We present a light-by-light photonic crystal configuration consisting of a bent waveguide with three embedded Kerr-type nonlinear rods and a T-branch waveguide. We show that such a configuration can also demonstrate all-optical AND gate operation with extremely high contrast between the OFF state and the ON state in its transmission. The photonic crystal configuration of all-optical light-by-light switching is simple and thus facilitates the fabrication of practical all-optical devices and further large-scale optical integration.
© 2006 Optical Society of America
All-optical information processing applications are key components for future integrated photonic circuits. One category of such devices is light-by-light switching. Recently, it was shown that light-by-light switching could be achieved in a nonlinear photonic crystal directional coupler and resonator [1–8]. For the directional coupler switching structure reported in Ref. , the optical power consumption for the control signal is as high as 1.56 W when the coupling length is around 1.1 mm (corresponding to about 2000 lattice constants), which limits the development of practical all-optical devices. The use of a photonic crystal resonator results in greatly reduced power requirements. However, the contrast ratio in the transmission between the ON state and the OFF state  is low and thus not very effective for many modern telecommunication devices.
In this paper we propose and discuss a novel photonic crystal light-by-light switching based on an interference waveguide between a bent waveguide with three embedded Kerr-type nonlinear rods and a T-branch waveguide. The novel switching can achieve a greatly improved contrast ratio in its transmission while maintaining low optical power consumption.
2. Principle of operation and performance analysis
The structure consists of a bent waveguide with three embedded Kerr-type nonlinear rods and a T-branch waveguide, as depicted in Fig. 1. The waveguides are formed by the removal of some of the rods from a photonic crystal, which consists of a square lattice of infinite circular rods made of linear dielectric material embedded in air. The relative dielectric constant is 11.56 and the cross-section radius is chosen equal to 0.18a, where a is the lattice constant. The three red rods creating the bend are considered to be of Kerr-type nonlinear material with a relative dielectric constant of 7 and the same radius as the linear rods. The nonlinear parameters of photonic crystals we study refer to Ref. .
We perform 2D nonlinear finite-difference time-domain (FDTD) with perfectly matched layer boundary condition [10–11] simulations for the TM case with the electric field parallel to the rod axis for this PC system. The simulations use 16×16 grid points per unit cell.
In the first numerical experiment, we launch continuous-wave (CW) signals with a frequency of ω = 0.341(2πc/a) and a power level of 1.0P0 (P 0 =2.5×10-4 a / n 2 and n 2 is the Kerr coefficient) into the waveguide A when the interference length L of the photonic crystal configuration equals 10a. The output power level at steady state from the waveguide F can be obtained and is 0.00014P 0. When we launch the same CW signals into the waveguide B, the output power level is 0.00019P 0. We vary the interference length L and measure the output power at steady state, as shown in Fig. 2. We observe that there are some very low transmissions when the interference length L equals 7a, 10a, and 13a. These low transmissions are the result of the nonlinear rod at the bottom of the interference waveguide being just around the nodes of the standing waves formed by interference between the incident and reflected waves, and nonlinear properties aren’t presented. Then we fix the interference length L at 10a. We separately launch the CW signals with a frequency of ω = 0341(2πc / a) and a power level of 1.0P0 into the waveguide A and launch the CW signals with a frequency of ω = 0.332(2πc / a) and a power level of 1.0P0 into the waveguide B. Then we launch the same signals into the waveguides A and B at the same time. The according electric field distribution at steady state can be obtained, as shown in Fig. 3, which more clearly shows the principle of light-by-light operation. Standing waves can be formed by interference between the incident and reflected waves in the interference waveguide when a signal light beam is injected into the waveguide A or waveguide B. If the embedded Kerr-type nonlinear rod at the bottom of the interference waveguide is in narrow regions around the nodes of the standing waves, regardless of the power level of the signal light, it cannot pass through the bent waveguide. So the OFF state is reached. If a control light with different frequencies or the same frequency is also launched into the waveguide B or waveguide A, the standing waves of the signal light can be cancelled because of nonlinear properties. The field localization in the nonlinear rod is enhanced, and the signal light can pass through the tunable optical switching. So the ON state and light-by-light switching are reached.
In a second numerical experiment, we fix the interference length L at 10a and the frequency of the incident signals at ω = 0.341(2πc / a) . We launch the separate CW signals with a power level of 1.0P 0 into the waveguides A and B. The output power level from the waveguide F can be obtained accordingly and is 0.00014P 0 and 0.00019P 0 . When we launch the same signals into the waveguides A and B at the same time, the total output power level is 1.84P 0 . We vary the input power from 0.1P 0 to 1.0P 0 and measure the output power at steady state, as shown in Fig. 4(a). In particular, we observe a light-by-light region between 0.315P 0 and 1.0P 0 , where the contrast ratio is about 40 dB.
Consider now a repetition of the above simulation but varying the frequency of the incident signals with a small interval 0.001(2πc / a) . The light-by-light operation can be obtained in a window of frequencies from 0.332(2πc / a) to 0.341(2πc / a) .
In optics, the OFF state is usually represented by low transmitted intensity whereas the ON state is represented by high transmitted intensity. Based on the previous calculations we can find that, if one of the inputs A and B is OFF and the other is ON, the output from F is OFF. IF both A and B inputs have the value of ON, the output from F is ON. Thus, F yields the result of a AND operation with a high switching contract of close to 40 dB between OFF and ON output states.
In order to more clearly demonstrate the AND gate operation, the incident signals consisting of a CW with a frequency of ω = 0.341(2πc / a) are modulated by a rectangular pattern shown in Figs. 5(a) and 5(b). The pulse duration modulated is 80,000 time steps. In Fig. 5 we plot the time traces of inputs and output power patterns illustrating AND gate operation. As shown in Fig. 5, when both A and B are ON, F is ON.
Since the profiles of our modes are so similar to the cross sections of the 3D modes described in Ref , we can use our 2D simulations to estimate the power needed to operate a true 3D device. According to what is shown in Ref. , we can safely assume that in a 3D device the profile of the mode at different positions in the third dimension will be roughly the same as the profile of the mode in the transverse direction of the 2D system. Thus, taking the Kerr coefficient to be n 2 =1.5×10-17 m 2 / W (a value achievable in many nearly instantaneous nonlinear materials), and a lattice constant a = 528.6nm corresponding to the carrier wavelength λ 0 =1.55μm, gives a minimum power to observe AND operation of Pmin =361mW .
The performance of a novel architecture for a light-by-light switching based on a photonic crystal interference waveguide between a bent waveguide with three embedded Kerr-type nonlinear rods and a T-branch waveguide has been proposed and demonstrated. Results show that the novel light-by-light switching can also demonstrate the AND gate operation with a wide bandwidth (approximately 0.009(2πc / a) ) and a greatly improved contrast ratio (approximately 40 dB) in its transmission, and the optical power consumption for the incident signal is 361mW. The mechanism explained in this paper may be easily extrapolated to other photonic crystal configurations made of holes with some of them filled with a nonlinear material, which is more feasible in an experimental device. As the use of photonic crystal technology facilitates further large-scale optical integration, this practical light-by-light switching structure may become a key building block of a larger and more-complex all-optical switching device. Moreover, the high contrast ratio is beneficial for maximum immunity to noise and detection error, and for fan-out considerations. Future work will deal with the practical implementation of the proposed switch.
References and links
1. E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, 7683–7686 (2000). [CrossRef]
2. 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 (2002). [CrossRef]
3. 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]
4. A. R. Cowan and J. F. Young, “Optical bistability involving photonic crystal microcavities and Fano line shapes,” Phys. Rev. E 68, 046606 (2003). [CrossRef]
5. M. Soljacic and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Mater. 3, 211–219 (2004), and references therein. [CrossRef]
6. S. F. Mingaleev and Y. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19, 2241–2249 (2002). [CrossRef]
7. F. Cuesta-Soto, A. Martínez, J. García, F. Ramos, P. Sanchis, J. Blasco, and J. Marti, “All-optical switching structure based on a photonic crystal directional coupler,” Opt. Express 12, 161–167 (2003). [CrossRef]
9. E. P. Kosmidou, T. D. Tsiboukis, and T. D. Tsiboukis, “An FDTD analysis of photonic crystal waveguides comprising third-order nonlinear materials,” Opt. Quantum Electron. 35, 931–946 (2003). [CrossRef]
10. M. Agio and C. M. Soukoulis, “Ministop bands in single-defect photonic crystal waveguides,” Phys. Rev. E 64, 055603–055606 (2001). [CrossRef]
11. T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107–125113 (2001). [CrossRef]
12. M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001). [CrossRef]