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Abstract
The interference between the long range surface plasmon (LRSP) mode and cladding mode in a gold stripe waveguide is theoretically investigated and experimentally demonstrated. Epoxy polymer SU-8 is used as the dielectric cladding. Long period relief gratings are formed on the SU-8 top surface by ultraviolet light bleaching. The cladding mode, which is excited due to the field mismatch between the LRSP mode and the lead-in fiber mode, interferes with the guiding mode supported by the surface plasmon waveguide. A sinusoidal interference pattern with a contrast ratio of over 12 dB is experimentally observed. Because of the diffraction of introduced SU-8 gratings at the leading edge of waveguide, dips in the transmission spectrum shift continuously with the input fiber position deviation. This waveguide mode interferometer has potential applications in plasmonic waveguide sensors.
© 2017 Optical Society of America
1. Introduction
Surface plasmon polaritons (SPPs) are hybridized excitations between light waves and collective charge density oscillations at metal-dielectric interfaces [1]. Symmetric thin metal film with finite width can offer two-dimensional confinement in the transverse plane. As the film thickness decreases, the first generated four fundamental modes (FMs) will form discrete values [2]. The symmetrical mode has a long propagation length, which is termed as long-range surface plasmon (LRSP) mode [2,3]. Due to characteristics of mode confinement, low loss and surface propagation, LRSP waveguides have been exploited intensively for their potential applications, such as filters [4,5], optical attenuators [6] and couplers [7,8]. In LRSP waveguide circuits, intermodal interference occurs when the mode field of LRSP mode mismatches with that of the incident fiber. Imperfect splicing induced mismatching between the numerical aperture of incident fiber and the LRSP mode field diameter may lead to intermodal interference, too. This interference decouples optical waves into lossy higher-order mode, which produces serious crosstalk noise and high transmitting signal loss. However, the intermodal interference may have favorable aspect. Different multimode fiber or single-mode photonic crystal fiber-based intermodal interferometers have been reported for applications in sensing measurement with advantages of compactness, low cost, and high stability [9–13]. Similar to fibers, LRSP waveguide intermodal interferometer also has a good potential for high precision sensing because of its sensitivity to external disturbance. In fact, long period waveguide grating (LPWG) devices based on the power coupling between the LRSP mode and the co-propagating cladding mode have been demonstrated experimentally [4,14,15]. However, the intrinsic character of mode excitation and interference, including the role of grating existence in LRSP waveguide, demands further investigation. As an epoxy negative photoresist, SU-8 has excellent optical properties over a wide wavelength range. Its refractive index and film thickness can be adjusted within a certain range by ultraviolet (UV) light bleaching [16]. Surface relief gratings can be formed on SU-8 film surface after UV light irradiation through a quartz plate mask with periodic chromium patterns. This grating configuration will have impacts on the intermodal interference in LRSP waveguide.
In this paper, we theoretically investigated and experimentally demonstrated the interference between the LRSP mode and cladding mode in the gold stripe waveguide. Thin gold stripe is embedded in the UV sensitive polymer SU-8 claddings. One-dimensional surface relief gratings on the top of SU-8 upper cladding are formed by UV-bleaching technique to enhance the mode excitation. A sinusoidal interference pattern with two wavelength dips in the C-band is experimentally observed. Due to the grating structure at the leading edge of waveguide, the transmission spectra shift continuously with the deviation of input fiber position. The dependence of resonance wavelength on the input fiber position is characterized. A high wavelength-input fiber position deviation sensitivity of 1.7 nm/μm is obtained. These results promise potential applications to displacement sensing and integrated LRSP waveguide circuits.
2. Theoretical design
The proposed LRSP waveguide intermodal interferometer is sketched in Fig. 1(a). The gold stripe with the thickness d = 25 nm and width w = 5 μm is embedded in SU-8 claddings. The claddings with a whole thickness t = 10 μm are coated on the silicon substrate. Gratings with a period Λ = 36 μm, groove height hg = 180 nm and length Lg = 1 mm are fabricated at the leading edge of waveguide to enhance the mode excitation. The refractive index of SU-8 can be adjusted from 1.561 to 1.582 by changing the UV-bleaching time and baking temperature [16]. In order to discrete the upper cladding mode index, the refractive index of SU-8 upper cladding is required to be larger than that of the SU-8 bottom cladding. More cladding modes will be excited with the increment of refractive index difference between the upper and bottom cladding. However, the LRSP mode requires the upper and bottom cladding has a small refractive index difference to restrain the propagation loss. Therefore, there exists a trade-off between the number of cladding modes and the propagation loss of LRSP mode. Here, the refractive indices of SU-8 bottom cladding nlow = 1.565, SU-8 upper cladding nup = 1.576, and gold film nAu = 0.55-11.5i at wavelength of 1550 nm are adopted [15]. Figure 1(b) shows the mechanism of mode excitation with the assistance of surface gratings when the gap h is 10 μm. The incident light from the input fiber is diffracted by UV defined SU-8 gratings. The cladding mode excited due to the mode field mismatch between the LRSP waveguide and the lead-in single mode (SM) fiber will interfere with the guiding mode, which results in sinusoidal interference transmission spectrum. The LRSP mode can be excited even as the input fiber deviates from the Au stripe end facet along y direction due to the diffraction effect of introduced SU-8 gratings.
Fig. 1 (a) Schematic diagram of proposed LRSP waveguide intermodal interferometer, and (b) mechanism of SU-8 grating assisted end-fire excitation of LRSP mode. The LRSP mode can be excited even as the input fiber deviates from the Au stripe end facet along y direction due to the introduced SU-8 gratings.
The intermodal interference is theoretically calculated by finite element method. Figure 2(a) presents the fundamental LRSP mode field distribution. This field with a diameter of 5.2 μm is well confined to SU-8 claddings, which is favorable to reduce the radiation loss. Figure 2(b) demonstrates the cladding mode field that distributes on both sides of the LRSP waveguide. Here, the mode field diameter of SM fiber is about 9.2 μm. Due to the field mismatch between the SM fiber and LRSP mode, the cladding mode therefore can be excited by end-fire coupling.
Fig. 2 Calculated field distribution of (a) fundamental LRSP mode, and (b) cladding modes with parameters of Au thickness d = 25 nm, Au stripe width w = 5 μm, and SU-8 thickness t = 10 μm.
For TM polarized waves, the output power can be calculated according to Eq. (1) [12]
where and are intensities of the LRSP mode and cladding mode, respectively. is the phase difference between these two modes, which can be defined aswhere L is the length of the intermodal interferometer, nLRSP and nclad are effective refractive indices of the LRSP mode and cladding mode, Δneff is the effective refractive index difference between two modes. Here, nLRSP and nclad are calculated to be 1.576 and 1.566, respectively. Assuming that the cladding mode is fully excited, according to Eq. (3) [17]the free spectral range (FSR) is approximated to be 30 nm in C-band when L = 8 mm.3. Experimental results
3.1 Gratings on SU-8 surface
A 10 μm-thick SU-8 (Microchem Co., USA) film was firstly spin-coated on the silicon substrate to investigate the impact of exposure time on the duty cycle of gratings. After prebaking at 65 °C for 10 min and 95 °C for 20 min, the SU-8 film received different UV exposure dose (14 mW/cm2) through a quartz plate mask with periodic chromium patterns. Post exposure bake at 65 °C for 10 min and 95 °C for 20 min was subsequently done. Atomic force microscope (AFM) was used to characterize the duty cycle change on the SU-8 surface. Figure 3 shows the duty cycle of gratings as a function of exposure dose. The duty cycle is 0.5, 0.63, 0.68 and 0.72 at a dose of 14, 70, 98, and 112 mJ/cm2, respectively. The duty cycle increases with the exposure dose because of the increment of exposure time. An exposure expose of 14 mJ/cm2 can form uniform gratings with a duty cycle of 50%, as shown in Fig. 4. The corrugation depth hg and period Λ are 180 nm and 36 μm, respectively.
Fig. 3 Duty cycle of SU-8 gratings as a function of UV light exposure dose. The light intensity and SU-8 film thickness are 14 mW/cm2 and 10 μm, respectively.
Fig. 4 AFM image of corrugations on the SU-8 film surface with a period of Λ = 36 μm and a duty cycle of 0.5.
3.2 Intermodal interferometer
Firstly, a layer of 5 μm-thick SU-8 was spin-coated over the silicon wafer as the bottom cladding. After prebaking, it was exposed to UV light for 10 s at an intensity of 14 mW/cm2. A hard baked at 150 °C for 30 min was conducted to realize full cross-linking and to enhance the adhesion of SU-8 on silicon substrate. The high-purity (>99.999%) gold was then deposited onto the bottom cladding by electron beam evaporation (Semicore Inc., USA). Photoresist BP212 (Kempur Microelectronics Inc., China) was used as the sacrifice layer, patterned by the UV photolithography machine (ABM Co. Inc., USA) to define waveguide patterns on the gold film. The gold film without the protection of BP212 was removed after wet chemical etching process [18,19]. The AFM image of gold stripe is shown in Fig. 5. A steep sidewall profile with a thickness of about 24 nm and width of 5 μm can be observed. Another SU-8 layer was spin-coated onto the gold stripe as the upper cladding. After prebaking, UV light irradiation for 1 s through a phase mask was implemented to construct 1 mm-long relief gratings at the leading edge of the waveguide. A post exposure bake at 95 °C for 10 min, which is different from the treatment to the bottom cladding, was adopted to realize a larger refractive index than that of the bottom cladding.
Fig. 5 AFM image of fabricated gold stripe on the SU-8 bottom cladding. The thickness and width of the gold stripe are 24 nm and 5 μm, respectively.
3.3 Measurement
The experimental setup is schematically shown in Fig. 6. The broadband light from an amplified spontaneous emission (ASE) source AS-4500 (ASE, B&A Co., China) is launched into the device by the input SM fiber. An optical spectrum analyzer AQ6317C (OSA, ANDO Co., Japan) is used to record the transmitting light from the output fiber.
Fig. 6 Experimental setup for intermodal interferometer performance characterization. The broadband light output from ASE source is launched into the device by end-fire coupling method. The output light is coupled into OSA to record the transmission spectrum.
4. Result and discussion
4.1 Effect of offset
The far field light output of the interferometer is shown in Fig. 7. Compared with simulation results, the observed bright spots confirm the excitation of cladding modes. Here, the brightest one corresponds to the field overlap between the LRSP mode and cladding mode. Other spots result from the weakly excited cladding modes. The optical transmission spectra of the interferometer are shown in Fig. 8. A transmission dip of 15 dB at the wavelength of 1541 nm can be observed when the input fiber is centrally aligned to the gold stripe. The sinusoid-like curve promises a transmission dip outside of C-band. To monitor the variation of the spectra, the input fiber alignment position deviates along y direction when the output fiber position is fixed. The spectrum blue shifts continuously when the input fiber position deviation df increases. This is attributed to the variation of mode index with the excitation angle and the increment of coupling spacing [20]. When df increases to be 4 μm, two transmission dips at 1534 and 1563 nm is emerging. The resonance wavelength difference Δλ between the resonance minima almost remains to be 29 nm for all dual-attenuation spectra. These results are well in accordance with the theoretical expectations.
Fig. 7 Far-field light output from the intermodal interferometer when the input SM fiber is centrally aligned to the Au stripe waveguide end facet.
Fig. 8 Optical transmission spectra of a 5-μm wide gold stripe waveguide with surface relief gratings when the input SM fiber deviates from the Au stripe waveguide end facet. The position deviation ranges from 0 to 12 μm.
When the input fiber moves continuously along the y direction, the transmission dip disappears because no LRSP mode is excited and no intermodal interference occurs. However, another dual resonance dips emerges at the position y = 19 μm, which exhibits a similar behavior to what has mentioned above. This originates from the excitation of LRSP mode by grating diffractions. Figure 9 shows the far-field light output when df = 21 μm. The LRSP mode can be excited at large deviation df of 21 μm. Figure 10 shows the transmission spectra shift with the position deviation from 19 to 23 μm. Here, the evanescent field of LPG and the end-fire coupling both contribute to the mode excitation. The transmission band gets shallower, which results from the fact that LRSP mode excitation and corresponding intermodal coupling weakens with the increment of deviation df. Besides, the resonance wavelength difference Δλ between each two transmission dips still remains at 29 nm.
Fig. 9 Far-field light output from the intermodal interferometer when the input SM fiber position deviation df is 21 μm.
Fig. 10 Optical transmission spectra of a 5-μm wide gold stripe waveguide with surface relief gratings when the input SM fiber deviates from the Au stripe waveguide end facet. The position deviation ranges from 19 to 23 μm.
In order to determine the power distribution of the interferential mode, the wavelength spectra are Fourier transformed to obtain the spacial frequency of interference patterns. As shown in Fig. 11, two interferential modes are confirmed to be excited. The peak overlapped at 0 nm−1 in the spatial frequency spectra corresponds to the LRSP mode. The peak at 0.08 nm−1 corresponds to the excited cladding mode, which interferes with the LRSP guiding mode, leading to main interferential fringes. Moreover, these two modes that develop the main interferential fringe can still be excited even at a large input fiber position deviation of 21 μm. This results from the diffraction of SU-8 corrugation gratings at the leading edge of the interferometer. However, the power of LRSP mode attenuates remarkably with the increment of deviation. All obtained experimental outcome confirms that the intermodal interference between the LRSP mode and cladding mode happens within the thin metal film waveguide. Figure 12 shows the shift of resonance wavelength with the input fiber position deviation, exhibiting a high sensitivity of 1.7 nm/μm.
Fig. 11 Spacial frequency distributions of transmission spectra when the position deviation is 4, 6, 19, and 21 μm, respectively.
We measured the transmission spectrum when the input fiber continues moving along the y direction to a deviation of over 20 μm, as shown in Fig. 13(a). The transmission dip disappears at first, while emerges again as the position deviation y increases to be 34 μm. However, a smaller extinction ratio of 6 dB is observed compared to that of over 10 dB in Fig. 8. The resonance wavelength exhibits less sensitivity of 1 nm/μm to the input fiber position deviation. Moreover, the transmission spectra become shallower, and the resonance wavelength no longer shifts linearly with df. In fact, a resonance dip can be observed even at a large deviation of 49 μm. Unfortunately, the extinction ratio decreases to 4 dB, which is mainly due to the increased transmission loss caused by the large deviation. Figure 13(b) shows the corresponding spacial frequency distribution of interference patterns when df is 34 and 39 μm, respectively. The peak overlapped at 0 nm−1 in the spatial frequency spectra corresponds to the guided mode. The peak at 0.12 nm−1 corresponds to the excited higher order cladding mode [12]. Comparatively, the cladding mode has a lower spacial frequency of 0.08 nm−1 at small df (0 ~25 μm). Therefore, the interference patterns vary greatly at large df because the dominant cladding mode has changed. Nevertheless, the proposed device still can work when the input fiber deviation is over 20 μm.
Fig. 13 (a) Transmission spectrum of a 5-μm wide gold stripe waveguide with surface relief gratings when the input SM fiber deviates from the Au stripe waveguide end facet. The position deviation varies from 34 to 60 μm, (b) corresponding spacial frequency distributions of transmission spectrum when df is 34 and 60 μm.
4.2 Effect of grating existence
In order to study the effect of grating structure existence on the mode excitation, a 5 μm-wide gold stripe waveguide without surface relief gratings is fabricated with the same process to that in Section 3. The interferential pattern with a maximum interference depth of 11 dB can be observed, as shown in Fig. 14(a). The cladding mode has been successfully excited by end-fire coupling. However, the spectrum distorts seriously once the input fiber deviates 0.5 μm from its original position. This can be explained that the deviation alters the optical mode field distribution at the gold stripe end facet, and then the excitement of guiding and cladding modes. The inset in Fig. 14(a) shows far field light outputs when df = 0 μm and df = 1 μm. The power of LRSP mode attenuates obviously once the input fiber position deviation emerges. Figure 14(b) shows the corresponding spacial frequency of the interference pattern. When an offset of 0.5 μm is introduced, the power of excited LRSP mode and cladding mode attenuate rapidly, resulting in a large variation in the spectrum. Above experimental results confirm the existence of a 1-mm long lead-in SU-8 gratings can enhance the excitation efficiency and stability of modes in surface plasmon waveguide.
Fig. 14 (a) Transmission spectrum of a 5-μm wide gold stripe waveguide without surface relief gratings, the insets exhibit far field light outputs when df is 0 and 1 μm, respectively, (b) corresponding spacial frequency distributions of transmission spectra of Fig. 14(a).
5. Conclusion
In summary, the intermodal interference in LRSP waveguide is demonstrated. A sinusoidal interference pattern with two wavelength dips in C-band is observed. Dips in the transmission spectra vary continuously and linearly with the input fiber position change within a certain range of incident deviation. The sensitivity of resonance wavelength to the input fiber position offset is about 1.7 nm/μm. The existence of the grating structure at the leading edge of waveguide enhances the efficiency and stability of modes excitation. The experimental result accords well with simulations. This work has potential applications for surface plasmon waveguide design and micro-displacement measurement.
Funding
National Key Research and Development Plan of China (Grant No.2016YFB0402502); National Natural Science Foundation of China (Nos. 61675087, 61475061, 61405070, 61575076, 61605057).
Acknowledgments
We gratefully acknowledge state key laboratory on integrated optoelectronics for experimental facilities support.
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