Bistability of a self-standing filmcaused by photothermal displacement

Kazuhiro Hane and Kentaro Suzuki

We report on the bistability of a self-standing thin film caused by photothermal displacement. Thesample consisted of a self-standing thin film placed in front of a mirror. By irradiating the self-standingthin film with continuous wave laser light, the self-standing thin film deflected with thermoelasticbending moment. Since a standing wave of the laser light was generated by the reflection of the mirror,the bending moment generated on the film was periodic along the optical axis. The displacement of thefilm was found to be bistable with the laser light intensity. Simultaneously, the light intensity reflectedfrom the sample was also bistable. These phenomena are explained by the photothermal displacementof thin film in the standing wave of laser light. © 1997 Optical Society of America

Key words: Bistability, photothermal displacement, interference fringe.

1. Introduction

There have been numerous reports on the opticalbistability of nonlinear materials. In particular,semiconductor structures have attracted a high levelof interest for high speed switching of incident laserbeams.1,2 The optical bistability of a Faraday me-dium in a Fabry–Perot resonator has also been dem-onstrated.3 In contrast, some bistabilities wereattributed to the thermal effects generated by laserirradiation. Surface expansion generates optical bi-stability by coupling with a prism placed close to asurface.4 Likewise, the slow bistability of a pendu-lum mirror displacement induced by radiation pres-sure has been investigated theoretically.5 Weinclude several interesting properties for thermal op-tical bistability.

Here we report on the bistability of a self-standingthin film caused by the photothermal effect. In thephotothermal technique, we used the surface dis-placement mainly for nondestructive evaluation andspectroscopic examination of materials.6 Displace-ment of the platelike structure with laser irradiationwas investigated recently to measure thermal diffu-sivity7 and to excite the resonator of vibration-typemicrosensors.8,9 When the resonator was activated,

The authors are with the Department of Mechatronics and Pre-cision Engineering, Tohoku University, Sendai 980-77, Japan.

Received 5 February 1996; revised manuscript received 19March 1997.

0003-6935y97y215006-04$10.00y0© 1997 Optical Society of America

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the self-excited vibration of the mechanical resonatorwas determined to be a nonlinear photothermal ef-fect.10,11 However, as far as we know, photothermalbistability of self-standing film has not been reported.

2. Experimental

Figure 1 shows a schematic diagram of the experi-mental setup. The self-standing film, consisting of a150-mm-thick glass plate covered with a 20-nm-thickaluminum layer, was used as a cantilever. Theglass plate was 45 mm long by 5 mm wide. Theenergy absorption coefficient of the aluminum layerwas approximately 10%. The cantilever and themirror were parallel with each other. When thesample was irradiated by continuous wave ~cw! Arlaser light ~wavelength l 5 514.5 nm!, part of thelaser light was absorbed by the aluminum layer andthe remainder traveled to the mirror. The light re-flected by the mirror interferes with the incident lightand produces a standing wave. Consequently, thealuminum layer absorbs the light energy of thestanding wave. The absorbed light energy is con-verted to heat ~i.e., the photothermal effect!, and theheat is transported along the thickness of the canti-lever. The temperature distribution generates thethermoelastic bending moment on the cantilever.The cantilever deflects with the thermoelastic bend-ing moment until it reaches equilibrium, where thethermoelastic bending moment is equal to the springmoment of the cantilever. Since the light intensityabsorbed by the aluminum layer changes periodicallyin the direction of the cantilever deflection, the equi-librium positions are located periodically.

To measure the displacement of the cantilever, weused two-beam interferometry of a He–Ne laser.The sample is irradiated perpendicularly by theHe–Ne laser beam at nearly the same position as thatwith an Ar laser beam. The two laser beams thatreflect from the surfaces of the cantilever and themirror interfere with each other. The intensity ofthe interference signal changes sinusoidally as afunction of cantilever displacement by as much as onehalf of the He–Ne laser wavelength. Displacementof the cantilever was determined from the phasechange of the interference signal.

3. Results and Discussion

Figure 2 shows the displacement of the cantilever asa function of incident light intensity. When the lightintensity increases, deflection of the cantilever in-creases abruptly at an intensity of 180 mW. In con-trast, when the light intensity decreases, deflectiondecreases at 130 mW. At an intensity that rangesbetween 130 and 180 mW, the cantilever has twostable positions. The cantilever jumps a distance ofapproximately 130 nm, which corresponds to approx-imately half of the wavelength of the standing wave~i.e., ly4!.

The transition time was measured to be approxi-mately 0.93. Moreover, when the cantilever was setprecisely parallel with the mirror, the transition time

Fig. 1. Schematic diagram of the experimental setup: P.D., pho-todetector; B.S., beam splitter; PZT, piezoelectric transducer.

Fig. 2. Displacement of the cantilever measured as a function ofincident light intensity.

became shorter and the cantilever was driven to self-excited vibration.10

Figure 3 shows the reflected light intensity as afunction of incident light intensity. The reflectedlight intensity decreases at an incident light intensityof 180 mW and increases at 130 mW. The reflectedlight intensity jumps at the same incident light in-tensity as for the cantilever displacement. Whenthe distance between the cantilever and the mirrorvaries, the bistability disappears. Bistability oc-curred at the period of ly2 because the distance in-creased between the cantilever and the mirror.

When the cantilever is irradiated by cw laser light,the incident laser light and the reflected laser lightinterfere with each other and produce the standingwave. Assuming that the transmittance of the alu-minum layer is close to unity, the intensity distribu-tion Q~r! of the standing wave at cantilever position rcan be written as

Q~r! 5 Q0H1 2 g cosF4p

l~r0 1 r!GJ, (1)

where Q0, g, and r0 denote the incident light inten-sity, the contrast of the standing wave, and the initialdistance of the cantilever from the mirror, respec-tively.

On the other hand, the thermoelastic model can beused frequently for thermal bending of a plate.12,13

In general, for precise analysis, one should considertwo- or three-dimensional heat distribution. Here,however, we tried to obtain the analytical equationsto enable us to explain the phenomenon observed inour experiment. When we apply the model to ourexperiment, displacement r~x! of the cantilever per-pendicular to its length ~x axis! is given as

r~x! 51

EI *L

MT~j!F~j, x!dj, (2)

where E, I, and j are Young’s modulus, moment ofinertia, and a point in irradiation region L, respec-tively, and MT and F denote bending moment and aGreen’s function, respectively. Here, deformationalong the width is assumed to be much smaller than

Fig. 3. Reflected light intensity measured as a function of inci-dent light intensity.

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that along the length. We note that F is expressedas a function of irradiation point j and observationpoint x. When the area irradiated by the laser beamis much smaller than the cantilever length, the valueof F is almost constant in integral region L in Eq. ~2!.Furthermore, according to the treatment of the bend-ing hot spot, the irradiation region is heated to gen-erate a constant bending moment whereas outsidethat region the temperature remains unchanged.Thus, displacement r is approximated from Eq. ~2!:

r~x! 51

EILMT~j0!F~j0, x!. (3)

Because the cantilever is attached at one end andunattached at the other end, the F~j0, x! is consideredto have a beamlike shape bent at irradiation point j0.In our experiments, however, displacement of thecantilever at the irradiation point is of the order ofthe laser light wavelength and much smaller than thecantilever length ~45mm!. Thus, it is assumed thatdeflection of the cantilever at the irradiation point isslight and displacement r~x! near the irradiationpoint is almost constant.

When the surface absorption is assumed and thetemperature distribution is approximated to be linearalong thickness h with the temperature differenceQmyG, where m and G are the absorption rate of lightand heat conductance, an approximation of momentMT is obtained from Ref. 12 and can be expressed as

MT~j0! 5EIamQ

hG. (4)

Note that the bending moment MT is proportional tolight intensity Q. The equilibrium equation is ob-tained from Eqs. ~1!, ~3!, and ~4!:

hGaLmF

1Q0

5

1 2 g cosF4p

l~r0 1 r!G

r. (5)

Since the right-hand side of Eq. ~5! expresses thedecreased amplitude of the sinusoidal curve with anincrease of r, the plural positions can be allowed for acertain value of Q0. The typical cantilever displace-ment r was obtained from Eq. ~5! as a function ofincident light intensity Q0. A typical result is shownin Fig. 4, which explains qualitatively the experimen-tal result shown in Fig. 2.

The jump of the cantilever deflection can be ex-plained as follows. When the incident light inten-sity increases, the node of the standing wave is anunstable position for cantilever deflection. An in-crease of the displacement causes an increase of thelight intensity that impinges on the cantilever andvice versa. Thus the cantilever deflects spontane-ously from the node of the standing wave when theincident light intensity increases. When the inci-dent light intensity decreases, the antinode of thestanding wave is an unstable position for cantileverdeflection. Thus the cantilever deflects abruptly

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from the antinode of the standing wave when inci-dent light intensity decreases.

On the other hand, the reflected light intensity,resulting from the interfering laser beams reflectedfrom the surfaces of the cantilever and the mirror,has maximum and minimum values at the node andthe antinode of the standing wave, respectively.When the incident light intensity increases, the can-tilever jumps from the node, and thus the reflectedlight intensity jumps from maximum to a smallvalue. When the incident light intensity decreases,the cantilever jumps from the antinode and thus thereflected light intensity jumps from minimum to alarge value.

4. Conclusions

In conclusion, we observed the bistabilities of thecantilever displacement and the reflected light inten-sity when the self-standing thin film located close tothe mirror was irradiated by cw laser light. Thecantilever deflected with the thermoelastic bendingmoment. The bistability of the cantilever displace-ment was explained by the intensity distribution ofthe standing wave and the thermoelastic bending mo-ment exerted to the cantilever by the photothermaleffect. Likewise, the bistability of the reflected lightintensity was explained by taking into considerationthe bistability of the cantilever displacement and theinterference of the laser light reflected from the sur-faces of the thin film and the mirror. Although thetransition time is long, the bistability can be used foroptical switching and memory, especially by adoptingthe micromachining technique.8,9

This research was supported in part by the Electro-Mechanic Technology Advancing Foundation and theSecom Science and Technology Foundation.

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