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Silicon optical diode based on cascaded photonic crystal cavities Yong Zhang,1 Danping Li,1 Cheng Zeng,1 Zengzhi Huang,1 Yi Wang,1 Qingzhong Huang,1 Ying Wu,2 Jinzhong Yu,1,3 and Jinsong Xia1,* 1
Wuhan National Laboratory for Optoelectronics and School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China 2
3
School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
Optoelectronic System Laboratory, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China *Corresponding author:
[email protected] Received October 3, 2013; revised December 20, 2013; accepted January 15, 2014; posted January 24, 2014 (Doc. ID 198225); published March 5, 2014 An all-silicon passive optical diode based on optical nonlinearity in cascaded photonic crystal (PhC) L3 cavities is proposed and demonstrated. A nonreciprocal transmission ratio (NTR) of 30.8 dB and insertion loss of 8.3 dB are realized in the device. The device has a relatively broad 17 dB operation bandwidth of 0.08 nm, and at least 16 dB of NTR is achieved when input power varies between −6.25 and −2.95 dBm. A nonlinear couple mode model for cascaded PhC cavities is established to analyze the behavior of the device, and numerical simulation results are in good agreement with the experiment results. © 2014 Optical Society of America OCIS codes: (230.3120) Integrated optics devices; (230.5298) Photonic crystals; (230.4320) Nonlinear optical devices. http://dx.doi.org/10.1364/OL.39.001370
Optical nonreciprocal transmission is fundamental to realize optical diodes, isolators, and circulators and is in great demand in all-optical signal processing systems. For a device to be an isolator it must block or divert all possible states for backward propagation [1]. However, it is still a large challenge to break Lorentz reciprocity and realize on-chip devices due to material integration and structure design. Numerous efforts have been made to solve this problem, including devices based on magneto-optic effect [2], nonlinear materials [3], and time-dependent refractive index [4] and so on. These approaches either are not compatible with complementary metal-oxide semiconductor (CMOS) processes or are complex in devices design and fabrication process. Fan et al. proposed and fabricated an all-silicon passive optical diode based on optical nonlinearity in cascaded high Q silicon microrings [5,6]. A high nonreciprocal transmission ratio (NTR) of 40 dB was realized in their device [7]. However, the device needs two microrings with identical resonant wavelengths; thus precise thermal tuning was required to compensate the resonances mismatch introduced in fabrication. Mu et al. demonstrated an optical nonreciprocal transmission system based on cascaded silicon microrings [8]. The devices operated under resonance mismatch condition. An NTR of 27 dB was realized at input power of 8.2 dBm. The operating power was relatively high due to the low Q and large mode volume of the microrings. The optical characteristics and loss mechanism of a photonic crystal (PhC) cavity was investigated in 2003 [9]. From that, the performance of PhC cavities has been improved greatly. Various high-Q, ultra-high-Q, and small mode volume PhC cavities were demonstrated [10,11]. Because of the strong optical confinement in high-Q PhC cavities with small mode volume, light-matter interaction was dramatically enhanced. PhC cavities have various applications, including thresholdless lasers [12], light emitting diodes [13], enhancing optical nonlinear effect [14], and so on. 0146-9592/14/061370-04$15.00/0
In this Letter, we demonstrate an all-silicon passive optical diode based on optical nonlinearity in cascaded PhC L3 cavities, which consists of a PhC membrane with a line of three holes missing. The device operates under resonance mismatch condition. Because of small mode volume of PhC L3 cavities, the operation power of the device is much lower than microring-based systems. The operation power is 8.2 dBm for systems based on cascaded resonance mismatch microrings. The proposed all-silicon optical diode is based on strong optical nonlinearity in high-Q PhC L3 cavities with small mode volume. It consists of two cascaded PhC L3 cavities coupling with a PhC waveguide; the scanning electron microscope (SEM) image of the fabricated optical diode is shown in Fig. 1(a). The footprint of the whole device is about 20 μm 10 μm. In the experiment, electron beam lithography (Vistec EBPG 5000 plus) and inductively coupled plasma etching are used to define patterns on a silicon-on-insulator (SOI) wafer (220 nm thick silicon on 3000 nm thick silica). The lattice constant is 420 nm, and the hole radius is 126 nm. The positions of
Fig. 1. (a) SEM image of fabricated optical diode. Red oval represents the strong nonlinearity effect region for forward transmission, blue oval represents the strong nonlinearity effect region for backward transmission. (b) Magnified micrograph of L3 cavity. The three holes adjacent to the cavity are laterally shifted by 0.175, 0.025, and 0.175 a, respectively, indicated by green arrows. (c) Ey profile for fundamental mode supported by L3 cavity calculated by 3D FDTD. © 2014 Optical Society of America
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the three holes adjacent to the cavities are optimized to obtain high Q factors [15]. The device is processed by diluted hydrofluoric acid solution to form the freestanding device. Figure 1(b) shows the magnified micrograph of the L3 cavity. Grating couplers are fabricated to couple TE polarization light in and out of the PhC waveguide with a fiber-chip-fiber loss of 13.7 dB at 1540 nm. All values of input power in this Letter are defined as the power coupled into the PhC waveguide, which is derived from output power of the tunable laser and coupling efficiency of grating couplers. The resonant wavelengths of fabricated two cascaded L3 cavities do not match exactly due to the process variation in nanofabrication. The detuning between the two resonances is Δλ λL − λR > 0, where λL and λR are the resonant wavelengths of the left and the right L3 cavities in Fig. 1(a), respectively. Light entering from Port I and exiting Port II is designated as forward transmission while light entering Port II and exiting Port I is designated as backward transmission. The forward and backward transmission spectra of cascaded PhC L3 cavities at input power of −27.6 dBm are shown in Fig. 2(a). The spectra show two dips corresponding to the resonances of the two cavities. At such low power, the dips are symmetric, and forward and backward transmission spectra are identical, indicating that the two L3 cavities are both working in the linear regime. The resonant wavelengths of the left and right cavities are 1540.76 and 1540.61 nm, respectively. The detuning Δλ is 0.15 nm. As input power increases, the resonance dips redshift due to the onset of nonlinearity induced by the thermooptic effect in the silicon cavity. As shown in Fig. 2(b), red and blue curves represent forward and backward transmission spectra of the device at input power of −7.0 dBm, respectively. The black curve shows transmission spectrum at input power of −27.6 dBm in the linear regime for comparison. Obviously, an NTR of 12.6 dB, which is defined as the contrast of transmitted optical power between forward and backward transmission, is observed at λ0 1540.76 nm. In the forward transmission, input light at λ0 is coupled into the left cavity (λL ) first. However, optical energy coupling into the left cavity is decreased by the redshift of λL induced by the
Fig. 2. Experimental forward and backward transmission spectra of the device at input powers of (a) −27.6 dBm. (b) −7.0 dBm. (c) −5.0 dBm.
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nonlinearity in the cavity, thus allowing the light to pass the left cavity with low attenuation. When the attenuated light reaches the right cavity (λR ), the coupling between the right cavity and PhC waveguide is weak because input light λ0 is far from λR . The coupling is increased by the redshift of λR induced by nonlinearity. However, the redshift is small since the light in the PhC waveguide is already attenuated by the left cavity. Thus, the light can pass the right cavity with low attenuation and achieve relatively high overall transmission. In the backward transmission, input light at λ0 from port II is coupled into the right cavity first. Since there is no attenuation before the light reaches the right cavity, the light intensity coupled into the right cavity will be relative higher comparing with forward transmission. Therefore, the redshift of λR is larger and the detuning between right cavity resonance and λ0 becomes smaller. Thus, the coupling is relatively stronger, leading to high attenuation. When the light reaches the left cavity, the redshift of λL is very small since the light is greatly attenuated by the right cavity. Therefore, the detuning between left cavity resonance and λ0 is small and the coupling is strong, leading to high attenuation. Thus, the overall transmission is significantly smaller comparing with forward transmission. As shown in Fig. 2(c), red and blue curves represent forward and backward transmission spectra of the device at input power of −5.0 dBm, respectively. An NTR of 30.8 dB is obtained at 1540.76 nm. In the forward transmission, input light at λ0 from port I is coupled into the left cavity (λL ) first. Left resonance redshifts due to the onset of nonlinearity through the thermo-optic effect of silicon, and a sharp rise is observed on the longer wavelength side of the left cavity dip. The slope of transmission waveform on the shorter wavelength side of left cavity dip decreases continually, which is an evidence of the bistable behavior in the cavity [16,17]. Input light passes the left cavity with low attenuation. The redshift of right cavity resonance is bigger than that at input power of −7.0 dBm. However, the right cavity resonance is still much shorter than λ0 . Input light can also pass the right cavity with low attenuation. In the backward transmission, the redshift of right cavity resonance is big due to high input power. It is a positive feedback between optical energy coupled into the right cavity and the redshift of resonant wavelength. The resonant wavelength of the right cavity moves close to λ0 . Therefore, the light passes the right cavity with large attenuation. When the light reaches the left cavity, it will be attenuated again by the strong coupling with the left cavity; thus the overall transmission is significantly reduced by both the right cavity and the left cavity. Figure 3(a) shows transmitted power for forward and backward transmission at various input powers at 1540.76 nm. Figure 3(b) shows NTR and insertion loss at various input powers at 1540.76 nm. Insertion loss is defined as the ratio between input power and forward transmitted power. As shown in Fig. 3, the NTR reaches a maximum value of 30.8 dB. At input power of −5.0 dBm in backward transmission, the right cavity resonance is redshifted close to 1540.76 nm, which is the resonant wavelength of left cavity. The light is significantly attenuated by both the right cavity and left cavity. When input power is smaller or bigger than −5.0 dBm, redshifted
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fabricated a titanium micro-heater around the diode to work across a large wavelength band [5]. We use nonlinear light propagation equations derived from coupled-mode theory to analyze operation principle of the proposed structure. Let us consider forward transmission first. Linear coupled mode equations at steady state for the two cavities are given by [19] Fig. 3. (a) Experimental transmitted power for forward and backward transmission at various input powers at 1540.76 nm. (b) NTR and insertion loss at various input powers at 1540.76 nm experimentally.
s ss 1 1 1 a jωL aL jωL − s a ; τtotal;L L τin;L 1 τin;L τin;R R
1
(1) resonant wavelength of the right cavity moves away from 1540.76 nm. The power reduction due to the right cavity decreases. The forward transmitted signal is weak with only −13 dBm at input power of −5.0 dBm. Optimizing the detuning between the two resonances to decrease insertion loss and decreasing the Q factor of L3 cavities to increase operation power can be adopted to increase the forward transmitted signal. As shown in Fig. 3(b), at least 16 dB of NTR is obtained at input power between −6.25 dBm and −2.95 dBm. The insertion loss is 8.3 dB at input power of −5.0 dBm, and decreases to 6.3 dB at input power of −2.95 dBm. The insertion loss of the device is much lower than previous reports [5,7,18]. The decrease of insertion loss is mainly due to much slower drop on the shorter wavelength side of the left cavity resonance for forward transmission, as shown in Fig. 2(c). The forward and backward transmitted spectra of the device at a fixed input power of −5.0 dBm at various input wavelengths are shown in Fig. 4. We fix the power and wavelength of tunable laser, the input light from tunable laser transmits the device, and then the transmitted power is recorded and characterized by an optical spectrum analyzer (OSA) with a resolution of 0.02 nm. The symbols in Fig. 4 are the data points recorded by OSA. The FWHM of transmitted spectrum is nearly 0.02 nm due to the limited resolution of OSA. The maximum NTR about 30.8 dB was obtained at 1540.76 nm, and an NTR larger than 17 dB is obtained between 1540.72 and 1540.80 nm. Similar to all resonance-enhanced optical devices, the operation bandwidth of the proposed optical diode is limited by the bandwidth of the resonant cavity. Its operation wavelength can be tuned by
jωR aR jωR −
τtotal;R
s ss 1 1 1 aR s1 − a ; τin;R τin;L τin;R L (2)
where aL and aR are the complex amplitude of light propagating in the left and right L3 cavities, which are normalized by letting jaL j2 and jaR j2 equal the mode energy, respectively. ωL and ωR are resonant angular frequency of the left and right L3 cavities at extremely low input power, respectively. 1∕τtotal;L and 1∕τtotal;R are the total decay rate of the left and right L3 cavities, respectively. 1∕τin;L and 1∕τin;R are the rate of decay into bus waveguide of the left and right L3 cavities, respectively. S 1 is the complex amplitude of input light in the PhC waveguide. Because of high Q factor, long resonant photon lifetimes and small mode volume of silicon PhC cavity, stored electromagnetic energy density could be extremely large in the cavity. Various nonlinear behaviors may occur in the cavity, including two-photon absorption, free-carrier absorption, thermo-optic effect, plasma dispersion effect, and Kerr effect. In addition, linear absorption of “cold nanocavity” (as opposed to radiation in “cold nanocavity”) should be also considered in our analysis. Under nonlinear condition, resonant angular frequency of the cavities would be ω0 ω Δωthermal Δωplasma Δωkerr ;
(3)
where Δωthermal , Δωplasma , Δωkerr are the shifts of resonant angular frequency, due to thermo-optic effect, plasma dispersion effect and Kerr effect, respectively. Total energy decay rates would be, 1 τtotal
Fig. 4. Experimental forward and backward transmitted spectra at various input wavelengths. The wavelength of input light is fixed for each curve. The curves with solid symbols represent forward transmitted spectra; curves with open symbols represent backward transmitted spectra.
1
1 1 1 1 1 ; τv τin τlin τTPA τFCA
(4)
where 1∕τv is the rate of decay into free space (vertical direction). 1∕τlin , 1∕τTPA , and 1∕τFCA are decay rates of linear absorption of “cold nanocavity,” TPA, and FCA, respectively. Detailed nonlinear effects formulas and physical parameters are given by [14,20]. Similarly, nonlinear light propagation equations for backward transmission can also be established. Using the nonlinear couple mode model established above,
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cascaded PhC cavities is established to analyze the behavior of the device. Simulation results show good agreement with our experiment results. The demonstrated optical diode has potential for on chip all-optical signal processing, and has advantages of simple design, easy fabrication process, compact footprint, high NTR and low operation power.
Fig. 5. Calculated forward and backward transmission spectra of the device at various input powers of (a) −27.6 dBm. (b) −6.8 dBm. (c) −4.1 dBm.
we can derive forward and backward transmission spectra of the proposed device at various input powers. In the simulation, at very low input power, the resonant wavelengths of the two cavities are 1540.76 and 1540.61 nm, respectively. The two cavities have identical Q factors and extinction ratios, which are 9000 and 21 dB, respectively. As shown in Fig. 5(a), red and blue curves represent calculated forward and backward transmission spectra of the proposed device at input power of −27.6 dBm, respectively. Obviously, forward and backward transmission spectra are identical. The black curve shows the experimental forward transmission spectrum at input power of −27.6 dBm. Calculated transmission spectra are in good agreement with experiment results. Figure 5(b) shows calculated transmission spectra of the device at input power of −6.8 dBm. As input power increases, the distance between the two resonances becomes bigger for forward transmission and becomes smaller for backward transmission. An NTR of 9.0 dB is observed at 1540.76 nm. When input power increases to −4.1 dBm, calculated transmission spectra are quite different, as shown in Fig. 5(c). For forward transmission, the distance between the two resonances becomes even bigger. For backward transmission, redshifted resonant wavelength of the right cavity moves closely to the resonant wavelength (λL ) of the left cavity. Thus, backward transmission at 1540.76 nm is significantly reduced by both the right cavity and left cavity. A calculated NTR of 31.3 dB is in good agreement with the experiment results, indicating that nonlinear coupled mode model for cascaded PhC cavities established above can simulate the behavior of the proposed diode structure effectively. In conclusion, we demonstrate an all-silicon passive optical diode based on optical nonlinearity in cascaded PhC L3 cavities. An NTR of 30.8 dB and insertion loss of 8.3 dB are realized. An NTR larger than 17 dB is achieved between 1540.72 and 1540.80 nm, and an NTR larger than 16 dB is obtained when input power varies between −6.25 and −2.95 dBm. Nonlinear couple mode model for
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