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Abstract
Silicon wire waveguide TE0/TE1 mode conversion Bragg grating can be used in wavelength add/drop and polarization rotation Bragg diffraction. The device can implement many filtering functionalities required in wavelength division multiplexing optical communications. In this paper we describe TE0/TE1 mode conversion Bragg grating device incorporating resonant cavity section to obtain narrow transmission wavelength peak. Theoretical calculation agreed with measured wavelength response.
© 2017 Optical Society of America
1. Introduction
Silicon waveguide technology [1–4] is promising in extending usage of optical technology into ubiquitous applications owing to its compactness and CMOS fabrication process enabling mass production. A very compact device can be obtained by using Si wire waveguide structure which enables steep curved waveguides. For a wavelength division multiplexing (WDM) optical communication, interconnection and optical sensing the wavelength filtering devices are required. A Bragg grating is one of the elements for selecting a wavelength and many types of devices have been implemented using many materials. Silicon is not an exception and many Bragg grating devices have been reported [5–10].
In a most basic form the forward propagating fundamental mode is diffracted into backward propagating fundamental mode with the same polarization which in most cases is the transverse electric (TE) mode. However, devices capable of diffracting a light into different polarization can be implemented using silicon waveguide structure [11–13]. There are also devices that can diffract a light into a mode with different order other than a fundamental mode (TE0) such as the first-order mode (TE1). Several silicon waveguide TE0/TE1 mode conversion Bragg grating were reported which are used in wavelength add/drop device and polarization rotation Bragg diffraction [14–16].
Bragg grating structure can be modified to generate functionalities which cannot be obtained by simple uniform grating structure. These are for example λ/4 shift [17], sampled [18] and super structure gratings [19]. Silicon waveguide λ/4 shift [20,21] and sampled grating [22] devices have been also reported. We have shown that λ/4 shift, sampled and super structure gratings can also be applied to Bragg grating capable of diffracting a light into different polarization [23].
A resonance cavity can be introduced into a Bragg grating to obtain a Fabry-Pérot or ring-resonator type wavelength response [24]. A very narrow transmission wavelength peak can be attained by strong diffraction efficiency even with a compact device. We reported that this type of device structure can be used for polarization rotator Bragg grating [25]. A tailored transmission wavelength peak such as with a flat-top characteristic is attained by double cavity structure. In this report we show a TE0/TE1 mode conversion Bragg grating using resonance cavity structure in Si wire waveguide showing flat-top response. There is only few report [26] on this device which used somewhat bulky thick Si rib waveguide.
This paper is organized as in the following. First we explain the basic device structure. Then the device operation is described using the transfer matrix method. We explain single and double cavity device structures. The experimental results are shown in the next section. We also propose a grating structure using a photonic crystal type to achieve very high diffraction efficiency. The paper is concluded with a summery.
2. TE0/TE1 mode conversion grating
The device structure is shown in Fig. 1. Figure 1(a) shows the basic device structure composed of one pair of mode conversion grating and a resonator cavity section where there is no grating. The basic structure shown in Fig. 1(a) can be connected to obtain a cascaded multiple resonator cavity structure shown in Fig. 1(b). The wavelength response of the multiple resonator cavity device can be changed from that of the single resonator cavity as will be shown.
Fig. 1 Device structure of TE0/TE1 mode conversion Bragg grating with resonator cavity section. (a) Single cavity and (b) double cavity structures are shown.
2.1 Analysis of device operation using transfer matrix
The device characteristics can be explained using transfer matrix. The transfer matrix is shown in Eqs. (1)-(4). The transfer matrices of the mode conversion grating [E] and resonator cavity [ϕ] are used to describe the total wavelength response of the device.
The forward propagating modes for the two modes t0(z), t1(z) and modes propagated in opposite direction r0(z), r1(z) are considered at end of the device with distance z. The two by two sub-matrix elements in the upper left corner of the matrix show diffraction of the fundamental to the first order modes. The two by two sub-matrix elements in the lower right corner show diffraction of the first order to the fundamental modes. The matrix elements are shown with ζ being the grating length, K the polarization rotation diffraction coupling coefficient and α the loss of the grating. The detuning is δ = β-βB and μ2 = K2 + (jδ -α/2)2. The propagation constant is β = π(N0 + N1)/λ where N0 and N1 are effective indices for the fundamental and the first-order modes respectively. The βB is related to Bragg wavelength as λB = π(N0B + N1B)/βB where N0B and N1B are effective indices for the fundamental and the first-order modes at Bragg wavelength respectively. The fundamental and the first-order mode phase effects introduced in the cavity section are given by c and c1, respectively, with k being the light wavenumber, αp0,1 the fundamental, the first-order mode propagation loss, and L is the cavity section length.
We assumed an ideal mode converter grating meaning that the diffraction to the counter propagating mode with the same order and conversion into the co-propagating mode are ignored. Equation (1) is similar to that for the polarization rotation grating [23].
The diffracted light r0(0), r1(0) and transmitted light t0(z), t1(z) are derived by putting all other components equal to zero except t0(0) = 1 or t1(0) = 1. The final results for the reflection and transmission derived from Eqs. (1)-(4) are as in Eqs. (5) and (6).
Using β = δ + βB the phase term can be written as k(N0 + N1)L = (δ + βB)L = δL + 2πL/Λ where Λ is the grating period.
2.2 Device operation of cascaded two resonators
The transfer matrix for device with cascaded two resonators is as in Eqs. (7)-(9). The amount of diffraction in the middle Bragg grating is assumed to be different from the others. The middle grating length can be different from the gratings placed at both ends in the simplest case, so that we define a’ and b’ as in Eq. (9) with ζ’ being the length of the middle grating.
The wavelength responses calculated using Eq. (6) and Eqs. (7)-(9) are shown in Fig. 2(a) and (b), respectively. We use 200 nm Si core thickness in the foundry and a device with this thickness is assumed. The detuning δ is related to the wavelength as λ = λB + λ2δ/π/(ng0 + ng1) in Fig. 2. The effective refractive indices were N0 = 2.6 and N1 = 2.1 for 850 nm wide waveguide at 1570 nm wavelength for the TE0 and TE1 modes, respectively. Relatively wide waveguide was selected to attain strong confinement for the TE1 mode and reduce the effect of width error. The width w dependence is dN0/dw = 3.4x10−4 nm−1 and dN1/dw = 1.5 x10−3 nm−1 for the TE0 and TE1 modes, respectively. The peak wavelength shift due to the 1σ width error will be contained in the peak width with the foundry’s capability [27]. The waveguide group indices we used for the TE0 and TE1 modes were ng0 = 3.86 and ng1 = 3.66, respectively. The resonator cavity and grating section lengths were 80Λ and 150Λ with grating period of Λ = λ/(N0 + N1) = 334 nm, respectively. Coupling coefficient of K = 0.027μm−1 is used in the calculation which is the value we could obtain in the real device. A grating section propagation loss α of 1 dB/mm is used.
Fig. 2 Calculated wavelength response of the device for (a) single and (b) double cavity structures using Eq. (6) and Eqs. (7)-(9) respectively.
The transmission maximum condition can be derived considering the phase component c and c1 in Eq. (6) as k(N0 + N1)L = (2m + 1)π for integer m when there is no loss. According to multiple m values multiple peaks are generated. The free spectral range between peaks is ΔλF = λB2/[L(ng0 + ng1)] with L being the resonator cavity length. The stop band width ΔλSB of sufficiently long grating is 2λB2K/[π(ng0 + ng1)] and the maximum number of the peaks becomes ΔλSB/ΔλF + 1 = 2LK/π + 1.
For the double cavity device the middle grating length was adjusted to obtain good flat-top response. The wavelength responses calculated using Eqs. (7)-(9) for different middle grating lengths are shown in Fig. 3. The length ratios of 1.0, 1.6 and 2.0 between gratings placed at middle and edge (each end) are shown for an example. Results for 0.15 and 0.5 dB/mm grating section propagation losses are shown. By using the middle/edge grating lengths ratio of 1.6 a good flat-top response is obtained irrespective of the propagation loss. We chose this length ratio in Fig. 2(b) and in the experiment.
Fig. 3 Calculated wavelength response of the device showing dependence on middle to edge grating lengths ratio for (a) 1.5 and (b) 5 dB/cm propagation losses, respectively using Eqs. (7)-(9).
3. Experiment
The devices were fabricated on silicon on insulator (SOI) wafer with 200 nm thick Si layer which is the standard thickness of the foundry. In the device fabrication, the ArF-immersion lithography was used for photo resist patterning. The waveguide was formed using RIE (reactive ion etching) method. The upper clad SiO2 was deposited using chemical vapor deposition (CVD). The device design is the same as described in previous sections on theory and Fig. 1 except for the grating period which was Λ = 343 nm in the experiment. The middle/edge grating ratio of 1.6 was used. The scanning electron microscopy photograph of the test grating is shown in Fig. 4(a). The right angle corners of the grating teeth are rounded by limitation of the fabrication resolution. The rounding of the corner lowers the grating diffraction efficiency. The grating diffraction efficiency of the fabricated device could be matched with the result of three-dimensional finite difference time domain (3D-FDTD) simulation when sinusoidal grating was used in the model.
Fig. 4 Experimental aspects: (a) scanning electron microscopy (SEM) photograph of test grating and (b) measurement setup for device characterization.
The measurement setup for device characterization is shown in Fig. 4(b). The wavelength response of the device was measured using super luminescent diode (SLD) as a white light source and optical spectrum analyzer. The fibers with lensed end are used. The spot size converters (SSC) with inverse width taper are used as at the waveguide facets. The measured response was obtained as an excess loss against the 480 nm wide reference waveguide with the same length and shown in Fig. 5. The propagation loss of the reference waveguide was 1.5 dB/cm.
A single transmission peak appeared in a stop band for both the single and double cavity devices. The peak width of 0.5 nm was attained. Flat-top response and steep peak slope were attained for the double cavity device as expected. The losses were 2.5 dB and 3 dB for the single and double cavity devices respectively. The ripple in the flat-top peak was 0.6 dB. Introducing apodization will improve the wavelength response but it’s not used in this experiment.
4. Grating structure for strong diffraction
The stop band width of the Bragg grating where the transmission wavelength peaks reside is proportional to the diffraction strength of the grating. To attain wide useable wavelength range a grating with very strong diffraction is required. We found that a very strong diffraction can be attained using a grating structure using a hole pierced through the Si layer resembling photonic crystal. The device structure is shown in Fig. 6. To control the diffraction efficiency of the hole grating, it can be partially occupied by Si in depth direction.
A 3D-FDTD simulation was used to calculate the device’s wavelength response. The simulated wavelength response is shown in Fig. 7. The waveguide width and thickness are 1 μm and 200 nm, respectively. The effective refractive indices were N0 = 2.7 and N1 = 2.3 for the TE0 and TE1 modes, respectively. The waveguide group indices for the TE0 and TE1 modes were ng0 = 3.81 and ng1 = 4.29, respectively. The hole diameter and depth are 120 nm and 70 nm, respectively. The center spacing between holes in the width direction is 500 nm. The resonator cavity length is 25Λ. Each grating section is 40Λ long and the device has total length of 105Λ. The period of holes is Λ = 308 nm. The 3D-FDTD results shows that the coupling coefficient of K = 0.18 μm−1 is obtained which is 6.7 times stronger than that obtained by conventional tooth type grating. The stop band width is proportional to the coupling coefficient and wide 33 nm stop band is observed in Fig. 7.
The circular shaped grating can be reliably fabricated with good reproducibility and has strong diffraction. The loss and unwanted diffraction induced at the edge of the grating section can be lowered by decreasing the hole depth.
A sidewall grating with deep teeth can also be used to attain strong diffraction. In this structure we found from 3D-FDTD simulations that apodization of the grating is required to obtain low loss. By gradually increasing the corrugation depth from the edge to the center of the grating section was able to suppress the loss generated at the edge of the grating section. Using teeth depth of 250 nm placed at sidewalls of the 850 nm wide waveguide a 100 nm wide stop band could be obtained in the simulation. An extinction ratio of 30 dB was obtained by using grating length of 35 periods with raised cosine type apodization.
5. Summary
We have reported TE0/TE1 mode conversion Bragg grating device incorporating resonant cavity section to obtain narrow transmission wavelength peak. The mode conversion Bragg grating can be used in many type of wavelength selective devices such as a wavelength add/drop and polarization rotator. Very narrow transmission peak is obtained in the stop band using resonant cavity section with compact device. We analyzed the device characteristics using transfer matrix method. Experimental device was fabricated using SOI wafer and immersion ArF lithography. The measured wavelength response agreed with the theoretical calculation. Peak width of 0.5 nm and flat-top response were obtained. The flatness of the top was 0.6 dB. A very strong diffraction is achieved by using photonic crystal type hole shaped grating so that very compact device and wide stop band is attained.
Funding
New Energy and Industrial Technology Development Organization (NEDO).
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