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A guided-mode resonance filter integrated in a waveguide cavity resonator constructed by two distributed Bragg reflectors is designed and fabricated for miniaturization of aperture size. Reflection efficiency of >90% and wavelength selectivity of 0.4 nm are predicted in the designed SiO2-based filter with 50-μm aperture by a numerical calculation using the finite-difference time-domain method. A maximum reflectance of 67% with 0.5-nm bandwidth is experimentally demonstrated by the fabricated device at around 850-nm wavelength.
©2012 Optical Society of America
1. Introduction
Guided-mode resonance filters (GMRFs) have been paid much attention as attractive devices in applications to wavelength filters, laser mirrors, and sensors because of their narrowband spectral characteristics and simple structures [1–12]. A GMRF consists of a thin-film waveguide and a surface-relief grating, and is a kind of grating couplers (GCs) from the viewpoint of the structure. A normally incident free-space wave at an operation wavelength is coupled into guided waves by the surface-relief grating, namely guided-mode resonance grating (GMRG), and the excited guided waves are coupled out to air and substrate radiation waves by the GMRG during the propagation in the waveguide. The air radiation wave interferes constructively with the direct reflection wave, whereas the substrate radiation wave interferes destructively with the direct transmission wave. In order to achieve high reflectance of about 100%, guided waves of sufficient power should be excited in the waveguide by the GMRG. The excitation efficiency depends on the coupling coefficient and the coupling length (the aperture size) of the GMRG. The coupling coefficient depends on the modulation depth of the refractive index and the groove depth of the surface-relief grating. Thus, GMRF formed with dielectric materials needs millimeter-size aperture and millimeter-size incident beam diameter for realization of high efficiency and narrow-band spectrum response [8,9].
In practical applications, lensless optical coupling between a narrowband reflection filter/mirror and a single-mode optical fiber or a semiconductor laser end is very attractive in terms of compactness, stability, and cost. Such the lensless direct coupling is, however, very difficult for the conventional GMRFs with dielectric materials due to the large difference in size. Although direct coupling between a diverging light and a GMRF has been investigated theoretically and experimentally by formation of a GMRF on a concave substrate [10,11], miniaturization of the aperture size of GMRF would be more suitable in compactness. A doubly periodic GMRF, where a function of distributed Bragg reflector (DBR) is superimposed on the GMRG by modification of the periodic structure, has been proposed for the aperture miniaturization, but the aperture size as well as the incident beam size are still in the vicinity of a hundred of micrometers [12]. On the other hand, we have recently proposed a vertical-coupling GC integrated in a waveguide cavity resonator constructed by a pair of DBRs for aperture miniaturization, and have demonstrated high-efficiency out-coupling from a guided wave to a free-space wave [13,14]. Such the integration of GC and DBRs would be utilized to the GMRF for miniaturization of the aperture size. A similar combination of GMRG and DBRs has been reported by using semiconductor materials, where the DBRs have been utilized for reduction of spectral bandwidth and a multi-layered mirror is also used on a substrate for suppression of transmission [15]. In this paper, we design and fabricate a cavity-resonator-integrated guided-mode resonance filter (CRIGF) in a SiO2-based waveguide for operation at about 850-nm wavelength. We predict the basic principle of the designed CRIGF by numerical calculation, and experimentally confirm spectral characteristics of the fabricated CRIGF.
2. Device configuration and design
A schematic cross-sectional structure and refractive index profile of the CRIGF designed for around 850-nm wavelength operation is illustrated in Fig. 1 . The device consists of a 0.2-μm-thick electron beam (EB) resist grating layer with refractive index of 1.5500 and a 0.8-μm-thick Ge-doped SiO2 core layer with refractive index of 1.5400 on a SiO2 substrate with refractive index of 1.4600. A surface-relief pattern for CRIGF is formed in the EB resist layer. In the GRIGF pattern, a GMRG is integrated between two DBRs with phase-shifting spaces (PSs). A schematic view of light propagation is also depicted in Fig. 1. A normally incident wave of resonant wavelength with transverse-electric (TE) polarization, which electric field is parallel to the grating lines of CRIGF, is partially reflected, is partially coupled by GMRG to guided waves propagating contra-directionally with each other, and partially transmits to the substrate. The excited guided waves propagate back and forth in a waveguide cavity constructed by a pair of DBRs with reflection efficiency of almost unity, while the excited guided waves are partially coupled out by GMRG to air and substrate radiation waves. The radiation waves from forward and backward guided waves are phase-matched with each other by adjusting the length of PS between GMRG and DBR. In this condition, the superposed substrate radiation wave interferes destructively with the direct transmitted wave, whereas the superposed air radiation wave interferes constructively with the direct reflected wave. Consequently, CRIGF acts as a high-reflectance mirror at the resonant wavelength.
The device parameters were designed at operation wavelength of 846 nm. The effective refractive index of TE0 guided mode at the patterned area was calculated to be 1.5033. GMRG period, DBR period, and PS length were determined to be 562.76 nm ( =Λ), 281.38 nm ( =Λ/2), and 70.345 nm ( =Λ/8), respectively. The radiation decay factor of GMRG between a free-space wave and TE0 guided wave was calculated to be 2.97 mm–1 by coupled-mode analysis. The coupling coefficient of DBR was calculated to be 19.1 mm–1 by coupled-mode analysis. The DBR reflectance of 99% and 99.9% would be realized by the DBRs with lengths of >157 μm and >218 μm, respectively. The wavelength dependence of CRIGF was numerically calculated using the finite-difference time-domain (FDTD) method (Rsoft FullWAVE). In the calculation, GMRG length (aperture size) and DBR length were set to be 50 μm and 160 μm, respectively, and the incident beam was assumed as a plane wave of 50 μm width. Figure 2 shows the calculated reflection and transmission spectra of the designed CRIGF. Figure 2 also shows the sum of the leakage waves passing through the DBRs. A maximum reflectance, a minimum transmittance, and full width at half maximum (FWHM) of wavelength selectivity were calculated to be 91.8%, 6.3%, and 0.4 nm, respectively. The residual of 1.9% was the leakage loss due to the imperfect confinement of the guided wave in the waveguide cavity caused by the DBR reflectance of 99.1%. The higher reflectance as well as the lower transmittance would be expected by using longer DBRs with higher reflectance. The reflection and transmission spectra of CRIGF are very sensitive to the PS length. However, it is impossible that only the PS length deviates from the designed value independently because the CRIGF pattern including GMRG, DBRs, and PSs is formed simultaneously. Therefore, an undesired error in fabrication would cause the shift of the operation wavelength with almost the same efficiency and bandwidth. The wavelength dependence of a conventional GMRF with the same composition was calculated by using the rigorous coupled-mode analysis (RCWA) method (Rsoft DiffractMOD) for comparison. In this calculation, the GMRF with an infinite aperture size and the normally incident light of a plane wave with infinite width were assumed. The calculated reflection and transmission spectra are shown in Fig. 3 . The conventional GMRF was predicted to have a maximum reflectance of almost unity and FWHM bandwidth of 0.8 nm. Thus, the high reflection efficiency with narrow bandwidth similar to a conventional GMRF is expected from the designed CRIGF with small aperture.
Fig. 3 Calculated wavelength dependence of the conventional GMRF with the same composition and an infinite aperture.
3. Fabrication and optical characterization
A Ge-SiO2 core layer with 0.8-μm thickness was deposited on a SiO2 glass substrate with refractive index of 1.4527 by plasma-enhanced chemical vapor deposition. The refractive index of the deposited Ge-SiO2 film was measured to be 1.5384. An EB-resist (Zeon ZEP520A) layer with 0.2-μm thickness was spin-coated on the deposited film. The CRIGF pattern with Λ of 562.74 nm was fabricated by EB direct writing and developing. Figure 4 shows an optical microscope photograph and scanning electron microscope (SEM) photographs of the fabricated CRIGF. The lengths of GMRG and DBRs were 50 μm and 275 μm, respectively. The DBR reflectance with 275-μm coupling length was predicted to be >99.98%. The width of CRIGF was determined to be 600 μm in order to avoid inessential complexity about lateral confinement. The grating patterns with a line/space ratio of 1:1 were obtained for both GMRG and DBR parts.
Fig. 4 (a) Microscope photograph of the fabricated CRIGF. SEM photographs of (b) GMRG and (c) DBR parts.
The optical experimental setup for measurement of transmission and reflection spectra is illustrated in Fig. 5 . A SiO2 wedge with apex angle of 3° was attached to backside surface of the SiO2 substrate via refractive-index-matching oil in order to reduce the influence of undesirable reflection from the backside surface. A TE-polarized beam of 1 mm diameter from a tunable laser diode (LD) was normally irradiated on the fabricated device through a beam splitter, so that the incident beam was regarded as a plane wave on the GMRG area. The images of the transmitted and reflected waves were observed by charge-coupled device (CCD) cameras through an objective (NA = 0.55) and a camera lens (Nikkon Micro-NIKKOR 55 mm f/2.8), respectively. The relative efficiencies of transmission and reflection of the CRIGF were estimated from the images observed on the GMRG part. Figure 6 shows the measured transmission and reflection spectra of the fabricated CRIGF. The vertical scale of Fig. 6(a) was estimated from transmittance through the fabricated substrate without the CGIGF pattern, which is theoretically calculated to be 91.3%. The vertical scale of Fig. 6(b) was estimated from reflectance at the surface of the fabricated substrate without the CRIGF pattern, which is theoretically estimated to be 5.4%. Both of the minimum transmittance of 16% and the maximum reflectance of 67% were obtained at 843.8-nm wavelength. The shift of the operation wavelength from the designed value is due to the difference of the effective refractive indices between the designed value and the fabricated one, which was estimated to be 1.4994. Such the difference is caused by the fabrication errors in the refractive indices and film thicknesses as well as the rough setting of refractive indices in the design. One of the reasons for the measured reflectance lower than the predicted value would be the difference in waveform between the incident beams assumed in the theoretical prediction and used in the experimental measurement. The waveform of the incident wave in our calculation was assumed to be a plane wave with the same width as the GMRG length in order to simulate the practical applications, while the incident beam in the measurement was much wider than the aperture in order to observe the transmitted and reflected images from the whole device for experimental convenience. This waveform difference might reduce the interference effect that suppresses the transmission and enhances the reflection. Another reason would be that the NA of the camera lens used in the reflectance measurement was insufficient to collect the whole of the wave reflected from the GMRG part. A stray light caused by reflection from the backside surface of the wedge would lead to the higher transmittance at the operating wavelength. FWHM of wavelength selectivity was measured to be about 0.5 nm, which was very close to the predicted value of 0.4 nm.
Fig. 6 Measured wavelength dependence of (a) transmission and (b) reflection for the fabricated CRIGF with 50 μm aperture.
4. Conclusions
We have designed and fabricated a guided-mode resonance filter integrated in a waveguide cavity resonator for realization of a high-efficiency narrow-band filter with small aperture for the first time. We have predicted that a narrowband filter with >90% reflection efficiency and 0.4-nm bandwidth would be expected in a SiO2-based 50-μm aperture device. We have experimentally confirmed a basic property of a narrowband reflection by the fabricated device with 50-μm aperture at around 850-nm wavelength. For future work, it is necessary to improve the device characteristics and to reduce aperture size furthermore for practical applications. Polarization independence and lateral confinement are another future issues in order to realize direct coupling with a single-mode fiber end.
Acknowledgments
This work was financially supported in part by the Foundation for Technology Promotion of Electronic Circuit Board.
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