Compact delay structure based on photonic crystal waveguide loop

Optics Communications 272 (2007) 529–533 www.elsevier.com/locate/optcom

Compact delay structure based on photonic crystal waveguide loop Zhenfeng Xu *, Ping Su, Qingsheng He, Guofan Jin Tsinghua-Foxcon Nanotechnology Research Center, State Key Laboratory of Precision Measurement Technology and Instruments, Tsinghua University, 100084 Beijing, China Received 14 August 2006; received in revised form 20 November 2006; accepted 21 November 2006

Abstract A new compact delay structure based on two-dimensional photonic crystal (PC) is presented. The delay structure consists of a PC waveguide loop and a PC coupler switch. The optical signal pulse is delayed when it circulates in the waveguide loop, and the delay process is controlled by the coupler switch. After the theoretical analysis and design, the behavior of the delay structure is verified using the finite-difference time-domain method.  2006 Elsevier B.V. All rights reserved.

1. Introduction In ultra-high speed optical communication networks, optical buffer is a significant device used to realize the data synchronization between the input and output devices. In the optical buffer, the delay structure is a key element to store the signal pulses temporarily. Traditional delay structures were mainly based upon the optical fiber-ring [1,2]. The radii of those optical fiber-rings were set greater than several centimeters to avoid radiation loss, which is far from the demand of compact integrated photonic devices. Therefore, many designs of delay structure based upon the photonic crystals (PCs) were proposed and demonstrated [3,4], owing to the fact that the PCs can manipulate the light wave with a size of several microns [5]. In this paper, we propose a new compact delay structure based on two-dimensional (2D) PC. This structure is formed by a PC waveguide (PCWG) loop and a PC directional coupler switch. The delayed optical signal pulse circulates in the waveguide loop when the switch is ‘off’, and then can be accessed when the switch is ‘on’. By optimizing the PCWG, low group velocity dispersion and transmission loss are realized simultaneously to reduce the distortion and loss of the optical signal pulse. After the theoretical *

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analysis, the performance of the delay structure is simulated using the finite-difference time-domain (FDTD) method. 2. Design and analysis The schematic layout of our delay structure is shown in Fig. 1. It consists of a waveguide loop and a directional coupler switch in a 2D PC with square lattice of dielectric rods in the air background. The signal in the form of ultrashort optical pulse is coupled into the input port; it will exit from the output port without delay if the switch is ‘off’; otherwise, it will be coupled into the PCWG loop. Then the optical pulse cannot be coupled back after the switch is turned from ‘on’ to ‘off’, and will circulate in the PCWG loop until the switch is again ‘on’. Thus, the optical signal pulse is delayed in this structure, and the delay time is nL/ vg, where n is the number of circulating cycles; L is the total length of the PCWG loop, and vg is the group velocity of the optical pulse. In the designed structure, there are mainly three rules that should be considered: First, when the optical signal pulse is delayed, it will propagate in the PCWG loop with a relatively long optical path, so the group velocity dispersion should be around zero for the spectral components of the signal pulse to reduce the pulse distortion [6].

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PCWG loop

a Input port

Output port

0.55

Fig. 1. The schematic layout of the delay structure based on PC, which consists of a PCWG loop and a PC directional coupler switch. The optical signal pulse is delayed when it circulates in the PCWG loop, and the delay process is controlled by the coupler switch.

Second, the signal pulse travels through 4n bends after n cycles and a slight reflection will decrease the energy of forward pulse drastically, so high transmission coefficient should also be achieved in the bends of the PCWG loop to reduce the transmission loss. Third, the delay structure should include an optical switch to control the delay process. In the following analysis and design, the refractive index of the dielectric rods in the PC bulk is assumed to be 3.4, and the radii of these rods is chosen as 0.20a, (a is the lattice constant) to get a relatively large gap size [5]. This 2D PC has a photonic band gap (PBG) only for the transverse magnetic (TM) modes, so only the TM modes are concerned. The PCWG is formed by removing one row of rods in the C–X direction. To obey the first and the second rules simultaneously, we adjust the radii of rods at the boundaries of PCWG from 0.20a to 0.25a. The supercell of the corresponding PCWG is shown in Fig. 2a. The projected dispersion curve of the TM guided modes is calculated with a preconditioned block-iterative plane wave expansion code [7] and plotted in Fig. 2b. A single non-degenerate TM guided mode extends from 0.304(2pc/a) to 0.433(2pc/a) (c is the velocity of light in free space). Based on the dispersion relation, the dispersion (d2k/dx2) for the guided modes is plotted in Fig. 3a. It can be seen that the dispersion is nearly zero around the frequency of 0.358(2pc/a). Therefore, the central frequency of the signal pulse is chosen at 0.358(2pc/a) to reduce its distortion caused by the group velocity dispersion. Meanwhile, the PCWG bend can be regarded as two C– X direction waveguides connected with a C–M direction waveguide. By adjusting the effective length of C–M section, nearly 100% transmission can be realized for several frequencies [8]. Considering that the high transmission frequencies should be near the frequency of 0.358(2pc/a),pthe ffiffiffi effective length of C–M section is set as L ¼ 2:33  2a, as indicated in Fig. 1. Fig. 3b shows the transmission

Normalized frequency (2π c/a)

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Fig. 2. (a) Supercell used to compute the dispersion relation of the PCWG modes. (b) The dispersion curve of the PCWG. The radii of dielectric rods in PC bulk is r = 0.20a, and refractive index of the rods is assumed to be 3.4. The PCWG is formed by removing one row of rods in the C–X direction.

coefficient through the PCWG bend as a function of the operating frequency. The detailed calculation method is demonstrated in [8]. It can be seen that nearly 99% transmission around the frequency of 0.358(2pc/a) is obtained. If the radii of the relevant rods was not tuned to 0.25a, the corresponding transmission coefficient only can reach 93%. Consequently, low dispersion and high transmission are realized simultaneously to reduce the distortion and loss of the optical signal pulse. For the third rule, a PC directional coupler switch is added to control the delay process. As shown in Fig. 4a, the coupler consists of two PCWGs with an interval of 4a, and the radii of one row of the dielectric rods is changed from 0.20a to 0.35a. The coupler structure remains symmetric to ensure the total energy transfer [6]. According to the coupled mode theory [9], for the frequency of 0.358(2pc/a), the coupling length is about 54a; when the refractive index of the three rows of rods between the two PCWGs decreases from 3.4 to 3.3 (i.e., 3% variation), the coupling length declines to 36a. So the interaction length of the two PCWGs of the coupler (or the length of the bottom part of PCWG loop) is designed as 108a, then the status of the coupler switch can be determined by the refractive index of the relevant rods: when the

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0.90 0.34

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Normalized frequency (2πc/a)

Fig. 3. (a) The dispersion of the guided modes as a function of normalized frequency. (b) Transmission coefficients of PCWG bend in the frequency range of 0.340 < xa/2pc < 0.370. In order to get high transmission coefficient and low group velocity dispersion in this range of frequency simultaneously, the radii of rods at the boundaries of PCWG is adjusted from 0.20a to 0.25a.

refractive index is 3.4, nearly total energy will be coupled back from PCWG1 to PCWG2, as shown in Fig. 4b, and we define the status of the switch as ‘off’; when the refractive index shifts to 3.3, nearly total energy will be coupled from PCWG2 to PCWG1, as shown in Fig. 4c, and we define the status of the switch as ‘on’. In order to shorten the switch time, less variation of the refractive index is need, and the index change can be achieved by the quantum dots system [10]. The further optimization of the coupler switch is under consideration. 3. Simulation Combining the PCWG loop with the PC directional coupler switch, the delay structure is formed as shown in Fig. 1. The behavior of the structure is simulated using the FDTD method. The length of the PCWG between the input port and the output port is 130a, and the PCWG loop is 2 · (108 + 25)a long. In order to avoid the reflection

c Fig. 4. (a) Schematic structure of the PC directional coupler switch, the electric filed patterns of (b) ‘off’ status, and (c) ‘on’ status in the coupler switch, respectively.

from the output port, a gradual taper transition is added to couple the pulse efficiently from the PCWG to the free space [11]. The total size of the structure is 130a · 40a. Then a Gaussian pulse is excited at the input port with a center frequency of 0.358(2pc/a), a full width at half maximum (FWHM)Dt = 0.5ps, and polarization parallel to the rods. Fig. 5a–h show the electric filed patterns in the delay structure at different times: (1) the excited optical pulse propagates in the PCWG, and nearly total of its energy is coupled into the PCWG loop when the switch is ‘on’, as shown in Fig. 5a and b; (2) Then the coupled pulse circulates in the PCWG loop with little loss when the switch shifts from ‘on’ to ‘off’, as shown in Fig. 5c–f; (3) when the switch is again ‘on’, the optical pulse circulating in the PCWG is coupled back and radiates from the output port, as shown in Fig. 5g and h. The time when the optical pulse propagates in the PCWG loop is the delay time, and it is controlled by the coupler switch.

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Z. Xu et al. / Optics Communications 272 (2007) 529–533 1.0 0.8

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Delay time (a/c) Fig. 6. The normalized intensity detected at the output port, the total delay time is about 2520a/c.

Fig. 6 shows the normalized intensity detected at the output port. The input optical pulse is excited at the time t = 0. And the optical pulse has circulated in the PCWG loop for 4 cycles before radiating out. It can be seen that a little portion of the pulse energy (i.e., 0.3% loss) leaks out for each cycle, which is mainly due to the relatively low extinction ratio of the PC coupler switch. The interval between the adjacent pulses is about 630a/c, and the total delay time is about 2520a/c. The total delay time can be enlarged by (1) increasing the total length of the PCWG loop; (2) decreasing the group velocity of the guided modes [12]; (3) enhancing the extinction ratio of the coupler switch to reduce the leakage of pulse in each cycle [13]. We can also see that the FWHM of the signal pulse is slightly broadened, which is mainly caused by the non-zero dispersion between the different spectral components of the signal pulse. The low loss and little pulse broadening indicate that the structure is valid when the pulse width is around 0.5 ps. 4. Conclusions

Fig. 5. The electric filed patterns in the delay structure at different time: (a) and (b): the excited optical pulse is coupled into the PCWG loop; (c) and (f): the coupled pulse is delayed in the PCWG loop with little loss; (g) and (h): the optical pulse circulating in the PCWG loop is coupled back and radiates from the output port.

In summary, we proposed a new compact delay structure based upon the 2D PCWG loop. After the structure optimizations of the PCWG and the PCWG bend, with the central frequency of 0.358(2pc/a), low group velocity dispersion and high transmission coefficient (i.e., 99%) are realized simultaneously in the PCWG loop to reduce the distortion and loss of the optical signal pulse; a symmetric PC directional coupler switch is added to control the delay process. Then the performance of the delay structure is verified using the FDTD method. The results agree well with the theoretical analysis. The simulated delay time is about 2520a/c, which can be enlarged by further design and optimization. This delay structure can work as a building block for the compact optical buffer. We notice that our FDTD simulation is based on the 2D model and the vertical leakage of light is not considered. For practical delay structure, the proposed design should

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be realized in different forms, such as PC slab [14], or sandwiched between two identical 1D PCs [15]. Then the performance of the delay structure will be degraded by imperfect vertical confinement. However, the theoretical analysis presented in this paper is still valid after including the out-ofplane loss. Acknowledgement This work was supported by the National Research Fund for Fundamental Key Projects No.973 (G19990330). References [1] K.L. Hall, J.D. Moores, K.A. Rauschenbach, W.S. Wong, E.P. Ippen, H.A. Haus, IEEE Photon. Technol. L. 7 (1995) 1093. [2] Aiming Liu, Chongqing Wu, Yandong Gong, P. Shum, IEEE Photon. Technol. L. 16 (2004) 2129. [3] Zheng Wang, Shanhui Fan, Phys. Rev. E 68 (2003) 066616. [4] Daisuke Mori, Toshihiko Baba, Appl. Phys. Lett. 85 (2004) 1101.

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