Abstract

The effect of aberrations in the recording beams of a holographic setup is discussed regarding the deterioration of properties of a reflecting volume Bragg grating. Imperfect recording beams result in a spatially varying grating vector, which causes broadening, asymmetry, and washed out side lobes in the reflection spectrum as well as a corresponding reduction in peak diffraction efficiency. These effects are more significant for gratings with narrower spectral widths.

© 2013 Optical Society of America

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References

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  1. A. Sevian, O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, and L. Glebov, “Efficient power scaling of laser radiation by spectral beam combining,” Opt. Lett. 33, 384–386 (2008).
    [CrossRef]
  2. O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
    [CrossRef]
  3. Z. Sun, Q. Li, H. Lei, Y. Hui, and M. Jiang, “Sub-nanosecond pulse, single longitudinal mode Q-switched Nd:YVO4 laser controlled by reflecting Bragg gratings,” Opt. Laser Technol. 48, 475–479 (2013).
    [CrossRef]
  4. D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013 (2)

Z. Sun, Q. Li, H. Lei, Y. Hui, and M. Jiang, “Sub-nanosecond pulse, single longitudinal mode Q-switched Nd:YVO4 laser controlled by reflecting Bragg gratings,” Opt. Laser Technol. 48, 475–479 (2013).
[CrossRef]

M. SeGall, D. Ott, I. Divliansky, and L. B. Glebov, “The effect of aberrated recording beams on reflecting Bragg gratings,” Proc. SPIE 8644, 864408 (2013).
[CrossRef]

2012 (1)

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

2011 (1)

2010 (1)

2009 (2)

T. Hieta, M. Vainio, C. Moser, and E. Ikonen, “External-cavity lasers based on a volume holographic grating at normal incidence for spectroscopy in the visible range,” Opt. Commun. 282, 3119–3123 (2009).
[CrossRef]

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

2008 (2)

2007 (1)

2006 (2)

1987 (1)

1985 (1)

1976 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick volume holograms,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Andrusyak, O.

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

A. Sevian, O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, and L. Glebov, “Efficient power scaling of laser radiation by spectral beam combining,” Opt. Lett. 33, 384–386 (2008).
[CrossRef]

Chen, N.

Ciapurin, I.

Creath, J.

J. Wyant and J. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. Shannon and J. Wyant, eds. (Academic, 1992), Vol. XI, pp. 1–53.

Dai, G.

G. Dai, Wavefront Optics for Vision Correction (SPIE, 2008).

Divliansky, I.

M. SeGall, D. Ott, I. Divliansky, and L. B. Glebov, “The effect of aberrated recording beams on reflecting Bragg gratings,” Proc. SPIE 8644, 864408 (2013).
[CrossRef]

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

Fujii, M.

Glebov, L.

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

A. Sevian, O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, and L. Glebov, “Efficient power scaling of laser radiation by spectral beam combining,” Opt. Lett. 33, 384–386 (2008).
[CrossRef]

Glebov, L. B.

Hieta, T.

T. Hieta, M. Vainio, C. Moser, and E. Ikonen, “External-cavity lasers based on a volume holographic grating at normal incidence for spectroscopy in the visible range,” Opt. Commun. 282, 3119–3123 (2009).
[CrossRef]

Hui, Y.

Z. Sun, Q. Li, H. Lei, Y. Hui, and M. Jiang, “Sub-nanosecond pulse, single longitudinal mode Q-switched Nd:YVO4 laser controlled by reflecting Bragg gratings,” Opt. Laser Technol. 48, 475–479 (2013).
[CrossRef]

Ikonen, E.

T. Hieta, M. Vainio, C. Moser, and E. Ikonen, “External-cavity lasers based on a volume holographic grating at normal incidence for spectroscopy in the visible range,” Opt. Commun. 282, 3119–3123 (2009).
[CrossRef]

Ishizuki, H.

Jiang, M.

Z. Sun, Q. Li, H. Lei, Y. Hui, and M. Jiang, “Sub-nanosecond pulse, single longitudinal mode Q-switched Nd:YVO4 laser controlled by reflecting Bragg gratings,” Opt. Laser Technol. 48, 475–479 (2013).
[CrossRef]

Koc, C.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick volume holograms,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Lei, H.

Z. Sun, Q. Li, H. Lei, Y. Hui, and M. Jiang, “Sub-nanosecond pulse, single longitudinal mode Q-switched Nd:YVO4 laser controlled by reflecting Bragg gratings,” Opt. Laser Technol. 48, 475–479 (2013).
[CrossRef]

Lequime, M.

Li, Q.

Z. Sun, Q. Li, H. Lei, Y. Hui, and M. Jiang, “Sub-nanosecond pulse, single longitudinal mode Q-switched Nd:YVO4 laser controlled by reflecting Bragg gratings,” Opt. Laser Technol. 48, 475–479 (2013).
[CrossRef]

Lumeau, J.

Ma, M.

Mahajan, V. N.

V. N. Mahajan, “Zernike polynomials and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (Wiley, 2007), pp. 498–546.

Mokhov, S.

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

V. Smirnov, J. Lumeau, S. Mokhov, B. Ya. Zeldovich, and L. B. Glebov, “Ultranarrow bandwidth moiré reflecting Bragg gratings recorded in photo-thermo-refractive glass,” Opt. Lett. 35, 592–594 (2010).
[CrossRef]

Mokhun, O.

Moser, C.

T. Hieta, M. Vainio, C. Moser, and E. Ikonen, “External-cavity lasers based on a volume holographic grating at normal incidence for spectroscopy in the visible range,” Opt. Commun. 282, 3119–3123 (2009).
[CrossRef]

Noll, R. J.

Ott, D.

M. SeGall, D. Ott, I. Divliansky, and L. B. Glebov, “The effect of aberrated recording beams on reflecting Bragg gratings,” Proc. SPIE 8644, 864408 (2013).
[CrossRef]

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

Rotar, V.

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

Ryasnyanskiy, A.

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

Saikawa, J.

Sakuda, K.

SeGall, M.

M. SeGall, D. Ott, I. Divliansky, and L. B. Glebov, “The effect of aberrated recording beams on reflecting Bragg gratings,” Proc. SPIE 8644, 864408 (2013).
[CrossRef]

Sevian, A.

Sirohi, R. S.

R. S. Sirohi, Optical Methods of Measurement: Wholefield Techniques, 2nd ed. (CRC Press, 2009).

Smirnov, V.

Spiegelberg, C.

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

Sun, Z.

Z. Sun, Q. Li, H. Lei, Y. Hui, and M. Jiang, “Sub-nanosecond pulse, single longitudinal mode Q-switched Nd:YVO4 laser controlled by reflecting Bragg gratings,” Opt. Laser Technol. 48, 475–479 (2013).
[CrossRef]

Syms, R. R. A.

R. R. A. Syms, Practical Volume Holography, Oxford Engineering Science Series (Clarendon, 1990), p. 24.

Taira, T.

Vainio, M.

T. Hieta, M. Vainio, C. Moser, and E. Ikonen, “External-cavity lasers based on a volume holographic grating at normal incidence for spectroscopy in the visible range,” Opt. Commun. 282, 3119–3123 (2009).
[CrossRef]

Venus, G.

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

A. Sevian, O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, and L. Glebov, “Efficient power scaling of laser radiation by spectral beam combining,” Opt. Lett. 33, 384–386 (2008).
[CrossRef]

Vorobiev, N.

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

Wang, F.

Wang, X.

Wyant, J.

J. Wyant and J. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. Shannon and J. Wyant, eds. (Academic, 1992), Vol. XI, pp. 1–53.

Yamada, M.

Zeldovich, B. Ya.

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick volume holograms,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, and L. Glebov, “Spectral combining and coherent coupling of lasers by volume Bragg gratings,” IEEE J. Sel. Top. Quantum Electron. 15, 344–353 (2009).
[CrossRef]

J. Holography Speckle (1)

L. B. Glebov, “Volume holographic elements in a photo-thermo-refractive glass,” J. Holography Speckle 5, 1–8 (2008).

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

T. Hieta, M. Vainio, C. Moser, and E. Ikonen, “External-cavity lasers based on a volume holographic grating at normal incidence for spectroscopy in the visible range,” Opt. Commun. 282, 3119–3123 (2009).
[CrossRef]

Opt. Laser Technol. (1)

Z. Sun, Q. Li, H. Lei, Y. Hui, and M. Jiang, “Sub-nanosecond pulse, single longitudinal mode Q-switched Nd:YVO4 laser controlled by reflecting Bragg gratings,” Opt. Laser Technol. 48, 475–479 (2013).
[CrossRef]

Opt. Lett. (6)

Proc. SPIE (2)

M. SeGall, D. Ott, I. Divliansky, and L. B. Glebov, “The effect of aberrated recording beams on reflecting Bragg gratings,” Proc. SPIE 8644, 864408 (2013).
[CrossRef]

D. Ott, V. Rotar, J. Lumeau, S. Mokhov, I. Divliansky, A. Ryasnyanskiy, N. Vorobiev, V. Smirnov, C. Spiegelberg, and L. Glebov, “Longitudinal mode selection in laser cavity by moiré volume Bragg grating,” Proc. SPIE 8236, 823621 (2012).
[CrossRef]

Other (5)

R. R. A. Syms, Practical Volume Holography, Oxford Engineering Science Series (Clarendon, 1990), p. 24.

J. Wyant and J. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. Shannon and J. Wyant, eds. (Academic, 1992), Vol. XI, pp. 1–53.

V. N. Mahajan, “Zernike polynomials and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (Wiley, 2007), pp. 498–546.

G. Dai, Wavefront Optics for Vision Correction (SPIE, 2008).

R. S. Sirohi, Optical Methods of Measurement: Wholefield Techniques, 2nd ed. (CRC Press, 2009).

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Figures (3)

Fig. 1.
Fig. 1.

Geometry of a grating recorded by two-beam interference where the nominal half angle of interference is θ. This grating acts as a reflecting grating for a probe beam incident in the plane orthogonal to the recording plane. All angles are angles inside the medium.

Fig. 2.
Fig. 2.

One-dimensional illustration of a grating recorded by two beams incident at local angles θeff,x. The local wavevector in the aberrated wavefront creates a local grating period and a local tilt angle ϕx

Fig. 3.
Fig. 3.

Reflection spectra in the presence of one wave of a given aberration for [(a), (b)] Grating A and [(c), (d)] Grating B. The probe beam is incident at [(a), (c)] the center of the grating and [(b), (d)] halfway between the center and the edge of the grating.

Equations (18)

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I(x,y,z)=I1+I2+2I1I2cos((k1k2)·r),
E(x¯,y¯,0)=E0(x¯,y¯,0)exp(iknZn(x¯,y¯)),
E(x¯,y¯,z¯)=F1{F{E(x¯,y¯,0)}e(fx2+fy2)z¯2k}eikz¯.
W(x¯,y¯,z¯)=1karctan(Im[E(x¯,y¯,z¯)]Re[E(x¯,y¯,z¯)])z¯.
k(x¯,y¯,z¯)=k1+(Wx¯)2+(Wy¯)2(Wx¯Wy¯1).
kg(x¯,y¯,z¯)=(cosθ0sinθ010sinθ0cosθ)k(x¯,y¯,z¯).
kg(xcosθzsinθ,y,xsinθ+zcosθ)=kg(x¯,y¯,z¯).
kg(x,y,0)=kg(x¯/cosθeff,x,y¯/sinθeff,y,0),
kg(x,y,z)=kg(x+ztanθeff,x,y+zcotθeff,y,0).
θeff,x=arctan(kg,x(0,0,0)kg,z(0,0,0))θeff,y=arccos(kg,y(0,0,0)k),
KTBG(x,y,z)=kg,1(x,y,z)kg,2(x,y,z).
KRBG=(001010100)KTBG
R(λ)=R(y,z,λ)Ip(y,z,λ)dydzIp(y,z,λ)dydz.
(E+(0)E(0))=T(E+(t)E(t)).
T11=[cosh(γt)+iΔksinh(γt)/γ]exp(ikBraggt)T12=κtsinh(γt)exp(i(kBraggt+ζ))/(γt)T21=κtsinh(γt)exp(i(kBraggt+ζ))/(γt)T22=[cosh(γt)iΔksinh(γt)/γ]exp(ikBraggt).
K=2kBragg(sinθysinϕycos(ϕxθx)+cosθycosϕy),
T=i=1NTi,
R(y,z,λ)=|T21T11|2.

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