July 1, 1990 / Vol. 15, No. 13 / OPTICS LETTERS 731

Optical bistability and multistability in an active interferometer

Junji Ohtsubo and Yun Liu

Faculty of Engineering, Shizuoka University, Johoku 3-5-1, Hamamatsu, 432 Japan

Received March 8, 1989; revised manuscript received December 29, 1989; accepted April 12, 1990

Optoelectronic hybrid bistability and multistability in an active interferometer using a laser diode are demonstrated

experimentally. The active laser-diode interferometer is composed of a Twyman-Green interferometer with an

electronic feedback circuit. By feeding back the interferometer output together with an external light inputthrough a detector to control the laser-diode injection current, the optical bistable and multistable states of theoutput power from the laser diode are observed. Bistable operation does not require cutoff or saturation in theamplifier. The theoretical background of the phenomena is discussed.

Optical bistability has been observed in many differ-ent systems by using intrinsic or hybrid optical cir-cuits. A system is considered optically bistable if ithas two output states for the same value of input oversome range of input values. The two optical statesoriginate from the steady-state and transient charac-teristics of a nonlinear-optical system under some op-erating conditions. Multistability also occurs whenthe input and output relation is described by a multi-valued function and has many steady and transientstates in a nonlinear system. Optical bistability andmultistability in various configurations have been ex-tensively investigated and reviewed by Gibbs.1

Recently, optical bistability and multistability inoptoelectronic feedback using a laser diode have beenreported.2 Yoshino et al.

3 have discussed a laser-di-ode feedback interferometer for stabilization of theinterferometer and for displacement-measurementapplications. They observed bistability of the photo-detector signal in the feedback interferometer by vi-brating one of the interferometer arms.

In this Letter we describe optical bistability andmultistability using an active Twyman-Green inter-ferometer that consists of a laser diode, a photodiode,and an electronic feedback circuit. By mixing lightfrom an external source onto the interferometer pho-todetector, optical instability of the laser-diode out-put power is realized. Optical bistable operation usu-ally requires cutoff or saturation in a gain medium.However, such a mechanism is not necessary in theamplifier to observe optical bistability.

The photodiode detects the interferometer outputpower together with the power from another lightsource. Nonlinearity of the output power from thelaser diode is caused by electronic feedback. By feed-ing back the interferometer output signal through thelaser-diode injection current, the oscillation frequencyand the output power of the laser diode are dynamical-ly changed. The nonlinearity in the system changes,resulting in optical bistability and multistability.This is the first demonstration, to our knowledge, ofoptical bistability and multistability of laser outputpower in an interferometer system.

Figure 1 shows the experimental setup for optical

bistability and multistability in an active interferome-ter with a laser diode. The fundamental analysis isnearly the same as that used by Yoshino et al.,3 exceptfor a light input Pi.. The Twyman-Green interferom-eter used here has an unbalanced interferometer armwhose optical path difference is 2D. The optical pow-er Pm from the interferometer together with lightsource input Pin is detected by a photodiode (PD)through a pinhole that is much smaller than the fringeseparation.

In the optical setup shown in Fig. 1, the detectedpower is compared with the reference power Po, andthe difference signal is fed back to the laser-diodeinjection current. The output power Pout and fre-quencyf of the laser diode are changed by this current.The feedback current If to the laser diode is written as

If = A(Pm + Pin-PO), (1)

where A is the feedback gain and Pm is the detectedoptical power of the interferometer, given by

Pm = aPout(l + b cos 6), (2)

with aPout the average power over the interference

Fig. 1. Diagram of an active interferometer. LD, laserdiode; A, amplifier; H.M., half-mirror; LED, light-emittingdiode.

0146-9592/90/130731-03$2.00/0 © 1990 Optical Society of America

732 OPTICS LETTERS / Vol. 15, No. 13 / July 1, 1990

fringe times the detector area. The constant parame-ter b is the fringe visibility, which depends on thecoherence factor of the lasing condition and is a func-tion of the injection current. The phase 3 of the inter-ference fringe is a function of the laser frequency f = fo+ goIf and the optical path difference 2D,

3 = 47rD(fo + PoIf)/c, (3)

where fo is the oscillation frequency of the laser diodeat a dc bias current Ib, Po is the modulation ratio of thelaser frequency per unit current, and c is the velocityof light in vacuum. The optical output power of thelaser diode is given by

Pout = a(If + Ib - Ith), (4)

where a represents the laser-diode conversion efficien-cy and Ith is the laser-diode threshold current. Theoptical output power Pout is limited to a certain levelby saturation of the amplifier.

If Eqs. (3) and (4) are substituted into Eq. (2), thedetected power in the interferometer is given as afunction of the laser output power,

Pm = aPout[1 + b cos(b0 + #Pout)], (5)

where

60 = 47rD[fo - go(Ib - Ith)]Ic (6a)

and

# = 4-7rDpo/ac. (6b)

Then, by using Eqs. (1), (4), and (5), the fundamentalequation of the feedback loop is

Pout = aAaPout[l + b cos(bO + #P0 ut)] + aAPin

+ Ca(Ib-Ith-APO). (7)

On the right-hand side of Eq. (7) the first term repre-sents the nonlinear feedback of the loop through theinterferometer; the second term is the input signalfrom the external source, and the third term denotesthe constant that depends on the device parameters ofthe laser diode and the circuit constant in the feedbackloop. By choosing the parameters in Eq. (7) properly,optical bistability and multistability can be realizedfor the relation between the input and output power.

It is not easy to solve Eq. (7) directly; however, wecan graphically find the solutions by introducing twoequations obtained from Eq. (7),

y aAaPOut[1 + b cos(b0 + gPout)]

and

y = Pout-a (APi. + Ib-Ith-APo).

diode with a wavelength X of 0.785 Am at an injectioncurrent of 50 mA and a temperature of 251C. Thelaser-diode temperature is fixed by an automatic tem-perature-controlled assembly attached to a Peltier ele-ment. The threshold current of the laser diode usedin this experiment is Ith = 32 mA. The conversionefficiency a and the modulation ratio j 0 of the laserdiode are measured to be 0.1 mW/mA and 4.0 GHz/mA, respectively. The coefficient a, which is relatedto the detected power of the interference fringe, ismeasured as a = 4.5 X 10-4. The feedback gain A ischosen to be 2.6 X 104 mA/mW. The optical pathdifference D in the interferometer is fixed at 50 mmthroughout the experiment. The optical bistabilityand multistability of the laser-diode output power areinvestigated by varying the input power by a triangu-lar modulation signal at a frequency of 1 kHz. Acharge-coupled-device (CCD) television camera isused to monitor the interference fringes and to adjusttheir separation properly.

Figure 2 shows an example of the optical bistabilityat a bias current of Ib = 50 mA. The horizontal andvertical scales corresponding to the input and outputpower are 11.1 nW/division and 24.2 yW/division, re-spectively. The switching power required for opticalbistable operation is 15 nW and is dependent on feed-back gain and bias current. The switching outputpower of the laser diode for bistable operation is 53

POUTX

PIN

Fig. 2. Bistable states of the input and output relation forthe bias current Ib = 50 mA. The horizontal and verticalscales are 11.1 nW/division and 24.2 AW/division, respec-tively.

PIN

Fig. 3. Multistable state of the input and output relationfor the bias current Ib = 60 mA. The horizontal and verticalscales are 44.4 nW/division and 153 ,W/division, respective-ly.

POUT

(8)

(9)

When the input power Pin changes, one can graphical-ly solve the equations and obtain the output powerPout of the laser diode as a function of input power Pin.With these equations, bistable and multistable opera-tion of the interferometer can be explained.

The experiment for optical bistability and multista-bility is performed by using the setup shown in Fig. 1.The interferometer light source is a Hitachi HL7806Gsingle-mode AlGaAs channeled-substrate planar laser

July 1, 1990 / Vol. 15, No. 13 / OPTICS LETTERS 733

IuW, which corresponds to a frequency change of 2.1GHz. Usually, in optical bistability and multistab-ility experiments that use semiconductor light-emit-ting devices, photodiodes, and electronic active ele-ments, the cutoff and saturation characteristics of thedevices as well as their amplifications are required.However, optical bistability can be observed in thisexperiment with an active interferometer without theneed for amplifier cutoff and saturation characteris-tics. This phenomenon occurs owing to the depen-dence of the laser-diode output power on the cosinecharacteristics in the feedback loop as is representedin Eq. (7).

Figure 3 shows an example of the optical multistab-ility at a bias current of lb = 60 mA. The horizontaland vertical scales corresponding to the input andoutput powers are 44.4 nW/division and 153 ,W/divi-sion, respectively. The switching power required forsingle optical bistable operation is 40 nW.

We have demonstrated optical bistability and mul-tistability in an active interferometer with electronicfeedback. By changing the system parameters, opti-cal bistability and multistability are realized in theoptical and electronic hybrid feedback loop. Theswitching input power of ten to several tens ofnanowatts required for single bistable operation is

readily obtained in this experiment. The switchingpower can be varied by changing the loop gain and biascurrent. The switching time for bistable operation isnot evaluated in this experiment. Since a laser diodeusually has a rapid response time, it will be limited bythe detector response or the feedback circuit. Opticalinstability may occur either in negative or positivefeedback. The theoretical consideration is possibleby using Eq. (7). Finally, we point out that the outputpower Pout is time dependent in the actual experiment,so that it may be possible to realize optical chaos inthis feedback interferometer by introducing an appro-priate time delay to the feedback injection current.Such an experiment is currently being carried out, andthe results will be given in a future publication.

The authors thank N. Murakami for help with theexperiments.

References

1. H. M. Gibbs, Optical Bistability: ControllingLight withLight (Academic, Orlando, Fla., 1985).

2. C.-H. Lee, K.-H. Cho, S.-Y. Shin, and S.-Y. Lee, IEEE J.Quantum Electron. QE-24, 2063 (1988).

3. T. Yoshino, M. Nara, S. Mnatzakanian, B. S. Lee, and T.C. Strand, Appl. Opt. 26, 892 (1987).