April 1, 1992 / Vol. 17, No. 7 / OPTICS LETTERS 517 Bistable operation of a phase-conjugate resonator containing an intracavity saturable absorber S. W McCahon, G. J. Dunning, K. W Kirby, G. C. Valley, and M. B. Klein Hughes Research Laboratories, 3011 Malibu Canyon Road, Malibu, California 90265 Received December 10, 1991 We have demonstrated bistability in a phase-conjugate resonator containing an intracavity saturable absorber. The saturable absorber was a film of fluorescein-doped boric acid glass. The state of the resonator is deter- mined by an external control beam incident upon the saturable absorber. When the resonator is switched to the on state by means of the control beam, it remains in that state even with the control beam turned off. Phase-conjugate resonators (PCR's) are useful de- vices for optical processing because of their inherent high resolution and thresholding properties as well as their ability to correct for intracavity distortions. In earlier research' we demonstrated image thresh- olding in a linear PCR using an image-bearing erase beam incident upon the BaTiO3phase-conjugate mirror (PCM). In the research reported here, we have improved on the sharpness of the threshold by introducing a saturable absorber in the PCR. In this architecture the input image is brought in on a control beam inci- dent upon the saturable absorber. Using a plane- wave input, we have demonstrated that such a device is bistable, with an output that switches from the off state to the on state at a specific threshold intensity and then remains on for any value of control beam intensity. This switching and latching behavior can be important for optical memory or optical logic ap- plications as well as for image thresholding. Re- cently a saturable absorber was used inside a PCR to control the transverse modes, 2 but no evidence of bistability was reported. The device described here is closely related to a bistable laser, which consists of a conventional reso- nator containing a saturable gain medium and a sat- urable absorber. 3 ' 4 In our device (shown in Fig. 1) the saturable gain medium is replaced by an exter- nally pumped BaTiO3 PCM, in which the reflectivity exceeds unity. In the PCM the saturation of the reflectivity with input intensity is due to pump depletion. As mentioned above, the information to be thresholded is amplitude encoded as a two- dimensional array of pixels on an auxiliary incoher- ent control beam that is incident upon the saturable absorber (a single pixel is illustrated in Fig. 1). If the intensity at a given pixel is above a threshold intensity, the saturable absorber will bleach locally by an amount sufficient to switch on the PCR. The PCR will continue to oscillate at these pixel loca- tions even when the control beam is removed. In order to turn off the resonator the loss must be in- creased, for example, by blocking the resonator path. The saturable absorber that we chose for our ex- periments is a film of fluorescein-doped boric acid glass. This material has an extremely low value of saturation intensity, Is = 20 mW/cm 2 at the absorp- tion peak at 450 nm. It was initially developed as a nonlinear material for four-wave mixing by Todorov et al.' and later investigated by Kramer et al. 6 The fluorescein-doped boric acid glass samples were syn- thesized following a modified technique presented by Todorov et al.' The technique consists of mixing boric acid and a prescribed amount of fluorescein, melting the mixture in a small test tube, and then sandwiching the molten glass between two pre- heated microscope slides. The solidified glass-slide composite is then annealed below the melting point of the borate glass for approximately 30 min before being cooled to room temperature to alleviate stresses that can lead to cracking. This procedure has produced good-quality 60-100-/,tm-thick samples with few cracks. Figures 2(a)-2(c) show the transmission of the saturable absorber, the reflectivity of the PCM, and the combined reflectivity of the saturable absorber/ PCM system as a function of input intensity. The open circles correspond to the measured data, and the solid curves correspond to theoretical calcula- tions. We operated the system at the argon-laser wavelength of 457.9 nm, since this is near the ab- sorption peak of the fluorescein-doped glass film. The transmission of the saturable absorber can be modeled by using an absorption coefficient of the BACKWARD PUMP PARTIAL SATURABLE/ REFLECTOR ABSORBER 7 ,XCONTROL RWARD INTENSITY Fig. 1. Schematic diagram of a linear PCR containing an intracavity saturable absorber. Information is read into the resonator by means of a separate control beam incident upon the saturable absorber. 0146-9592/92/070517-03$5.00/0 C 1992 Optical Society of America
Bistable operation of a phase-conjugate resonator containingan intracavity saturable absorber
S. W McCahon, G. J. Dunning, K. W Kirby, G. C. Valley, and M. B. KleinHughes Research Laboratories, 3011 Malibu Canyon Road, Malibu, California 90265
Received December 10, 1991
We have demonstrated bistability in a phase-conjugate resonator containing an intracavity saturable absorber.The saturable absorber was a film of fluorescein-doped boric acid glass. The state of the resonator is deter-mined by an external control beam incident upon the saturable absorber. When the resonator is switched tothe on state by means of the control beam, it remains in that state even with the control beam turned off.
Phase-conjugate resonators (PCR's) are useful de-vices for optical processing because of their inherenthigh resolution and thresholding properties as wellas their ability to correct for intracavity distortions.In earlier research' we demonstrated image thresh-olding in a linear PCR using an image-bearing erasebeam incident upon the BaTiO3 phase-conjugatemirror (PCM).
In the research reported here, we have improvedon the sharpness of the threshold by introducing asaturable absorber in the PCR. In this architecturethe input image is brought in on a control beam inci-dent upon the saturable absorber. Using a plane-wave input, we have demonstrated that such a deviceis bistable, with an output that switches from the offstate to the on state at a specific threshold intensityand then remains on for any value of control beamintensity. This switching and latching behavior canbe important for optical memory or optical logic ap-plications as well as for image thresholding. Re-cently a saturable absorber was used inside a PCR tocontrol the transverse modes,2 but no evidence ofbistability was reported.
The device described here is closely related to abistable laser, which consists of a conventional reso-nator containing a saturable gain medium and a sat-urable absorber.3'4 In our device (shown in Fig. 1)the saturable gain medium is replaced by an exter-nally pumped BaTiO3 PCM, in which the reflectivityexceeds unity. In the PCM the saturation ofthe reflectivity with input intensity is due to pumpdepletion. As mentioned above, the information tobe thresholded is amplitude encoded as a two-dimensional array of pixels on an auxiliary incoher-ent control beam that is incident upon the saturableabsorber (a single pixel is illustrated in Fig. 1). Ifthe intensity at a given pixel is above a thresholdintensity, the saturable absorber will bleach locallyby an amount sufficient to switch on the PCR. ThePCR will continue to oscillate at these pixel loca-tions even when the control beam is removed. Inorder to turn off the resonator the loss must be in-creased, for example, by blocking the resonator path.
The saturable absorber that we chose for our ex-periments is a film of fluorescein-doped boric acid
glass. This material has an extremely low value ofsaturation intensity, Is = 20 mW/cm2 at the absorp-tion peak at 450 nm. It was initially developed as anonlinear material for four-wave mixing by Todorovet al.' and later investigated by Kramer et al.6 Thefluorescein-doped boric acid glass samples were syn-thesized following a modified technique presentedby Todorov et al.' The technique consists of mixingboric acid and a prescribed amount of fluorescein,melting the mixture in a small test tube, and thensandwiching the molten glass between two pre-heated microscope slides. The solidified glass-slidecomposite is then annealed below the melting pointof the borate glass for approximately 30 min beforebeing cooled to room temperature to alleviatestresses that can lead to cracking. This procedurehas produced good-quality 60-100-/,tm-thick sampleswith few cracks.
Figures 2(a)-2(c) show the transmission of thesaturable absorber, the reflectivity of the PCM, andthe combined reflectivity of the saturable absorber/PCM system as a function of input intensity. Theopen circles correspond to the measured data, andthe solid curves correspond to theoretical calcula-tions. We operated the system at the argon-laserwavelength of 457.9 nm, since this is near the ab-sorption peak of the fluorescein-doped glass film.The transmission of the saturable absorber can bemodeled by using an absorption coefficient of the
BACKWARDPUMP
PARTIAL SATURABLE/REFLECTOR ABSORBER
7
,XCONTROL RWARD
INTENSITY
Fig. 1. Schematic diagram of a linear PCR containing anintracavity saturable absorber. Information is read intothe resonator by means of a separate control beam incidentupon the saturable absorber.
0146-9592/92/070517-03$5.00/0 C 1992 Optical Society of America
Fig. 2. (a) Transmission of the fluorescein-doped boricacid film as a function of input intensity. (b) Reflectionfrom the BaTiO3 PCM as a function of probe intensity.(a) Joint reflectivity of the saturable absorber/PCM as afunction of probe intensity.
form a = ao/(l + I/Isat), where Isat is the saturationintensity and a0 is the low-intensity absorption coef-ficient. Solution of the equation dI/dz = aI yieldsan equation for the transmitted intensity Iout as afunction of input intensity Iin, with the solutionshown in Fig. 2(a). The best fit is obtained forIsat = 17 mW/cm 2 , aoL = 1.45 (L is the thickness ofthe glass film), and an unsaturable transmission of0.58 (the high-intensity value of transmission).This saturation intensity is among the lowest re-ported in organic molecules and corresponds to ananomalously long excited-state lifetime of -0.1 S.56
The data shown in Fig. 2(b) are obtained from aseparate experiment in which we measured the de-generate four-wave mixing reflectivity as a functionof probe intensity for the externally pumped BaTiO3
PCM. The dimensions of the BaTiO3 crystal were5 mm X 5 mm X 2 mm, with the c axis orientedalong one of the 5-mm edges. The probe beam wasincident nearly normal to the 5 mm X 5 mm faces,while the pump angles and intensities were adjustedto optimize the PCM reflectivity. All beams werep polarized to couple into the large electro-optic co-efficient r.12 in BaTiO3. The 5 mm X 5 mm faceswere antireflection coated to prevent parasitic oscil-lation within the crystal. Typical operating intensi-ties were 3.2 and 0.8 W/cm2 for the forward and
backward pump beams, respectively, which yieldeda reflectivity greater than 70 at small probe inten-sities. We modeled the reflectivity by a phe-nomenological expression of the form R = Ro/[1 +(I/IpcM)057], where Ro is the reflectivity at smallprobe intensities and Ipcm represents the saturationintensity of the PCM. The fit shown in Fig. 2(b)corresponds to Ro = 70.4 and Ipcm = 1.85 mW/cm2 .
The joint (combined) reflectivity (Rj) of thedouble-pass saturable absorber/PCM system isshown in Fig. 2(c). Note that for intensities aboveapproximately 0.1 W/cm2 the PCM reflectivity mul-tiplied by the square of the unsaturable componentof the glass film absorption is obtained, while for in-tensities below approximately 1 mW/cm2 we obtainthe square of the low-intensity transmission coeffi-cient times the PCM reflectivity. The modelingproceeds as discussed above with the modificationthat the fluorescein-doped glass film is saturated byboth the forward and backward beams. The result-ing solutions for the coupled absorber/PCM systemare implicit equations that are readily solved with amodern symbolic manipulation program (e.g., Math-ematica) to obtain the fit shown in Fig. 2(c).
The bistability in our device results from thedouble-valued nature of the joint reflectivity andcan be analyzed along the same lines as the approachof Lininger et al.7 for a different device. First let usconsider forming a linear resonator by adding a con-ventional partial reflecting mirror (reflectivity Rpr)in place of the probe beam. The oscillation condi-tion of the resonator can be written as Rj(Iin)Rpr =1, where Iin is the resonator intensity incident uponthe saturable absorber. If we examine the case forRpr = 47%, Fig. 3 shows that there are two solutionsfor the intracavity intensity, with one value that isunstable with respect to. changes in intensity. Inaddition, there is a third operating point for theresonator, when the intracavity intensity equals zero.Thus if the intracavity intensity is initially zero, itwill remain at that level, because loss exceeds gain.In order to switch the resonator to the stable on state,
0id
U-
zso
0.1 '1 0X5 10-3 lo-' lo'
INPUT INTENSITY [in (W/cm2 )
Fig. 3. Calculated joint reflectivity of the saturable ab-sorber/PCM combination as a function of input intensityfor several values of control beam intensity. The horizon-tal line corresponds to the joint reflectivity required whena resonator is formed by adding a partial reflecting mirrorwith Rpr = 47%. The intersections of this line with theplots of the joint reflectivity represent solutions for theintracavity intensity.
Fig. 5. Measured resonator buildup time as a function ofcontrol beam intensity. The measured buildup time ofthe empty resonator is also shown.
it is convenient to use a separate control beam tobias the transmission of the saturable absorber (seeFig. 1). In Fig. 3 we have plotted the joint reflectiv-ity calculated from our model for several values ofcontrol beam intensity (h). When I = 6 mW/cm2,the device will switch to the on state (for Rpr = 0.47).Still higher values of I, have little effect on the reso-nator output intensity. Furthermore, even if I, isnow reduced to zero, the resonator remains in theon state.
Motivated by the above analysis, we measured sev-eral properties of a PCR formed by adding a high-relecting conventional mirror opposite the saturableabsorber/PCM combination characterized above.The PCM and saturable absorber were operated un-der the same conditions as described above. Thecontrol beam was generated from the same laser (at457.9 nm) that provided the pump beams for thePCM. The control beam was spatially filtered inorder to provide a uniform intensity at the saturableabsorber. The incident angle of the control beamwas approximately 30° from the resonator axis.The polarization of the control beam was set orthog-onal to that of the pump beams, in order to avoidfeedback into the resonator. The diameter of the
resonator mode (-2 mm) was determined by thepumped area of the PCM.
Based on the analysis presented above, one wouldexpect the PCR to switch at I, h 6 mW/cm 2 for R pr =47%. In our experiment we found that switchingat this control beam intensity required Rpr= 95%.This suggests that resonator operation is subject toother losses, such as aperturing of transverse modesat the PCM.
In Fig. 4 we plot the resonator intensity (incidentupon the saturable absorber) as a function of thecontrol beam intensity. The device is seen toswitch at Ic = 6 mW/cm 2 . The output intensityvaries by less than 20% for a variation in controlbeam intensity by more than 3 orders of magnitude.
We have also studied the transient buildup of theresonator output as a function of control beam inten-sity. The temporal response can be approximatedby a single exponential, and fits to the data weremade by using this approximation. The resultingexponential time constant is plotted as a function ofcontrol beam intensity in Fig. 5. Note the substan-tial increase in buildup time near the switchingthreshold; this is characteristic of bistable devices.8
In summary, we have demonstrated bistability ina PCR containing an intracavity saturable absorber.The resonator output was controlled by a separateuniform beam incident upon the saturable absorber.In our most recent experiments we have demon-strated a simple form of image storage using a metalmask consisting of a 2 X 6 array of 250-sam-diameterholes (spaced by 500 [tm on center) placed in front ofthe saturable absorber. We found that individualpixels could be switched on with a focused controlbeam or switched off with a spatially selective beamblock.
We acknowledge helpful technical discussionswith G. Burdge and D. M. Pepper and skilled techni-cal support from R. V Harold.
References
1. M. Klein, G. Dunning, G. Valley, R. Lind, andT. O'Meara, Opt. Lett. 11, 575 (1986).
2. B. Fischer, 0. Werner, M. Horowitz, and A. Lewis,Appl. Phys. Lett. 58, 2729 (1991).
3. P. H. Lee, P. B. Schoefer, and W B. Barker, Appl. Phys.Lett. 13, 373 (1968).
4. D. G. Hall and T. G. Dziura, Opt. Commun. 49, 146(1984).
5. T. Todorov, L. Nikolova, N. Tomova, and V Dragostinova,Opt. Quantum Electron. 13, 209 (1981).
6. M. A. Kramer, W R. Tompkin, and R. W Boyd, Phys.Rev. A 34, 2026 (1986).
7. D. M. Lininger, D. D. Crouch, P. J. Martin, and D. Z.Anderson, Opt. Commun. 76, 89 (1990).
8. H. M. Gibbs, Optical Bistability: Controlling LightWith Light (Academic, Orlando, Fla., 1985).
