We demonstrate experimentally two widely tunable optical couplers formed with parallel long-period polymer waveguide gratings. One of the couplers consists of two parallel gratings and shows a peak coupling efficiency of ~34%. The resonance wavelength of the coupler can be tuned thermally with a sensitivity of 4.7 nm/°C. The experimental results agree well with the coupled-mode analysis. The other coupler consists of an array of ten widely separated gratings. A peak coupling efficiency of ~11% is obtained between the two best matched gratings in the array and the resonance wavelength can be tuned thermally with a sensitivity of -3.8 nm/°C. These couplers have the potential to be further developed into practical broadband add/drop multiplexers and signal dividers.
© 2006 Optical Society of America
A fiber grating with a pitch of the order of 100 µm, which is commonly referred to as a long-period fiber grating (LPFG), enables transfer of light energy from the guided mode to selected cladding modes of the fiber at specific resonance wavelengths . In most applications with LPFGs, the light energy coupled to the cladding mode of the fiber is lost (see, for example, the review paper  and the references therein) and the gratings function as no more than band-rejection filters. Recently, it has been shown both theoretically and experimentally that the light coupled to the cladding mode can be collected by using two parallel LPFGs [3, 4]. The outputs from the two gratings are complementary to each other, one showing band-rejection characteristics and the other showing band-pass characteristics. The structure of two parallel LPFGs thus operates as a broadband add/drop multiplexer. However, packaging of two critically aligned parallel gratings to provide stable and efficient add/drop operation remains a practical challenge. It is also difficult to scale up the device by increasing the number of parallel gratings, regardless of the recent demonstration of a six-port add/drop multiplexer using three gratings . To remove the geometry and material constraints of the fiber, long-period waveguide gratings (LPWGs), namely, long-period gratings fabricated in planar waveguides, have been proposed [6, 7]. In fact, a number of LPWGs fabricated in various waveguide structures with different materials have been reported over the last few years [8–14]. The idea of forming parallel LPWGs on the same substrate to realize robust add/drop multiplexers has also been analyzed very recently [15, 16]. According to the theoretical analysis [15, 16], it should be possible to achieve effective power transfer between widely separated parallel LPWGs over a short distance. Furthermore, one can take advantage of the large temperature sensitivity of polymer LPWGs to achieve effective wavelength tuning.
In this paper, we demonstrate two widely tunable LPWG couplers: one consisting of two parallel gratings and the other consisting of ten parallel gratings, both of which were fabricated with polymer channel waveguides. The two-grating coupler shows a peak coupling efficiency of ~34% and a wavelength-tuning sensitivity of 4.7 nm/°C, while the ten-grating coupler shows a peak coupling efficiency of ~11% between the two best matched gratings in the array and a wavelength-tuning sensitivity of -3.8 nm/°C. Simulation results are also presented for the two-grating couplers and compared with the experimental results. Issues in the design and fabrication of such couplers are discussed.
2. LPWG coupler
The two-grating coupler considered in this paper is shown schematically in Fig. 1(a). The coupler consists of two parallel identical gratings (LPWG1 and LPWG2) introduced along two single-mode cores, which are formed on an oxidized silicon substrate (SiO2/Si) and covered with a common cladding. The materials of the cores and the cladding are benzocyclobutene (BCB) and epoxy (OPTOCAST 3505), respectively.
The operation principle of the LPWG coupler is different from that of an LPFG coupler. In an LPFG coupler, light is coupled between the guided mode and the cladding mode of the individual fiber by the respective grating and energy transfer between the two fibers is through evanescent-field coupling between the cladding modes of the two fibers [3, 4]. In the LPWG coupler, light launched into one core is coupled to the cladding mode of the entire structure by the grating on the launching core, so the output from the launching core shows band-rejection characteristics. At the same time, light is coupled from the cladding mode of the entire structure to the other core by the other grating. The output from the coupled core therefore shows band-pass characteristics. When the two cores are sufficiently separated, evanescent-field coupling between the two cores can be ignored. Unlike an LPFG coupler, there is no evanescent-field coupling involved in the LPWG coupler. Under appropriate conditions, 100% energy exchange between the two waveguides can be achieved by using pure grating effects .
2.1 Experimental results
We fabricated the coupler in our laboratory by standard procedures [9–11]. A BCB thin film was first spin-coated on a SiO2/Si wafer (the SiO2 layer was 3 µm thick) to a thickness of 1.8 µm. It was next etched into two identical rectangular cores with a width of 3 µm by photolithography and reactive ion etching (RIE). The core separation was 8 µm. Two identical gratings with a pitch of 107 µm and a length of 9 mm were then etched on the BCB cores by the RIE process. The corrugation depth of the gratings was approximately 80 nm. An epoxy (OPTOCAST 3505) film was then spin-coated on the entire structure to a thickness of 7 µm. Finally, the epoxy film was etched into a rectangular cladding, which was supposed to have a width of 10 µm as measured from the outer side of each core. The refractive indices of the BCB and epoxy films (prior to being patterned) were measured with a prism coupler system (Metricon 2010) and the values for the TE polarization (at 20.4°C) were 1.542 and 1.512, respectively. Figure 1(b) shows an SEM image of the fabricated LPWG coupler, where the gratings along the left and right cores of the coupler are labeled as LPWG1 and LPWG2, respectively. As shown in Fig. 1(b), the two cores are not located symmetrically within the rectangular cladding. The distance from the left core to the left side of the cladding is 9 µm, while the distance from the right core to the right side of the cladding is 11 µm. The deviation from the design value 10 µm for each side was caused by the slight misalignment of the mask in the process of patterning the waveguide cladding.
The transmission spectrum of the LPWG filter was measured with a commercial (C+L)-band amplified spontaneous emission (ASE) source and an optical spectrum analyzer. A heat pump was placed underneath to control the temperature of the device. Figure 2(a) shows the transmission spectra measured from the launching core for the TE polarization at different temperatures. As expected, band-rejection characteristics are obtained. As shown in the figure, the resonance wavelength for the case that light was launched into LPWG1 and detected from LPWG1 (LPWG1 in, LPWG1 out) agrees reasonably well with that for the case that light was launched into LPWG2 and detected from LPWG2 (LPWG2 in, LPWG2 out). The slight difference (less than 4 nm) between the resonance wavelengths of the two LPWGs is believed to be due to the slight difference in the dimensions of the two BCB cores. On the other hand, the contrasts at the resonance wavelengths for the two cases are significantly different. Figure 2(b) shows the normalized transmission spectra measured from the coupled core. Band-pass characteristics are clearly seen. The coupling efficiency of the coupler is defined as the fractional power coupled to the tapping core when light is launched only into the launching core . The band-pass spectrum shown in Fig. 2(b) is normalized with respect to the average of the background light levels used in the normalization of the band-rejection spectra of the two LPWGs, so that the effects due to the input launching efficiency and the output waveguide coupling efficiency are eliminated. In practice, the rejection band of each LPWG was thermally tuned away from the (C+L)-band to provide a clean background light level for normalization. The normalized band-pass spectrum in Fig. 2(b), therefore, gives directly the coupling efficiency of the coupler. In the case that light was launched into LPWG1 and detected from LPWG2 (LPWG1 in, LPWG2 out), a maximum coupling efficiency of ~33% was obtained at 29.2°C. In the case that light was launched into LPWG2 and detected from LPWG1 (LPWG2 in, LPWG1 out), a maximum coupling efficiency of ~34% was obtained at 21.8°C. Unlike the band-rejection characteristics, the band-pass characteristics for the two launching conditions are comparable. The transmission spectra shown in Fig. 2 are not clean, which may be due to any material and geometry non-uniformities along the coupler. The band-pass resonance wavelengths shown in Fig. 2(b) agree reasonably well with the band-rejection wavelengths shown in Fig. 2(a). As the resonance wavelengths of the launching and tapping LPWGs are slightly different, the band-pass resonance wavelengths in the two cases are slightly different from each other, which are also slightly different from the band-rejection resonance wavelengths.
The temperature dependences of the resonance wavelengths for different cases are shown in Fig. 3, which indicates that LPWG1 and LPWG2 have close temperature sensitivities. The wavelength-tuning sensitivity is ~4.7 nm/°C, which allows the operating wavelength of the coupler to be tuned over the (C+L)-band with a control of only ~20°C. The slight difference between the resonance wavelengths of the two LPWGs and the uncertainties in the control of the temperature across the coupler account for the small differences in the temperature sensitivities in different cases.
2.2 Theoretical analysis
To explain the experimental results, we analyzed the fabricated coupler with coupled-mode theory. Light coupling in an LPWG coupler with two widely separated cores is described by the following coupled-mode equations that ignore evanescent-field coupling between the two cores :
where A 1 and A 2 are the amplitudes of the guided modes in the individual cores, respectively, B is the amplitude of the coupled cladding mode of the entire waveguide structure, δ=(2π/λ)(λ 0/λ-1) is a phase-detuning parameter that measures the deviation of the free-space operating wavelength λ from the resonance wavelength λ 0, and κ 1 and κ 2 are the coupling coefficients of LPWG1 and LPWG2, respectively. The coupling coefficient is a measure of the spatial overlap between the guided mode of the individual core and the coupled cladding mode over the area of the grating region . In the theory reported in Ref. , a symmetric coupler is assumed, which implies that the magnitudes of the coupling coefficients of the two gratings are equal, i.e., |κ 1|=|κ 2|. The present coupler structure, however, is asymmetric, because the two cores are located asymmetrically within the cladding, as shown by the SEM image in Fig. 2(b). Therefore, in our analysis, the coupling coefficients κ 1 and κ 2 are not equal. By following the procedures detailed in Ref. , analytical solutions for Eqs. (1) and (2) can be derived. To obtain numerical results, it is necessary to identify the coupled cladding mode and evaluate the coupling coefficients.
In our simulation, we used the physical dimensions given by the SEM image in Fig. 1(b) and the measured refractive indices of BCB and epoxy. We first calculated the mode indices and the field distributions for the guided mode and the cladding modes of the waveguide structure using a commercial full-vector mode solver FIMMWAVE (Photon Design). From the mode indices, we determined the relationship between the resonance wavelength and the grating pitch for couplings to different cladding modes . The results are shown in Fig. 4(a). Because of the asymmetry of the composite structure and the presence of two high-index cores, it is difficult to label the cladding modes of our coupler according to their electric-field patterns as for a perfect rectangular waveguide. Given the grating pitch 107 µm, we identified the cladding mode that gave rise to the observed resonance wavelength as the sixth lowest-order cladding mode, which is marked by the vertical dashed line in Fig. 4(a). The corresponding electric-field patterns of the guided mode of one of the cores and the coupled cladding mode at the wavelength 1600 nm are shown in Figs. 4(b) and 4(c), respectively. The field pattern in Fig. 4(c) indicates that the coupled cladding mode resembles the E61 mode of a perfect rectangular waveguide. With the knowledge of the field distributions of the cladding mode and the guided modes of the individual cores, the coupling coefficients for the LPWG1 and LPWG2 were calculated to be κ 1=213.5m-1 and κ 2=68.7m-1 at the wavelength 1600 nm for a corrugation depth of 80 nm.
The transmission spectra calculated for the band-rejection and band-pass outputs are shown in Fig. 4(d), where a grating length of 9 mm is assumed. In our calculation, we assume that the two cores are identical, so the mode indices of the guided modes of the individual cores are equal, which leads to identical band-rejection and band-pass resonance wavelengths for both LPWGs, as shown in Fig. 4(d). The slight difference in the observed resonance wavelengths of the two LPWGs, as shown in Fig. 2, is believed to be due to any slight difference in the dimensions of the two cores. For the band-rejection outputs, the calculated contrast at the resonance wavelength is -10.5 dB for LPWG1 and -1.3 dB for LPWG2. The large difference in the contrast at the resonance wavelength between the two gratings is consistent with the experimental results shown in Fig. 2(a). Our simulation shows that the slight asymmetry in the fabricated waveguide structure is significant enough to cause a large difference in the contrasts of the rejection dips of the two gratings. For the band-pass outputs, however, we find that the coupling efficiencies are the same, regardless of which core is the launching core, which agrees with the experimental results shown in Fig. 2(b). That the coupling efficiency is independent of the launching core can be explained intuitively by the fact that the coupling efficiency is the combined result of both gratings; the combined effect of a strong radiation grating (LPWG1) and a weak receiving grating (LPWG2) is just the same as the combined effect of a weak radiation grating (LPWG2) and a strong receiving grating (LPWG1). This is a manifestation of the reciprocity property of the coupler. The calculated coupling efficiency at the resonance wavelength is 17.5%. Considering the large uncertainties in the values of the waveguide dimensions, the refractive indices of the materials, and the corrugation depth in our calculation, the agreement between the simulation results and the experimental results is quite reasonable. Our study shows the importance of having a symmetric structure to optimize the performance of the coupler. On the other hand, since the difference between the coupling coefficients κ 1 and κ 2 depends sensitively on the field distribution of the cladding mode, it seems possible to select a cladding mode that is more tolerant of structure deformation. Such a possibility is worth pursuing in the future.
3. LPWG array
To demonstrate the potential of integrating a large number of LPWGs on the same substrate, we consider a coupler that consists of an array of ten widely separated BCB single-mode cores, each of which contains a corrugation grating, as shown schematically in Fig. 5(a). The operation principle of the coupler can be explained qualitatively in the following way . At the resonance wavelength, light is coupled to the cladding mode of the entire composite structure and the cladding mode, at the same time, is coupled to the guided modes of the individual waveguides through the respective gratings in the waveguides. The coupling efficiency for each waveguide depends on the coupling dynamics of the entire system as well as the spatial overlap over the grating area between the cladding mode and the guided mode of the waveguide. The cladding mode of the entire structure serves as a common light source for all the waveguides to tap into. Such a grating array can provide an effective means to distribute signals among widely separated waveguides , which would be difficult to achieve with conventional couplers.
The array was fabricated in the same way as the two-grating coupler and also with the same materials. Each BCB core was 2 µm thick and 5.5 µm wide. The grating pitch was 83 µm and the grating length was 10 mm. The corrugation depth of the grating was ~80 nm. The core separation was 80 µm, which was ten times larger than that of the two-grating coupler. The nominal thickness of the epoxy cladding was 4.7 µm. An SEM image of the fabricated LPWG array is shown in Fig. 5(b).
The ten gratings are labeled sequentially as LPWG1 to LPWG10 from left to right. Figure 6(a) shows the transmission spectra measured for the band-rejection outputs (i.e., when light was launched into and detected from the same core) for the TE polarization at 35.9°C. As shown in Fig. 6(a), a good matching in the resonance wavelength is found between LPWG1 and LPWG9 and, to a less extent, between LPWG2 and LPWG8. The other gratings do not show obvious resonance dips in the (C+L)-band. The non-uniformity in the grating characteristics is believed to be due to the non-uniformity in the cladding thickness together with large modal dispersion. Because the cladding of the structure is relatively thin, the mode index of the guided mode of each core depends sensitively on the thickness of the cladding above that core. A non-uniform cladding across the array can thus give rise to different mode indices for the guided modes across the array and hence different resonance wavelengths for different gratings. Large modal dispersion can further enhance the sensitivity of the dependence of the resonance wavelength on the cladding thickness [10, 11]. The large bandwidths of the rejection bands shown in Fig. 6(a) confirm a large modal dispersion factor . It just happens that the thickness of the cladding above LPWG1 is close to that above LPWG9, so the two gratings have close resonance wavelengths. The cladding thickness profile of the LPWG array, measured with an alpha-step profiler, is presented in Fig. 6(b), which shows that the cladding thickness is non-uniform across the LPWGs. The cladding thickness above LPWG1 is indeed close to that above LPWG9, which suggests strong coupling between LPWG1 and LPWG9. Significant coupling is also expected between LPWG2 and LPWG8. There might exist other coupled LPWG pairs, but their resonance wavelengths are outside the (C+L)-band. A comparison of the resonance wavelengths of LPWG1 and LPWG2 in Fig. 6(a) and their corresponding cladding thicknesses in Fig. 6(b) shows that a change of the cladding thickness by 0.05 µm can shift the resonance wavelength by more than 70 nm. Such a high sensitivity is the result of a large modal dispersion factor . It is possible to design waveguides that are more tolerant to changes in waveguide dimensions .
Figure 7(a) shows the TE transmission spectra measured at 35.9°C when broadband light was launched into the LPWG1 core and detected from the other cores. As shown in the figure, a strong passband appears in the output spectrum of the LPWG9 core, which confirms that strongest coupling takes place between LPWG1 and LPWG9, in agreement with the results in Fig. 6. The coupling efficiency reaches ~11%. Weaker passsbands are observed at the outputs of some non-resonant gratings, because of the overlap of the main lobe and the side lobe in the transmission spectra of the two gratings (e.g., LPWG1 and LPWG2), as shown in Fig. 6. The near-field patterns of the array were also measured with a tunable laser and a CCD camera and the results are shown in Fig. 7(b). At an off-resonance wavelength 1460 nm, light stays in the LPWG1 core, while at the resonance wavelength 1540 nm, light is coupled to other cores, especially the LPWG9 core. The two sets of results in Fig. 7 agree with each other. Figure 7(c) shows the TE transmission spectra measured at 35.9°C when broadband light was launched into the LPWG9 core and detected from other cores. Again, strongest coupling between LPWG1 and LPWG9 is seen and the coupling efficiency is also ~11%, which confirms the reciprocity property of the coupler. There are also weak couplings to other non-resonant cores. The near-field patterns measured for this launching condition are shown in Fig. 7(d), which can be interpreted in the same way as Fig. 7(b). We should point out that the physical separation between the two best matched gratings LPWG1 and LPWG9 is very large (640 µm) and the grating length is only 10 mm. Our results show clearly the possibility of achieving effective energy transfer between widely separated waveguides over a short distance by using only the grating effects. Such long-range coupling is difficult to achieve with conventional waveguide couplers.
Figure 8 shows the temperature dependences of the resonance wavelengths measured for LPWG1 and LPWG9 when light was launched into the LPWG1 core. The wavelength-tuning sensitivity is about -3.8 nm/°C, which allows the resonance wavelength to be tuned over the (C+L)-band with a temperature control of only ~25°C. The negative sign of the wavelength-tuning sensitivity is due to the relatively large core dimension that results in a negative modal dispersion factor .
The transmission spectra measured from the coupled cores at 35.9°C for the TE polarization are shown in Fig. 9 when broadband light was launched into the LPWG2 core and the LPWG8 core, respectively. Strong coupling between LPWG2 and LPWG8 is seen and a peak coupling efficiency of ~10% is obtained. The results are consistent with the band-rejection spectra shown in Fig. 6.
We demonstrate experimentally two LPWG couplers fabricated with polymer waveguides: one consisting of two gratings and the other consisting of an array of ten gratings. The operation of these couplers relies solely on grating effects and no evanescent-field coupling is involved. A peak coupling efficiency of ~34% is achieved with the two-grating coupler and ~11% with the ten-grating coupler. Strong coupling between two cores separated by as far as 640 µm with a grating length of only 10 mm is demonstrated. Both couplers allow the operating wavelength to be tuned thermally over a wide range, which is difficult to achieve with other types of couplers. Experimental results are also compared with the theoretical analysis for the two-grating coupler and a good agreement is obtained. Our results show clearly that such LPWG couplers have the potential to be developed into compact optical add/drop multiplexers and signal dividers for applications in optical communications. It should be noted that only experimental results for the TE polarization are presented. We did not observe any rejection bands for the TM polarization in the (C+L)-band, which is consistent with our calculated results that the resonance wavelengths of the two samples for the TM polarization are located below the C-Band. As the resonance wavelength of a LPWG coupler depends on the mode indices of the core mode and the cladding mode, both of which are polarization-dependent [7–11], the performance of the coupler is in general polarization-dependent [15,16]. In our future work, we expect significant improvement of the performance of the coupler by improving the quality of the waveguide structure (e.g., structure symmetry and cladding uniformity) and using more controllable and flexible grating fabrication techniques (e.g., real-time UV-writing techniques  and thermal-optically induced gratings [13, 18]). The polarization-dependence issue of the coupler may be solved with a careful waveguide design [7, 10].
This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China, [Project No. City U 112005].
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