Abstract

We report the study, both theoretical and experimental, of the finite-beam Bragg diffraction behavior of an electro-optic (EO) volume grating made of a periodically poled lithium niobate (PPLN) crystal. When a Gaussian laser beam is used, the experimental observations show that the diffraction characteristics of the PPLN EO Bragg device, including the diffraction mode pattern and diffraction efficiency, are closely related to the interaction beam size and applied voltage, which cannot be modeled properly by a simplified theory using the plane-wave approximation. In this work, we have developed a theoretical model for describing the diffraction behavior of a PPLN EO Bragg device based on the coupled-wave theory with the aid of the plane-wave decomposition method. Specifically, we found that it is the angular distribution (or the dephasing bandwidth) of the plane wave elements decomposed from the incident Gaussian beam and grating strength that determine the Bragg coupling behavior of the device. We also identified some other electro-optically induced effects in the PPLN grating as an important mechanism in affecting the diffraction performance of the present device, especially at high working voltages.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Yamada, M. Saitoh, and H. Ooki, “Electric-field induced cylindrical lens, switching and deflection devices composed of the inverted domains in LiNbO3 crystals,” Appl. Phys. Lett. 69, 3659–3661 (1996).
    [CrossRef]
  2. M. Yamada, “Electrically induced Bragg-diffraction grating composed of periodically inverted domains in lithium niobate crystals and its application devices,” Rev. Sci. Instrum. 71, 4010–4016 (2000).
    [CrossRef]
  3. Y. Y. Lin, S. T. Lin, G. W. Chang, A. C. Chiang, Y. C. Huang, and Y. H. Chen, “Electro-optic periodically poled lithium niobate Bragg modulator as a laser Q-switch,” Opt. Lett. 32, 545–547 (2007).
    [CrossRef]
  4. Y. H. Chen, W. K. Chang, H. P. Chung, B. Z. Liu, C. H. Tseng, and J. W. Chang, “Tunable, pulsed multiline intracavity optical parametric oscillator using two-dimensional MgO: periodically poled lithium niobate–aperiodically poled lithium niobate,” Opt. Lett. 38, 3507–3509 (2013).
    [CrossRef]
  5. H. Gnewuch, C. N. Pannell, G. W. Ross, P. G. R. Smith, and H. Geiger, “Nanosecond response of Bragg deflectors in periodically poled LiNbO3,” IEEE Photon. Technol. Lett. 10, 1730–1732 (1998).
    [CrossRef]
  6. J. A. Abernethy, C. B. E. Gawith, R. W. Eason, and P. G. R. Smith, “Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared,” Appl. Phys. Lett. 81, 2514–2516 (2002).
    [CrossRef]
  7. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  8. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  9. N. Kato, “A theoretical study of pendellosung fringes,” Acta Crystallogr. 14, 526–532 (1961).
    [CrossRef]
  10. B. Benlarbi, P. St. J. Russell, and L. Solymar, “Bragg diffraction of finite beams by thick gratings: two rival theories,” Appl. Phys. B 28, 63–72 (1982).
    [CrossRef]
  11. L. Paul and R. C. Dale, Electromagnetic Fields and Waves (W. H. Freeman, 1972), Chap. 12.
  12. M. Müller, E. Soergel, and K. Buse, “Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals,” Appl. Opt. 43, 6344–6347 (2004).
    [CrossRef]
  13. M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
    [CrossRef]
  14. M. Müller, E. Soergel, K. Buse, and M. C. Wengler, “Light deflection from ferroelectric domain boundaries,” Appl. Phys. B 78, 367–370 (2004).
    [CrossRef]
  15. J. A. Fleck and M. D. Feit, “Beam propagation in uniaxial anisotropic media,” J. Opt. Soc. Am. 73, 920–926 (1983).
    [CrossRef]

2013

2007

2004

M. Müller, E. Soergel, and K. Buse, “Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals,” Appl. Opt. 43, 6344–6347 (2004).
[CrossRef]

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
[CrossRef]

M. Müller, E. Soergel, K. Buse, and M. C. Wengler, “Light deflection from ferroelectric domain boundaries,” Appl. Phys. B 78, 367–370 (2004).
[CrossRef]

2002

J. A. Abernethy, C. B. E. Gawith, R. W. Eason, and P. G. R. Smith, “Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared,” Appl. Phys. Lett. 81, 2514–2516 (2002).
[CrossRef]

2000

M. Yamada, “Electrically induced Bragg-diffraction grating composed of periodically inverted domains in lithium niobate crystals and its application devices,” Rev. Sci. Instrum. 71, 4010–4016 (2000).
[CrossRef]

1998

H. Gnewuch, C. N. Pannell, G. W. Ross, P. G. R. Smith, and H. Geiger, “Nanosecond response of Bragg deflectors in periodically poled LiNbO3,” IEEE Photon. Technol. Lett. 10, 1730–1732 (1998).
[CrossRef]

1996

M. Yamada, M. Saitoh, and H. Ooki, “Electric-field induced cylindrical lens, switching and deflection devices composed of the inverted domains in LiNbO3 crystals,” Appl. Phys. Lett. 69, 3659–3661 (1996).
[CrossRef]

1985

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

1983

1982

B. Benlarbi, P. St. J. Russell, and L. Solymar, “Bragg diffraction of finite beams by thick gratings: two rival theories,” Appl. Phys. B 28, 63–72 (1982).
[CrossRef]

1969

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

1961

N. Kato, “A theoretical study of pendellosung fringes,” Acta Crystallogr. 14, 526–532 (1961).
[CrossRef]

Abernethy, J. A.

J. A. Abernethy, C. B. E. Gawith, R. W. Eason, and P. G. R. Smith, “Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared,” Appl. Phys. Lett. 81, 2514–2516 (2002).
[CrossRef]

Benlarbi, B.

B. Benlarbi, P. St. J. Russell, and L. Solymar, “Bragg diffraction of finite beams by thick gratings: two rival theories,” Appl. Phys. B 28, 63–72 (1982).
[CrossRef]

Buse, K.

M. Müller, E. Soergel, and K. Buse, “Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals,” Appl. Opt. 43, 6344–6347 (2004).
[CrossRef]

M. Müller, E. Soergel, K. Buse, and M. C. Wengler, “Light deflection from ferroelectric domain boundaries,” Appl. Phys. B 78, 367–370 (2004).
[CrossRef]

Chang, G. W.

Chang, J. W.

Chang, W. K.

Chen, Y. H.

Chiang, A. C.

Chung, H. P.

Dale, R. C.

L. Paul and R. C. Dale, Electromagnetic Fields and Waves (W. H. Freeman, 1972), Chap. 12.

de Angelis, M.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
[CrossRef]

De Nicola, S.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
[CrossRef]

Eason, R. W.

J. A. Abernethy, C. B. E. Gawith, R. W. Eason, and P. G. R. Smith, “Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared,” Appl. Phys. Lett. 81, 2514–2516 (2002).
[CrossRef]

Feit, M. D.

Ferraro, P.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
[CrossRef]

Finizio, A.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
[CrossRef]

Fleck, J. A.

Gawith, C. B. E.

J. A. Abernethy, C. B. E. Gawith, R. W. Eason, and P. G. R. Smith, “Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared,” Appl. Phys. Lett. 81, 2514–2516 (2002).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Geiger, H.

H. Gnewuch, C. N. Pannell, G. W. Ross, P. G. R. Smith, and H. Geiger, “Nanosecond response of Bragg deflectors in periodically poled LiNbO3,” IEEE Photon. Technol. Lett. 10, 1730–1732 (1998).
[CrossRef]

Gnewuch, H.

H. Gnewuch, C. N. Pannell, G. W. Ross, P. G. R. Smith, and H. Geiger, “Nanosecond response of Bragg deflectors in periodically poled LiNbO3,” IEEE Photon. Technol. Lett. 10, 1730–1732 (1998).
[CrossRef]

Grilli, S.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
[CrossRef]

Huang, Y. C.

Kato, N.

N. Kato, “A theoretical study of pendellosung fringes,” Acta Crystallogr. 14, 526–532 (1961).
[CrossRef]

Kogelnik, H.

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

Lin, S. T.

Lin, Y. Y.

Liu, B. Z.

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Müller, M.

M. Müller, E. Soergel, K. Buse, and M. C. Wengler, “Light deflection from ferroelectric domain boundaries,” Appl. Phys. B 78, 367–370 (2004).
[CrossRef]

M. Müller, E. Soergel, and K. Buse, “Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals,” Appl. Opt. 43, 6344–6347 (2004).
[CrossRef]

Ooki, H.

M. Yamada, M. Saitoh, and H. Ooki, “Electric-field induced cylindrical lens, switching and deflection devices composed of the inverted domains in LiNbO3 crystals,” Appl. Phys. Lett. 69, 3659–3661 (1996).
[CrossRef]

Pannell, C. N.

H. Gnewuch, C. N. Pannell, G. W. Ross, P. G. R. Smith, and H. Geiger, “Nanosecond response of Bragg deflectors in periodically poled LiNbO3,” IEEE Photon. Technol. Lett. 10, 1730–1732 (1998).
[CrossRef]

Paturzo, M.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
[CrossRef]

Paul, L.

L. Paul and R. C. Dale, Electromagnetic Fields and Waves (W. H. Freeman, 1972), Chap. 12.

Pierattini, G.

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
[CrossRef]

Ross, G. W.

H. Gnewuch, C. N. Pannell, G. W. Ross, P. G. R. Smith, and H. Geiger, “Nanosecond response of Bragg deflectors in periodically poled LiNbO3,” IEEE Photon. Technol. Lett. 10, 1730–1732 (1998).
[CrossRef]

Russell, P. St. J.

B. Benlarbi, P. St. J. Russell, and L. Solymar, “Bragg diffraction of finite beams by thick gratings: two rival theories,” Appl. Phys. B 28, 63–72 (1982).
[CrossRef]

Saitoh, M.

M. Yamada, M. Saitoh, and H. Ooki, “Electric-field induced cylindrical lens, switching and deflection devices composed of the inverted domains in LiNbO3 crystals,” Appl. Phys. Lett. 69, 3659–3661 (1996).
[CrossRef]

Smith, P. G. R.

J. A. Abernethy, C. B. E. Gawith, R. W. Eason, and P. G. R. Smith, “Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared,” Appl. Phys. Lett. 81, 2514–2516 (2002).
[CrossRef]

H. Gnewuch, C. N. Pannell, G. W. Ross, P. G. R. Smith, and H. Geiger, “Nanosecond response of Bragg deflectors in periodically poled LiNbO3,” IEEE Photon. Technol. Lett. 10, 1730–1732 (1998).
[CrossRef]

Soergel, E.

M. Müller, E. Soergel, and K. Buse, “Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals,” Appl. Opt. 43, 6344–6347 (2004).
[CrossRef]

M. Müller, E. Soergel, K. Buse, and M. C. Wengler, “Light deflection from ferroelectric domain boundaries,” Appl. Phys. B 78, 367–370 (2004).
[CrossRef]

Solymar, L.

B. Benlarbi, P. St. J. Russell, and L. Solymar, “Bragg diffraction of finite beams by thick gratings: two rival theories,” Appl. Phys. B 28, 63–72 (1982).
[CrossRef]

Tseng, C. H.

Wengler, M. C.

M. Müller, E. Soergel, K. Buse, and M. C. Wengler, “Light deflection from ferroelectric domain boundaries,” Appl. Phys. B 78, 367–370 (2004).
[CrossRef]

Yamada, M.

M. Yamada, “Electrically induced Bragg-diffraction grating composed of periodically inverted domains in lithium niobate crystals and its application devices,” Rev. Sci. Instrum. 71, 4010–4016 (2000).
[CrossRef]

M. Yamada, M. Saitoh, and H. Ooki, “Electric-field induced cylindrical lens, switching and deflection devices composed of the inverted domains in LiNbO3 crystals,” Appl. Phys. Lett. 69, 3659–3661 (1996).
[CrossRef]

Acta Crystallogr.

N. Kato, “A theoretical study of pendellosung fringes,” Acta Crystallogr. 14, 526–532 (1961).
[CrossRef]

Appl. Opt.

Appl. Phys. B

M. Müller, E. Soergel, K. Buse, and M. C. Wengler, “Light deflection from ferroelectric domain boundaries,” Appl. Phys. B 78, 367–370 (2004).
[CrossRef]

B. Benlarbi, P. St. J. Russell, and L. Solymar, “Bragg diffraction of finite beams by thick gratings: two rival theories,” Appl. Phys. B 28, 63–72 (1982).
[CrossRef]

Appl. Phys. Lett.

J. A. Abernethy, C. B. E. Gawith, R. W. Eason, and P. G. R. Smith, “Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared,” Appl. Phys. Lett. 81, 2514–2516 (2002).
[CrossRef]

M. Yamada, M. Saitoh, and H. Ooki, “Electric-field induced cylindrical lens, switching and deflection devices composed of the inverted domains in LiNbO3 crystals,” Appl. Phys. Lett. 69, 3659–3661 (1996).
[CrossRef]

M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785–2787 (2004).
[CrossRef]

Bell Syst. Tech. J.

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

IEEE Photon. Technol. Lett.

H. Gnewuch, C. N. Pannell, G. W. Ross, P. G. R. Smith, and H. Geiger, “Nanosecond response of Bragg deflectors in periodically poled LiNbO3,” IEEE Photon. Technol. Lett. 10, 1730–1732 (1998).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Proc. IEEE

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Rev. Sci. Instrum.

M. Yamada, “Electrically induced Bragg-diffraction grating composed of periodically inverted domains in lithium niobate crystals and its application devices,” Rev. Sci. Instrum. 71, 4010–4016 (2000).
[CrossRef]

Other

L. Paul and R. C. Dale, Electromagnetic Fields and Waves (W. H. Freeman, 1972), Chap. 12.

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.

Schematic of a PPLN EO Bragg grating used as an illustration for our theoretical development.

Fig. 2.
Fig. 2.

Development of a beam propagating through a high-refractive-index domain layer and passing through the dielectric interface between the layer and its neighboring low-refractive-index layer in a PPLN EO grating when the incident angle (a) θB1>θi(V) or (b) θB1<θi(V). (c) (Calculated) specific incident angle [θi(V)] of the beam that leads to its refracted beam incident at the critical angle θC(V) of the dielectric interface as a function of applied voltage.

Fig. 3.
Fig. 3.

Calculated penetrating distance q as a function of applied voltage. The dashed line denotes the voltage in which the device operates in the situation with θB1=θi(V).

Fig. 4.
Fig. 4.

(a) Schematic configuration of a PPLN EO grating device. (b) A typical microscopic image of the hydrofluoric acid-etched +z surface of the fabricated PPLN crystal.

Fig. 5.
Fig. 5.

Measured (solid black and gray curves) and calculated (dotted and dashed curves for square-wave and cosinusoidal-wave shape gratings, respectively) zeroth-order transmittances of a 1064-nm laser after traversing the PPLN EO Bragg device as a function of applied voltage for beam waist radii of (a) 28 μm and (b) 135 μm. (c) Same measurement results (solid black and gray curves) as those plotted in (a) and (b), but with simulations (dashed and dotted curves) based on a modified Fourier amplitude of the modulated permittivity (see text). (d) A periodic trapezoidal grating form.

Fig. 6.
Fig. 6.

(a) Transmittance of the zeroth-order harmonic wave as a function of the driving voltage of the PPLN EO Bragg device for plane wave elements of different absolute values of the dephasing factor D. The lower figures show the angular spectra and the corresponding dephasing factor distribution of the incident Gaussian beams with waist radii of (b) 28 μm and (c) 135 μm.

Fig. 7.
Fig. 7.

Measured (solid curves) and calculated (dashed curves) beam intensity distribution along the central horizontal line of the beam profiler (corresponding to the dashed lines in the insets) for various specific operating voltages of the device for incident Gaussian beam waist radii of 28 μm (left figures) and 135 μm (right figures). The insets show the captured images of the corresponding 2D intensity distributions.

Fig. 8.
Fig. 8.

Calculated output angular spectra of the two Gaussian beams of waist radii 28 μm (left figures) and 135 μm (right figures) after traversing the PPLN EO Bragg device under the specific operating voltages used in Fig. 7. The vertical scales are directly comparable for the results obtained with the same incident beam size.

Equations (14)

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

ε(x)=ε0+h=1εhcos(hKx),
εh=8neΔnesin(hπ/2)hπ
2E(x,y)+k2ε(x)E(x,y)=0,
E(x,y)=i=Ai(y)ej(kxiK)xej[k2(kxiK)2]1/2y,
dAi(y)dy=jπ2ϑiλ2h=1[εhej(ϑiϑih)yAih(y)+εhej(ϑiϑi+h)yAi+h(y)],
E(x,y=0)=mAmejkmxx,
Em(x,y)=iAm,i(y)ej(kmxiK)xej[k2(kmxiK)2]1/2y,
dAm,i(y)dy=jπ2ϑm,iλ2h=1[εhej(ϑm,iϑm,ih)yAm,ih(y)+εhej(ϑm,iϑm,i+h)yAm,i+h(y)],
kmx=kmx.
Am,i=0(y=0)=AmandAm,i0(y=0)=0.
E(x,y)=mi=i=Am,iej[kmx,ix+kmy,i(yd)],
kmx,i=kmxiK,
Am,i=Am,i(y=d)ej[k2(kmxiK)2]1/2d.
q(V)=λ/(2πnL(V)){(nH(V)/nL(V))2sin2(θi2(V))1}1/2,

Metrics