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We put forward a route-asymmetrical optical transmission scheme employing optical gradient force, which means that forward and backward propagation of an optical device have different transmittance provided they are not present simultaneously. The device is based on optical gradient force between two single-mode waveguides followed by a Mach-Zehnder interferometer. Our numerical investigation shows that the forward transmittance is about −6 dB while the backward transmittance is suppressed below −20.5 dB in C + L bands. The proposed device is passive, wideband, and compatible with complementary metal-oxide semiconductor (CMOS) process. Furthermore, we demonstrate the applications of route-asymmetrical transmission such as an all-optical switch and all-optical AND gate for all-optical information processing.
© 2014 Optical Society of America
1. Introduction
Photonic integrated circuit has a special charm to optical communication and optical computing. Among all kinds of photonic integrated circuits, silicon photonics is the leading candidate due to its ability to integrate both photonic and electronic devices, compatibility with complementary metal-oxide semiconductor (CMOS) process, as well as low fabrication costs [1]. A device which is built with silicon photonics will have great advantages. Many optical components have been realized with complete silicon photonics, such as filter [2], polarization splitter [3], optical switch [4, 5] in the field of optical communication, and all-optical logic gate [6, 7] in the field of optical computing.
The force exerted by photons is of fundamental importance in light-matter interactions [8]. Optical force can be mainly divided into three categories, optical scattering force, optical gradient force and optical dissipative force [9]. With the development of the nano-fabrication technology, optical gradient force in integrated photonic circuits has been theoretically and experimentally investigated in many works [10–13]. The operation of optical force is adequately wideband, the device is compatible with CMOS process, and the design is flexible. All of these advantages make optical force a potential technology for optical communication and optical computing. A lot of optical components have been proposed based on optical forces, such as an optically tunable filter [14], a static and dynamic wavelength router [15], a broadband phase shifter [13]. As far as we know, very few works about route-asymmetric transmission were reported using optical force. Route-asymmetrical transmission means that forward and backward propagation of an optical device have different transmittance provided they are not present simultaneously. It is realized with many other approaches, such as optical nonlinearities in silicon resonant devices [16, 17].
In this paper, we propose an all-optical component to realize route-asymmetrical transmission based on optical gradient force. The device consists of two close single-mode waveguides with cantilever structure to arouse attractive force and a following Mach-Zehnder interferometer (MZI) to improve the bidirectional transmission difference. The proposed device is passive, wideband, and compatible with CMOS process. All-optical switch and logic AND gate are also demonstrated as the applications of the route-asymmetrical transmission.
2. Operation principle and simulation results
The device of route-asymmetrical transmission is fabricated on silicon-on-insulator (SOI) wafer, as shown in Fig. 1(a). A part of silica is dug out so that silicon waveguide in that region is suspended in the air. Two single-mode waveguides with width of w1 is separated by gap of g1. One of them is tapered to a needle at the end to reduce light reflection which is named as cantilever, and the other ends with a curved waveguide which will be fixed on the silica substrate. The cross section of the two single-mode waveguides is shown in Fig. 1(b). The height and width of the waveguide is 220 nm and 350 nm, respectively, the gap g1 is 70 nm and the height of the silica is 1 μm. The suspended distance of the coupling region of the two single mode waveguides is 30 μm. An MZI structure is subsequently employed with an optical path difference of half a wavelength between the two arms when input optical wavelength is set at 1550 nm. Thus the free spectral range (FSR) of the MZI will be 387 THz. The cantilever and the two arms of the MZI are separated by the equal gap of 100 nm. The width of the arms of MZI is 500 nm.
Fig. 1 (a) Schematic structure of the proposed device, (b) Cross section of the two single-mode waveguides, w1 = 350 nm, g1 = 70 nm, h = 220 nm. The coupling length of the two single-mode waveguides is 30 μm, (c) and (d) are the transverse components of the electric field of the symmetric mode and anti-symmetric mode, respectively, (e) and (f) show the distribution of the magnitude of the electric field in the backward and forward propagation, respectively, (g) transverse components of the electric field transmitted in the two single mode waveguides, (h) and (i) show the electric magnitude of the cross section labeled in (g).
The asymmetric transmission is caused by the different deformations of cantilever imposed by optical forces between two single-mode waveguides in the two propagation directions. In the backward propagation, the input light is firstly split to two beams propagating in the two arms of MZI, then undergoing completely destructive interference (due to an initial π phase difference) in the cantilever when the wavelength is set at 1550 nm, thus there is no output power. Figure 1(e) shows an example of backward optical field propagation without output power. However, in the forward propagation, the input light will be transferred to two eigenmodes of the two single-mode waveguides, i.e., symmetric mode and anti-symmetric mode, respectively. Figures 1(c) and 1(d) show the mode field distributions of these two super-modes. Then attractive or repulsive optical force will arise [11]. Attractive optical force will be dominant in our scheme, which will be discussed later in this paper. Thus the cantilever will be deformed to get close to the upper arm of the MZI, more light energy will propagate in the upper arm of the MZI, and less propagate in the lower arm, resulting in a partial destructive interference. The output power is not zero as shown in Fig. 1(f). Figure 1(g) shows the coupling light between the two single mode waveguides, and Fig. 1(h) and 1(i) describe the electric magnitude of the cross section labeled in Fig. 1 (g). It should be noted that we ignore the optical force between the cantilever and the two arms of the MZI, because the coupling length (2~3 μm) is too small to induce a distinct deflection in our structure.
We calculate the effective refractive indexes of symmetric and anti-symmetric modes varying with the gap between the two single-mode waveguides, as shown in Fig. 2(a), the insets are zoom-in effective refractive index of the anti-symmetric mode, one can see that the variation of the effective refractive index of the anti-symmetric mode is much smaller than that of the symmetric mode. The optical gradient force is described by [18, 19]
where is the optical force between the two single-mode waveguides, L and d is the coupling length and gap, respectively. neff is the effective refractive index of symmetric mode and anti-symmetric mode. P is the input power. c is the speed of light in vacuum.Fig. 2 (a) Effective refractive index of symmetric mode (red line) and anti-symmetric mode (blue line) in the waveguide dependent on the gap. Inset: Zoom-in display of anti-symmetric mode, (b) Optical force of symmetric mode (red line) and anti-symmetric mode (blue line) dependent on the gap. Inset: Zoom-in display of anti-symmetric mode, (c) Optical force of symmetric and anti-symmetric mode for different wavelengths.
Then we calculate the optical force according to Eq. (1). The optical force as a function of the gap between the two single-mode waveguides is shown in Fig. 2(b), and the inset shows the zoom-in optical force induced by the anti-symmetric mode. One can see that the optical force caused by the anti-symmetric mode is much smaller than the one by the symmetric mode. The effective refractive index and the optical force is dependent on the wavelength of the input light. Therefore we calculate the optical forces of symmetric mode and anti-symmetric mode for different wavelengths, i.e., 1530 nm, 1550 nm and 1625 nm, as shown in Fig. 2(c). One can see that the variation of the optical forces for different wavelengths is very small. Besides, in the forward propagation, most of the power will be transferred to the symmetric mode in our structure according to the simulation by finite-difference time-domain (FDTD) method [20]. Therefore, in an adequate bandwidth, we can neglect the repulsive optical force caused by the anti-symmetric mode and consider that the cantilever will always be attracted to get close to the upper arm of the MZI due to the attractive optical force caused by the symmetric mode.
The deflection is determined by the Euler-Bernoulli beam theory [21]
where u is the deflection, z is the position along the waveguide, A = w1, E = 169GPa stands for the silicon’s Young’s modulus [22].When the wavelength of input light is set to 1550 nm, the maximum deflection of the cantilever is dependent on the power of the symmetric mode which is shown in Fig. 3(a). One can see that the maximum deflection increases with the power, thus the difference of the gaps between the cantilever and the two arms of MZI will be bigger when we increase the power, which will result in a higher forward transmittance. But when we increase the power up to 3.73 mW, the movable end of the cantilever will touch the fixed waveguide, further increasing the power will not increase the maximum deflection which means that the forward transmittance will not be improved. In our simulation, the power of the symmetric mode is set to 3.62 mW, resulting in a maximum deflection of about 45 nm. Figure 3(b) shows the deflection of the waveguide changing with the position along the waveguide.
Fig. 3 (a) The maximum deflection of the cantilever changing with the power of the symmetric mode. (b) Deflection curve of the cantilever waveguide with the power set to 3.62 mW. (c) Forward and backward transmission spectra.
It is always attainable to get a maximum deflection of 45 nm by changing the power of symmetric mode for different wavelengths. Therefore we simulate the transmission with the same structure for different wavelengths without loss of generality (The maximum deflection is 45 nm). The transmission spectra of forward and backward propagation are shown in Fig. 3(c). A distinct asymmetric transmission spectra can be observed. The backward transmittance is suppressed deeply to below −20.5 dB, which means that the device acts as a ‘close door’ state when there is no light coming forward. But the forward transmittance is about −6 dB in conventional (C) and long wavelength (L) band, when light with enough power propagates in the two single-mode waveguides. Thus the device has a route-asymmetric transmission spectra when the forward and backward beams are not present simultaneously.
3. Applications
3.1. All-optical switch
One of the typical applications of route-asymmetric transmission is optical switch. Figure 4(a) shows an example of optical switch, where the schematic is the same as Fig. 1(a) except that a 50:50 coupler is employed at Port 1. The signal light (week signal) is launched from Port 2 (Backward propagation), which is controlled by a strong control light launched from Port 1 (Forward propagation). We simulate the structure by setting the optical wavelength at 1550 nm. When the control light is turned off, the cantilever waveguide is not deformed and locates at the middle of two arms of MZI. Thus the signal light could not reach the output port, resulting in the transmittance of −27.5 dB, as shown in Fig. 4(b). On the contrary, when the control light is turned on, the cantilever gets close to the upper arm of MZI due to optical force. Thus the signal light can arrive at the output port, and the transmittance is −10.3 dB, as shown in Fig. 4(c). We may notice that the response time of our device is tens to hundreds microsecond due to the mechanical vibration effect [13]. Although the response time is relatively low compared with other all-optical switches with silicon photonics [4, 5], our device has a wide bandwidth and a simple fabrication process, which may has special applications in photonic networks with low bitrate routing. Besides, the optical switch here could also act as an all-optical modulator, although the modulation frequency is relatively low compared with other all-optical modulators [23–26], our device is realized with complete silicon photonics.
Fig. 4 (a) The schematic structure of the all-optical switch, as well as an all-optical AND gate. (b) and (c) show the distribution of the magnitude of the electric field when the control light is turned off and turned on, respectively.
3.2. All-optical AND gate
Another application of route-asymmetric transmission is optical logic. Here we demonstrate logic AND gate as an example. As shown in Fig. 4(a), the AND gate function is defined that the light of output port is present if the light of Port 1 and Port 2 is present simultaneously. Setting the optical wavelength at 1550 nm, we simulate the optical field transmission of different states using FDTD method [20], as shown in Fig. 5, where Fig. 5(a) describes the case that Port 1 has no light incidence (‘0’) and Port 2 has incident light (‘1’). One can see there is no light output (‘0’). In this case, the cantilever is not deformed, and the backward light could not propagate along the cantilever. Similarly, Fig. 5(b) describes the case of Port 1 with light incidence and Port 2 without. In this case, the output is zero because backward light does not exit. Figure 5(c) shows the case of light existences at both Port 1 and Port 2. The cantilever is deformed, thus the backward light can arrive at the output port. Table 1 shows the power efficiency of the AND gate. The power of the output port is normalized to the total power launched in Port 1 and Port 2. The power referring to state ‘1’ of Port 1 should be large enough to deform the cantilever. From Table 1, one can see the device can act as an all-optical AND gate.
Fig. 5 The AND gate function described by the distribution of the magnitude of the electric field. The status of the output port is dependent on the status of the input ports, (a) logic signal ‘0’ AND ‘1’ gets ‘0’, (b) logic signal ‘1’ AND ‘0’ gets ‘0’, (c) logic signal ‘1’ AND ‘1’ gets ‘1’.
Table 1. Efficiency of the AND Gate
Conclusion
We have designed a device which has an asymmetric forward and backward transmission when forward and backward beams are not present simultaneously. The device is passive and compatible with CMOS process. Within the scope of a wide bandwidth of 95 nm (C and L band), the forward transmittance is about −6 dB, but the backward transmittance is suppressed below −20.5 dB. Our device has potential applications in highly integrated photonic information processing chip, such as an all-optical switch and an all-optical AND gate.
Acknowledgments
This work was partially supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 201139), the National Natural Science Foundation of China (Grant No. 11174096 and 61475052). The authors thank Li Liu, Mengyuan Ye, Hailong Zhou and Aoling Zheng for helpful discussion.
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