Abstract

The saturated photorefractive index determines the information storage capacity of a photorefractive crystal. Therefore, it is important to be able to measure this quantity precisely. We report a technique for measuring the saturated amplitude of the photorefractive index grating Δn0 with a precision of 2%, by measuring the diffraction efficiency as a function of time. We also report the measurement of the half-growth time τ of the grating. The Δn0 and τ are also verified by substitution into the theoretical formula derived from the coupled wave theory. The resulting theoretical prediction is shown to be consistent with the experimental data. The results also show that Δn0 is almost linearly proportional to light modulation up to unit light modulation for 0.01% Fe doped LiNbO3, which may be understood from the work of Vaveliuk et al. [Phys. Rev. B 59, 10985 (1999)] work for the nonlinear regime. We will now be able to quantify the photorefractive effect of those crystals for which this method is applicable.

© 2008 Optical Society of America

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References

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  1. J. H. Hong, P. Yeh, D. Psaltis, and D. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 334-346 (1990).
    [CrossRef]
  2. S.-F. Chen, Y. C. Liu, Y. J. Huang, and M. T. Chen, “A quantitative measurement for the photorefractive index modulation of reflection gratings in LiNbO3,” Opt. Commun. 238, 57-67 (2004).
    [CrossRef]
  3. C.-C. Sun, C. C. Tu, M. C. Chen, and S. C. Donn, “Precise measurement for the amplitude of photorefractive index grating,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications V, F.T.S.Yu and S.Yin, eds., Proc. SPIE 3801, 53-57 (1999).
  4. S. C. Donn, C.-C. Tu, C.-C. Sun, and M.-T. Chen, “Quantitative measurement for the modulation of photorefractive index gratings,” Opt. Eng. (Bellingham) 41, 1346-1349 (2002).
    [CrossRef]
  5. H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in undoped LiNbO3,” Appl. Phys. Lett. 22, 626-627 (1973).
    [CrossRef]
  6. R. Grousson, M. Henry, S. Mallick, and S. L. Xu, “Measurement of bulk photovoltaic and photorefractive characteristics of iron doped LiNbO3,” J. Appl. Phys. 54, 3012-3016 (1983).
    [CrossRef]
  7. P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199-299 (1982).
    [CrossRef]
  8. D. Makgerefteh and J. Feinburg, “Erasure rate and coasting in photorefractive barium titanate at high optical power,” Opt. Lett. 13, 1111-1113 (1988).
    [CrossRef]
  9. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, 1988), Chap. 6.
  10. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electropic crystals. 1. Steady state,” Ferroelectrics 22, 949-960 (1979).
    [CrossRef]
  11. R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sublinear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259-268 (1989).
    [CrossRef]
  12. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, 1988), Chap. 7.
  13. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).
  14. G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature at LiNbO3,” J. Appl. Phys. 38, 1941-1943 (1967).
    [CrossRef]
  15. P. Vaveliuk, B. Ruiz, and N. Bolognini, “Analysis of the steady-state photorefractive harmonic gratings,” Phys. Rev. B 59, 10985-10991 (1999).
    [CrossRef]

2004

S.-F. Chen, Y. C. Liu, Y. J. Huang, and M. T. Chen, “A quantitative measurement for the photorefractive index modulation of reflection gratings in LiNbO3,” Opt. Commun. 238, 57-67 (2004).
[CrossRef]

2002

S. C. Donn, C.-C. Tu, C.-C. Sun, and M.-T. Chen, “Quantitative measurement for the modulation of photorefractive index gratings,” Opt. Eng. (Bellingham) 41, 1346-1349 (2002).
[CrossRef]

1999

P. Vaveliuk, B. Ruiz, and N. Bolognini, “Analysis of the steady-state photorefractive harmonic gratings,” Phys. Rev. B 59, 10985-10991 (1999).
[CrossRef]

1990

J. H. Hong, P. Yeh, D. Psaltis, and D. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 334-346 (1990).
[CrossRef]

1989

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sublinear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259-268 (1989).
[CrossRef]

1988

1983

R. Grousson, M. Henry, S. Mallick, and S. L. Xu, “Measurement of bulk photovoltaic and photorefractive characteristics of iron doped LiNbO3,” J. Appl. Phys. 54, 3012-3016 (1983).
[CrossRef]

1982

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199-299 (1982).
[CrossRef]

1979

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electropic crystals. 1. Steady state,” Ferroelectrics 22, 949-960 (1979).
[CrossRef]

1973

H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in undoped LiNbO3,” Appl. Phys. Lett. 22, 626-627 (1973).
[CrossRef]

1967

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature at LiNbO3,” J. Appl. Phys. 38, 1941-1943 (1967).
[CrossRef]

Bolognini, N.

P. Vaveliuk, B. Ruiz, and N. Bolognini, “Analysis of the steady-state photorefractive harmonic gratings,” Phys. Rev. B 59, 10985-10991 (1999).
[CrossRef]

Bond, W. L.

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature at LiNbO3,” J. Appl. Phys. 38, 1941-1943 (1967).
[CrossRef]

Boyd, G. D.

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature at LiNbO3,” J. Appl. Phys. 38, 1941-1943 (1967).
[CrossRef]

Brady, D.

J. H. Hong, P. Yeh, D. Psaltis, and D. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 334-346 (1990).
[CrossRef]

Carter, H. L.

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature at LiNbO3,” J. Appl. Phys. 38, 1941-1943 (1967).
[CrossRef]

Chen, M. C.

C.-C. Sun, C. C. Tu, M. C. Chen, and S. C. Donn, “Precise measurement for the amplitude of photorefractive index grating,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications V, F.T.S.Yu and S.Yin, eds., Proc. SPIE 3801, 53-57 (1999).

Chen, M. T.

S.-F. Chen, Y. C. Liu, Y. J. Huang, and M. T. Chen, “A quantitative measurement for the photorefractive index modulation of reflection gratings in LiNbO3,” Opt. Commun. 238, 57-67 (2004).
[CrossRef]

Chen, M.-T.

S. C. Donn, C.-C. Tu, C.-C. Sun, and M.-T. Chen, “Quantitative measurement for the modulation of photorefractive index gratings,” Opt. Eng. (Bellingham) 41, 1346-1349 (2002).
[CrossRef]

Chen, S.-F.

S.-F. Chen, Y. C. Liu, Y. J. Huang, and M. T. Chen, “A quantitative measurement for the photorefractive index modulation of reflection gratings in LiNbO3,” Opt. Commun. 238, 57-67 (2004).
[CrossRef]

Donn, S. C.

S. C. Donn, C.-C. Tu, C.-C. Sun, and M.-T. Chen, “Quantitative measurement for the modulation of photorefractive index gratings,” Opt. Eng. (Bellingham) 41, 1346-1349 (2002).
[CrossRef]

C.-C. Sun, C. C. Tu, M. C. Chen, and S. C. Donn, “Precise measurement for the amplitude of photorefractive index grating,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications V, F.T.S.Yu and S.Yin, eds., Proc. SPIE 3801, 53-57 (1999).

Feinburg, J.

Goldner, R. B.

H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in undoped LiNbO3,” Appl. Phys. Lett. 22, 626-627 (1973).
[CrossRef]

Grousson, R.

R. Grousson, M. Henry, S. Mallick, and S. L. Xu, “Measurement of bulk photovoltaic and photorefractive characteristics of iron doped LiNbO3,” J. Appl. Phys. 54, 3012-3016 (1983).
[CrossRef]

Günter, P.

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199-299 (1982).
[CrossRef]

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, 1988), Chap. 6.

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, 1988), Chap. 7.

Henry, M.

R. Grousson, M. Henry, S. Mallick, and S. L. Xu, “Measurement of bulk photovoltaic and photorefractive characteristics of iron doped LiNbO3,” J. Appl. Phys. 54, 3012-3016 (1983).
[CrossRef]

Hong, J. H.

J. H. Hong, P. Yeh, D. Psaltis, and D. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 334-346 (1990).
[CrossRef]

Huang, Y. J.

S.-F. Chen, Y. C. Liu, Y. J. Huang, and M. T. Chen, “A quantitative measurement for the photorefractive index modulation of reflection gratings in LiNbO3,” Opt. Commun. 238, 57-67 (2004).
[CrossRef]

Huignard, J.-P.

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, 1988), Chap. 6.

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, 1988), Chap. 7.

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electropic crystals. 1. Steady state,” Ferroelectrics 22, 949-960 (1979).
[CrossRef]

Liu, Y. C.

S.-F. Chen, Y. C. Liu, Y. J. Huang, and M. T. Chen, “A quantitative measurement for the photorefractive index modulation of reflection gratings in LiNbO3,” Opt. Commun. 238, 57-67 (2004).
[CrossRef]

Maillard, A.

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sublinear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259-268 (1989).
[CrossRef]

Makgerefteh, D.

Mallick, S.

R. Grousson, M. Henry, S. Mallick, and S. L. Xu, “Measurement of bulk photovoltaic and photorefractive characteristics of iron doped LiNbO3,” J. Appl. Phys. 54, 3012-3016 (1983).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electropic crystals. 1. Steady state,” Ferroelectrics 22, 949-960 (1979).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electropic crystals. 1. Steady state,” Ferroelectrics 22, 949-960 (1979).
[CrossRef]

Psaltis, D.

J. H. Hong, P. Yeh, D. Psaltis, and D. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 334-346 (1990).
[CrossRef]

Ruiz, B.

P. Vaveliuk, B. Ruiz, and N. Bolognini, “Analysis of the steady-state photorefractive harmonic gratings,” Phys. Rev. B 59, 10985-10991 (1999).
[CrossRef]

Rupp, R. A.

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sublinear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259-268 (1989).
[CrossRef]

Serreze, H. B.

H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in undoped LiNbO3,” Appl. Phys. Lett. 22, 626-627 (1973).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electropic crystals. 1. Steady state,” Ferroelectrics 22, 949-960 (1979).
[CrossRef]

Sun, C.-C.

S. C. Donn, C.-C. Tu, C.-C. Sun, and M.-T. Chen, “Quantitative measurement for the modulation of photorefractive index gratings,” Opt. Eng. (Bellingham) 41, 1346-1349 (2002).
[CrossRef]

C.-C. Sun, C. C. Tu, M. C. Chen, and S. C. Donn, “Precise measurement for the amplitude of photorefractive index grating,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications V, F.T.S.Yu and S.Yin, eds., Proc. SPIE 3801, 53-57 (1999).

Tu, C. C.

C.-C. Sun, C. C. Tu, M. C. Chen, and S. C. Donn, “Precise measurement for the amplitude of photorefractive index grating,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications V, F.T.S.Yu and S.Yin, eds., Proc. SPIE 3801, 53-57 (1999).

Tu, C.-C.

S. C. Donn, C.-C. Tu, C.-C. Sun, and M.-T. Chen, “Quantitative measurement for the modulation of photorefractive index gratings,” Opt. Eng. (Bellingham) 41, 1346-1349 (2002).
[CrossRef]

Vaveliuk, P.

P. Vaveliuk, B. Ruiz, and N. Bolognini, “Analysis of the steady-state photorefractive harmonic gratings,” Phys. Rev. B 59, 10985-10991 (1999).
[CrossRef]

Vinetski, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electropic crystals. 1. Steady state,” Ferroelectrics 22, 949-960 (1979).
[CrossRef]

Walter, J.

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sublinear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259-268 (1989).
[CrossRef]

Xu, S. L.

R. Grousson, M. Henry, S. Mallick, and S. L. Xu, “Measurement of bulk photovoltaic and photorefractive characteristics of iron doped LiNbO3,” J. Appl. Phys. 54, 3012-3016 (1983).
[CrossRef]

Yeh, P.

J. H. Hong, P. Yeh, D. Psaltis, and D. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 334-346 (1990).
[CrossRef]

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

Appl. Phys. A

R. A. Rupp, A. Maillard, and J. Walter, “Impact of the sublinear photoconductivity law on the interpretation of holographic results in BaTiO3,” Appl. Phys. A 49, 259-268 (1989).
[CrossRef]

Appl. Phys. Lett.

H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in undoped LiNbO3,” Appl. Phys. Lett. 22, 626-627 (1973).
[CrossRef]

Ferroelectrics

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, “Holographic storage in electropic crystals. 1. Steady state,” Ferroelectrics 22, 949-960 (1979).
[CrossRef]

J. Appl. Phys.

G. D. Boyd, W. L. Bond, and H. L. Carter, “Refractive index as a function of temperature at LiNbO3,” J. Appl. Phys. 38, 1941-1943 (1967).
[CrossRef]

R. Grousson, M. Henry, S. Mallick, and S. L. Xu, “Measurement of bulk photovoltaic and photorefractive characteristics of iron doped LiNbO3,” J. Appl. Phys. 54, 3012-3016 (1983).
[CrossRef]

Opt. Commun.

S.-F. Chen, Y. C. Liu, Y. J. Huang, and M. T. Chen, “A quantitative measurement for the photorefractive index modulation of reflection gratings in LiNbO3,” Opt. Commun. 238, 57-67 (2004).
[CrossRef]

Opt. Eng. (Bellingham)

S. C. Donn, C.-C. Tu, C.-C. Sun, and M.-T. Chen, “Quantitative measurement for the modulation of photorefractive index gratings,” Opt. Eng. (Bellingham) 41, 1346-1349 (2002).
[CrossRef]

Opt. Lett.

J. H. Hong, P. Yeh, D. Psaltis, and D. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 334-346 (1990).
[CrossRef]

D. Makgerefteh and J. Feinburg, “Erasure rate and coasting in photorefractive barium titanate at high optical power,” Opt. Lett. 13, 1111-1113 (1988).
[CrossRef]

Phys. Rep.

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199-299 (1982).
[CrossRef]

Phys. Rev. B

P. Vaveliuk, B. Ruiz, and N. Bolognini, “Analysis of the steady-state photorefractive harmonic gratings,” Phys. Rev. B 59, 10985-10991 (1999).
[CrossRef]

Other

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, 1988), Chap. 7.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, 1988), Chap. 6.

C.-C. Sun, C. C. Tu, M. C. Chen, and S. C. Donn, “Precise measurement for the amplitude of photorefractive index grating,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications V, F.T.S.Yu and S.Yin, eds., Proc. SPIE 3801, 53-57 (1999).

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Figures (9)

Fig. 1
Fig. 1

Experimental setup for measuring the modulation of a photorefractive index grating.

Fig. 2
Fig. 2

(a) Diffracted He–Ne laser beam power as a function of time for the phase-matching measurement from the grating constructed by two interference beams whose intensity ratio was 400 mW : 400 mw and intersected at an angle of 30.4° on a 0.1% Fe doped Li Nb O 3 . (b) Diffracted beam power versus Bragg angle deviation for the phase-mismatching measurement for the experiment described in (a).

Fig. 3
Fig. 3

Mach–Zehnder interferometer used in measuring the refractive index due to laser heating.

Fig. 4
Fig. 4

Geometrical considerations for calculating the refractive index of the crystal in one of the arms in the Mach–Zehnder interferometer.

Fig. 5
Fig. 5

Refractive index change of the crystal as a function of time after the crystal is exposed to laser heating for various incident powers.

Fig. 6
Fig. 6

Typical diffracted beam power is plotted as a function of time for both experimental and calculated results, which overlaps at least on the first maximum and the first minimum. The calculated result uses the interaction length computed by the method proposed by Sun et al. [3] and Donn et al. [4].

Fig. 7
Fig. 7

Typical diffracted beam power is plotted as a function of time for both experimental and calculated results, which does not overlap at least on the first maximum and the first minimum. The calculated result uses the interaction length approximated by the crystal thickness.

Fig. 8
Fig. 8

(a) Plot of saturated photorefractive index (measured by using expanded and collimated laser beam) as a function of light modulation for a 0.01% Fe doped LiNbO3. (b) Plot of saturated photorefractive index (measured by using expanded and collimated laser beam) as a function of light modulation for a 0.1% Fe doped LiNbO3.

Fig. 9
Fig. 9

(a) Plot of the maximum space charge field (calculated by the formula of Vaveliuk et al. [15]) as a function of light modulation for the grating period near the Debye screening length for a 0.01% Fe doped Li Nb O 3 . (b) The plot of the maximum space charge field (calculated by the formula of Vaveliuk et al. [15]) as a function of light modulation for the grating period much larger than the Debye screening length for a 0.1% Fe doped Li Nb O 3 .

Tables (3)

Tables Icon

Table 1 Computation Summary

Tables Icon

Table 2 Interaction Length and Saturated Photorefractive Index for Li Nb O 3 with 0.01% Fe Doping

Tables Icon

Table 3 Interaction Length and Saturated Photorefractive Index for Li Nb O 3 with 0.1% Fe Doping

Equations (21)

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

η = sin 2 κ L = sin 2 π Δ n ( t ) λ cos θ B L ,
κ = π Δ n ( t ) λ cos θ B ,
η = sin 2 π Δ n 0 ( 1 e t τ ) λ cos θ B L ,
Δ n = N λ cos θ B L ,
η = κ 2 κ 2 + ( Δ α 2 ) 2 sin 2 { κ L [ 1 + ( Δ α 2 K g ) 2 ] 1 2 } ,
κ L [ 1 + ( Δ α 2 κ ) 2 ] 1 2 = m π , m = 1 , 2 , 3 .
L = ( m 2 2 m 1 2 ) 1 2 λ 2 n sin θ B ( Δ θ 2 2 Δ θ 1 2 ) 1 2 ,
Δ n 1 ( t 1 ) = 1 2 λ cos θ B L ,
Δ n 2 ( t 2 ) = 1 λ cos θ B L .
Δ n 1 ( t 1 ) = Δ n 0 ( 1 e t 1 τ ) ,
Δ n 2 ( t 2 ) = Δ n 0 ( 1 e t 2 τ ) .
Δ n 1 ( 1 e t 2 τ ) = Δ n 2 ( 1 e t 1 τ ) .
Δ n m ( t ) = 1 2 n e 3 ( t , T ) γ 33 E 1 ( t ) ,
Δ n c ( t ) = 1 2 n e 3 ( t = 0 , T ) γ 33 E 1 ( t ) .
Δ n c ( t ) = Δ n m ( t ) n e 3 ( t = 0 ) n e 3 ( t ) = Δ n m ( t ) n e 3 ( t = 0 ) [ n e ( t = 0 ) + Δ n e ] 3 .
n Δ d ( t ) = Δ m ( t ) λ .
n = ( 1 cos θ ) ( d λ Δ m 2 ) d ( 1 cos θ ) λ Δ m .
I = 1 2 E T E T * = 1 8 E 0 2 ( 1 + e i δ ) ( 1 + e i δ ) = 1 4 E 0 2 ( 1 + cos δ ) ,
Δ n ( t ) d = Δ m ( t ) λ ,
m 1 = 2 , Δ θ 1 = 0.038 ° ± 0.001 ° .
m 2 = 3 , Δ θ 2 = 0.072 ° ± 0.001 ° .

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