Abstract

Volume Bragg gratings serve an important role in laser development as devices that are able to manipulate both the wavelength and angular spectrum of light. A common method for producing gratings is holographic recording of a two collimated beam interference pattern in a photosensitive material. This process requires stability of the recording system at a level of a fraction of the recording wavelength. A new method for measuring and stabilizing the phase of the recording beams is presented that is extremely flexible and simple to integrate into an existing holographic recording setup and independent of the type of recording media. It is shown that the presented method increases visibility of an interference pattern and for photo-thermo-refractive glass enables enhancement of the spatial refractive index modulation. The use of this technique allows for longer recording times that can lead to the use of expanded recording beams for large aperture gratings.

© 2014 Optical Society of America

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References

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  1. R. R. Syms, Practical Volume Holography (Clarendon, 1990), pp. 21–26.
  2. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode by UV exposure through a phase mask photosensitive optical fiber,” Appl. Phys. Lett. 62, 1035–1037 (1993).
    [CrossRef]
  3. A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41, 176–178 (2005).
    [CrossRef]
  4. G. Venus, A. Sevian, V. Smirnov, and L. Glebov, “Stable coherent coupling of laser diodes by a volume Bragg grating in photothermorefractive glass,” Opt. Lett. 31, 1453–1455 (2006).
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    [CrossRef]
  13. C. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
    [CrossRef]
  14. G. M. Kuan and S. J. Moser, “Sensitivity of optical metrology calibration to measured corner cube retroreflector parameters for the space interferometry mission,” Proc. SPIE 4852, 795–802 (2013).
    [CrossRef]
  15. L. Glebov, V. Smirnov, C. Stickley, and I. Ciapurin, “New approach to robust optics for HEL systems,” Proc. SPIE 4724, 101–109 (2002).
    [CrossRef]
  16. L. Glebov, “Volume holographic elements in a photo-thermo-refractive glass,” J. Hologr. Speckle 5, 77–84 (2009).
  17. H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  18. I. Ciapurin, D. Drachenberg, V. Smirnov, G. Venus, and B. Glebov, “Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors,” Opt. Eng. 51, 058001 (2012).
    [CrossRef]

2013 (1)

G. M. Kuan and S. J. Moser, “Sensitivity of optical metrology calibration to measured corner cube retroreflector parameters for the space interferometry mission,” Proc. SPIE 4852, 795–802 (2013).
[CrossRef]

2012 (1)

I. Ciapurin, D. Drachenberg, V. Smirnov, G. Venus, and B. Glebov, “Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors,” Opt. Eng. 51, 058001 (2012).
[CrossRef]

2010 (1)

C. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
[CrossRef]

2009 (1)

L. Glebov, “Volume holographic elements in a photo-thermo-refractive glass,” J. Hologr. Speckle 5, 77–84 (2009).

2006 (2)

2005 (2)

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41, 176–178 (2005).
[CrossRef]

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

2002 (1)

L. Glebov, V. Smirnov, C. Stickley, and I. Ciapurin, “New approach to robust optics for HEL systems,” Proc. SPIE 4724, 101–109 (2002).
[CrossRef]

1993 (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode by UV exposure through a phase mask photosensitive optical fiber,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

1988 (1)

1986 (1)

1985 (1)

1977 (1)

1969 (1)

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

1967 (1)

Albert, J.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode by UV exposure through a phase mask photosensitive optical fiber,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Bennion, I.

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41, 176–178 (2005).
[CrossRef]

Bilodeau, F.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode by UV exposure through a phase mask photosensitive optical fiber,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Caputo, R.

Cescato, L. H.

Chen, Y.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Ciapurin, I.

I. Ciapurin, D. Drachenberg, V. Smirnov, G. Venus, and B. Glebov, “Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors,” Opt. Eng. 51, 058001 (2012).
[CrossRef]

L. Glebov, V. Smirnov, C. Stickley, and I. Ciapurin, “New approach to robust optics for HEL systems,” Proc. SPIE 4724, 101–109 (2002).
[CrossRef]

Clausnitzer, T.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Corke, M.

De Luca, A.

De Sio, L.

Deshpande, A.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Drachenberg, D.

I. Ciapurin, D. Drachenberg, V. Smirnov, G. Venus, and B. Glebov, “Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors,” Opt. Eng. 51, 058001 (2012).
[CrossRef]

Francis, O.

C. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
[CrossRef]

Frejlich, J.

Gaylord, T. K.

Glebov, B.

I. Ciapurin, D. Drachenberg, V. Smirnov, G. Venus, and B. Glebov, “Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors,” Opt. Eng. 51, 058001 (2012).
[CrossRef]

Glebov, L.

L. Glebov, “Volume holographic elements in a photo-thermo-refractive glass,” J. Hologr. Speckle 5, 77–84 (2009).

G. Venus, A. Sevian, V. Smirnov, and L. Glebov, “Stable coherent coupling of laser diodes by a volume Bragg grating in photothermorefractive glass,” Opt. Lett. 31, 1453–1455 (2006).
[CrossRef]

L. Glebov, V. Smirnov, C. Stickley, and I. Ciapurin, “New approach to robust optics for HEL systems,” Proc. SPIE 4724, 101–109 (2002).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 297–298.

Guest, C. C.

Hill, K. O.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode by UV exposure through a phase mask photosensitive optical fiber,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Johnson, D. C.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode by UV exposure through a phase mask photosensitive optical fiber,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Kamshilin, A. A.

Khrushchev, I. Y.

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41, 176–178 (2005).
[CrossRef]

Kley, E.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Kogelnik, H.

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

Kuan, G. M.

G. M. Kuan and S. J. Moser, “Sensitivity of optical metrology calibration to measured corner cube retroreflector parameters for the space interferometry mission,” Proc. SPIE 4852, 795–802 (2013).
[CrossRef]

Leilabady, P.

MacQuigg, D.

Malo, B.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode by UV exposure through a phase mask photosensitive optical fiber,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Martinez, A.

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41, 176–178 (2005).
[CrossRef]

Moser, S. J.

G. M. Kuan and S. J. Moser, “Sensitivity of optical metrology calibration to measured corner cube retroreflector parameters for the space interferometry mission,” Proc. SPIE 4852, 795–802 (2013).
[CrossRef]

Mueller, G.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Muhs, J.

Neumann, D. B.

Quetschke, V.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Reitze, D.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Rose, H. W.

Rothleitner, C.

C. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
[CrossRef]

Sevian, A.

Smirnov, V.

I. Ciapurin, D. Drachenberg, V. Smirnov, G. Venus, and B. Glebov, “Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors,” Opt. Eng. 51, 058001 (2012).
[CrossRef]

G. Venus, A. Sevian, V. Smirnov, and L. Glebov, “Stable coherent coupling of laser diodes by a volume Bragg grating in photothermorefractive glass,” Opt. Lett. 31, 1453–1455 (2006).
[CrossRef]

L. Glebov, V. Smirnov, C. Stickley, and I. Ciapurin, “New approach to robust optics for HEL systems,” Proc. SPIE 4724, 101–109 (2002).
[CrossRef]

Stickley, C.

L. Glebov, V. Smirnov, C. Stickley, and I. Ciapurin, “New approach to robust optics for HEL systems,” Proc. SPIE 4724, 101–109 (2002).
[CrossRef]

Sukhov, A. V.

Syms, R. R.

R. R. Syms, Practical Volume Holography (Clarendon, 1990), pp. 21–26.

Tanner, D.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Tünnermann, A.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Umeton, C.

Veltri, A.

Venus, G.

I. Ciapurin, D. Drachenberg, V. Smirnov, G. Venus, and B. Glebov, “Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors,” Opt. Eng. 51, 058001 (2012).
[CrossRef]

G. Venus, A. Sevian, V. Smirnov, and L. Glebov, “Stable coherent coupling of laser diodes by a volume Bragg grating in photothermorefractive glass,” Opt. Lett. 31, 1453–1455 (2006).
[CrossRef]

Whiting, B.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Wise, S.

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Appl. Opt. (6)

Appl. Phys. Lett. (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode by UV exposure through a phase mask photosensitive optical fiber,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Bell Syst. Tech. J. (1)

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

Electron. Lett. (1)

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41, 176–178 (2005).
[CrossRef]

J. Hologr. Speckle (1)

L. Glebov, “Volume holographic elements in a photo-thermo-refractive glass,” J. Hologr. Speckle 5, 77–84 (2009).

Metrologia (1)

C. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
[CrossRef]

Opt. Eng. (1)

I. Ciapurin, D. Drachenberg, V. Smirnov, G. Venus, and B. Glebov, “Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors,” Opt. Eng. 51, 058001 (2012).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

S. Wise, V. Quetschke, A. Deshpande, G. Mueller, D. Reitze, D. Tanner, B. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Proc. SPIE (2)

G. M. Kuan and S. J. Moser, “Sensitivity of optical metrology calibration to measured corner cube retroreflector parameters for the space interferometry mission,” Proc. SPIE 4852, 795–802 (2013).
[CrossRef]

L. Glebov, V. Smirnov, C. Stickley, and I. Ciapurin, “New approach to robust optics for HEL systems,” Proc. SPIE 4724, 101–109 (2002).
[CrossRef]

Other (2)

R. R. Syms, Practical Volume Holography (Clarendon, 1990), pp. 21–26.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 297–298.

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Figures (9)

Fig. 1.
Fig. 1.

General recording and readout for a VBG. Rays marked purple indicate the recording beams that generate the interference pattern at a wavelength within the photosensitivity spectrum of the medium. After recording and development, the grating can be used as a transmitting grating for beams at a different wavelength marked as green or at yet another wavelength the grating can be used as a reflecting grating for beams indicated by red.

Fig. 2.
Fig. 2.

Dependence of interference pattern visibility on phase fluctuations during recording. Phase variation σ is shown as a fraction of the recording wavelength. Inset shows fringe visibility for small phase fluctuations.

Fig. 3.
Fig. 3.

VBG recording setup showing the paths of the recording/probe beam. BS, beam splitter; M1 and M2, mirrors; PZT, piezoelectric transducer. The side view shows how the beam is split between a recording portion and a probe portion for measuring phase.

Fig. 4.
Fig. 4.

Phase shift between recording beams measured by the detector in Fig. 3 as a function of voltage applied to the PZT that causes a position change of the recording mirror, M2. The red line shows a sinusoidal fit to the experimental data in blue dots.

Fig. 5.
Fig. 5.

Diagram of a retroreflector in a phase stabilization system with designation of variables for calculating lateral sensitivity.

Fig. 6.
Fig. 6.

Experimental setup to study the sensitivity of phase measurement to lateral displacement for (A) a transmitting VBG and for (B) a corner cube retroreflector. The PZT is used to shift the respective measurement device. The effect of lateral shift on the signal measured at the detector is monitored.

Fig. 7.
Fig. 7.

Dependence of signals measured by the detectors in Figs. 6(A) and 6(B) on a signal applied to the PZT controlling lateral displacement of a TBG (red) and a retroreflector (blue). The difference in the visibility of these fringes is not inherent to the measurement device but is determined by alignment of components.

Fig. 8.
Fig. 8.

Phase fluctuations at a detector depicted in Fig. 3 for the recording of gratings (A) without and (B) and (C) with phase stabilization. The relative phase of the recording beams with no stabilization shows both high-frequency noise and long-term variations. The relative phase of the recording beams with stabilization shows dramatic decrease of both high-frequency noise and long-term variations. The correction voltage applied to the PZT is shown in blue.

Fig. 9.
Fig. 9.

Transmission spectra of 3.75 mm thick gratings with the same periods recorded (A) without and (B) and (C) with phase stabilization. The FWHM bandwidths are 430, 660, and 670 pm for plots (A), (B), and (C), respectively. Red, experiment; blue, coupled wave theory simulation.

Equations (7)

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

I(x)=I1+I2+2I1I2cos(2kxsinθ+φ),
Ifinal(x)=I1+I2+0T2I1I2cos(2kxsinθ+φ(t))dt.
W(φ)=12πσe(φ22σ2),
Ifinal(x)=I1+I2+W(φ)·2I1I2cos(2kxsinθ+φ)dφ.
V=ImaxIminImax+Imin.
OPD=2n0((x+δ)2+y2(xδ)2+y2),wherey=x/tanθglass,
OPD=4n0δsinθglass.

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