” Opt. Mater. 25(4), 413–418 (2004).
[Crossref]

J. Lumeau, L. Glebova, V. Golubkov, E. Zanotto, and L. B. Glebov, “Origin of crystallization-induced refractive index changes in photo-thermo-refractive glass,” Opt. Mater. 32(1), 139–146 (2009).
[Crossref]

Opt. Mater. Express (1)

Proc. SPIE (2)

A. L. Glebov, O. Mokhun, A. Rapaport, S. Vergnole, V. Smirnov, and L. B. Glebov, “Volume Bragg gratings as ultra-narrow and multiband optical filters,” Proc. SPIE 8428, 84280C (2012).
[Crossref]

L. Cao, Y. Zhao, Q. He, and G. Jin, “Angle amplifier based on multiplexed volume holographic gratings,” Proc. SPIE 6832, 683216 (2007).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

DE of the transmitted minus first diffracted order as a function of the deviation from Bragg angle and index modulation under different beam divergence.

Fig. 2
Fig. 2

DE of the transmitted minus first diffracted order as a function of the deviation from Bragg angle and index modulation for different incident wavelengths and polarization states.

Fig. 3
Fig. 3

Scheme of DE measurement of VBGs.

Fig. 4
Fig. 4

Dependence of coefficient of coincidence for experimental and theoretical values of diffraction efficiency on refractive index modulation for VBG-1# (a) and VBG-2# (b). Wavelengths and states of polarization are shown in inserts.

Fig. 5
Fig. 5

Experimental angle selectivity curves and theoretical angle selectivity curves plotted according to the evaluated RIM values of VBG-1#(a-d) and VBG-2#(e-h).

Tables (1)

Tables Icon

Table 1 Evaluated RIM values of VBGs under different measurement conditions.

Equations (9)

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η= sin 2 ( ν 2 + ξ 2 ) 1 2 1+ ξ 2 / ν 2 .
ν={ πΔnd λ (cos θ r cos θ s ) 1 2 TE mode -πΔndcos(2(ϕ θ r )) λ (cos θ r cos θ s ) 1 2 TM mode .
ξ= d 2cos θ s [ (Kcos(ϕ θ r ) K 2 λ 4π n 0 ) ].
G( θ, θ i ,b )=exp[ 2 ( θ θ i b ) 2 ].
b= 2 λ 0 πD .
η θ,b ( θ i )= η( θ )G( θ, θ i ,b )dθ G( θ, θ i ,b )dθ .
η θ,b ( θ i )= 2 π 1 b η( θ )G( θ, θ i ,b )dθ .
CC= { 1 N i [D E exp ( θ i )D E the ( θ i )] 2 } 1/2 .
η= I 1T I 0T + I 1T .