- Email: [email protected]
Dynamic control of Q factor in photonic crystal microcavity employing Kerr effect
Optics Communications 285 (2012) 5508–5511
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Dynamic control of Q factor in photonic crystal microcavity employing Kerr effect Pengfei Zhu a, Bo Fang b, Chaomin Zhang a, Yunxia Ping a, Fuxin Wang a, Chun Jiang b,n a b
College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China State Key Laboratories of Advanced Optical Communication System and Network, Shanghai Jiao Tong University, Shanghai 200240, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 September 2011 Received in revised form 10 April 2012 Accepted 21 July 2012 Available online 4 August 2012
We design an in-plan hetero-photonic crystal (IP-HPC) structure which can dynamically control the quality (Q) factor of the nanocavity by using Kerr effect. In both theoretical derivation and numerical simulation, the Q factor could be dynamically turned with a larger scale than reported before. We study the effect of distance between the cavity and the hetero-photonic crystal on the Q factor. With optimal parameters, the Q factor of the nanocavity can be changed from 130,000 to 880,000 in the IP-HPC system. & 2012 Elsevier B.V. All rights reserved.
Keywords: Photonic crystal Nanocavity Hetero Q factor Kerr effect
1. Introduction Photonic crystals (PhC) have attracted much interest for integrated photonic circuits because they exhibit a photonic band gap (PBG) resulting in the ability to forbid propagation of light within a frequency range [1–3]. Because confinement by the PBG is the most efficient way to confine light in a wavelength-scale volume, the PhC cavities have rapid progress recently and have been considered as the most advantageous in terms of Q per unit mode volume (V), that is, Q/V. Especially two dimensional (2D) PhC slab cavities have been widely studied by utilizing well established fabrication processes in the semiconductor industry [4–8]. In such 2D Photonic crystal slab structures, photons can be confined horizontally by the 2D PBG and vertically by total internal reflection (TIR). The Q factor has achieved 109 in the latest report in a 2D PhC structure [9]. Although the high quality (Q) factor photonic crystal nanocavities have achieved so high value, there are a few researches [10–12] about dynamical control of the Q factor up to now. They used the interference effect and the nonlinear effect of the material to turn Q factor by optical method. The previous work [11] successfully dynamically controlled the Q factor of the nanocavity in a photonic crystal from 3,000 to 12,000. If dynamic control over the Q factor could be achieved within the lifetime of a photon pulse, significant advances would be expected
n
Corresponding author. E-mail address: [email protected] (C. Jiang).
0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.07.065
in areas of physics and engineering such as the slowing or stopping light [13,14] and quantum information processing [15,16]. For these applications, it is desirable that the transfer, storage and exchange of photons in nanocavity systems in such a timescale. This means that it is very important to design a small optical system with high and dynamically controllable Q. In this study, we design a novel structure and simulate the dynamically controlled Q factor by injecting pump light which can change the refractive index of the waveguide due to the Kerr effect. We study that how the distance between the cavity and PC2 influence the Q factor, which is very useful to initialize the state of the structure when dynamically tuning the value of Q factor. Moreover, we optimize several parameters of this structure, and the numerical simulation is performed by using the FDTD method with perfectly matched layer (PML) as absorbing boundary conditions [17], and the spatial resolution of the numerical simulation is 40 pixels/a. The results show that the Q factor can be dynamically tuned from 130,000 to 880,000 with photon pulse in photonic crystal.
2. Design of the structure The base structure is a 2D photonic crystal which is composed of silicon with a triangular lattice of air holes whose radii are r1 ¼ 1 and r2 ¼0.355 in PC1 and PC2 respectively. Fig. 1 shows a schematic of the proposed structure consisting of two photonic crystals (PC1 and PC2) having different lattice constants (a1 ¼1
P. Zhu et al. / Optics Communications 285 (2012) 5508–5511
5509
0.32
Frequency (c/a)
0.3 0.28 0.26 0.24
ω=0.2416 (2πc/a)
0.22 0.2
0
0.1
Fig. 1. Structure diagram of nanocavity with a hetero-photonic crystal.
0.2 0.3 Wave vector (2π/a)
0.4
0.5
Fig. 2. Waveguide mode dispersion curves in PC1.
and a2 ¼0.98) with line-defect waveguides in PC1 [18]. And the initial structure of the cavity is made with three missing air holes in a line separated from the waveguide by two rows of hole as shown in Fig. 1. The width of the waveguide (line pffiffiffidefect) whose refractive index is 3.5 in PC1 region equals to b1 ¼ 3a1. In order to create an electric field distribution in the form of a Gaussian-like function[5], two air holes at the cavity edges are shifted by 0.13a1. L is the distance between the center of the cavity and the first layer on the left of PC2. The space of the junction between PC1 and PC2 is defined as parameter d, which is studied in our simulation for initializing the state of the structure when we dynamically control the value of Q factor.
3. Theoretical analysis There are two factors that determine the quality factor in the case of a two-dimensional photonic crystal nanocavity: (1) the in-plan Q factor (Qin) which is determined by the optical coupling between the nanocavity and the waveguide, and (2) the vertical Q factor (Qv), which is determined by the optical coupling between the nanocavity and free-space. The Qv is fixed by the structure of the cavity and is mainly determined by TIR condition for the vertical direction. But the Qin can be influenced by the environment of the cavity which we refer to the mirror (PC2) as shown in Fig. 1. Qtotal is the total quality factor of the nanocavity. In our model, the total Q factor of the nanocavity is governed by [11] 1 1 þ cos y 1 ¼ þ Q total Qv Q in0
ð1Þ
where y is the phase difference between the two light waves (the light waves emitted from the nanocavity to the backward direction and to the forward direction) and Qin0 is the in-plane quality factor in the absence of the hetero-photonic crystals. The Qtotal could be theoretically changed from minimum Qin0/2 to maximum Qv by changing y from 0 to p when Qv*Qin0. Although the PhC with the same lattice constant as PC1 can act as the mirror, we use the hetero-photonic crystal for tuning the initialization state of structure before we dynamically tune Q factor in the next section. The value of y can be changed by irradiating an optical pulse onto the waveguide which is marked with blue block in Fig. 1 to change the refractive index by the Kerr effect. If the duration of the optical pulse is several picoseconds, the refractive index changes in the same timescale. Although the free carrier can change the refractive index too, in present simulation we
mainly consider the Kerr effect and do not set the carrier effect in the software. And for the ideal condition we assume the loss of the nonlinear material which is marked with blue block in Fig. 1 is zero in the simulation. In the simulation, we use a pump and a signal beam to demonstrate dynamic control of the Q factor using the system shown in Fig. 1. The PBG of PC1 is from 0.1980(c/a) to 0.3315(c/a). And Fig. 2 shows the waveguide mode dispersion relationship in PC1. As the calculated resonant frequency of the cavity is 0.2416(c/a) which is marked with a dot in Fig. 2. So we select this frequency for signal beam which is put in the cavity. The rule of the pump frequency we select is that the pump frequency should be outside the resonant frequency of the cavity and inside the PBG of PC1. A pump pulse whose normalized frequency is 0.4832(c/a) is used to irradiate onto the waveguide to change the refractive-index of the waveguide due to the Kerr effect and thus the phase difference y. As the phase difference is 2mp (m is integer), the signal and backward pump waves will constructively interfere, at this time the signal wave will couple from the nanocavity into input port and thus Q decrease. As the phase difference is (2mþ1)p, the two waves will destructively interfere, the signal wave is not able to couple from the nanocavity into input port and thus Q nearly does not change. The characteristics of the light radiation from the nanocavity strongly depended on the relative time of signal beam and pump pulse. The pump pulse and signal pulse arrive simultaneously to make sure the Q factor achieving the maximum. If the distance between the nanocavity and PC2 is too large, the Qtotal is still at its lowest possible value because all the energy has emitted from the cavity before the backward light reaches the nanocavity so that the pump pulse is useless when we dynamically control the Q factor. On the other hand, if the distance is too short, the Qtotal will increase since much backward light will couple into the nanocavity so that the calculated value would not be accurate. Therefore, it is important to choose a proper position for the nanocavity from PC2 in order to satisfy two conditions: (1) the backward light has little effect on increasing the quality factor of the nanocavity, and (2) the pump pulse can modulate the quality factor.
4. Results and discussion It is shown from the Ref. [19] that the high Qtotal needs high Qv nanocavity. So we design the high Qv first by shifting the air holes
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P. Zhu et al. / Optics Communications 285 (2012) 5508–5511
at the cavity edges in order to create an electric-field distribution in the form of a Gaussian-like function. We shift the two air holes about 0.13a1 at the cavity edges without waveguide for calculating the Qv of the cavity with 2D FDTD method and obtain the maximum Q factor in this structure. The calculated Qv of this nanocavity is 880,000. Then we put the signal laser in the nanocavity and obtain the Qin0 130,000 when PC2 is moved away. Next, we investigate the rule of Q factor of the cavity with the distance (L, the unit is a1) between the cavity and the first layer of PC2. The method we take is to find a proper position for the cavity by fixing PC2 and shortening the space (d, the unit is a1) of the junction between PC1 and PC2 from the maximum value P ¼Max {a1, a2}. In our design, the P value equals to a1 ¼1.According to the method, we firstly change the position of the cavity in the horizontal direction when the PC2 is fixed and the results are shown in Fig. 3. The Q factor is close to Qin0, when the distance between the nanocavity and the hetero-photonic crystal is L¼11a1. Secondly, when PC1 and the cavity is fixed, the PC2 is x 105
1.52
1.48
Q
1.44
1.4
1.36
1.32
8
12
16
20
L Fig. 3. Q factor plotted versus the distance between the center of the nanocavity and the hetero-photonic crystal when we fix PC1 and PC2.
1.5
moved close to PC1 piece by piece from the original position (d ¼P) with the step of 0.01a1. The calculated results of the Q factors are shown in Fig. 4. Note that the quality factor of the nanocavity is rising slowly with the distance abridging, i.e., the Q factor has the smallest value in this structure when the parameter d equals to a1. We further investigate the dynamic control of Q factor of the nanocavity with pump pulse in our simulation. From the results we analyzed before, we fix the distance (L) as 11a1 between the nanocavity and PC2 and we set up the parameter d to equal to a1. The results in Fig. 5 show that when pump and signal pulses arrive simultaneously, we can achieve the maximum Q factor whose value is 880,000. The pump power can also influence Q factor of the nanocavity due to the Kerr effect. So, in the simulation we study the relationship between the Q values and pump power. The results are shown in Fig. 5. Since we change the pump power by changing the amplitude of the pump field in the simulation, the unit of the power is normalized in Fig. 5. The results show that the Q factor can be dynamically controlled by pump pulse. And there is a threshold value of pump power to change Q factor from 550,000 to higher value. The timescale of pump pulse is in picoseconds. When compared with the theoretical analysis described above, the simulation clearly indicates that dynamic control of the Q factor from 130,000 to 880,000 can be achieved.
5. Conclusion
x 105
We have designed a novel structure which could dynamically control the Q factor of the nanocavity in a photonic crystal with a hetero-photonic crystal by the Kerr effect. This structure was modeled and also numerically calculated by using 2D FDTD method, both of which proved the Q factor could be dynamically controlled by a pump pulse. We have studied the effect of the distance between the cavity and the hetero-photonic crystal, which was very useful when the state of the structure is initialized. We successfully turned the Q factor of the nanocavity of the photonic crystal from 130,000 to 880,000 by a pump pulse whose timescale is in picoseconds.
1.46
Q
Fig. 5. Q factor plotted versus the normalized pump power.
1.42
1.38
Acknowledgments 1.34 0.84
0.88
0.92 d
0.96
1
Fig. 4. Q factor plotted versus the steps (unit a1) of hetero-photonic crystal budging close to PC1 from the original position (d ¼P ¼a1) when PC1 and the nanocavity is fixed.
This work was supported by National Natural Science Foundation of China (Grant no. 60672017) and Shanghai Pujiang Program and Scholastic Research Foundation of Shanghai University of Engineering Science (No. 2011XY35) and the Innovation Program of Shanghai Municipal Education Commission (Nos. 11YZ216 and A-3500-11-10).
P. Zhu et al. / Optics Communications 285 (2012) 5508–5511
References [1] [2] [3] [4] [5] [6] [7] [8]
[9] [10]
E. Yablonovitch, Physical Review Letters 58 (1987) 2059. S. John, Physical Review Letters 58 (1987) 2486. S. Noda, K. Tomoda, N. Yamamoto, A. Chutinan, Science 289 (2000) 604. O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. O’Brien, P.D. Dapkus, I. Kim, Science 284 (1999) 1819. Y. Akahane, T. Asano, B.S. Song, S. Noda, Nature 425 (2003) 944. B.S. Song, S. Noda, T. Asano, Y. Akahane, Nat. Mater. 4 (2005) 207. T. Asano, B.S. Song, Y. Akahane, S. Noda, IEEE J. Sel. Top. Quantum Electron 12 (2006) 1123. Eiichi Kuramochi, Masaya Notomi, Satoshi Mitsugi, Akihiko Shinya, Takasumi Tanabe, Toshifumi Watanabe, Applied Physics Letters 88 (2006) 041112. Y. Tanaka, T. Asano, S. Noda, Journal of Lightwave Technology 26 (2008) 1532. M.F. Yanik, W. Suh, Z. Wang, S. Fan, Physical Review Letters 93 (2004) 903.
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[11] Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, S. Noda, Nat. Mater. 6 (2007) 862. [12] M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, M. Morita, Optics Express 15 (2007) 17458–17481. [13] M.F. Yanik, S. Fan, Physical Review Letters 92 (2004) 083901. [14] Tanaka, Y., Asano, T. and Noda S., CWE4-3, Tokyo, Japan, July 11–15, 2005, pp. 1024. [15] J.H. Hartmann, F.G.S.L. Brandao, M.B Plenio, Nat. Phys. 2 (2006) 849. [16] K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E.L. Hu, A. Imamoglu, Nature 445 (2007) 896. [17] A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J.D. Joannopoulos, S.G. Johnson, G. Burr, Optics Letters 31 (2006) 2972. [18] Bong-shik Song, Takashi Asno, Yoshihiro Akahane, Yoshinri Tanaka, Susumu Noda, Applied Physics Letters 85 (2004) 4591. [19] Yoshihiro Akahane, Masamitsu Mochizuki, Takashi Asano, Yoshinori Tanaka, Susumu Noda, Applied Physics Letters 82 (2003) 1341.
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Dynamic control of Q factor in photonic crystal microcavity employing Kerr effect Pengfei Zhu a, Bo Fang b, Chaomin Zhang a, Yunxia Ping a, Fuxin Wang a, Chun Jiang b,n a b
College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China State Key Laboratories of Advanced Optical Communication System and Network, Shanghai Jiao Tong University, Shanghai 200240, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 September 2011 Received in revised form 10 April 2012 Accepted 21 July 2012 Available online 4 August 2012
We design an in-plan hetero-photonic crystal (IP-HPC) structure which can dynamically control the quality (Q) factor of the nanocavity by using Kerr effect. In both theoretical derivation and numerical simulation, the Q factor could be dynamically turned with a larger scale than reported before. We study the effect of distance between the cavity and the hetero-photonic crystal on the Q factor. With optimal parameters, the Q factor of the nanocavity can be changed from 130,000 to 880,000 in the IP-HPC system. & 2012 Elsevier B.V. All rights reserved.
Keywords: Photonic crystal Nanocavity Hetero Q factor Kerr effect
1. Introduction Photonic crystals (PhC) have attracted much interest for integrated photonic circuits because they exhibit a photonic band gap (PBG) resulting in the ability to forbid propagation of light within a frequency range [1–3]. Because confinement by the PBG is the most efficient way to confine light in a wavelength-scale volume, the PhC cavities have rapid progress recently and have been considered as the most advantageous in terms of Q per unit mode volume (V), that is, Q/V. Especially two dimensional (2D) PhC slab cavities have been widely studied by utilizing well established fabrication processes in the semiconductor industry [4–8]. In such 2D Photonic crystal slab structures, photons can be confined horizontally by the 2D PBG and vertically by total internal reflection (TIR). The Q factor has achieved 109 in the latest report in a 2D PhC structure [9]. Although the high quality (Q) factor photonic crystal nanocavities have achieved so high value, there are a few researches [10–12] about dynamical control of the Q factor up to now. They used the interference effect and the nonlinear effect of the material to turn Q factor by optical method. The previous work [11] successfully dynamically controlled the Q factor of the nanocavity in a photonic crystal from 3,000 to 12,000. If dynamic control over the Q factor could be achieved within the lifetime of a photon pulse, significant advances would be expected
n
Corresponding author. E-mail address: [email protected] (C. Jiang).
0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.07.065
in areas of physics and engineering such as the slowing or stopping light [13,14] and quantum information processing [15,16]. For these applications, it is desirable that the transfer, storage and exchange of photons in nanocavity systems in such a timescale. This means that it is very important to design a small optical system with high and dynamically controllable Q. In this study, we design a novel structure and simulate the dynamically controlled Q factor by injecting pump light which can change the refractive index of the waveguide due to the Kerr effect. We study that how the distance between the cavity and PC2 influence the Q factor, which is very useful to initialize the state of the structure when dynamically tuning the value of Q factor. Moreover, we optimize several parameters of this structure, and the numerical simulation is performed by using the FDTD method with perfectly matched layer (PML) as absorbing boundary conditions [17], and the spatial resolution of the numerical simulation is 40 pixels/a. The results show that the Q factor can be dynamically tuned from 130,000 to 880,000 with photon pulse in photonic crystal.
2. Design of the structure The base structure is a 2D photonic crystal which is composed of silicon with a triangular lattice of air holes whose radii are r1 ¼ 1 and r2 ¼0.355 in PC1 and PC2 respectively. Fig. 1 shows a schematic of the proposed structure consisting of two photonic crystals (PC1 and PC2) having different lattice constants (a1 ¼1
P. Zhu et al. / Optics Communications 285 (2012) 5508–5511
5509
0.32
Frequency (c/a)
0.3 0.28 0.26 0.24
ω=0.2416 (2πc/a)
0.22 0.2
0
0.1
Fig. 1. Structure diagram of nanocavity with a hetero-photonic crystal.
0.2 0.3 Wave vector (2π/a)
0.4
0.5
Fig. 2. Waveguide mode dispersion curves in PC1.
and a2 ¼0.98) with line-defect waveguides in PC1 [18]. And the initial structure of the cavity is made with three missing air holes in a line separated from the waveguide by two rows of hole as shown in Fig. 1. The width of the waveguide (line pffiffiffidefect) whose refractive index is 3.5 in PC1 region equals to b1 ¼ 3a1. In order to create an electric field distribution in the form of a Gaussian-like function[5], two air holes at the cavity edges are shifted by 0.13a1. L is the distance between the center of the cavity and the first layer on the left of PC2. The space of the junction between PC1 and PC2 is defined as parameter d, which is studied in our simulation for initializing the state of the structure when we dynamically control the value of Q factor.
3. Theoretical analysis There are two factors that determine the quality factor in the case of a two-dimensional photonic crystal nanocavity: (1) the in-plan Q factor (Qin) which is determined by the optical coupling between the nanocavity and the waveguide, and (2) the vertical Q factor (Qv), which is determined by the optical coupling between the nanocavity and free-space. The Qv is fixed by the structure of the cavity and is mainly determined by TIR condition for the vertical direction. But the Qin can be influenced by the environment of the cavity which we refer to the mirror (PC2) as shown in Fig. 1. Qtotal is the total quality factor of the nanocavity. In our model, the total Q factor of the nanocavity is governed by [11] 1 1 þ cos y 1 ¼ þ Q total Qv Q in0
ð1Þ
where y is the phase difference between the two light waves (the light waves emitted from the nanocavity to the backward direction and to the forward direction) and Qin0 is the in-plane quality factor in the absence of the hetero-photonic crystals. The Qtotal could be theoretically changed from minimum Qin0/2 to maximum Qv by changing y from 0 to p when Qv*Qin0. Although the PhC with the same lattice constant as PC1 can act as the mirror, we use the hetero-photonic crystal for tuning the initialization state of structure before we dynamically tune Q factor in the next section. The value of y can be changed by irradiating an optical pulse onto the waveguide which is marked with blue block in Fig. 1 to change the refractive index by the Kerr effect. If the duration of the optical pulse is several picoseconds, the refractive index changes in the same timescale. Although the free carrier can change the refractive index too, in present simulation we
mainly consider the Kerr effect and do not set the carrier effect in the software. And for the ideal condition we assume the loss of the nonlinear material which is marked with blue block in Fig. 1 is zero in the simulation. In the simulation, we use a pump and a signal beam to demonstrate dynamic control of the Q factor using the system shown in Fig. 1. The PBG of PC1 is from 0.1980(c/a) to 0.3315(c/a). And Fig. 2 shows the waveguide mode dispersion relationship in PC1. As the calculated resonant frequency of the cavity is 0.2416(c/a) which is marked with a dot in Fig. 2. So we select this frequency for signal beam which is put in the cavity. The rule of the pump frequency we select is that the pump frequency should be outside the resonant frequency of the cavity and inside the PBG of PC1. A pump pulse whose normalized frequency is 0.4832(c/a) is used to irradiate onto the waveguide to change the refractive-index of the waveguide due to the Kerr effect and thus the phase difference y. As the phase difference is 2mp (m is integer), the signal and backward pump waves will constructively interfere, at this time the signal wave will couple from the nanocavity into input port and thus Q decrease. As the phase difference is (2mþ1)p, the two waves will destructively interfere, the signal wave is not able to couple from the nanocavity into input port and thus Q nearly does not change. The characteristics of the light radiation from the nanocavity strongly depended on the relative time of signal beam and pump pulse. The pump pulse and signal pulse arrive simultaneously to make sure the Q factor achieving the maximum. If the distance between the nanocavity and PC2 is too large, the Qtotal is still at its lowest possible value because all the energy has emitted from the cavity before the backward light reaches the nanocavity so that the pump pulse is useless when we dynamically control the Q factor. On the other hand, if the distance is too short, the Qtotal will increase since much backward light will couple into the nanocavity so that the calculated value would not be accurate. Therefore, it is important to choose a proper position for the nanocavity from PC2 in order to satisfy two conditions: (1) the backward light has little effect on increasing the quality factor of the nanocavity, and (2) the pump pulse can modulate the quality factor.
4. Results and discussion It is shown from the Ref. [19] that the high Qtotal needs high Qv nanocavity. So we design the high Qv first by shifting the air holes
5510
P. Zhu et al. / Optics Communications 285 (2012) 5508–5511
at the cavity edges in order to create an electric-field distribution in the form of a Gaussian-like function. We shift the two air holes about 0.13a1 at the cavity edges without waveguide for calculating the Qv of the cavity with 2D FDTD method and obtain the maximum Q factor in this structure. The calculated Qv of this nanocavity is 880,000. Then we put the signal laser in the nanocavity and obtain the Qin0 130,000 when PC2 is moved away. Next, we investigate the rule of Q factor of the cavity with the distance (L, the unit is a1) between the cavity and the first layer of PC2. The method we take is to find a proper position for the cavity by fixing PC2 and shortening the space (d, the unit is a1) of the junction between PC1 and PC2 from the maximum value P ¼Max {a1, a2}. In our design, the P value equals to a1 ¼1.According to the method, we firstly change the position of the cavity in the horizontal direction when the PC2 is fixed and the results are shown in Fig. 3. The Q factor is close to Qin0, when the distance between the nanocavity and the hetero-photonic crystal is L¼11a1. Secondly, when PC1 and the cavity is fixed, the PC2 is x 105
1.52
1.48
Q
1.44
1.4
1.36
1.32
8
12
16
20
L Fig. 3. Q factor plotted versus the distance between the center of the nanocavity and the hetero-photonic crystal when we fix PC1 and PC2.
1.5
moved close to PC1 piece by piece from the original position (d ¼P) with the step of 0.01a1. The calculated results of the Q factors are shown in Fig. 4. Note that the quality factor of the nanocavity is rising slowly with the distance abridging, i.e., the Q factor has the smallest value in this structure when the parameter d equals to a1. We further investigate the dynamic control of Q factor of the nanocavity with pump pulse in our simulation. From the results we analyzed before, we fix the distance (L) as 11a1 between the nanocavity and PC2 and we set up the parameter d to equal to a1. The results in Fig. 5 show that when pump and signal pulses arrive simultaneously, we can achieve the maximum Q factor whose value is 880,000. The pump power can also influence Q factor of the nanocavity due to the Kerr effect. So, in the simulation we study the relationship between the Q values and pump power. The results are shown in Fig. 5. Since we change the pump power by changing the amplitude of the pump field in the simulation, the unit of the power is normalized in Fig. 5. The results show that the Q factor can be dynamically controlled by pump pulse. And there is a threshold value of pump power to change Q factor from 550,000 to higher value. The timescale of pump pulse is in picoseconds. When compared with the theoretical analysis described above, the simulation clearly indicates that dynamic control of the Q factor from 130,000 to 880,000 can be achieved.
5. Conclusion
x 105
We have designed a novel structure which could dynamically control the Q factor of the nanocavity in a photonic crystal with a hetero-photonic crystal by the Kerr effect. This structure was modeled and also numerically calculated by using 2D FDTD method, both of which proved the Q factor could be dynamically controlled by a pump pulse. We have studied the effect of the distance between the cavity and the hetero-photonic crystal, which was very useful when the state of the structure is initialized. We successfully turned the Q factor of the nanocavity of the photonic crystal from 130,000 to 880,000 by a pump pulse whose timescale is in picoseconds.
1.46
Q
Fig. 5. Q factor plotted versus the normalized pump power.
1.42
1.38
Acknowledgments 1.34 0.84
0.88
0.92 d
0.96
1
Fig. 4. Q factor plotted versus the steps (unit a1) of hetero-photonic crystal budging close to PC1 from the original position (d ¼P ¼a1) when PC1 and the nanocavity is fixed.
This work was supported by National Natural Science Foundation of China (Grant no. 60672017) and Shanghai Pujiang Program and Scholastic Research Foundation of Shanghai University of Engineering Science (No. 2011XY35) and the Innovation Program of Shanghai Municipal Education Commission (Nos. 11YZ216 and A-3500-11-10).
P. Zhu et al. / Optics Communications 285 (2012) 5508–5511
References [1] [2] [3] [4] [5] [6] [7] [8]
[9] [10]
E. Yablonovitch, Physical Review Letters 58 (1987) 2059. S. John, Physical Review Letters 58 (1987) 2486. S. Noda, K. Tomoda, N. Yamamoto, A. Chutinan, Science 289 (2000) 604. O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. O’Brien, P.D. Dapkus, I. Kim, Science 284 (1999) 1819. Y. Akahane, T. Asano, B.S. Song, S. Noda, Nature 425 (2003) 944. B.S. Song, S. Noda, T. Asano, Y. Akahane, Nat. Mater. 4 (2005) 207. T. Asano, B.S. Song, Y. Akahane, S. Noda, IEEE J. Sel. Top. Quantum Electron 12 (2006) 1123. Eiichi Kuramochi, Masaya Notomi, Satoshi Mitsugi, Akihiko Shinya, Takasumi Tanabe, Toshifumi Watanabe, Applied Physics Letters 88 (2006) 041112. Y. Tanaka, T. Asano, S. Noda, Journal of Lightwave Technology 26 (2008) 1532. M.F. Yanik, W. Suh, Z. Wang, S. Fan, Physical Review Letters 93 (2004) 903.
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