Optics Communications 255 (2005) 46–50

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Optical bistable device based on one-dimensionalphotonic crystal waveguide

Ming Chen a,*, Chunfei Li a, Mai Xu b, Weibiao Wang b, Yuxue Xia b,Shaojie Ma b

a Department of Applied Physics, Harbin Institute of Technology, Harbin 150001, PR Chinab Laboratory of Excited-state Processes, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences,

Changchun 130033, PR China

Received 15 November 2004; received in revised form 18 April 2005; accepted 31 May 2005

Abstract

Optical bistability occurs when the effects of nonlinear behavior of materials cause hysteresis in the transmission andthe reflection of a device. An optical bistable device based on one-dimensional photonic crystal waveguide is designedand fabricated. Doped semiconductor CdSxSe1 � x glass, which has large nonlinear refractive index coefficient and fastnonlinear responding time, is used. The threshold light intensity of the optical bistability is 1.65 · 105 W/cm2 and theoptical switching time is 63 ps.� 2005 Elsevier B.V. All rights reserved.

PACS: 42.65.Pc; 42.65.�k; 73.21.Ac; 73.21.Cd

Keywords: Optical bistability; Photonic crystal; Nonlinear

1. Introduction

Optical bistability is characterized by the non-linear variation of light intensity though some kindof optical devices [1]. The light output as a func-tion of light input exhibits hysteresis, i.e., thereare two or more stable output levels for the same

0030-4018/$ - see front matter � 2005 Elsevier B.V. All rights reserv

doi:10.1016/j.optcom.2005.05.036

* Corresponding author. Tel./fax: +86 431 617 6339.E-mail address: m_chen@126.com (M. Chen).

input intensity. Optical bistable device has beendeveloped rapidly because of its significant appli-cations [1–6]. One of the main goals of the appliedresearch in bistability is the development of a fast(picosecond), solid state, low-power (milliwatt)bistable optical device that operates at room tem-perature, which has led to search for materialswith large nonlinear refractive index coefficientand short nonlinear response time. Nonlinear pho-tonic crystal would meet this demand.

ed.

M. Chen et al. / Optics Communications 255 (2005) 46–50 47

Photonic crystal is periodic array of dielectricmaterials where the period is chosen so that lightis strongly reflected, refracted and confined [7–9].This is a promising class of structures for inte-grated optical functions chip, due to the fact thatboth the individual elements performing opticalfunctions and interconnects in this structure canbe very small. Nonlinear photonic crystal maymake the vision of light controlling light in micro-scale photonic circuits to a reality. We fabricated abistable optical device based on one-dimensionalphotonic crystal waveguide in this paper. It couldbe used in all-light digital computing systems andoptical processing due to its low threshold lightpower and short switching time.

2. Theoretical review

Optical bistability in one-dimensional periodicstructures with Kerr nonlinearity has been studiedby many authors [4,10–13]. Here, we summarizethe theory very briefly. The nonlinear photoniccrystal structure under consideration is shown inFig. 1. It is a period corrugation of the boundary.K is the period of the nonlinear photonic crystaland L is the length of the periodic structure. h isthe height of peak-groove. nc is the refractive indexof air. nf(z) and ns denote the refractive indices ofthe waveguide and the substrate, respectively.The effective refractive index distribution nf(z) is

Fig. 1. Side view of nonlinear one-dimensional photonic crystalwaveguide and the inset shows effective refractive indexdistribution of the waveguide film.

z-dependent and light intensity-dependent. It isexpressed as follows:

nfðzÞ ¼ n0fðzÞ þ n2S; ð1Þn0fðzÞ ¼ n0 þ Dn � sinðKzÞ; ð2Þ

where n0f(z) is the effective refractive index of theone-dimensional photonic crystal with very lowincident light intensity. n0 is the linear refractive in-dex of the nonlinear materials CdSxSe1 � x, Dn isthe reflective index modulation amplitude of theone-dimensional photonic crystal, K = 2p/K, n2 isthe nonlinear refractive index coefficient of thematerials and S denotes the light intensity. Thisis weak refractive index modulation periodic struc-ture as Dn � n0. The field in this structure is takenas a sum of two counter-propagating waves:

EðzÞ ¼ eþðzÞ expðibzÞ þ e�ðzÞ expð�ibzÞ. ð3ÞAnd the wave propagation is described by twocoupled wave equations as follows [12,13]:

� ioeþoz

¼ je� expð�i2DbzÞ þ cðjeþj2 þ 2je�j2Þeþ;

ð4Þ

ioe�oz

¼ jeþ expði2DbzÞ þ cðje�j2 þ 2jeþj2Þe�; ð5Þ

where b = 2pn0/k, b0 = 2pn0/K, Db = b � b0, k isthe vacuum wavelength of the light, j = pDn/K,c = pn2/K, n2 = 12pv(3)/n0, and v(3) is the thirdorder susceptibility tensor.

3. Design and fabrication

Superior optical bistable device requires thatthe materials with large nonlinear refractive indexcoefficient and fast speed nonlinear response. Inour device, doped semiconductor glassCdSxSe1 � x was used. The nonlinear refractive in-dex coefficient and the nonlinear responding timeof this glass are �1.0 · 10�9 cm2/W and 3.5 ps,respectively. We firstly fabricated a planar wave-guide on the substrate by K–Na ion exchange tech-nique, and then obtained the one-dimensionalphotonic crystal waveguide shown in Fig. 1 byetching technique. The total length of the nonlin-ear photonic crystal L is 3 mm.The linear refrac-

48 M. Chen et al. / Optics Communications 255 (2005) 46–50

tive index of the waveguide materials CdSxSe1 � x

n0 � 1.551. The refractive index of the substratematerials ns � 1.523. The height of the peak-groove h � 0.1 lm. The period of the photoniccrystal K � 507 nm. The Bragg condition is

2N 0K ¼ qk0; ð6Þwhere N0 is the effective refractive index of TE0

mode and q is diffraction order. We let q = 3 con-sidering our condition of fabricating technique.k0 = 514.5 nm. The band gaps of the photoniccrystal depended on incident intensity becausethe refractive index of the waveguide is light inten-sity-dependent. This dependence on incident inten-sity can be called dynamical effect of band gap ofnonlinear photonic crystal, which is the physicalbasis of many interesting nonlinear phenomenaof photonic crystal [11,13]. In Fig. 2, we demon-strated the band gaps of the nonlinear photoniccrystal for incident intensity 0 W/cm2 (solid curve)and 1.40 · 105 W/cm2 (dashed curve), respectively.The band gap of the photonic crystal was shiftedtoward short wavelength when the incident inten-sity increased because of the negative nonlinearrefractive index of the CdSxSe1 � x glass (n2 < 0).The wavelength, 514.5 nm, the center of the bandgap for incident intensity 0 W/cm2, was whollyshifted out the band gap with incident intensity1.40 · 105W/cm2.

Fig. 2. The band gaps of the nonlinear photonic crystal withthe incident intensity 0 W/cm2 (solid curve) and 1.40 · 105 W/cm2 (dashed curve), respectively.

4. Experimental measurement

The experimental setup, which was used to testthe characteristics of optical bistability of the non-linear one-dimensional photonic crystal wave-guide, is shown in Fig. 3. A mode-locking pulsedArgon ion laser of 514.5 nm was used. The repeat-ing frequency and the pulse width of the laser are82 MHz and 200 ps, respectively. The laser beamwas split into two beams by the beam-splitter, asshown in this figure. One beam was received by afast light-detector after reflected by two reflectorsand then be translated into electric signal thatwas sent into a 7904 oscillograph. Then we canrecord the pulse waveform of the incident light.The other beam was coupled into the nonlinearone-dimensional photonic crystal waveguide afterthrough an attenuator by a prism coupler. Thecoupling efficiency of the prism coupler is about6%. The light losses, including absorbed loss andscatting loss of the materials and diffraction lossof the nonlinear one-dimensional photonic crystal,are ignored in experiment. The diameter of thebeam waist is 1.0 mm. The effective high of the0-order mode is about 2.883 lm in the nonlinearone-dimensional photonic crystal waveguide. Theoutput average power of the Argon ion laser was1.28 W. The laser beam, output from the wave-guide through other prism coupler, was receivedby the fast light-detector. We can also record thepulse waveform of the output light from the wave-guide. The two pulse waveforms are shown in Fig.4. The solid curve denotes the incident pulse

Fig. 3. Experimental setup for the characteristic of the opticalbistable device measurements.

Fig. 4. Waveform of the input pulse (solid curve) and that ofoutput pulse (dashed curve). Fig. 5. Experimental curve of the optical bistability of the one-

dimensional photonic crystal waveguide.

M. Chen et al. / Optics Communications 255 (2005) 46–50 49

waveform and the dashed curve denotes the outputpulse waveform. The input pulse width is 200 ps.The output pulse width from the one-dimensionalphotonic crystal waveguide is about 180 ps. Theoutput pulse is compressed. This pulse compres-sion is the total result of the short wavelength shiftof the band gap with increasing incident lightintensity [14] and the hysteresis effect due to thenonlinear response time of the materials. We usethe input pulse waveform and output pulse wave-form to obtain the optical bistable curve of thephotonic crystal waveguide. We obtain the valuesof the input pulse and these of the output pulseevery 5.73 ps, respectively. The curve of opticalbistability is shown in Fig. 5. The time interval be-tween every two neighboring points is about5.73 ps. The threshold light intensity and theswitching time of the optical bistability are1.65 · 105 W/cm2 (it is equivalent to averagepower of 77 mW) and 63 ps (11 time intervals),respectively. The peak power of the laser pulses,required for switching of the optical bistability, isabout 4.699 W.

5. Conclusion and analysis

We designed and fabricated an optical bistabledevice based on one-dimensional photonic crystalwaveguide. In order to obtain a fast (picosecond)

and low-power (milliwatt) optical bistable devicethat operates at room temperature, we selecteddoped semiconductor CdSxSe1 � x glass as materi-als which has large nonlinear refractive index coef-ficient and very short nonlinear responding time tocompose the one-dimensional photonic crystalwaveguide. Using the theory demonstrated in thetheoretical review of this paper, we obtained thatthe threshold light intensity and switching timeof the optical bistable device is 1.40 · 105 W/cm2

and 50 ps in theory, respectively. In experiment,the threshold light intensity of the device is1.65 · 105 W/cm2, and the switching time is63 ps. The peak power of the laser pulses, requiredfor switching of the optical bistability, is about4.699 W. The testing data agree well with theoret-ical predictions.

Because the doped semiconductor CdSxSe1 � x

glass is self-defocus materials (n2 < 0), the bandgaps will be shifted toward short wavelength whenthe incident intensity increased, as shown in Fig. 2.The optical bistable device operates at the dynam-ical long-wavelength side of the photonic bandgap. At low input intensity, the incident lightwavelength is in the band gap so that its transmis-sion is low. When the input intensity is increased,more light enters the device and changes therefractive index of the nonlinear medium thusshifts the band gap to shorter wavelength. Eventu-ally the incident light wavelength is wholly shifted

50 M. Chen et al. / Optics Communications 255 (2005) 46–50

out the band gap and the device turns on to a hightransmission state. If the input is reduced, the dis-tributed feedback mechanism enables the device toretain a sufficiently large internal field so that thehigh transmission state is maintained. The inputhas to drop below the original switch-up intensitybefore the transmission falls to a low value. Thehysteretic curve was shown in Fig. 5.

This device may be useful in all-light digitalcomputing systems and high-speed optical process-ing in the near future.

Acknowledgments

The authors thank the National Nature ScienceFoundation of China under Contract Nos.60177021 and 60277030.

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