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A cavity-resonator-integrated guided-mode resonance filter is a kind of narrowband filters, which uses a resonance effect of a waveguide cavity. Two experimental methods for determining the cavity length were investigated in order to estimate the response time of the filter. SiO2-based filters for operation at 1540-nm wavelength were fabricated and their cavity lengths were determined from measured resonance wavelengths. In the both of methods, the cavity length determined to be 65 μm and the response time was estimated to be 4 psec.
© 2015 Optical Society of America
1. Introduction
A guided-mode resonance filter (GMRF) consisting of a surface grating in a thin-film waveguide has attracted much attention in applications to laser mirrors as well as wavelength filters, because of its great advantage of high fabrication-throughput in comparison with multilayer dielectric mirrors [1–8]. However, GMRF normally needs a sub-millimeter aperture as well as a sub-millimeter incident beam diameter [9, 10], and it is impossible to be directly coupled to an optical fiber or waveguide end of much smaller core size of microns. Therefore, miniaturization of GMRF is attractive to provide a laser mirror for a very compact waveguide laser or vertical-cavity surface-emitting laser (VCSEL) for example.
Recently, we have proposed a new type of GMRF, namely, a cavity-resonator-integrated guided-mode resonance filter (CRIGF) [11–13]. Basic characteristics and several types of CRIGFs have been investigated and demonstrated [12–16]. A schematic cross-sectional view of CRIGF is illustrated in Fig. 1. A grating coupler (GC) is integrated between a pair of distributed Bragg reflectors (DBRs) constructing a waveguide cavity. Gratings are formed on a guiding core layer on a substrate. Light wave propagations are also shown schematically in Fig. 1. A wave vertically-injected to the CRIGF from the air is partly coupled by a GC to guided waves propagating contra-directionally with each other, and partly transmits to the substrate. The excited guided wave coupled out by the same GC to radiation waves propagating into the air and substrate. The radiation waves are superposed to the direct transmission and reflection of the incident wave. The length of the phase-adjusting gaps between GC and DBR is determined so that the radiation waves from forward and backward guided waves are phase-matched with each other. When the reflectance of both DBRs is unity, the guided wave power is accumulated enough to cancel the direct transmission or reflection. As a result, only a reflection or transmission remains according to the relative phase of radiation waves. The relative phase strongly depends on wavelength in resonance regime.
When CRIGF is utilized as a laser mirror in a waveguide laser or VCSEL for optical communications, its response time is important because it limits the direct modulation performance. The response time is equal to a photon lifetime in the cavity resonator. An amplitude decay ξ of the guided wave in a round-trip in the resonator is expressed by
where t0 and τ are the time required for the round-trip and the response time, respectively. t0 is given bywhere c is the light speed in vacuum, N is an effective refractive index of the guided mode, and Lcav is a length of the waveguide cavity. When a guided wave decays only by a radiation in GC, the amplitude decay ξ is expressed bywhere α and LGC is a radiation decay factor and a coupling length of GC, respectively. Therefore, τ is obtained from Eqs. (1)-(3) as follows.Because the waveguide cavity of CRIGF consists of a pair of DBRs, Lcav is given bywhere Ldis is a gap between two DBRs and Leff is an effective DBR length from the edge to the equivalent reflection point. Leff is theoretically predicted bywhere κ and LDBR are the coupling coefficient and length of DBR, respectively [17].In this work, we investigated two methods for determining the cavity length of CRIGF. One method is measurement of cavity length dependence of resonance wavelength. The other is measurement of longitudinal mode spacing.
2. Measurement of cavity length dependence of resonance wavelength
2.1 Measurement method
Resonance wavelength λr must satisfy
The following equation is obtained from Eq. (7).Therefore, the cavity length can be determined by the dependence of resonance wavelength upon the cavity length.2.2 Design examples and fabrication
CRIGF of an 11.5-μm aperture was designed for an operation wavelength of 1540 nm. Schematic view of the designed CRIGF is illustrated in Fig. 2. A GeO2:SiO2 guiding core layer and a Si-N cladding layer were stacked on a SiO2 glass substrate. The cladding layer is shaped into an 11.5-μm-width strip to form a waveguide channel. Gratings with line/space ratio of 1 were formed by corrugation of the cladding layer. The effective refractive index of the fundamental guided mode was calculated to be 1.476. The grating periods of GC and DBR were determined to be 1043.6 nm ( = Λ) and 521.8 nm ( = Λ/2), respectively. The phase-adjusting gap was determined to be 391.4 nm ( = 3Λ/8). The radiation decay factor of GC and the coupling coefficient of DBR were calculated to be 6.6 mm−1 and 37.2 mm−1, respectively. The reflectance of each DBR was calculated to be higher than 99.99% with a coupling length of 244 μm. The cavity length of the CRIGF was predicted to be 39 μm by Eqs. (5) and (6).
CRIGFs of different cavity lengths were fabricated in order to measure the cavity length dependence of resonance wavelength. GeO2:SiO2 and Si-N layers was deposited by plasma-enhanced chemical vapor deposition and DC sputtering, respectively. Grooves of the gratings and surrounding area of the strip were formed by electron-beam (EB) direct writing lithography. CRIGFs were formed with different phase-adjusting gaps from 3Λ/8-3Λ/15 to 3Λ/8 in steps of Λ/15 to provide different cavity lengths. Figure 3 shows optical microscope photographs of fabricated CRIGFs. Different phase-adjusting gaps were successfully formed.
Fig. 3 Optical microscope photographs of fabricated CRIGFs of phase-adjusting gaps of (a) 3Λ /8-3Λ/15, (b) 3Λ /8-2Λ/15, (c) 3Λ /8-Λ/15, and (d) 3Λ /8.
2.3 Optical measurement
An experimental setup for measuring a reflection spectrum is illustrated in Fig. 4. A beam launched from a wavelength-tunable laser diode (LD) was focused by an objective lens of 20x so that the beam waist of 11.5-μm diameter was located on the GC surface. The reflected beam from the CRIGF is collimated by the same lens, reflected by a beam splitter, focused by another objective lens of 10x, and coupled to a single-mode optical fiber connected to an optical spectrum analyzer.
The measured resonance wavelengths of CRIGFs of different phase-adjusting gaps are shown in Fig. 5. The gradient dλr/dLgap was 0.046. The cavity length of the fabricated CRIGF was calculated to be 67 μm by Eq. (8). This value is expected by assuming the coupling coefficient of DBR is about 18 mm−1. This reduction of the coupling coefficient would be caused by deformation of grating corrugation due to fabrication errors in EB direct writing lithography.
3. Measurement of longitudinal mode spacing
3.1 Measurement method
When resonance wavelengths of the waveguide cavity in m-th and n-th modes are λr,m and λr,n, respectively, the following equation is obtained from Eq. (7).
Therefore, the cavity length can be determined by measuring the longitudinal mode spacing. Resonance-mode intensity distributions of this CRIGF are shown schematically in Fig. 6. The incident wave is coupled to the resonance mode when nodes of the intensity distribution within GC are located on boundaries of GC grating grooves. Even modes in Fig. 6 does not satisfy this condition because of a symmetrical structure of CRIGF. Then only odd modes can be excited. Therefore, we can determine Lcav by substituting neighboring wavelengths of observed resonances to3.2 Design examples and fabrication
Shorter mode spacing gives more observable modes, meaning that longer cavity is better. Then CRIGF having long phase-adjusting gaps was fabricated. Schematic cross-sectional view of the designed CRIGF is illustrated in Fig. 7. This CRIGF is the same as one illustrated in Fig. 2 with the exception of phase-adjusting gaps and DBR length. The reflectance of each DBR was calculated to be higher than 99.99% with a coupling length of 190 μm.
This CRIGF was fabricated by the process described in section 2.2. Figure 8 shows an optical microscope photograph of the fabricated CRIGF. Long phase-adjusting gaps are formed.
3.3 Optical measurement
The experimental setup described in section 2.3 was used. The measured reflection spectrum is shown in Fig. 9. Peaks showing resonance wavelengths were observed at 1537.6 nm and 1546.8 nm. Ripples seen in the spectrum would result from an interference effect due to unexpected reflections in the experimental optical system. The cavity length of the fabricated CRIGF was calculated to be 172 μm by Eq. (10). This means that the cavity length of CRIGF with the phase-adjusting gap of 3Λ/8 is expected to be 63 μm. This is almost the same value obtained from the measurement of cavity length dependence of resonance wavelength.
4. Conclusions
We investigated two methods of the cavity length determination for estimating the response time of CRIGF. In the first method, the cavity length was determined from the dependence of resonance wavelength upon cavity length. CRIGFs of different phase-adjusting gaps were fabricated and the dependence was measured. In the second method, it was determined from the longitudinal mode spacing. CRIGF having the long phase-adjusting gaps was formed to observe multiple longitudinal modes. The cavity length was determined to be 65 μm and the response time was estimated to be 4 psec.
Acknowledgments
The authors would like to express sincere thanks to Prof. H. Kikuta and Mr. S. Oue in Osaka Prefecture University for their support on EB direct writing process.
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