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Abstract
We propose a double-stage guided-mode converter for pillar photonic-crystal (PhC) waveguide devices. The converter consists of a pillar-to-wire waveguide coupler and a transverse-magnetic-mode-selective spot-size converter. The former secures high-efficiency wide-band optical coupling of a pillar-PhC waveguide to a wire waveguide. The latter improves the coupling efficiency of the wire waveguide and an outside waveguide such as an optical fiber and also the signal-to-noise ratio of light guided in the pillar-PhC waveguide. The transmission band of a fabricated pillar-PhC waveguide having the converters on both ends was 88 nm in wavelength. The cutoff at the band edge was steep and deep with an extinction ration of 40 dB in a 4-nm wavelength range.
© 2017 Optical Society of America
1. Introduction
During the past decade, optical circuit integration based on silicon (Si) wire waveguides has attracted much attention because it enables drastic miniaturization of optical-circuit devices. For 25-Gbps optical transmitters, large bandwidths, small power consumptions, and high packing densities were achieved [1,2]. Increasing demands for data communication are, however, urging us to pursue even higher levels of these indices [3]. Instead of introducing new materials or elaborating totally novel devices, a simpler solution would be to introduce new functional waveguides with enhanced optical properties. Two-dimensional (2D) pillar photonic-crystal (PhC) waveguides stand among such waveguides [4–6], with which a lot of compact and miniaturized waveguide devices have been proposed. Most of them were designed by taking advantage of slow-light properties in addition to zero-radius bends of line-defect waveguides [7–11]. Sometimes, defect cavities with high quality-(Q)-factors were combined [12,13].
As far as device application is concerned, hole-PhC waveguides have been more intensely investigated than pillar-PhC waveguides [14], since compatibility of hole-PhC waveguides with conventional Si wire waveguides was higher [15]. However, most research efforts were made mainly on high-Q cavities and phase shifters [16–27], and light guiding along integrated optical circuits has been left in the charge of Si wire waveguides. This is because bends of hole-PhC waveguides are inherently of narrow transmission-bands, requiring fine topological modifications [28–30]. Hence applications of hole-PhC waveguides tend to be limited to non-circuit ones of enhanced slow-light properties or Q-factors, although their excessive enhancement would lead to undesirable backscattering in optical circuits [31]. On the other hand, pillar-PhC waveguide bends, especially those of square lattices, can exhibit high transmission in wide bands [32]. Pillar-PhC waveguides are, therefore, drawing attention again to promote overall miniaturization of optical integrated circuit devices, as tried in Ref [33].
Prior to implementing pillar-PhC waveguide devices, the optical loss of pillar-PhC waveguides should be small. Fortunately, the propagation loss of waveguides can be decreased thanks to continuous advances in Si-based fabrication technologies such as CMOS and micro electro mechanical systems (MEMS). In addition, pillar-PhC-waveguide amplifiers may be used to recover optical losses of devices, since slow light can efficiently interact with the constituent materials of pillar PhCs [34,35]. The remaining problem is to establish efficient optical coupling to pillar-PhC waveguides, where a pillar-to-wire waveguide (PWWG) coupler between pillar-PhC and wire waveguides plays an important role. Theoretically, long PWWG couplers based on adiabatic transition appear to be the simplest and most reliable structures from the view point of wide coupling bands [36–39]. In practice, however, it is difficult to experimentally show their potential performance, because of the limited lengths of couplers and the limited critical dimensions of fabrication processes used [40]. To solve this dilemma, the authors previously developed a semi-adiabatic PWWG coupler. In Ref [41], it has been reported that a semi-adiabatic PWWG coupler exhibited a high coupling efficiency in a wide band in both a three-dimensional simulation and an experiment. In the literature, they also demonstrated excellent experimental performances of directional couplers and Mach-Zehnder interferometers (MZIs) of pillar-PhC waveguides equipped with their couplers. However, details of the working mechanism and the method of design optimization of the coupler are still to be revealed.
Recently, we found that, in experiments, input of pure transverse-magnetic-(TM)-mode light is very important for proper operation of pillar-PhC-waveguide circuits, even if they are equipped with the semi-adiabatic PWWG coupler. In this paper, we propose a double-stage guided-mode converter comprised of the PWWG coupler and a TM-mode-selective spot-size converter (SSC), as a complete form of optical coupling device for pure-TM-mode guiding in a pillar-PhC waveguide. The TM-mode-selective SSC improves the signal-to-noise-(S/N) ratio of light transmitted to a pillar-PhC waveguide. In the following section, we present detailed designs and functions of the individual components of the double-stage guided-mode converter for the first time. We explain a problem that we noticed about light guiding in pillar-PhC waveguides and also how the TM-mode-selective SSC in the double-stage converter helps to solve the problem. For experiments, we describe the fabrication process of the double-stage converter, which includes our original process for forming vertical Si tapers. The effect of the double-stage converter on pure TM-mode guiding in a pillar-PhC waveguide is experimentally demonstrated with a transmission result of a pillar-PhC waveguide equipped with the converters. The cutoff of a pillar-PhC waveguide we observed is the steepest and deepest among ever reported.
2. Designs and functions
The double-stage guided-mode converter consists of a semi-adiabatic PWWG coupler and a TM-mode-selective SSC, as shown in Fig. 1. In the following subsections, first the PWWG coupler is described in detail, and next, explanation of problems and requirements for improvement is provided. Then the SSC added as a new component is described.
Fig. 1 Schematic illustration of double-stage guided-mode converter comprised of semi-adiabatic pillar-to-wire waveguide (PWWG) coupler and transverse-magnetic-(TM)-mode-selective spot-size converter (SSC) between pillar photonic-crystal-(PhC) waveguide and outside waveguide such as optical fiber.
2.1 Semi-adiabatic pillar-to-wire waveguide coupler
Guided light in a pillar-PhC waveguide is a Bloch-wave beam, which can be decomposed into light beams with different wave-vectors in the guiding direction. On the other hand, guided light in an input/output waveguide coupled to the pillar-PhC waveguide is usually a non-Bloch-wave beam with a single wave-vector. The role of a PWWG coupler is to convert a Bloch-wave beam to a non-Bloch-wave beam, and vice versa. A PWWG coupler is desired to be adiabatic but compact to work in a wide wavelength range at a small propagation loss. A velocity coupler, in which two oppositely tapered waveguides are laid out side by side, is known as a waveguide coupler of those characteristics. We introduced it to our PWWG coupler by adjacently disposing line defects with graded diameters and a horizontally tapered wire-waveguide. Figure 2(a) shows a schematic of our PWWG coupler illustrating individual functional regions contained in it. In the joint region labeled “Joint,” the single line of defect pillars of a pillar-PhC waveguide from the left is branched into two parallel lines with a T-shaped branch and 90°-bends. In the region labeled “Taper 1”, a wire waveguide (more precisely, wire-waveguide core) is inserted between the two lines of defect pillars to form a velocity coupler, in which light energy is transferred between the defect lines and the wire-waveguide core. In the region labeled “Taper 2”, pillars on both sides of the wire-waveguide core deviate from the core as they go to the right. Taper 2 converts guided light from a Bloch wave to a non-Bloch wave, and vice versa. Figure 2(b) shows a more detailed illustration of the coupler. Note that, in Fig. 2(b), the diameters of the defect pillars in the velocity-coupler region, which corresponds to Taper 1 in Fig. 2(a), gradually increase as they go to the right up to the diameter of the non-defect pillars.
Fig. 2 (a) Schematic and (b) more detailed illustration of semi-adiabatic PWWG coupler for coupling pillar-PhC and wire waveguides. Main parts are in yellow (PhC pillars), green (line-defect pillars), red (branch and bends of line-defect pillars), blue (line-defect pillars in Taper 1), and purple (wire-waveguide core in Taper 1, Taper 2, and outside of coupler). (c) Snapshot of electric-field distribution of light propagating through two-dimensional-(2D) coupler. Field is superimposed on line drawing of coupler, and is normalized between –1 (blue) and 1 (red).
We calculated the electric-field distribution of guided light propagating through a coupler by carrying out a 2D finite-difference time-domain (FDTD) simulation. Figure 2(c) shows a snapshot of the electric-field distribution, which is superimposed on a line drawing of the coupler. In the 2D simulation model, the refractive index of pillars np and that of the surrounding material ns were set to 3.480 and 1.442, respectively. The lattice constant a was 0.40 µm. The diameters of the non-defect pillars D and that of the defect pillars Dd were 0.24 µm (D/a = 0.600) and 0.160 µm (Dd/a = 0.400), respectively. The tip width of the inserted wire-waveguide core wtip was set to 0.080 µm (wtip/a = 0.200), and the width of the core was gradually increased as it went to the right to be larger than that of the single-mode wire-waveguide wch = 0.110 µm (wch/a = 0.275). The grid size of the model was a/8. In Fig. 2(c), the TM-polarized light, for which the electric field is parallel to the pillars, at a wavelength of 1680 nm was input from the wire waveguide on the right-hand side. As confirmed in Fig. 2(c), no resonance occurred in the joint region, although it was an abrupt structure. This is because the joint region consisted of a high-efficiency wide-band T-shaped branch and 90° bends of the pillar-PhC waveguide [32].
All parts of the coupler must have guided modes that overlap each other in wavelength (or frequency) for smooth energy transfer of electromagnetic wave of light through the coupler. We calculated the dispersion relations of modes for the individual parts, except the joint region, as shown in Figs. 3(a)–3(e). The plane-wave-expansion method was used for the calculation. Note that the lower horizontal scales of the figures are written in wavelength instead of frequency to finally align with that of the transmission spectrum shown in Fig. 3(f). The gray areas in Figs. 3(b)–3(e) denote the continua of extended modes of the bulk pillar-PhC. According to Fig. 3(e), the photonic band gap (PBG) of the pillar PhC ranged from 1496 to 1767 nm, and the guided mode of the pillar-PhC waveguide ranged from 1591 to 2090 nm. By eliminating the range outside the PBG, the effective guided mode was within the range from 1591 to 1767 nm. As shown in Fig. 3(d), there were three guided modes labeled “1”, “2”, and “3” for Taper 1 (the velocity coupler region). Note that the whole structure comprised of the wire-waveguide core and the adjacent defect pillars works as a waveguide core of Taper 1, which is too wide to maintain single-mode guiding. Fortunately, only the lowest mode 1 can be excited due to its symmetry. It is, thus, confirmed that the guided modes of all the consecutive parts of the coupler cover the effective guided mode of the pillar-PhC waveguide.
Fig. 3 Dispersion-relation diagrams of (a) wire waveguide, (b) and (c) Taper 2 at two different positions, (d) Taper 1 at one position, and (e) line-defect waveguide, all of which are contained in 2D semi-adiabatic PWWG coupler shown in Fig. 2(c). Specific waveguide structure of each part is illustrated on right-hand side of its diagram. Excited guided modes are indicated with bold black curves. Gray areas denote continua of extended modes of bulk pillar-PhC. (f) Transmission spectrum calculated for entire PWWG coupler.
Figure 3(f) shows the transmission spectrum of the entire PWWG coupler. The spectrum includes those of the effective guided mode of the line-defect waveguide and the extended mode of the bulk pillar-PhC. In Fig. 3(f), the extinction ratio of the transmittance around the cutoff wavelength of 1591 nm was over 60 dB, which is large enough for applications such as wavelength filters, optical power modulators, and on/off switches. Note the notch at 1713 nm in the spectrum; carrying out an FDTD simulation, we verified that resonance occurred in the joint region of the coupler at this wavelength. Our further investigation revealed that this notch can be shifted to the longer wavelength side by narrowing the tip of the inserted wire-waveguide core. Also, the notch depth can be reduced by starting the pillar deviation immediately at the tip of the wire-waveguide core, which is equivalent to merging Taper 1 and Taper 2 shown in Fig. 2(a). The Q-factor of the joint region is decreased by this means.
These findings can be used to optimize a semi-adiabatic PWWG coupler. Figure 4 shows a top-view schematic of an essential part of the coupler. In Fig. 4, non-defect pillars of a pillar-PhC waveguide are in black. Taper 1 and Taper 2 that were separately depicted in Fig. 2(b) are unified into a single taper region labeled “Taper,” by which the length of the coupler can be shorter than before. The tip width of the wire-waveguide core wtip is the most important parameter to establish high continuity of the dispersion relations of guided modes throughout the coupler. The deviation angle and the diameter-increasing rate of the defect pillars in Taper are adjusted in search of the shortest length of Taper and the smallest Q-factor of Joint at the same while the optical loss of the coupler is sufficiently suppressed. Finally, for further reduction of optical loss, the pillars of the T-shaped branch in Joint are slightly shifted from the lattice points of the pillar PhC in the directions denoted with red arrows in Fig. 4.
Fig. 4 Top-view schematic of essential part of semi-adiabatic PWWG coupler illustrating optimization method. Tip width of wire-waveguide core (in purple) wtip is most important parameter to establish high continuity of dispersion relations of guided modes throughout coupler. Deviation angle and diameter-increasing rate of defect pillars in Taper (blue circles) are adjusted in search of shortest length of Taper and smallest Q-factor of Joint while optical loss is sufficiently suppressed. Finally, pillars of T-shaped branch in Joint (red circles) are slightly shifted from lattice points of pillar PhC in directions denoted with red arrows.
Note that blue shift of the transmission spectrum occurs for a practical PWWG coupler because of electric-field penetration into the over- and under-claddings. We have previously reported the electric-field distribution and the transmission spectrum calculated for a finite-thickness PWWG coupler [41], for which the pillars were 1.00-µm-high and were fully immersed in the surrounding material. The results were almost the same as those of the fully 2D coupler, except that the cutoff wavelength of the finite-thickness coupler was about 1500 nm though that of the fully 2D coupler is 1591 nm.
2.2 Problems and requirements for improvement
As stated in the previous subsection, a pillar-PhC waveguide with a semi-adiabatic PWWG coupler can exhibit the extinction ratio of 60 dB around the cutoff wavelength. From our experience, however, it is difficult to observe such a deep extinction ratio in experiments in which optical fibers are directly coupled to the wire-waveguide ends of the couplers. The illustration shown in Fig. 5 explains how an extinction ratio can deteriorate. The TM guided mode of the pillar-PhC waveguide that we designed is degenerate with the transverse-electric-(TE) bulk-mode of the PhC. The problem is that this TE bulk-mode light can reach the output end of the waveguide along with the TM guided-mode light, even if the TE bulk-mode light is unintentionally mixed with the TM guided-mode light during measurement. In addition, particularly near the cutoff wavelength, the TM guided-mode light is “slow light” and has a small group velocity. It is known that the optical loss of light propagating along a waveguide at a group velocity vg is in inverse proportion to vg [42]. This fact means that an optical device utilizing a small group velocity can suffer a large propagation loss. Particularly for a long pillar-PhC waveguide, most of the mixed TE light can survive to the output end of the waveguide while the properly input TM light may die out, which will disturb observation of light extinction at the cutoff wavelength. Therefore, a pure TM-light input and a short waveguide are indispensable in order to observe a clear cutoff of transmission spectrum.
Fig. 5 Illustrated relation of decaying TM- and transverse-electric-(TE) light beams propagating along pillar-PhC line-defect waveguide and its bulk-PhC, respectively.
The finite-thickness pillar-PhC waveguide we designed has a pillar height of 1.00 µm. Hence a semi-adiabatic PWWG coupler applied to it and a wire waveguide extending from the coupler have the same height. A Si wire waveguide with this height will support a single mode for the TM-polarized light, if its width is 0.110 µm or smaller. Generally, a waveguide for optical coupling should support only a single mode for preventing multimode coupling. On the other hand, a single-mode waveguide having a vertically long cross-section is unsuitable for efficient input of the TM-polarized light, while the TE-polarized light can be more easily input to it. The coupling efficiency of the TM-polarized light may be increased by horizontally widening the coupling end of the waveguide through a taper waveguide; however, the problem of multimode coupling will remain.
2.3 TM-mode-selective spot-size converter
For efficient input of the TM-polarized light, the coupling end of a wire waveguide should be horizontally wide and vertically thin. We developed such a structure, as shown in Fig. 6(a). It works as a TM-mode-selective SSC (TM-SSC). The materials of the core and the cladding of the SSC are Si and SiO2, respectively. A taper length of 50 µm is sufficient for adiabatic guiding of light in the converter. The Si core of the TM-SSC at the coupling end is 0.100 µm in height and 2.500 µm in width, which were determined for efficient coupling to a lensed optical fiber of a 2.0-µm beam-waist diameter. These core dimensions allow the waveguide to support only a single mode for the TM-polarized light. Figure 6(b) shows a colored contour map of the vertical electric field Ey of the fundamental TM-like mode at the coupling end, which was calculated by the finite-element method. For comparison, the horizontal electric field Ex of the fundamental TE-like mode is shown in Fig. 6(c). In Figs. 6(b) and 6(c), the solid lines denote the outer limits of the mode fields, at which the magnitudes of electric field are 1/e of the maxima. As shown in Fig. 6(b), the field of the TM-like mode was round, while that of the TE-like mode was flat, being tightly confined in the core, as shown in Fig. 6(c).
Fig. 6 (a) Illustrated TM-mode-selective SSC (TM-SSC) having vertical taper, and calculated electric fields of (b) TM-like and (c) TE-like guided modes of TM-SSC at coupling end.
By means of the Gaussian-beam approximation, we estimated the coupling efficiency of the TM-SSC for an input light beam of a 2-µm diameter. The coupling efficiency of two Gaussian beams is given by
where w1x and w1y are the spot sizes of the SSC mode in the x and y directions, respectively, and w2x and w2y are the beam-waist sizes of the input light, which are all radii. For the TM-like mode shown in Fig. 6(b), w1x = 1.310 µm and w1y = 0.745 µm under the Gaussian beam approximation. For the 2-µm-diameter beam, w2x = w2y = 1.00 µm. Then the η for the TM-like mode ηTM was calculated to be 0.92 (–0.34 dB). Note that this value does not include the reflection loss at the end face of the SSC. The effective index of the mode shown in Fig. 6(b) was calculated to be 1.481. This is only 3% larger than the refractive index of 1.442 of SiO2, which indicate that most of the light energy propagates in the cladding. The power reflectance R at the interface of two adjacent dielectrics having refractive indices n1 and n2, is given byAt the interface to the air, n1 = 1.442 and n2 = 1.000; accordingly, the R for the TM-like mode RTM was calculated to be 3.8% (0.16 dB). Consequently, the total coupling loss for the TM-like mode was estimated to be 0.50 dB. Similarly, the η for the TE-like mode ηTE was calculated to be 0.34 (–4.65 dB) from w1x = 0.974 µm, w1y = 0.177 µm, and Eq. (1). The effective index of the TE-like mode shown in Fig. 6(c) was 2.069, and the R for the TE-like mode RTE was calculated to be 12.1% (0.56 dB) from Eq. (2). As a result, the total coupling loss of the TE-like mode was estimated to be 5.21 dB. Finally, the difference of the total coupling losses for the TM- and TE-polarized light beams was found to be 4.71 dB for one coupling. Considering both input and output ends of a waveguide, we can expect a total extinction ratio of about 9 dB for the TM-polarized light beam against the TE-polarized one, which will improve the S/N ratio of light guided in a pillar-PhC waveguide having the TM-SSCs as parts of the double-stage guided-mode converters.3. Experiments
3.1 Device fabrication
We fabricated pillar-PhC waveguides having guided-mode converters using a silicon-on-insulator (SOI) wafer. The thicknesses of the buried oxide layer and the top Si layer of the wafer were 3.00 and 1.00 µm, respectively. The biggest challenge in the fabrication process was to form long vertical Si tapers for TM-SSCs. We describe here the fabrication process including convenient vertical-Si-taper-forming steps, in which pattern alignment may be inaccurate. It was developed for small experiments. For mass production, fine alignment between semi-adiabatic PWWG couplers and vertical Si tapers of TM-SSCs is required for many guided-mode converters on a wafer. We will describe such a process elsewhere [43].
Figures 7(a)–7(c) illustrate the process steps for forming vertical Si tapers on an SOI chip. First, a small covering chip of Si with a polished surface was placed on a SOI chip face-to-face right after removing the surface oxide of the SOI chip and dipping the covering chip into deionized water, as shown in Fig. 7(a). Immediately after that, the two chips were clamped as they were to hold a thin water film between them by using tweezers, as shown in Fig. 7(b). The clamped chips were then soaked in an isotropic Si etchant, as shown in Fig. 7(c). The etchant was a solution of 49% hydrofluoric acid (HF) and 69.5% nitric acid (HNO3) mixed at a ratio of HF:HNO3 = 1:300. The Si etching rate of the etchant was about 145 nm/min. During the wet etching step, the surface of the SOI chip under the covering chip was gradually eroded from the edge of the covering chip to the inside. As a result, a gentle Si slope was formed on the SOI chip along the edge of the covering chip. The water film helped to suppress excessive infiltration of the etchant into under the covering chip. After the etching, the covering chip was removed and the SOI chip was rinsed in deionized water.
Fig. 7 Fabrication process steps for forming (a)–(c) vertical Si tapers, (d)–(f) pillar-PhC waveguide devices, and (g) smooth end faces of waveguides.
Figures 7(d)–7(f) illustrate the process steps for defining and forming pillar-PhC waveguide devices. Electron beam (EB) direct writing on EB resist was carried out, as shown in Fig. 7(d). To compress writing data, the circles of the pillars’ cross-sections were approximated into octagons. The top Si layer of the SOI chip was vertically etched by the Bosch process with a gas mixture of sulfur hexafluoride (SF6) and octafluorocyclobutane (C4F8), as shown in Fig. 7(e). The switching times of gas mixture ratios were shortened to about five seconds in order to reduce so-called scallops on the side walls. After the EB resist was removed, an over-cladding of epoxy polymer was formed by spin-coating a liquid monomer and subsequently illuminating ultra-violet (UV) light for curing, as shown in Fig. 7(f). It was followed by hot-plate heating for further hardening. The epoxy polymer we used was an optical adhesive, GA700H, commercially available from NTT-AT. The refractive index of the polymer was adjusted to be nearly 1.442, which ensures symmetrical distribution of refractive indices in the PhC in the thickness direction. Finally, the sides of the SOI chip were cleaved off to form smooth end faces of waveguides, as shown in Fig. 7(g).
Figure 8(a) shows a top-view photograph of a vertical taper formed on the top Si layer of an SOI chip. The thinnest part of the taper looks metallic yellow, which is the color characteristic of a 100-nm-thick Si film. In practice, to leave the 100-nm thickness of the top Si layer for TM-SSCs, we stopped etching when the metallic yellow was recognized during the vertical-taper-etching step. As shown in Fig. 8(a), the vertical taper appeared rainbow-colored in accordance with the varying thickness of the top Si layer. The length of the taper was nearly 200 µm. Since the thickness of the top Si layer was 1.00 µm, the average slope angle was about 0.3°, which is small enough for adiabatic conversion of the guided mode along a TM-SSC that will be formed on the slope. As-dry-etched waveguides and pillars were observed by the scanning electron microscopy (SEM). Figures 8(b)–8(e) are oblique SEM micrographs of a tip of a TM-SSC, a halfway wire-waveguide to a PWWG coupler, the entrance of the coupler, and the tip of a wire-waveguide core inserted in the coupler, respectively. The structures shown in Figs. 8(d) and 8(e) are not of an optimized PWWG coupler. Figure 8(f) shows a top-view micrograph of the joint region of a PWWG coupler optimized in accordance with the method explained in the subsection 2.1. The pillars of the T-shaped branch were slightly shifted from the lattice points of the pillar PhC. The tip width of the wire-waveguide core resulted in 60 nm, while we designed it to be 80 nm since the critical dimension was thought to be 80 nm. In fact, the width of 60 nm was more preferable than 80 nm for better transmission of light. The deviation angles of the pillars on both sides of the wire-waveguide core were set to be 8.4°. By adjusting the diameter-increasing rate of the defect pillars, the length of the taper region from the coupler entrance to the tip of the wire-waveguide core was reduced to 8 µm.
Fig. 8 (a) Top-view photograph of Si vertical taper. Oblique scanning-electron-microscopy (SEM) micrographs of (b) TM-SSC tip, (c) halfway waveguide to PWWG coupler, (d) entrance of PWWG coupler, and (e) end of wire-waveguide core inserted in PWWG coupler, all of which compose double-stage guided-mode converter. (f) Top-view SEM micrograph of joint region of optimized PWWG coupler.
3.2 Measurement
We measured the transmission spectra of the fabricated waveguide devices. The measurement system we used is schematically illustrated in Fig. 9. Laser light from a tunable light source was coupled to a device under test (DUT) with a lensed optical fiber. The fiber had a tip radius of 5 µm to emit light with a beam-waist size of 1µm, which corresponds to a diameter of 2 µm. The polarization of light input to the DUT was controlled with a polarization controller inserted between the light source and the lensed optical fiber. The light output from the DUT was collected with another 5-µm lensed fiber, and the TE-polarized light was filtered out by using a polarization analyzer, which was an in-line polarizer. Finally, the light was introduced to a photo detector.
Fig. 9 Schematic illustration of measurement system for measuring transmission spectra of waveguide devices. Devices under test (DUTs) were pillar-PhC waveguide with semi-adiabatic PWWG couplers, wire waveguide with TM-SSCs only, and pillar-PhC waveguide with semi-adiabatic PWWG couplers and TM-SSCs as complete double-stage guided-mode converters.
Before starting measurement, we confirmed settings of the polarization controller and the polarization analyzer for the highest precision of measurement. First, the polarization of light output from the input fiber was adjusted to be TE or TM by using the polarization controller and a polarizer that was temporarily put in front of the fiber tip. Then, the input fiber was directly coupled to the output fiber, and the settings of the polarization analyzer for maximum and minimum transmissions for each of the TE- and TM-polarized light inputs were read. When the polarization controller was set for the TM-polarized light input, the extinction ratio of the detected light between the TM and TE settings of the polarization analyzer was 24 dB at a wavelength of 1550 nm. The same extinction ratio was obtained, when the polarization controller was set for the TE-polarized light input. This extinction ratio was appropriate for our measurement, since an excessive extinction ratio of the measurement system could hide the effect of the guided-mode converter due to the limited dynamic range of the measurement system. In addition, we note that this level of extinction ratio would be common in practical applications.
First, we measured a pillar-PhC waveguide having only the optimized semi-adiabatic PWWG couplers on both ends. The wire waveguides extending from the couplers were 0.110 µm in width throughout the entire lengths, and hence a single mode was supported for the TM-polarized light. The wire waveguides were defined to reach the end faces of the chip for optical coupling. The length of the pillar-PhC waveguide and that of the wire waveguides in total were 2.4 and 2.3 mm, respectively. Figure 10(a) shows the transmission spectrum measured for the TM-polarized light, for which both the polarization controller and the polarization analyzer were set to the TM settings. As shown in Fig. 10(a), no clear cutoff was observed in the spectrum. For comparison, the spectrum for the TE-polarized light is shown in Fig. 10(b). Note that the tested device was more transparent for the TE-polarized light than the TM-polarized light, which occurred mainly because the coupling efficiencies of the wire-waveguide ends and the optical fibers for the TM-polarized light were smaller than those for the TE-polarized light. The fine and large ripple of the spectrum observed in Fig. 10(a) can be attributed to the reflection at the wire-waveguide ends and/or the back scattering in the long pillar-PhC waveguide. These results strongly suggest the necessity of TM-SSCs for better transmission of the TM-polarized light in addition to using shorter pillar-PhC waveguides.
Fig. 10 Transmission spectra of pillar-PhC waveguide with semi-adiabatic PWWG couplers only, measured for (a) TM- and (b) TE-polarized light inputs. Lensed optical fibers were coupled to ends of single-mode wire-waveguides extending from couplers.
To examine the effect of adding TM-SSCs to semi-adiabatic PWWGs, we next tested a wire waveguide having TM-SSCs only and then a pillar-PhC waveguide having both PWWG couplers and TM-SSCs as complete double-stage guided-mode converters. These waveguides were formed on a single SOI chip, though they are separately illustrated in Fig. 9 to express changing DUTs. The total lengths of both waveguides were about 5 mm. For the wire-waveguide device, the waveguide width was 2.5 µm all the way. The coupling ends of the TM-SSCs were of the same width. Figure 11 (a) shows transmission spectra of the wire waveguide measured for the TM- and TE-polarized light inputs. The optical losses included in the spectra are insertion losses of the waveguide. As shown in Fig. 11(a), the extinction ratio of the TM-polarization spectrum to the TE-polarization one was as large as about 40 dB. Since the extinction ratio of the measurement system was 24 dB, the extinction effect of the two TM-SSCs was found to be 16 dB. This value is larger than 9 dB expected for two TM-SSCs in the subsection 2.3. The difference between the measured and expected extinction ratios can be attributed to the extra loss of the TE-polarized light guided along the thin waveguide regions of the TM-SSCs. Figure 11(b) shows the TM-light transmission spectrum of the wire waveguide, which is reproduced from Fig. 11(a), and that of the pillar-PhC waveguide having the double-stage guided-mode converters. The length of the pillar-PhC waveguide between the two PWWG couplers of the guided-mode converters was 4 µm, which was ten times the lattice constant a. As shown in Fig. 11(b), a clear cutoff was successfully observed at a wavelength of 1527 nm. The extinction ratio was about 40 dB in a wavelength range of 4 nm between 1525 and 1529 nm, and was comparable to the extinction ratio of the TM-polarized light to the TE-polarized light shown in Fig. 11(a). The efficient-transmission range of wavelength was 88 nm from 1527 to 1615 nm, which covers well the entire C-band (1530–1565 nm) of telecommunication wavelength.
Fig. 11 (a) Transmission spectra of wire waveguide with TM-SSCs measured for TM- and TE-light inputs and (b) those of wire waveguide with TM-SSCs again and pillar-PhC waveguide with both PWWG couplers and TM-SSCs as complete double-stage guided-mode converters measured for TM-light input.
4. Summary and conclusion
We proposed a double-stage guided-mode converter for efficient optical coupling to pillar-PhC waveguide devices. The converter consisted of a compact and wide-band semi-adiabatic PWWG coupler and a TM-SSC. The TM-SSC helped to improve the S/N ratio of guided light in devices by reducing unintentional mixing of the TE-polarized light with the properly input TM-polarized light. We have experimentally demonstrated a steep and deep cutoff of a pillar-PhC waveguide having the converters with a large extinction ration of about 40 dB in a 4-nm-wavelength range. It is, thus, concluded that our double-stage guided-mode converter enables pillar-PhC waveguide devices to be used in practical applications. We expect that pillar-PhC waveguides with our converters will accelerate miniaturization of optical integrated circuit devices for higher bit-rates and improved energy-efficiencies.
Acknowledgments
This work is partly based on results obtained from a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO).
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