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Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 7 — Apr. 4, 2005
  • pp: 2678–2687
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Optical bistable switching action of Si high-Q photonic-crystal nanocavities

Masaya Notomi, Akihiko Shinya, Satoshi Mitsugi, Goh Kira, Eiichi Kuramochi, and Takasumi Tanabe  »View Author Affiliations


Optics Express, Vol. 13, Issue 7, pp. 2678-2687 (2005)
http://dx.doi.org/10.1364/OPEX.13.002678


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Abstract

We have demonstrated all-optical bistable switching operation of resonant-tunnelling devices with ultra-small high-Q Si photonic-crystal nanocavities. Due to their high Q/V ratio, the switching energy is extremely small in comparison with that of conventional devices using the same optical nonlinear mechanism. We also show that they exhibit all-optical-transistor action by using two resonant modes. These ultrasmall unique nonlinear bistable devices have potentials to function as various signal processing functions in photonic-crystal-based optical-circuits.

© 2005 Optical Society of America

1. Introduction

The smallest size and driving energy of photonic devices are limited by the poor confinement of light in a small space and weak light-matter interaction. Photonic crystals (PhCs), which are structures whose refractive index is periodically modulated, are expected to overcome this limitation [1

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

, 2

2. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997). [CrossRef]

]. Recently, ultrasmall high-Q (quality factor) nanocavities [3

3. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). [CrossRef] [PubMed]

] were demonstrated by PhCs as a result of their strong confinement [4

4. Y. Akahane, T. Asano, B-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

, 5

5. K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003). [CrossRef]

]. Although theories predicted that optical nonlinear switch employing these nanocavities will exhibit significant reduction of switching energy for large Q/V (V: the cavity mode volume) ratio as a result of light-matter interaction enhancement [6

6. E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000). [CrossRef]

, 7

7. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002). [CrossRef]

, 8

8. M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003). [CrossRef]

, 9

9. A. R. Cowan and J. F. Young, “Optical bistability involving photonic crystal microcavities and Fano line shapes,” Phys. Rev. E 68, 046606 (2003). [CrossRef]

, 10

10. M. Soljacic and J.D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004), and references therein. [CrossRef] [PubMed]

] and very recently optical bistability in the reflection spectrum of PhC nanocavities was indicated [24

24. P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Optics Express 13, 801–820 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801 [CrossRef] [PubMed]

], these predictions have not yet been demonstrated in actual optical device operation.

Here we show that carefully-designed silicon high-Q PhC nanocavities (Q~9×104) coupled to input and output waveguides [11

11. S. Mitsugi, A. Shinya, E. Kuramochi, M. Notomi, T. Tsuchizawa, and T. Watanabe, “Resonant tunneling wavelength filters with high Q and high transmittance based on photonic crystal slabs,” in Proceedings of 16th Annual Meeting of IEEE LEOS (Institute of Electrical and Electronics Engineers, New York, 2003), pp. 214–215.

, 12

12. M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H-Y. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12,1551–1561 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551 [CrossRef] [PubMed]

] can operate as on-chip optical bistable switching devices at significantly low energy by employing optical nonlinearity. The switching energy is reduced over six orders of magnitude from that of conventional devices employing the same optical nonlinear mechanism. This is the first demonstration of clear all-optical bistable switching action with predicted large reduction of switching energy. We also show that they exhibit all-optical-transistor action by using two modes. These ultrasmall unique nonlinear bistable devices have potentials to function as various signal processing and logic functions in PhC-based optical-circuits.

2. Design

Our devices are based on two-dimensional Si PhC slabs fabricated on silicon-on-insulator substrates by electron-beam lithography and etching [13

13. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001). [CrossRef] [PubMed]

]. The fabricated hexagonal air-hole arrays in Si form PhCs with a large photonic bandgap. High-Q point-defect PhC nanoresonators are coupled to input and output line-defect PhC waveguides [13

13. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001). [CrossRef] [PubMed]

] (Figs. 1(a), 1(b)). The structural parameters are as follows: the Si layer thickness t=200 nm, the lattice constant a=420 nm, the hole radius r=0.275a, the radius of the h-holes r h=0.15a, the radius of the q-holes r q=0.125a, and the total length of the device l=25 µm. The cavity is located in the Γ-M direction from the waveguide terminal because the field decay is most gradual in this direction and thus the cavity-waveguide coupling is easy to control. Only light whose wavelength matches the cavity resonance transmits to the output waveguide by resonant-tunnelling.

If the refractive index n depends on the light intensity, the resonant wavelength becomes intensity-dependent. Since this change produces the positive feedback to the resonant-tunnelling process, it operates as a bistable switch as was discussed in theoretical papers [6

6. E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000). [CrossRef]

, 7

7. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002). [CrossRef]

, 8

8. M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003). [CrossRef]

, 9

9. A. R. Cowan and J. F. Young, “Optical bistability involving photonic crystal microcavities and Fano line shapes,” Phys. Rev. E 68, 046606 (2003). [CrossRef]

, 10

10. M. Soljacic and J.D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004), and references therein. [CrossRef] [PubMed]

, 14

14. S. F. Mingaleev and Y. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Sci. Am. B 19, 2241–2249 (2002). [CrossRef]

]. This phenomenon is basically similar to nonlinear Fabry-Perot etalons which were extensively studied in the past [15

15. H.M. Gibbs, Optical bistability: controlling light with light. (Academic Press, Orlando, 1985).

, 16

16. S. D. Smith, A. C. Walker, F. A. P. Tooley, and B. S. Wherrett, “The demonstration of restoring digital optical logic,” Nature 325, 27–31 (1987). [CrossRef]

], but the device size is greatly reduced. This size reduction and high Q leads to switching-energy reduction because the switching energy roughly scales as V/Q 2 if the nonlinear index shift is proportional to the light intensity [7

7. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002). [CrossRef]

, 10

10. M. Soljacic and J.D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004), and references therein. [CrossRef] [PubMed]

]. In the case for the present PhC nanocavities, this reduction is huge as will be shown later. In addition, simple single-wavelength operation is two-terminal (input/output) operation, but for logic operation, three-terminal (input/output/control) operation is required [17

17. S. D. Smith, “Optical bistability, photonic logic, and optical computation,” Appl. Opt. 25, 1550–1564 (1986). [CrossRef] [PubMed]

]. In PhC resonant-tunnelling devices, three-terminal operation can be realized by using two resonant modes (one for signal and the other for control). Double resonance for control and signal provides a further advantage.

To achieve nonlinear operation, the light intensity in the cavity must be high, namely, Q and T (transmittance) must be high. This is not a straightforward task because if the cavity-waveguide coupling is too large the loaded Q (Q L) decreases, and if too small, T decreases due to vertical radiation. This relationship is expressed as

T=(QLQC)2,where1QL=1QU+1QC.
(1)

Q U and Q C correspond to unloaded Q and cavity-waveguide coupling, respectively [18

18. H.A. Haus, Waves and fields in optoelectronics (Prince-Hall, New Jersey, 1984).

]. For achieving high-Q U cavity with two resonant modes, we utilized four-point defects and optimised the size of the q-holes (Fig. 1(b)) to minimize the radiation loss [4

4. Y. Akahane, T. Asano, B-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

]. Next, we designed the cavity-waveguide coupling Q C to keep Q L and T high by varying the size of the h-holes. Since the cavity-waveguide coupling is very sensitive to the size of h-holes, we can control Q C smoothly by changing r h. The description of this h-hole control will be reported elsewhere. Following this design, we determined the structural parameters as described before using the 3D finite-difference time-domain method.

Fig. 1. Photonic resonant-tunnelling device based on photonic-crystal nanocavity. (a) Scanning electron microscope image of a fabricated device. (b) Schematic description of our device.

3. Experiment

3.1. Transmission spectra in linear regime

Figures 2(a), 2(d) and 2(e) show the transmission spectra taken by sweeping of a tunable laser with a small power (thus in the linear regime), which shows the resonant-tunneling behavior. We observed two resonant peaks (mode A at 1568.7 nm and mode B at 1535 nm, in Figs. 2(b) and 2(c)). The measured Q L and T are 33400 and 40% (for mode A), and 7350 and 30% (for mode B). The estimated Q U are 9.0×104 (A) and 1.6×104 (B). Note that mode A has larger Q and mode B has stronger cavity-waveguide coupling.

Fig. 2. Resonant modes of resonant-tunneling devices. (a) Transmission spectrum in a linear regime. (b, c) Field distribution of resonant modes. The calculated mode volumes are 0.102 µm3 (A) and 0.080 µm3 (B). (d, e) Detailed transmission spectra near the resonant wavelength. The transmittance is normalized at the peak. The width is estimated by Lorentzian fitting.

3.2. Transmission spectra in non-linear regime

When we increased input power (P IN), the spectrum dramatically changed due to optical nonlinearity, as shown in Fig. 3(a). We varied the intensity by a combination of an optical amplifier and an attenuator, and the spectra were taken under wavelength upsweeping condition. We estimated the power in the input and output waveguides (PIN and POUT) using the coupling efficiency deduced from independent transmission measurements of the same PhC waveguide sample without a cavity. The uncertainty of the coupling is 0.5dB in our measurement. Note that the propagation loss in our PhC waveguide [12

12. M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H-Y. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12,1551–1561 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551 [CrossRef] [PubMed]

] (<1dB/mm) is negligible because of its short length.

Fig. 3. Bistable operation using single wavelength. (a) Intensity-dependent transmission spectra taken by a tunable laser in the upsweep condition. The wavelength sweep direction is indicated by arrows. (b) Output power (POUT) versus input power (PIN) for various detuning (δ) values. The sweep direction of PIN is indicated by arrows. The nonlinear regime starts from 10 µW, and the bistable regime starts from 40 µW.

We analysed the origin of this nonlinearity by time-dependent measurements and rate equation simulation, which suggested that it is thermal nonlinearity [15

15. H.M. Gibbs, Optical bistability: controlling light with light. (Academic Press, Orlando, 1985).

] primarily due to two-photon absorption (TPA) in Si [19

19. H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80, 416–418 (2002). [CrossRef]

]. The detail of the time-dependent measurements will be reported elsewhere. The spectrum shape is broadened for longer wavelength and there is a sharp drop at the long wavelength end. This broadening is explained by the resonance locking due to the positive feedback between the laser sweeping (upwardly swept) and the resonance red-shift. The most important point is the sharp drop, which indicates that bistable states exist.

3.3. Single-wavelength bistable operation

To observe bistability directly, we fixed the laser at a wavelength detuned by δ from the mode A resonance and measured PIN versus POUT for upward and downward sweeps of the power level. The result is plotted in Fig. 3(b). When δ exceeded 60 pm, we observed clear hysteresis between the OFF and ON branches. The switching characteristics largely depend on δ. The width of the hysteresis grows as δ becomes larger. At δ=180 pm, the width is 8dB and the switching contrast is larger than 14dB. The switching power decreases as δ becomes smaller. At 10 µW, we still observe nonlinear behaviour. The smallest bistable-switching power is approximately 40 µW.

To observe bistability directly, we fixed the laser at a wavelength detuned by δ from the mode A resonance and measured PIN versus POUT for upward and downward sweeps of the power level. The result is plotted in Fig. 3(b). When δ exceeded 60 pm, we observed clear hysteresis between the OFF and ON branches. The switching characteristics largely depend on δ. The width of the hysteresis grows as δ becomes larger. At δ=180 pm, the width is 8dB and the switching contrast is larger than 14dB. The switching power decreases as δ becomes smaller. At 10 µW, we still observe nonlinear behaviour. The smallest bistable-switching power is approximately 40 µW.

3.4. Transient response and switching energy

Next, we investigate the switching energy of this bistable operation. The switching energy for non-instantaneous nonlinear devices is roughly determined by the input power and relaxation time. To measure the switch-off time, we simultaneously excited the mode B with a CW weak probe signal and the mode A with a 400-nsec rectangular pulse pump signal. Figure 4(a) shows the temporal response of the output signal at the probe wavelength. The measured decay time for the initial state is approximately 100 nsec, which corresponds to the thermal relaxation time after the switch-off of the mode A excitation and is significantly smaller than that for thermal-nonlinear etalons because of the extremely small size. The estimated incident switching energy is roughly 4 pJ. From our estimation for the cavity Q=33000 and the incident power of P=40 µW using the parameters listed in Table 1, only 7% of PIN is absorbed by TPA process, which means that the consumed energy is 280 fJ. We calculated the heat energy required to be stored inside the cavity to shift the resonant wavelength by δ min (the smallest detuning required for bistable switching), using the parameters listed in Table 1. The calculated heat energy (~210 fJ) is not far from the consumed energy of 280 fJ.

Fig. 4. Switch-off time and switching energy. (a) Temporal response of the probe output. At t=800 nsec, the pump signal was switched off. The input instantaneous power for the pump is 64 µW. The pulse width and period are 400 nsec/40 µsec. (b) Estimated switch-on energy which is the product of the incident energy and the time required for switch-on.

Thus both results indicates that the switching energy is order of pJ and the consumed energy is a few hundred fJ. The reported switching energy of low-power thermal nonlinear etalons is µJ to several tens µJ [20

20. G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, and F. Van Milligen, “Microsecond room-temperature optical bistability and crosstalk studies in ZnS and ZnSe interference filters with visible light and milliwatt powers,” Appl. Phys. Lett. 45, 1031–1033 (1984). [CrossRef]

, 21

21. B. S. Wherrett, A. K. Darzi, Y. T. Chow, B. T. McGuckin, and E. W. Van Stryland, “Ultrafast thermal refractive nonlinearities in bistable interference filters,” J. Opt. Soc. Am. B 7, 215–219 (1990). [CrossRef]

], and the switching energy of our device is roughly 106–107 times smaller, which is close to the expected Q 2/V enhancement (106–107) against conventional nonlinear etalons (Q 2/V: 104/10µm3~106/100 µm3) [20

20. G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, and F. Van Milligen, “Microsecond room-temperature optical bistability and crosstalk studies in ZnS and ZnSe interference filters with visible light and milliwatt powers,” Appl. Phys. Lett. 45, 1031–1033 (1984). [CrossRef]

, 21

21. B. S. Wherrett, A. K. Darzi, Y. T. Chow, B. T. McGuckin, and E. W. Van Stryland, “Ultrafast thermal refractive nonlinearities in bistable interference filters,” J. Opt. Soc. Am. B 7, 215–219 (1990). [CrossRef]

]. Therefore, this result directly demonstrates the large reduction of switching energy in ultrasmall high-Q PhC cavities.

Table 1. Material parameters for Si used for estimation.

table-icon
View This Table

3.5. Two-wavelength bistable operation: All-optical bistable switch and memory

We move on to two-wavelength operation. The index change caused by mode A excitation should affect the resonance condition for mode B. Thus, the light in mode A can control the signal light in mode B (Fig. 5(a)). First, we studied how mode A affects the mode B

transmission spectrum. The control and signal light from two tunable lasers (λA and λB) was led to the input waveguide. Figure 5(b) show three mode B spectra when mode A was ON or OFF. We first reduced PIN of λA (PIN(A)) from 1 mW to 85µW (ON), then decreased it further to 68µW (OFF), and increased it again to 85 µW (OFF). The mode B spectrum jumped between two positions of ON and OFF (~200 pm apart), and the spectral shift showed clear hysteresis.

To see this clearly, we fixed λB at the peak (δ B=0), and measured P OUT(B) versus P IN(A). The result is shown in Fig. 5(c). Apparent bistable switching is observed for the signal light (λB). Because of the small P IN(B) and relatively low Q of mode B, there is no nonlinear contribution from mode B.

Fig. 5. All-optical switching operation using two wavelengths. (a) Schematic of operation. (b) Change in the transmission spectrum for mode B during the bistable switching of mode A. Conditions 1, 2, 3 correspond to 1, 2, 3 in curve (a). P IN(B) was approximately 1 µW. (c) Bistability of POUT(B) versus PIN(A) for various δA. δB is set at zero. The sweep direction of PIN(A) is indicated by arrows. We used a bandpass filter to measure P OUT(B). (d) Bistability of POUT(B) versus PIN(A) for two different δB. δA is set at 180 pm.

When δ B≠0, the bistable behaviour of mode B changes greatly, as shown in Fig. 5(d). Here, δ A was fixed but we changed δ B to 20 and 260 pm. The switching polarity is inversed when δ B=260 pm.

Figure 6(a) shows the transmission change at the switching condition as a function of δ B. The polarity inversion occurred when δ B=100 pm. The behaviour in Fig. 6(a) can be understood if we consider the width of the mode B resonance. The above results showed that three-terminal control of the light transmission is possible with this configuration. By choosing δ B appropriately, we can realize AND or NOT operations. In the case of δ B=260 pm, P OUT(B) corresponds to P IN(A) ∩ P IN(B). In the case of δ B=20 pm, P OUT(B) corresponds to PIN(B).

In addition, we can realize signal amplification by using the region where the nonlinearity is large but the hysteresis width is negligible. Figure 6(b) shows such an example where we chose δ A=60 pm and δ B=145 pm. When we used an input with a small AC signal (0.7dB) for λA, the resultant λB output exhibited a larger AC signal (~3dB).

Fig. 6. (a) Change in the transmission intensity at the switching (ΔPOUT(B)) as a function of δ B. δ A is set at 180 pm. The positive maximum of ΔPOUT(B) occurs at δB=0, and the negative maximum of ΔPOUT(B) occurs at δB~200 pm, which equals the width of mode B. (b) AC signal amplification experiment. A detuning condition is chosen where the hysteresis is small but the nonlinearity is large.

4. Summary

These represent the first clear demonstrations of the all-optical bistable switch using PhC nanocavities. The operation is equivalent to optical transistor action, [15

15. H.M. Gibbs, Optical bistability: controlling light with light. (Academic Press, Orlando, 1985).

, 17

17. S. D. Smith, “Optical bistability, photonic logic, and optical computation,” Appl. Opt. 25, 1550–1564 (1986). [CrossRef] [PubMed]

] and can be used for fundamental logic, such as flip-flop. Therefore, when PhC-based DWDM (dense-wavelength-division-multiplexing) photonic circuits are realized in future, we believe the present device may play an important role in logic functions in such circuits. Optical bistable switches based on nonlinear etalons had been extensively studied in 80’–90’s mainly intended for optical computing [15

15. H.M. Gibbs, Optical bistability: controlling light with light. (Academic Press, Orlando, 1985).

, 17

17. S. D. Smith, “Optical bistability, photonic logic, and optical computation,” Appl. Opt. 25, 1550–1564 (1986). [CrossRef] [PubMed]

], but it was found that realization of practical logic circuits was rather difficult. The main problems were too high switching energy, slow operating speed and difficulty in cascading/integrating a large number of elements. Our study showed that PhC bistable switches have definitely advantages as regards switching energy and integratability [10

10. M. Soljacic and J.D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004), and references therein. [CrossRef] [PubMed]

]. A large number of nonlinear cavities operating in different wavelengths with small switching energy can be effectively connected in a single chip, which is not easy in other systems.

Although the observed switching time is rather faster than conventional thermal photonic switching speed and it may be applicable to some area such as photonic burst switching network, the present device speed is limited by relatively slow thermal nonlinearity. However, the basic physics of the bistable operation and switching-energy reduction does not depend on the origin of nonlinearity (in the case for instantaneous nonlinearity, the reduction occurs for switching intensity), and we believe that our design scenario and what we observed here (reduction of switching energy and various bistable operation) must be general even when employing faster optical nonlinearity [6

6. E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000). [CrossRef]

].

Acknowledgments

We acknowledge Satoki Kawanishi in NTT Network Innovation Laboratories, Koji Yamada in NTT Microsystem Laboratories and Hiroyuki Tsuda in Keio University for fruitful discussion, and Shingo Kondo, Daisuke Takagi, and Toshiaki Tamamura for their help in the course of this work.

References and links

1.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

2.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997). [CrossRef]

3.

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). [CrossRef] [PubMed]

4.

Y. Akahane, T. Asano, B-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef] [PubMed]

5.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, “Experimental demonstration of a high quality factor photonic crystal microcavity,” Appl. Phys. Lett. 83, 1915–1917 (2003). [CrossRef]

6.

E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686(R) (2000). [CrossRef]

7.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002). [CrossRef]

8.

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003). [CrossRef]

9.

A. R. Cowan and J. F. Young, “Optical bistability involving photonic crystal microcavities and Fano line shapes,” Phys. Rev. E 68, 046606 (2003). [CrossRef]

10.

M. Soljacic and J.D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004), and references therein. [CrossRef] [PubMed]

11.

S. Mitsugi, A. Shinya, E. Kuramochi, M. Notomi, T. Tsuchizawa, and T. Watanabe, “Resonant tunneling wavelength filters with high Q and high transmittance based on photonic crystal slabs,” in Proceedings of 16th Annual Meeting of IEEE LEOS (Institute of Electrical and Electronics Engineers, New York, 2003), pp. 214–215.

12.

M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H-Y. Ryu, “Waveguides, resonators and their coupled elements in photonic crystal slabs,” Opt. Express 12,1551–1561 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551 [CrossRef] [PubMed]

13.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001). [CrossRef] [PubMed]

14.

S. F. Mingaleev and Y. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Sci. Am. B 19, 2241–2249 (2002). [CrossRef]

15.

H.M. Gibbs, Optical bistability: controlling light with light. (Academic Press, Orlando, 1985).

16.

S. D. Smith, A. C. Walker, F. A. P. Tooley, and B. S. Wherrett, “The demonstration of restoring digital optical logic,” Nature 325, 27–31 (1987). [CrossRef]

17.

S. D. Smith, “Optical bistability, photonic logic, and optical computation,” Appl. Opt. 25, 1550–1564 (1986). [CrossRef] [PubMed]

18.

H.A. Haus, Waves and fields in optoelectronics (Prince-Hall, New Jersey, 1984).

19.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80, 416–418 (2002). [CrossRef]

20.

G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, and F. Van Milligen, “Microsecond room-temperature optical bistability and crosstalk studies in ZnS and ZnSe interference filters with visible light and milliwatt powers,” Appl. Phys. Lett. 45, 1031–1033 (1984). [CrossRef]

21.

B. S. Wherrett, A. K. Darzi, Y. T. Chow, B. T. McGuckin, and E. W. Van Stryland, “Ultrafast thermal refractive nonlinearities in bistable interference filters,” J. Opt. Soc. Am. B 7, 215–219 (1990). [CrossRef]

22.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Select. Top. Quantum Electron. 8, 705–713 (2002). [CrossRef]

23.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia “A high-speed silicon optical modulator based on a metal-oxidesemiconductor capacitor,” Nature 427, 615–618 (2004). [CrossRef] [PubMed]

24.

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Optics Express 13, 801–820 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801 [CrossRef] [PubMed]

25.

V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004). [CrossRef] [PubMed]

26.

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5 µm in silicon etalon,” Electron. Lett. 28, 83–85 (1992). [CrossRef]

27.

O. Madelung, M. Schulz, and H. Weiss, Numerical Data and Functional Relationships in Science and Technology, Landolt-Börnstein, New Series, Vol. 17 (Springer-Verlag, Berlin, 1982).

OCIS Codes
(190.1450) Nonlinear optics : Bistability
(200.4660) Optics in computing : Optical logic
(230.1150) Optical devices : All-optical devices
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Research Papers

History
Original Manuscript: February 28, 2005
Revised Manuscript: March 23, 2005
Published: April 4, 2005

Citation
Masaya Notomi, Akihiko Shinya, Satoshi Mitsugi, Goh Kira, Eiichi Kuramochi, and Takasumi Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-7-2678


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  20. G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, and F. Van Milligen, �??Microsecond room-temperature optical bistability and crosstalk studies in ZnS and ZnSe interference filters with visible light and milliwatt powers,�?? Appl. Phys. Lett. 45, 1031-1033 (1984). [CrossRef]
  21. B. S. Wherrett, A. K. Darzi, Y. T. Chow, B. T. McGuckin, and E. W. Van Stryland, �??Ultrafast therma refractive nonlinearities in bistable interference filters,�?? J. Opt. Soc. Am. B 7, 215-219 (1990) [CrossRef]
  22. V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, P-T. Ho, �??Optical signal processing using nonlinear semiconductor microring resonators,�?? IEEE J. Select. Top. Quantum Electron. 8, 705-713 (2002). [CrossRef]
  23. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia �??A high-speed silicon optical modulator based on a metal-oxidesemiconductor capacitor,�?? Nature 427, 615-618 (2004). [CrossRef] [PubMed]
  24. P. E. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper," Opt. Express 13, 801-820 (2005). <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-801</a>. [CrossRef] [PubMed]
  25. V. R. Almeida and M. Lipson, "Optical bistability on a silicon chip," Opt. Lett. 29, 2387-2389 (2004). [CrossRef] [PubMed]
  26. G. Cocorullo and I. Rendina, "Thermo-optical modulation at 1.5 µm in silicon etalon," Electron. Lett. 28, 83- 85 (1992). [CrossRef]
  27. O. Madelung, M. Schulz, and H. Weiss, Numerical Data and Functional Relationships in Science and Technology, Landolt-Börnstein, New Series, Vol. 17 (Springer-Verlag, Berlin, 1982).

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