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Hologram recording and reading in discrete resonance ring cavity
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Optics Communications 280 (2007) 296–299 www.elsevier.com/locate/optcom
Hologram recording and reading in discrete resonance ring cavity Hyunsung Kim, Seung-Dae Sohn, Yeon H. Lee
*
School of Information and Communication Engineering, Sungkyunkwan University, Suwon, Kyongkido 440-746, Republic of Korea Received 15 June 2007; accepted 16 August 2007
Abstract Holograms are recorded and restored in a resonant ring cavity. The experimental data shows enhanced diffraction efficiencies off the holograms. To maintain the optical resonance of the cavity during writing or reading the hologram we propose discrete resonance ring cavity system. The experimental data is compared with those of the conventional system with no cavity resonance. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction In the early studies of the photorefractive effect, a photorefractive crystal was coupled with a resonant cavity for self-oscillation [1–3]. Since then many researches associated with a resonant cavity were reported. The optical feedback provided by a ring cavity was employed in associative memory [4]. A highly efficient light deflection system was designed by placing a grating in a resonant cavity [5]. In a recent research report conventionally recorded holograms were placed inside a resonant cavity for greatly enhanced diffraction efficiency [6]. In this paper we report, for the first time to our knowledge, recording of a hologram using two resonant cavity modes that rotate in a ring resonator in the opposite directions. The hologram is then read by one of the resonant cavity modes for an enhanced diffraction efficiency. In general, it is very hard to maintain the optical resonance in the ring cavity for a period of time long enough to write a hologram because the cavity mirrors continually vibrate due to the ambient air flow, floor vibration in the laboratory and so on. To solve this problem we propose ‘so called’ discrete resonance ring cavity (DRRC) system. DRRC system is based on the following ideas; when one of the cavity mirrors is deliberately moved back and forth, the optical path length of the ring cavity will change peri*
Corresponding author. E-mail address: [email protected] (Y.H. Lee).
0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.08.034
odically and cause the round-trip beam to have an additional phase delay. The cavity resonance is achieved only when the phase delay of the round-trip beam is given by either 0 or an integer multiple of 2p. One can note in this case that the cavity resonance will occur at discrete times t1, t2, t3, and so on as the optical path length of the ring cavity is varied periodically by one of the cavity mirrors moved back and forth. The resonance time tn will be perfectly periodic with period T if other cavity mirrors are perfectly still in their positions without any influence by the laboratory environment. In a real laboratory, the other cavity mirrors may vibrate due to the ambient air flow, floor vibration and so on. In this case the resonance time tn will not be periodic. However, the nth resonance will always occurs after tn1 within approximately the time interval T because the deliberately moved cavity mirror supplies an additional phase delay. This can be compared with an ordinary ring cavity where no mirror is moved deliberately. The cavity mirrors of the ordinary ring cavity will vibrate randomly due to the laboratory environment. In this case the resonances occur at randomly distributed times. A photorefractive crystal of LiTaO3 is inserted into the DRRC system to record a hologram. An interference fringe is formed by the two counter-propagating beams, called the reference and the signal beams, inside the crystal. The intensity of the reference and the signal beams will fluctuate inside the ring cavity and the crystal due to the cavity mirror deliberately moved back and forth. For
H. Kim et al. / Optics Communications 280 (2007) 296–299
example, the intensity of the reference beam will be at its maximum when its phase delay after one round-trip in the cavity is zero and minimum when the phase delay is p. However, the intensity fluctuations of the reference and the signal beams are synchronized because a small movement of the cavity mirror causes exactly the same phase delay to the reference and the signal beams at the same time. When the two beams interfere in the crystal to form a fringe pattern, the intensity modulation index is given by a value constant in time regardless of the intensity fluctuations. In the real experimental setup a rotation plate is inserted in the ring cavity to change the optical path length of the ring cavity instead of moving one of the cavity mirrors back and forth. The rotation plate is a simple transparent plate with optically flat surfaces. The incident beam will traverse a different distance inside the plate when the plate is slightly rotated about an axis perpendicular to the beam propagation direction. Our DRRC system consists of a resonant ring cavity and a rotation plate. The rotation plate is an optically flat parallel plate with anti-reflection coating. It is mounted on a motor driven rotation stage and controlled by a computer. It is made of fused silica with the diameter of 25 mm and the thickness of 10 mm. Its surface quality is specified as k/10. When it is rotated by a small angle, the optical path length of the ring cavity changes since the effective thickness of the plate changes along the beam direction. It is assumed in our experiment that there is no change in the beam direction due to the rotation of the plate. The rotation plate can continuously change the phase of the round-trip beam in the ring cavity. Then, the round-trip beams interfere constructively or destructively depending on the rotation angle of the plate. In this case, even if the cavity resonance is broken by unwanted small vibration of the cavity mirrors, the rotation plate can restore the cavity resonance by changing the phase of the round-trip beams. Since the rotation plate produces the constructive interference in the ring cavity only at discrete times, this system is called discrete resonance ring cavity. 2. Experimental setup Fig. 1 is the experimental setup to record a hologram in DRRC system and then read it. A 515 nm beam from ArIon laser first passes through a Faraday rotator to block the return beam entering the laser. The beam is expanded to a diameter of 12 mm and split into the reference and the signal beams. They enter DRRC, which is basically a ring cavity formed by mirrors M1–M3 and the additional rotation plate, through beam splitters BS1 and BS2 and rotate counter-clockwise and clockwise, respectively, in the ring cavity. Both the reference and the signal beams are focused to a common focal point in space by identical lenses L1 and L2 with the same focal length of 200 mm. The lenses are used to make a smaller beam size in the crys-
297
Fig. 1. Experimental setup to record and read a hologram in DRRC.
tal. The power of the reference beam before L1 is measured 92.0 ± 2.5 mW during our experiments. The exactly counter-propagating beams pass through a 45°-cut lithium tantalate double doped with 100 ppm of Fe and 200 ppm of Eu. The crystal is positioned such that the common focus of the two counter-propagating beams is located at the left entrance surface of the crystal. Next, all the optical elements of DRRC including lenses L1 and L2 are carefully aligned until only a bright disk appears in the beams leaving the cavity through BS3. One may observe a fringe in the beam when the optical components are not aligned perfectly. In this case he will never obtain a resonance in the ring cavity. 3. Bragg diffraction In this experimental setup Bragg diffraction efficiency can be derived analytically as follows. When the reference beam, Ein R , enters the ring cavity through BS1, it will rotate the ring cavity counter-clockwise many times. The total electric field of the reference beam just before the crystal can be derived as Etotal ¼ Ein R R rBS1
1 ; 1 a expðj/p Þ
ð1Þ
where a = tBS1tBS2tBS3tcrytaltPlatetlensesrmirrors with the reflection and transmission coefficients r and t. /p is the phase shift caused by the rotation plate. Non-depletion of pump is assumed in the derivation to ignore the depletion of the reference beam during the energy coupling in the crystal. In our experimental setup a is measured to be 0.21. The signal beam, Ein S , enters the ring cavity through BS2. It rotates the ring cavity clockwise many times and grows to Etotal at a S
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position between BS2 and the crystal. Etotal is also given as S in Eq. (1) with Ein R rBS1 replaced by E S rBS2 . A hologram is recorded by an interference of Etotal and Etotal in the crystal. R S When the hologram is read, shutter S2 is blocked. The reference beam Etotal enters the crystal from the left. In this R case the resulting Bragg diffraction ED propagates backward and rotates the ring cavity clockwise many times. It grows to Etotal at a position between BS1 and the crystal. D Etotal is also given as Eq. (1) with Ein D R rBS1 replaced by ED. The Bragg diffraction leaves the DRRC through BS3 and its electric field is given by total Eout D ¼ t BS1 rM3 r BS3 E D :
ð2Þ
We define the diffraction efficiency of the crystal as 2 go ¼ jED =Etotal R j , which represents the intensity ratio of the input reference beam and the output Bragg diffraction from the crystal. We also define the diffraction efficiency of in 2 DRRC as g ¼ jEout D =E R j , which represents the intensity ratio of the input and the output of the DRRC system. The diffraction efficiency of DRRC can be derived as out 2 E g ¼ Din ER " 2 # h i R 1 BS1 total 2 ; ¼ T BS1 RM3 RBS3 jED j total 2 1 a expðj/ Þ jER j p ð3Þ out where 1=Ein R of Eq. (1) and ED of Eq. (2) are used. R and T are intensity reflectance and transmittance. Using Etotal ¼ ED =f1 a expðj/p Þg in the Eq. (3) one can obtain D the diffraction efficiency of DRRC as ( ) 4 E D 2 1 : g ¼ total T BS1 RBS1 RBS3 ð4Þ 1 a expðj/p Þ ER
Fig. 2. Energy-coupled signal beam and Bragg diffracted beam are measured by rotating the plate.
tion of time. The figure shows that the signal beam intensity oscillates rapidly because of the rotation of the rotational plate and that the envelope increases exponentially because of the energy coupling between the signal and the reference beams. From t = 500 s to t = 1000 s the signal beam was blocked by S2 and the reference beam was diffracted from the hologram. The Bragg diffracted beam rotated the ring cavity many times and left the system through BS3. The measured intensity peaks of the energycoupled signal beam and the Bragg diffracted beam are
Here, assumed is RM3 1. It is noted in the equation that all the crystal parameters are included in the term 2 jED =Etotal R j . The hologram recorded in the crystal can be also read as in the conventional method. In this case only the beamsplitter BS1 is required together with the crystal. The reference beam enters the crystal after reflected from BS1. The resulting Bragg diffraction propagates backward and passes through BS1 before it is measured. The brace {.} term of Eq. (4) equivalently represents the intensity ratio of the incident reference beam and the output Bragg diffraction measured in this method. We call this as the diffraction efficiency of the conventional method. 4. Experimental data Fig. 2 shows the process of the hologram recording and reading in our DRRC system. From t = 70 s to t = 480 s two counter rotating beams in DRRC recorded a hologram in the crystal. During this time period the energy-coupled signal beam rotated the ring cavity clockwise and left the system through BS3. Its intensity was measured as a func-
Fig. 3. The peaks of data in Fig. 2 are plotted as dots. The energy coupling and the Bragg diffraction both fit to exponential functions.
H. Kim et al. / Optics Communications 280 (2007) 296–299
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the calculated Bragg diffraction efficiency of our DRRC system using Eq. (4). In this calculation the first data set was used for the brace term {..} of Eq. (4) together with the measured value of a. The experimental data shows that the diffraction efficiency of our DRRC system is enhanced by 30% compared with the conventional system with no cavity resonance when the intensity modulation is varied from 0.2 to 0.6. The analytic expression of Eq. (4) predicts increased diffraction efficiencies by 30% to 40% for the intensity modulation varied from 0.2 to 0.6. 5. Conclusion Fig. 4. Circles; hologram recording and reading are done by just two counter-propagating beams without cavity resonance. Squares; hologram recording and reading are done in DRRC. Open squares: Analytical predictions of the diffraction efficiencies.
plotted as dots in Figs. 3(a) and (b), respectively. Exponential curves are fitted to the peak values and shown by the solid curves. When the experiment was repeated by varying the rotation speed of the plate from 0.05°/s to 0.2°/s, there was little change in the strength of the Bragg diffraction with a variation less than 2.5%. In Fig. 4 the diffraction efficiency is plotted as a function of the writing-beam intensity modulation. In the first data set represented by closed circles, holograms were recorded with shutter S3 closed. This corresponds to the hologram record in the conventional method with two counter-propagating beams and with no cavity resonance. The diffraction efficiency was measured by the ratio of the Bragg diffraction transmitted through BS1 to the beam incident to BS1. In the second data set represented by closed squares, S3 was opened to employ the cavity resonance and the rotation plate. In this case the diffraction efficiency is measured as the ratio of the Bragg diffraction reflected from BS3 to the reference beam intensity incident into BS1. The third data set represented by open squares is
In conclusions, holograms were recorded and restored in a resonant ring cavity. Discrete resonance ring cavity (DRRC) system was first employed in our experiment to maintain the resonance of the beams, which include the writing, the reading and the Bragg diffracted beams. Experimental data showed increased diffraction efficiencies compared with the conventional method. The analytic expression for the diffraction efficiency was derived in the region of small intensity modulation and was shown that its predictions agreed well with the experimental data. Acknowledgement This paper was supported by Samsung Research Fund, Sungkyunkwan University, 2006. References [1] P.A. Belanger, A. Hardy, A.E. Siegman, Appl. Opt. 19 (1980) 602. [2] J. Feinberg, R.W. Hellwarth, Opt. Lett. 5 (1980) 519. [3] J.O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40 (1982) 450. [4] D. Psaltis, N. Farhat, Opt. Lett. 10 (1985) 98. [5] W.H. Steier, G.T. Kavounas, R.T. Sahara, J. Kumar, Appl. Opt. 27 (1988) 1603. [6] A. Sinha, G. Barbastathis, Opt. Lett. 27 (2002) 385.
Optics Communications 280 (2007) 296–299 www.elsevier.com/locate/optcom
Hologram recording and reading in discrete resonance ring cavity Hyunsung Kim, Seung-Dae Sohn, Yeon H. Lee
*
School of Information and Communication Engineering, Sungkyunkwan University, Suwon, Kyongkido 440-746, Republic of Korea Received 15 June 2007; accepted 16 August 2007
Abstract Holograms are recorded and restored in a resonant ring cavity. The experimental data shows enhanced diffraction efficiencies off the holograms. To maintain the optical resonance of the cavity during writing or reading the hologram we propose discrete resonance ring cavity system. The experimental data is compared with those of the conventional system with no cavity resonance. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction In the early studies of the photorefractive effect, a photorefractive crystal was coupled with a resonant cavity for self-oscillation [1–3]. Since then many researches associated with a resonant cavity were reported. The optical feedback provided by a ring cavity was employed in associative memory [4]. A highly efficient light deflection system was designed by placing a grating in a resonant cavity [5]. In a recent research report conventionally recorded holograms were placed inside a resonant cavity for greatly enhanced diffraction efficiency [6]. In this paper we report, for the first time to our knowledge, recording of a hologram using two resonant cavity modes that rotate in a ring resonator in the opposite directions. The hologram is then read by one of the resonant cavity modes for an enhanced diffraction efficiency. In general, it is very hard to maintain the optical resonance in the ring cavity for a period of time long enough to write a hologram because the cavity mirrors continually vibrate due to the ambient air flow, floor vibration in the laboratory and so on. To solve this problem we propose ‘so called’ discrete resonance ring cavity (DRRC) system. DRRC system is based on the following ideas; when one of the cavity mirrors is deliberately moved back and forth, the optical path length of the ring cavity will change peri*
Corresponding author. E-mail address: [email protected] (Y.H. Lee).
0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.08.034
odically and cause the round-trip beam to have an additional phase delay. The cavity resonance is achieved only when the phase delay of the round-trip beam is given by either 0 or an integer multiple of 2p. One can note in this case that the cavity resonance will occur at discrete times t1, t2, t3, and so on as the optical path length of the ring cavity is varied periodically by one of the cavity mirrors moved back and forth. The resonance time tn will be perfectly periodic with period T if other cavity mirrors are perfectly still in their positions without any influence by the laboratory environment. In a real laboratory, the other cavity mirrors may vibrate due to the ambient air flow, floor vibration and so on. In this case the resonance time tn will not be periodic. However, the nth resonance will always occurs after tn1 within approximately the time interval T because the deliberately moved cavity mirror supplies an additional phase delay. This can be compared with an ordinary ring cavity where no mirror is moved deliberately. The cavity mirrors of the ordinary ring cavity will vibrate randomly due to the laboratory environment. In this case the resonances occur at randomly distributed times. A photorefractive crystal of LiTaO3 is inserted into the DRRC system to record a hologram. An interference fringe is formed by the two counter-propagating beams, called the reference and the signal beams, inside the crystal. The intensity of the reference and the signal beams will fluctuate inside the ring cavity and the crystal due to the cavity mirror deliberately moved back and forth. For
H. Kim et al. / Optics Communications 280 (2007) 296–299
example, the intensity of the reference beam will be at its maximum when its phase delay after one round-trip in the cavity is zero and minimum when the phase delay is p. However, the intensity fluctuations of the reference and the signal beams are synchronized because a small movement of the cavity mirror causes exactly the same phase delay to the reference and the signal beams at the same time. When the two beams interfere in the crystal to form a fringe pattern, the intensity modulation index is given by a value constant in time regardless of the intensity fluctuations. In the real experimental setup a rotation plate is inserted in the ring cavity to change the optical path length of the ring cavity instead of moving one of the cavity mirrors back and forth. The rotation plate is a simple transparent plate with optically flat surfaces. The incident beam will traverse a different distance inside the plate when the plate is slightly rotated about an axis perpendicular to the beam propagation direction. Our DRRC system consists of a resonant ring cavity and a rotation plate. The rotation plate is an optically flat parallel plate with anti-reflection coating. It is mounted on a motor driven rotation stage and controlled by a computer. It is made of fused silica with the diameter of 25 mm and the thickness of 10 mm. Its surface quality is specified as k/10. When it is rotated by a small angle, the optical path length of the ring cavity changes since the effective thickness of the plate changes along the beam direction. It is assumed in our experiment that there is no change in the beam direction due to the rotation of the plate. The rotation plate can continuously change the phase of the round-trip beam in the ring cavity. Then, the round-trip beams interfere constructively or destructively depending on the rotation angle of the plate. In this case, even if the cavity resonance is broken by unwanted small vibration of the cavity mirrors, the rotation plate can restore the cavity resonance by changing the phase of the round-trip beams. Since the rotation plate produces the constructive interference in the ring cavity only at discrete times, this system is called discrete resonance ring cavity. 2. Experimental setup Fig. 1 is the experimental setup to record a hologram in DRRC system and then read it. A 515 nm beam from ArIon laser first passes through a Faraday rotator to block the return beam entering the laser. The beam is expanded to a diameter of 12 mm and split into the reference and the signal beams. They enter DRRC, which is basically a ring cavity formed by mirrors M1–M3 and the additional rotation plate, through beam splitters BS1 and BS2 and rotate counter-clockwise and clockwise, respectively, in the ring cavity. Both the reference and the signal beams are focused to a common focal point in space by identical lenses L1 and L2 with the same focal length of 200 mm. The lenses are used to make a smaller beam size in the crys-
297
Fig. 1. Experimental setup to record and read a hologram in DRRC.
tal. The power of the reference beam before L1 is measured 92.0 ± 2.5 mW during our experiments. The exactly counter-propagating beams pass through a 45°-cut lithium tantalate double doped with 100 ppm of Fe and 200 ppm of Eu. The crystal is positioned such that the common focus of the two counter-propagating beams is located at the left entrance surface of the crystal. Next, all the optical elements of DRRC including lenses L1 and L2 are carefully aligned until only a bright disk appears in the beams leaving the cavity through BS3. One may observe a fringe in the beam when the optical components are not aligned perfectly. In this case he will never obtain a resonance in the ring cavity. 3. Bragg diffraction In this experimental setup Bragg diffraction efficiency can be derived analytically as follows. When the reference beam, Ein R , enters the ring cavity through BS1, it will rotate the ring cavity counter-clockwise many times. The total electric field of the reference beam just before the crystal can be derived as Etotal ¼ Ein R R rBS1
1 ; 1 a expðj/p Þ
ð1Þ
where a = tBS1tBS2tBS3tcrytaltPlatetlensesrmirrors with the reflection and transmission coefficients r and t. /p is the phase shift caused by the rotation plate. Non-depletion of pump is assumed in the derivation to ignore the depletion of the reference beam during the energy coupling in the crystal. In our experimental setup a is measured to be 0.21. The signal beam, Ein S , enters the ring cavity through BS2. It rotates the ring cavity clockwise many times and grows to Etotal at a S
298
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position between BS2 and the crystal. Etotal is also given as S in Eq. (1) with Ein R rBS1 replaced by E S rBS2 . A hologram is recorded by an interference of Etotal and Etotal in the crystal. R S When the hologram is read, shutter S2 is blocked. The reference beam Etotal enters the crystal from the left. In this R case the resulting Bragg diffraction ED propagates backward and rotates the ring cavity clockwise many times. It grows to Etotal at a position between BS1 and the crystal. D Etotal is also given as Eq. (1) with Ein D R rBS1 replaced by ED. The Bragg diffraction leaves the DRRC through BS3 and its electric field is given by total Eout D ¼ t BS1 rM3 r BS3 E D :
ð2Þ
We define the diffraction efficiency of the crystal as 2 go ¼ jED =Etotal R j , which represents the intensity ratio of the input reference beam and the output Bragg diffraction from the crystal. We also define the diffraction efficiency of in 2 DRRC as g ¼ jEout D =E R j , which represents the intensity ratio of the input and the output of the DRRC system. The diffraction efficiency of DRRC can be derived as out 2 E g ¼ Din ER " 2 # h i R 1 BS1 total 2 ; ¼ T BS1 RM3 RBS3 jED j total 2 1 a expðj/ Þ jER j p ð3Þ out where 1=Ein R of Eq. (1) and ED of Eq. (2) are used. R and T are intensity reflectance and transmittance. Using Etotal ¼ ED =f1 a expðj/p Þg in the Eq. (3) one can obtain D the diffraction efficiency of DRRC as ( ) 4 E D 2 1 : g ¼ total T BS1 RBS1 RBS3 ð4Þ 1 a expðj/p Þ ER
Fig. 2. Energy-coupled signal beam and Bragg diffracted beam are measured by rotating the plate.
tion of time. The figure shows that the signal beam intensity oscillates rapidly because of the rotation of the rotational plate and that the envelope increases exponentially because of the energy coupling between the signal and the reference beams. From t = 500 s to t = 1000 s the signal beam was blocked by S2 and the reference beam was diffracted from the hologram. The Bragg diffracted beam rotated the ring cavity many times and left the system through BS3. The measured intensity peaks of the energycoupled signal beam and the Bragg diffracted beam are
Here, assumed is RM3 1. It is noted in the equation that all the crystal parameters are included in the term 2 jED =Etotal R j . The hologram recorded in the crystal can be also read as in the conventional method. In this case only the beamsplitter BS1 is required together with the crystal. The reference beam enters the crystal after reflected from BS1. The resulting Bragg diffraction propagates backward and passes through BS1 before it is measured. The brace {.} term of Eq. (4) equivalently represents the intensity ratio of the incident reference beam and the output Bragg diffraction measured in this method. We call this as the diffraction efficiency of the conventional method. 4. Experimental data Fig. 2 shows the process of the hologram recording and reading in our DRRC system. From t = 70 s to t = 480 s two counter rotating beams in DRRC recorded a hologram in the crystal. During this time period the energy-coupled signal beam rotated the ring cavity clockwise and left the system through BS3. Its intensity was measured as a func-
Fig. 3. The peaks of data in Fig. 2 are plotted as dots. The energy coupling and the Bragg diffraction both fit to exponential functions.
H. Kim et al. / Optics Communications 280 (2007) 296–299
299
the calculated Bragg diffraction efficiency of our DRRC system using Eq. (4). In this calculation the first data set was used for the brace term {..} of Eq. (4) together with the measured value of a. The experimental data shows that the diffraction efficiency of our DRRC system is enhanced by 30% compared with the conventional system with no cavity resonance when the intensity modulation is varied from 0.2 to 0.6. The analytic expression of Eq. (4) predicts increased diffraction efficiencies by 30% to 40% for the intensity modulation varied from 0.2 to 0.6. 5. Conclusion Fig. 4. Circles; hologram recording and reading are done by just two counter-propagating beams without cavity resonance. Squares; hologram recording and reading are done in DRRC. Open squares: Analytical predictions of the diffraction efficiencies.
plotted as dots in Figs. 3(a) and (b), respectively. Exponential curves are fitted to the peak values and shown by the solid curves. When the experiment was repeated by varying the rotation speed of the plate from 0.05°/s to 0.2°/s, there was little change in the strength of the Bragg diffraction with a variation less than 2.5%. In Fig. 4 the diffraction efficiency is plotted as a function of the writing-beam intensity modulation. In the first data set represented by closed circles, holograms were recorded with shutter S3 closed. This corresponds to the hologram record in the conventional method with two counter-propagating beams and with no cavity resonance. The diffraction efficiency was measured by the ratio of the Bragg diffraction transmitted through BS1 to the beam incident to BS1. In the second data set represented by closed squares, S3 was opened to employ the cavity resonance and the rotation plate. In this case the diffraction efficiency is measured as the ratio of the Bragg diffraction reflected from BS3 to the reference beam intensity incident into BS1. The third data set represented by open squares is
In conclusions, holograms were recorded and restored in a resonant ring cavity. Discrete resonance ring cavity (DRRC) system was first employed in our experiment to maintain the resonance of the beams, which include the writing, the reading and the Bragg diffracted beams. Experimental data showed increased diffraction efficiencies compared with the conventional method. The analytic expression for the diffraction efficiency was derived in the region of small intensity modulation and was shown that its predictions agreed well with the experimental data. Acknowledgement This paper was supported by Samsung Research Fund, Sungkyunkwan University, 2006. References [1] P.A. Belanger, A. Hardy, A.E. Siegman, Appl. Opt. 19 (1980) 602. [2] J. Feinberg, R.W. Hellwarth, Opt. Lett. 5 (1980) 519. [3] J.O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40 (1982) 450. [4] D. Psaltis, N. Farhat, Opt. Lett. 10 (1985) 98. [5] W.H. Steier, G.T. Kavounas, R.T. Sahara, J. Kumar, Appl. Opt. 27 (1988) 1603. [6] A. Sinha, G. Barbastathis, Opt. Lett. 27 (2002) 385.