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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 23 — Nov. 9, 2009
  • pp: 21108–21117
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Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity

Laurent-Daniel Haret, Takasumi Tanabe, Eiichi Kuramochi, and Masaya Notomi  »View Author Affiliations


Optics Express, Vol. 17, Issue 23, pp. 21108-21117 (2009)
http://dx.doi.org/10.1364/OE.17.021108


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Abstract

We demonstrate optical bistability in silicon using a high-Q (Q>105) one-dimensional photonic crystal nanocavity at an extremely low 1.6 µW input power that is one tenth the previously reported value. Owing to the device’s unique geometrical structure, light and heat efficiently confine in a very small region, enabling strong thermo-optic confinement. We also showed with numerical analyses that this device can operate at a speed of ~0.5 µs.

© 2009 Optical Society of America

1. Introduction

Several approaches have recently been tried in order to create all-optical devices [1

1. T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low switching-energy and high-repetition-frequency all optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102 ( 2006). [CrossRef]

3

3. A. Shinya, S. Mitsugi, T. Tanabe, M. Notomi, I. Yokohama, H. Takara, and S. Kawanishi, “All-optical flipflop circuit composed of coupled two-port resonant tunneling filter in two-dimensional photonic crystal slab,” Opt. Express 14, 1230–1235 ( 2006). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-3-1230 [CrossRef] [PubMed]

] that behave similarly to electronics components such as transistors. The interest in integrated all-optical logic devices has been triggered by the idea that the elimination of optical-to-electrical signal conversion will lead to the fabrication of very low-power signal processor systems. Therefore, it is reasonable to require an all-optical logic gate to be very small and to operate at very low power.

Optical bistability is a fundamental physical phenomenon that makes it possible to realize all-optical logic gates [4

4. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).

, 5

5. H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of two optical triodes,” Appl. Phys. Lett. 57, 1724 ( 1990). [CrossRef]

]. It implies that the optical response of the component is nonlinear, thus the resonant wavelength and absorption depend on the optical power. There are many possible candidate techniques for achieving the nonlinearity, including carrier-plasma dispersion, the optical Kerr effect, saturable absorption, and the thermo-optic effect, which usually appear only when a high optical power density is attained. For this reason, optical bistable operation has been difficult to demonstrate at a reasonably low input power. However, the recent fabrication of micro- and nano-cavities, with favorable designs for integration, has enabled the operation of optical bistability at a reasonably low power [6

6. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. 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 [CrossRef] [PubMed]

8

8. Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett. 31, 341–343 ( 2006). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-3-341 [CrossRef] [PubMed]

]. This is due to the high quality factor Q and small mode volume V of the cavities, because the optical power density in the cavity scales with Q/V.

The two-dimensional (2D) photonic crystal (PhC) nanocavity is a good candidate for an optical bistable device, because some of the best values for V [9

9. K. Nozaki and T. Baba, “Lasing characteristics with ultimate-small modal volume in point shift photonic crystal nanolasers,” Appl. Phys. Lett. 88, 211101 ( 2006). [CrossRef]

] and Q [10

10. T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 ( 2007). [CrossRef]

,11

11. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Photon. 1, 449–458 ( 2007). [CrossRef]

] have been obtained with this structure. Indeed, we have demonstrated a low-power optical bistable threshold power P tr of just 25 µW using a 2D silicon (Si) PhC nanocavity [6

6. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. 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 [CrossRef] [PubMed]

]. The use of Si is challenging because its material parameters, including its two-photon absorption coefficient, thermo-optic coefficient and thermal capacity, make it more difficult to obtain low power bistability than with other materials. Similar experiments have been undertaken by some research groups using GaAs, and the smallest reported value of P tr=1 µW was obtained by De Rossi et al. in a GaAs 2D PhC nanocavity [12

12. E. Weidner, S. Combrié, A. de Rossi, N. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118 ( 2007). [CrossRef]

]. However, because Si technology fabrication processes are now well known and widely used, and because the development of Si photonics will allow the on-chip integration of electronic and photonic devices, there is still a great interest in Si photonics, despite the material’s intrinsic disadvantages.

In this paper, we focus on Si material and demonstrate thermo-optic bistability at a significantly reduced Ptr by utilizing 1D PhC nanocavities to fulfill the criteria for low power optical processing. 1D PhC nanocavities have interesting geometrical and mechanical properties, [13

13. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16, 11095–11102 ( 2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-15-11095 [CrossRef] [PubMed]

16

16. M. Eichenfield, R. Camacho, J. Chan, K. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 ( 2009). [CrossRef] [PubMed]

] while their Q and V are comparable to those of the best 2D PhC cavities. Having fabricated 1D PhC nanocavities [17

17. E. Kuramochi, H. Taniyama, K. Kawasaki, and M. Notomi, “Fabrication of ultrahigh-Q nanocavity with one-dimensional photonic gap,” in Extended Abstracts of 70th Autumn JSAP Meeting, (Jpn. Soc. Appl. Phys., Tokyo, 2009), 9p-B-14. (in Japanese)

, 18

18. E. Kuramochi, NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi-shi, Kanagawa 243–0198, Japan, H. Taniyama, K. Kawasaki, and M. Notomi are preparing a manuscript to be called “Ultrahigh-Q nanocavity with 1D mode-gap barrier in silicon on insulator.”

], we thought it would be interesting to investigate their nonlinear bistable properties, because the structures are well isolated optically, electrically and thermally, and this may allow us to realize a significant reduction in P tr.

2. Optical properties of 1D PhC nanocavities

2.1. Describing the structure

Figure 1 shows schematic illustrations and scanning electron microscope images of fabricated 1D Si PhC nanocavities. We call Fig. 1(a) a “stack” cavity on SiO2 and 1(d) an air-bridged “ladder” cavity. Figures 1(b) and 1(e) are scanning electron microscope images of the fabricated samples. Figures 1(c) and 1(f) are the mode profiles calculated by 3D finite-difference time-domain method. Stack cavities can be simply described as Si boxes laid on SiO2, whereas in air-bridged ladder cavities, Si boxes are connected by two Si bridges, which allows the underlying SiO2 to be removed and the cavity to be suspended in air. The position and size of the Si boxes are modulated, which enables the creation of a mode gap and allows light to be confined [13

13. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16, 11095–11102 ( 2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-15-11095 [CrossRef] [PubMed]

]. The theoretical Q and V for these two types of cavities are; Q=1.9×107 with V⋍2.0(λ/n)3 for a stack cavity [17

17. E. Kuramochi, H. Taniyama, K. Kawasaki, and M. Notomi, “Fabrication of ultrahigh-Q nanocavity with one-dimensional photonic gap,” in Extended Abstracts of 70th Autumn JSAP Meeting, (Jpn. Soc. Appl. Phys., Tokyo, 2009), 9p-B-14. (in Japanese)

, 18

18. E. Kuramochi, NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi-shi, Kanagawa 243–0198, Japan, H. Taniyama, K. Kawasaki, and M. Notomi are preparing a manuscript to be called “Ultrahigh-Q nanocavity with 1D mode-gap barrier in silicon on insulator.”

], and Q=2.0×108 with V⋍1.4(λ/n)3 for an air-bridged ladder cavity [13

13. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16, 11095–11102 ( 2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-15-11095 [CrossRef] [PubMed]

]. The coupling between the cavity and the input/output waveguides is controlled by changing the number of boxes. A typical sample has about 30 boxes, which gives a total length of ~15 µm. Further details of a numerical study and the fabrication of these cavities have been published elsewhere [17

17. E. Kuramochi, H. Taniyama, K. Kawasaki, and M. Notomi, “Fabrication of ultrahigh-Q nanocavity with one-dimensional photonic gap,” in Extended Abstracts of 70th Autumn JSAP Meeting, (Jpn. Soc. Appl. Phys., Tokyo, 2009), 9p-B-14. (in Japanese)

, 18

18. E. Kuramochi, NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi-shi, Kanagawa 243–0198, Japan, H. Taniyama, K. Kawasaki, and M. Notomi are preparing a manuscript to be called “Ultrahigh-Q nanocavity with 1D mode-gap barrier in silicon on insulator.”

].

We employed these two structures as candidates for ultra low power thermo-optic bistable devices because they should have superior heat confinement characteristics owing to the very small thermal conductivities of SiO2 and the air that surrounds the cavity.

2.2. Demonstration of low-power thermo-optic bistability

Our experiment for demonstrating thermo-optic bistability consists of sweeping a continuous-wave laser light from short to long wavelengths at a speed of 0.5 nm/s and measuring the spectral response of the cavity with a power meter. The cavity Q and power transmittance T r are measured at a very low input power (about 100 nW in the waveguide) to ensure that there is no nonlinear effect that can alter these values. The fabricated stack cavity exhibits a very high Q of 8.2×104 (T r⋍3%) and an even higher Q of 2.5×105 (T r⋍0.3%) is obtained for an air-bridged ladder cavity. As noted before, higher T r is also possible by reducing the number of boxes (at the cost of slightly lowering the high-Q).

Fig. 1. (a) Schematic illustration of stack cavity. (b) Scanning electron microscope image of a fabricated stack cavity. (c) Magnetic field (Hz 2) profile of a stack cavity obtained by using 3D finite-difference time-domain method. (d) Schematic illustration of ladder cavity. (e) Scanning electron microscope image of a fabricated ladder cavity. (f) Magnetic field (Hz 2) profile of a ladder cavity obtained by using 3D finite-difference time-domain method.

The high concentration of optical energy in high-Q cavities results in non-negligible two photon absorption (TPA), which leads to the generation of heat through the relaxation of the TPA carriers. Thus the temperature T of Si increases. Since the refractive index n of Si is described as follows,

nTnT)=+1.87×104K1,
(1)

the resonant wavelength of a Si nanocavity should become longer when the input power increases (red shift). At an efficient high input power, the cavity resonance can lock to the wavelength of the input light, which leads to the modification of the measured transmittance spectrum. As regards thermo-optic bistability, it is well known that the resonance of the cavity follows the wavelength of the input and drops sharply at a certain wavelength when the input is swept from shorter to longer wavelengths. Such a sharp drop in the spectrum is direct evidence of the existence of optical bistability [4

4. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).

, 6

6. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. 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 [CrossRef] [PubMed]

]. We observed this spectrum shape in our cavities, and the results with the lowest P tr are plotted in Fig. 2

P tr is experimentally obtained by considering the lowest input power P in for which a sharp drop can be observed. P in is the power at the PhC waveguide. It is obtained by measuring the power at the input fiber and subtracting the coupling efficiency. The coupling efficiency is estimated by measuring the transmittance of a sample without a cavity (only a PhC waveguide).

Fig. 2. (a) Stack cavity transmission spectrum, plotted for different P in. (b) Ladder cavity transmission spectrum, plotted for different P in.

In order to achieve high accuracy, the fiber aligner is automated, which enables an alignment reproducibility of less than 0.2 dB. Since we can obtain a hysteresis curve of the input and output power by increasing and decreasing the power at a fixed wavelength, we can determine P tr from the power threshold appearing in a hysteresis curve. However the value obtained by using this method is usually not as accurate as that obtained from the nonlinear spectra as we employed in this study. It is because the determination of Ptr by nonlinear spectra measurement is more robust to the temperature fluctuation, particularly when the linewidth of the cavity is very small.

2.3. Simple analysis of thermal properties obtained from experiment

Here we try to understand the property of thermo-optic confinement in two different types of 1D PhC nanocavities. Since the experiments were performed with two types of 1D nanocavities whose Q, T r and geometrical structures were different, we should discuss the effects of optical confinement (i.e. Q and T r) and thermal confinement (i.e. geometrical effect) separately.

To understand the physics involved, and in line with our experimental results, we accept that the wavelength shift δλ approximately scales with the energy in the cavity as follows,

δλPinQTr.
(2)

A complete model of the physics will take account of such effects as free-carrier absorption and inherent linear absorption, as found in [19

19. P. 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). http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-801 [CrossRef] [PubMed]

] and [20

20. T. Uesugi, B. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express 14, 377–386 ( 2006). http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-377 [CrossRef] [PubMed]

], and should make it possible to obtain a more accurate model for the calculation of δλ. However, as suggested by the experiment, the following study is undertaken using the simple relation Eq. (2). Theoretically, the wavelength shift needed to reach a bistable threshold is δλtr=32Δλ=32λ0Q, where Δλ is the resonance width [4

4. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).

, 19

19. P. 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). http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-801 [CrossRef] [PubMed]

]. Thus our simple model expresses the threshold power as,

Ptr1=rnTRthTrQ2
(3)

where r is the ratio of the optical energy converted into thermal energy and R th is the thermal resistance of the cavity.

Optical characteristic: For the same R th, we should obtain a small P tr when the √T r Q 2 product is large. This product is a figure of merit that reflects the optical confinement property of a cavity. In our experiment, this product is 3 times higher for an air-bridged ladder cavity than for a stack cavity, which means the air-bridged ladder cavity has better overall optical characteristics for exhibiting low power optical bistability. Indeed, an air-bridged ladder cavity has a higher unloaded Q of ~2.4×105 compared with the unloaded Q of 8.2×104 for a stack cavity.

3. Numerical analysis of thermal properties of 1D photonic crystal nanocavities

3.1. Comparison of stack cavity and ladder cavity

The purpose now is to evaluate the thermal capacity of the cavity to convert the heat source into an effective temperature increase.

We use the following considerations in our elaboration of the numerical model. The calculations are made in the steady-state regime. TPA is considered to be a heat source located in a position where the electromagnetic field is intense. With the stack cavity, the heat source is assumed to be uniformly distributed in the three Si boxes at the center of the cavity, where the optical mode is located. This is sufficiently accurate because the carriers cannot diffuse outside the box. With the air-bridged ladder cavity, we also assume that the heat source is uniformly distributed at the center of the cavity. It should be noted that there is the possibility of the carriers diffusing. However, a numerical simulation of the carriers taking the surface recombination into account [21

21. T. Tanabe, H. Taniyama, and M. Notomi, “Carrier diffusion and recombination in photonic crystal nanocavity optical switches,” J. Lightwave Technol. 26, 1396–1403 ( 2008). [CrossRef]

] shows that, even in this case, the free carriers (and therefore the heat source) remain in the majority located at the center of the cavity, which indicates that our approximations are sufficiently accurate. The differential equation of the model is the classic heat equation

ΔT+pkSiSiO2=0,
(4)

with k being the conductivity of Si or SiO2, and p the power source density (W/m3). The source term is null except at the center of the device. Before solving this, we must choose appropriate boundary conditions. The temperatures of Si and SiO2 far from the cavity are assumed to be room temperature T 0. Also, it can be confirmed numerically that the effect of air convection is totally negligible, and henceforth air will be considered a perfect insulator. A numerical simulation gives a temperature increase δT taken at the center, from which the thermal resistance R th=δT/Φ is deduced. Φ is the total power of the source.

Now, what can we expect? The stack cavity has one advantage in terms of achieving high thermal resistance. Because there is no physical connection between the Si boxes, heat can only be evacuated through the underlying SiO2. By contrast, heat can escape via the bridge in the air-bridged ladder cavity. But the air-bridged ladder cavity also has an advantage; the cavity is completely surrounded by air, whereas the box type cavity is on SiO2, and SiO2 is not as good an insulator as air. The question is which of these two factors has the most important effect.

Fig. 3. (a) Steady-state heat distribution for stack cavity: The calculated thermal resistance is 2.33×105 K·W-1. (b) Heat flux lines in stack cavity: A significant proportion of heat escapes through SiO2. (c) Heat distribution for ladder cavity: The calculated thermal resistance is 5.53×105 K·W-1. (d) Heat flux lines for ladder cavity: Heat mainly escapes via the Si bridge.

3.2. Geometrical study of air-bridged cavity

Heat can only escape from the air-bridged ladder cavity by diffusing into the Si bridge. Intuitively, the thermal energy left in the cavity will be larger if the only path allowing it to escape is thinner. Mathematically speaking, when e is the bridge width, 2l the length of the cavity, h the slab thickness and δ T the temperature difference between the center and the edge of the cavity, Fourier’s law j th=-k SiT gives

δTl=jk,
(5)

where j th is the heat flux. Moreover, if 𝒱 represents the volume of the entire air-bridged cavity and 𝓢 its boundary, conservation of thermal energy gives,

Φ=𝓥pdr=𝒮jdS4ehj,
(6)

from which we derive

Rth=δTΦ=l4kh1e.
(7)

Equation (7) predicts a linear increase in temperature with e -1. As this is an approximation that does not take all geometric details into account, we also performed 3D FEM calculations of the cavity thermal resistance for several e values, and the results are shown in Fig. 4 (black dots). Figure 4 also shows the thermal resistance versus width e curve (in blue) derived from Eq. (7), which reveals the good agreement between our simple model and the numerical results. A thin bridge is the key to achieving thermal confinement. We can see in Fig. 4 that if e is larger than 250 nm, the thermal resistance of the air-bridged ladder cavity is lower than that of the stack cavity. Since e is 96 nm in our case, we succeeded in achieving a lower P tr for air-bridged ladder cavity. In addition, Eq. (7) shows that a very long bridge would realize better insolation. We performed experiments with cavities whose lengths varied from 14.5 to 17 µm. P tr decreases with l, thus reaching its minimum value for l=17 µm. (P tr=63,6.3,2.5, and 1.6 µW for l=14.6,15.4,16.2, and 17, respectively.) Although the fabrication of a very long thin bridge poses a challenge, we may be able to reduce the operating power even further by taking these factors into account.

Fig. 4. Dependence of cavity thermal resistance on Si bridge width: Black dots show the results of numerical calculation, the red line represents the thermal resistance of a stack cavity. The blue and the green curve are derived from Eq. (7) and Eq. (8) respectively.

Here we would like to make a brief comment about the accuracy of the model given by Eq. (7). As the inset of Fig. 3(d) shows, the heat straightly flows along the Si bridge without passing through the Si ladders. Therefore, the structure can be regarded as equivalent to two thin beams, which makes Eq. (7) a good approximation. On the other hand, when we separately consider the thermal resistance for the a and b region [Fig. 3(d) inset] and connect them in series, the total resistance is given as,

Rth=Ra+Rb=l4kh(12e+1w+2e)
(8)

Although Eq. (8) seems to give a better fit of the first point, the resulting fit, shown by the green line in Fig. 4, is not as good as the one given by Eq. (7), which is due to the considerations about thermal flux discussed above.

4. Comparison with 2D PhC cavities

4.1. Thermal resistance

Fig. 5. (a) Schematic illustration of 2D cavity. (b) Steady-state heat distribution of 2D cavity: The calculated thermal resistance is 1.99×104 K·W-1.

The chart in Table 1 summarizes important parameters and results for the three cavity types. The possibility of fabricating high-Q 1D photonic cavities, combined with better heat confinement than with 2D, explains our low P tr value.

Table 1. Parameters and results for the three cavity types

table-icon
View This Table

4.2. Operation time

Fig. 6. Simulated time-dependent heat relaxation for 1D and 2D cavities.

5. Conclusion

We demonstrated low input power bistable behavior using 1D PhC nanocavities. These cavities have a noteworthy property; they can confine both light and heat very efficiently. In the air-bridged ladder cavity, a high Q and a favorable design allowed us to reach an optical bistable threshold value lower than 1.6 µW, which we believe to be the lowest reported value for Si. This result depends crucially on the sample design, particularly the width of the Si bridge (96 nm). We also note that we may be able to reduce the operating power further by taking advantage of the material parameters of, for example, InP [3

3. A. Shinya, S. Mitsugi, T. Tanabe, M. Notomi, I. Yokohama, H. Takara, and S. Kawanishi, “All-optical flipflop circuit composed of coupled two-port resonant tunneling filter in two-dimensional photonic crystal slab,” Opt. Express 14, 1230–1235 ( 2006). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-3-1230 [CrossRef] [PubMed]

] or GaAs [12

12. E. Weidner, S. Combrié, A. de Rossi, N. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118 ( 2007). [CrossRef]

, 23

23. S. Combrié, A. De Rossi, Q. Tran, and H. Benisty, “GaAs photonic crystal cavity with ultrahigh Q: Microwatt nonlinearity at 1.55 µm,” Opt. Lett. 33, 1908–1910 ( 2008). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-16-1908 [CrossRef] [PubMed]

].

In addition, we estimated the speed of this switch to be about 0.5 µs, which is very fast for a thermo-optic device. Although this value still remains large compared with current electronics standards, we may be able to increase the speed by employing the carrier-plasma dispersion effect [7

7. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30, 2575–2577 ( 2005). http://www.opticsinfobase. org/ol/abstract.cfm?URI=ol-30-19-2575 [CrossRef] [PubMed]

]. We can expect very low power carrier-plasma bistability, because the similar structures of the heat diffusion equation and free carrier diffusion equation indicate that the good thermal properties of the air-bridged 1D structure should be converted into good carrier confinement.

We believe this type of design will become more generally applicable for achieving viable all-optical signal processors.

Acknowledgment

The first author thanks Prof. H. Benisty for his support, and NTT Basic Research Laboratories for financing his internship program.

References and links

1.

T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low switching-energy and high-repetition-frequency all optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102 ( 2006). [CrossRef]

2.

M. Hill, H. Dorren, T. de Vries, X. Leijtens, J. Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. Smit, “A fast low-power optical memory based on coupled micro-ring lasers” Nature 432, 206–209 ( 2004). [CrossRef] [PubMed]

3.

A. Shinya, S. Mitsugi, T. Tanabe, M. Notomi, I. Yokohama, H. Takara, and S. Kawanishi, “All-optical flipflop circuit composed of coupled two-port resonant tunneling filter in two-dimensional photonic crystal slab,” Opt. Express 14, 1230–1235 ( 2006). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-3-1230 [CrossRef] [PubMed]

4.

H. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).

5.

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of two optical triodes,” Appl. Phys. Lett. 57, 1724 ( 1990). [CrossRef]

6.

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. 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 [CrossRef] [PubMed]

7.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30, 2575–2577 ( 2005). http://www.opticsinfobase. org/ol/abstract.cfm?URI=ol-30-19-2575 [CrossRef] [PubMed]

8.

Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett. 31, 341–343 ( 2006). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-3-341 [CrossRef] [PubMed]

9.

K. Nozaki and T. Baba, “Lasing characteristics with ultimate-small modal volume in point shift photonic crystal nanolasers,” Appl. Phys. Lett. 88, 211101 ( 2006). [CrossRef]

10.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 ( 2007). [CrossRef]

11.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Photon. 1, 449–458 ( 2007). [CrossRef]

12.

E. Weidner, S. Combrié, A. de Rossi, N. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118 ( 2007). [CrossRef]

13.

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16, 11095–11102 ( 2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-15-11095 [CrossRef] [PubMed]

14.

A. Zain, N. Johnson, M. Sorel, and R. De La Rue, “Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16, 12084–12089 ( 2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-12084 [CrossRef] [PubMed]

15.

P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 ( 2009). [CrossRef]

16.

M. Eichenfield, R. Camacho, J. Chan, K. Vahala, and O. Painter, “A picogram- and nanometer-scale photonic crystal opto-mechanical cavity,” Nature 459, 550–555 ( 2009). [CrossRef] [PubMed]

17.

E. Kuramochi, H. Taniyama, K. Kawasaki, and M. Notomi, “Fabrication of ultrahigh-Q nanocavity with one-dimensional photonic gap,” in Extended Abstracts of 70th Autumn JSAP Meeting, (Jpn. Soc. Appl. Phys., Tokyo, 2009), 9p-B-14. (in Japanese)

18.

E. Kuramochi, NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi-shi, Kanagawa 243–0198, Japan, H. Taniyama, K. Kawasaki, and M. Notomi are preparing a manuscript to be called “Ultrahigh-Q nanocavity with 1D mode-gap barrier in silicon on insulator.”

19.

P. 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). http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-801 [CrossRef] [PubMed]

20.

T. Uesugi, B. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express 14, 377–386 ( 2006). http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-377 [CrossRef] [PubMed]

21.

T. Tanabe, H. Taniyama, and M. Notomi, “Carrier diffusion and recombination in photonic crystal nanocavity optical switches,” J. Lightwave Technol. 26, 1396–1403 ( 2008). [CrossRef]

22.

M. Watts, W. Zortman, D. Trotter, G. Nielson, D. Luck, and R. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” In Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference (CLEO/QELS’09), CPDB10, Baltimore, May 31-June 5 ( 2009). [PubMed]

23.

S. Combrié, A. De Rossi, Q. Tran, and H. Benisty, “GaAs photonic crystal cavity with ultrahigh Q: Microwatt nonlinearity at 1.55 µm,” Opt. Lett. 33, 1908–1910 ( 2008). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-16-1908 [CrossRef] [PubMed]

OCIS Codes
(160.6840) Materials : Thermo-optical materials
(190.1450) Nonlinear optics : Bistability
(140.3948) Lasers and laser optics : Microcavity devices
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: August 27, 2009
Revised Manuscript: November 1, 2009
Manuscript Accepted: November 1, 2009
Published: November 4, 2009

Citation
Laurent-Daniel Haret, Takasumi Tanabe, Eiichi Kuramochi, and Masaya Notomi, "Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity," Opt. Express 17, 21108-21117 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-23-21108


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References

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  4. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic Press, Orlando, 1985).
  5. H. Tsuda and T. Kurokawa, "Construction of an all-optical flip-flop by combination of two optical triodes," Appl. Phys. Lett. 57, 1724 (1990). [CrossRef]
  6. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. 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 [CrossRef] [PubMed]
  7. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip," Opt. Lett. 30, 2575-2577 (2005). http://www.opticsinfobase. org/ol/abstract.cfm?URI=ol-30-19-2575 [CrossRef] [PubMed]
  8. Q. Xu and M. Lipson, "Carrier-induced optical bistability in silicon ring resonators," Opt. Lett. 31, 341-343 (2006). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-3-341 [CrossRef] [PubMed]
  9. K. Nozaki and T. Baba, "Lasing characteristics with ultimate-small modal volume in point shift photonic crystal nanolasers," Appl. Phys. Lett. 88, 211101 (2006). [CrossRef]
  10. T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, "Trapping and delaying photons for one nanosecond in an ultra-small high-Q photonic-crystal nanocavity," Nat. Photonics 1, 49-52 (2007). [CrossRef]
  11. S. Noda, M. Fujita, and T. Asano, "Spontaneous-emission control by photonic crystals and nanocavities," Nat. Photonics 1, 449-458 (2007). [CrossRef]
  12. E. Weidner, S. Combrié, A. de Rossi, N. Tran, and S. Cassette, "Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity," Appl. Phys. Lett. 90, 101118 (2007). [CrossRef]
  13. M. Notomi, E. Kuramochi, and H. Taniyama, "Ultrahigh-Q nanocavity with 1D photonic gap," Opt. Express 16, 11095-11102 (2008). http://www.opticsinfobase.org/oe/abstract.cfm?URI= oe-16-15-11095 [CrossRef] [PubMed]
  14. A. Zain, N. Johnson, M. Sorel, and R. De La Rue, "Ultra high quality factor one dimensional photonic crystal/ photonic wire micro-cavities in silicon-on-insulator (SOI)," Opt. Express 16, 12084-12089 (2008). http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-12084 [CrossRef] [PubMed]
  15. P. Deotare, M. McCutcheon, I. Frank, M. Khan, and M. Lončar, "High quality factor photonic crystal nanobeam cavities," Appl. Phys. Lett. 94, 121106 (2009). [CrossRef]
  16. M. Eichenfield, R. Camacho, J. Chan, K. Vahala, and O. Painter, "A picogram- and nanometer-scale photonic crystal opto-mechanical cavity," Nature 459, 550-555 (2009). [CrossRef] [PubMed]
  17. E. Kuramochi, H. Taniyama, K. Kawasaki, and M. Notomi, "Fabrication of ultrahigh-Q nanocavity with onedimensional photonic gap," in Extended Abstracts of 70th Autumn JSAP Meeting, (Jpn. Soc. Appl. Phys., Tokyo, 2009), 9p-B-14. (in Japanese)
  18. E. Kuramochi, NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan, H. Taniyama, K. Kawasaki, and M. Notomi are preparing a manuscript to be called "Ultrahigh-Q nanocavity with 1D mode-gap barrier in silicon on insulator."
  19. P. 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). http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-13-3-801 [CrossRef] [PubMed]
  20. T. Uesugi, B. Song, T. Asano, and S. Noda, "Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab," Opt. Express 14, 377-386 (2006). http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-377 [CrossRef] [PubMed]
  21. T. Tanabe, H. Taniyama, and M. Notomi, "Carrier diffusion and recombination in photonic crystal nanocavity optical switches," J. Lightwave Technol. 26, 1396-1403 (2008). [CrossRef]
  22. M. Watts, W. Zortman, D. Trotter, G. Nielson, D. Luck, and R. Young, "Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics," In Conference on Lasers and Electro-Optics / Quantum Electronics and Laser Science Conference (CLEO/QELS’09), CPDB10, Baltimore, May 31-June 5 (2009). [PubMed]
  23. S. Combrié, A. De Rossi, Q. Tran, and H. Benisty, "GaAs photonic crystal cavity with ultrahigh Q: Microwatt nonlinearity at 1.55 μm," Opt. Lett. 33, 1908-1910 (2008). http://www.opticsinfobase.org/ol/ abstract.cfm?URI=ol-33-16-1908 [CrossRef] [PubMed]

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