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Abstract
A robust and efficient bidirectional coupler for whispering gallery mode (WGM) excitation based on a long-period grating (LPG) inscribed in D-fiber is theoretically and experimentally demonstrated. The LPG coupling the fundamental core mode to the forward propagating cladding modes according to the phase-matching condition not only enhances the evanescent field of the fiber but also selectively excites the WGM in a wavelength band of interest. Experimental results show that a maximum resonance contrast as high as 10.5 dB and a quality factor (Q-factor) on the order of 104 can be achieved in an LPG coupled spherical silica WGM resonator with a diameter of 242 µm, where the LPG with a pitch of 680 µm is fabricated by arc-discharging in a side-polished D-fiber with a maximum polishing depth of 56 µm. In addition to high robustness and efficiency, such an LPG-based WGM coupler also demonstrates bidirectionality, i.e., it is independent of the injection direction of the input light, which provides a reliable and flexible fiber coupler for the WGM resonator based practical applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Whispering gallery mode (WGM) resonators with high quality factor and small mode volume can significantly enhance the light-matter interaction in both time and spatial domains, which have been used in label-free biosensing, add-drop multiplexing, narrow linewidth lasing, and micro-combs [1–5]. Efficiently exciting WGMs through evanescent field coupling is of critical importance for the above-mentioned applications. Among the reported optical fiber-based WGM couplers, tapered optical fiber with a waist diameter of less than 2 µm, has been extensively studied due to their inherent compatibility with the fiber pigtailed sources and detectors, circular symmetry, and long-haul propagation [6–8]. However, the thin waist diameter induced fragility and external contaminants induced deterioration restricts the tapered fiber to be only used under controlled laboratory conditions unless additional protection is adopted [9–14].
Recently, a tapered fiber with a waist diameter of 18 µm following an LPG has been demonstrated to excite WGMs in both silica sphere and micro-bottle resonators [15]. The waist diameter is about one order magnitude higher than that of commonly used tapered fiber coupler, by which the robustness of the tapered fiber coupler can be enhanced to some extent. While such a single LPG-based coupling configuration is unidirectional, i.e., the WGM can only be excited by the light transmitting from the LPG to the tapered section. Furthermore, the resonance contrast is limited to ∼22% by the multimode coupler, which has been improved to about 50-60% by a pair of identical LPG with a tapered section in between [16,17]. Acoustically inducing an LPG in a hydrofluoric acid etched single-mode fiber (SMF) with a diameter of about 20.68 µm can also excite the WGMs in a silica capillary-based resonator, where the resonance contrast is ∼1 dB [18]. In comparison with the optical fiber with reduced diameter by tapering or chemical etching, side polished D-fiber or angle-polished fiber is more robust but less efficient [6,19–21]. For example, the coupling efficiency of a D-fiber coupler is limited to ∼20% for a sphere with a diameter of 1 mm, which will be much less for a sphere with a smaller size [6,20].
Herein, we demonstrate a robust and efficient bidirectional WGM coupler by inscribing an LPG in a D-fiber with a maximum polishing depth of 56 µm. The arc-discharging induced LPG couples the core mode to the phase-matched cladding mode, which significantly enhances the evanescent field of the D-fiber and efficiently excites the WGM in a selective wavelength band. WGMs around 1490 nm and 1550 nm have been experimentally demonstrated by two LPGs with different pitches. Specifically, for a silica spherical resonator with a diameter of 242 µm coupled by an LPG with a pitch of 680 µm and length of 8160 µm, a resonance contrast as high as 10.5 dB is experimentally observed around 1550 nm. Unlike the “thick” tapered fiber coupler following a long-period grating, the bidirectionality of the long-period D-fiber grating based coupler enables itself to be independent of the injection direction of the input light [15].
2. Principle and simulation
Figure 1 shows the schematic diagram of the WGM resonator coupled with an LPG inscribed in D-fiber, where the inset with the violet dotted outline is the zoom-in view of the coupling region. By ignoring both the self-coupling of core mode and cladding mode, the cladding mode (E3) coupled from the fundamental core mode (E1) depends on the coupling coefficient (κc) between them, the phase detuning (δ) and the grating length (L) as [22]
The phase detuning δ=(β1-β2-2π/Λ)/2, where β1, β2, and Λ are the propagation constants of core mode and cladding mode, and the grating period, respectively.
Bridged by the cladding modes (E3), part of the fundamental core mode can also be coupled to the WGMs (E4) with a coupling coefficient of κr, i.e.,
Given an LPG resonating at 1550 nm and a critical coupled WGM resonator with a radius of 75 µm, the LPG coupled WGM resonator demonstrates periodical resonance with an envelope, as shown in Fig. 2. The period of the resonance is identical to the free spectrum range (FSR) of the resonator. The envelope corresponds to the transmission spectrum of the LPG.
As a proof-of-principle, a two-dimensional simulation based on the finite difference in time domain (FDTD) method is conducted for simplicity. The radii of the core and cladding are respectively 4 µm and 62.5 µm. The refractive indexes of the core, the cladding, and the resonator are 1.45, 1.44, and 1.44, respectively. A uniform refractive index modification of 0.15 is introduced to form an LPG with a period of 600 µm in the core of a D-fiber with a maximum polish depth (i.e., h, as shown in Fig. 1) of 56 µm. Limited by the hardware configuration of the computer, the length of the LPG is set to 3600 µm. The ring resonator with outer and inner radii of 100 µm and 97 µm axially locates in the middle of the LPG. The lateral distance between the ring resonator and the D-fiber is zero, meaning that the ring resonator is in contact with the D-fiber. A Gaussian field with a mode diameter of 10.4 µm is injected along the z-axis (as defined in Fig. 1) as the input.
The simulated transmission spectrum of the LPG coupled resonator is shown by the red line in Fig. 3(a). Resonances with a period corresponding to the theoretical FSR indicate that the WGM can be excited even in the case that the cladding thickness between the core and the resonator is 2.5 µm. The envelope of the resonances is identical to the transmission spectrum of the LPG, as shown by the solid blue line in Fig. 3(a). The transmission spectrum of the resonator coupled with the same D-fiber without the LPG is shown by the black line in Fig. 3(a), indicating that the WGM cannot be excited without the aid of the LPG. Figure 3(b) shows the field distribution at 1538.71 nm, which is the resonant wavelength of the WGM resonator and close to the dip of the LPG. The zoom-in view of the field distribution in Fig. 3(b) is shown in Fig. 3(c), where the white dotted lines and red lines represent the boundaries of the core and upper cladding, respectively.
Fig. 3. (a) Simulated transmission spectra of the resonator without LPG, the LPG, and the LPG coupled resonator. (b) Field distribution of the LPG coupled WGM resonator at 1538.71 nm. (c) Zoom-in view of the field distribution in (b).
To study the effect of the polishing depth of D-fiber on coupling, the polishing depth is varied from 56.5 µm to 48.5 µm with a step of 2 µm, where the corresponding cladding thickness above the core varies from 2 µm to 10 µm. The simulated transmission spectra are shown in Fig. 4(a) to Fig. 4(e), where the lateral coupling gaps (g shown in Fig. 1) between the D-fiber and the resonator are zero. As the polishing depth decreases, the envelope of the spectrum shifts towards the shorter wavelength and the maximum resonance contrast in the wavelength range from 1400 nm to 1600 nm slightly decreases. WGMs can still be excited by the LPG coupler when the cladding thickness above the core is 10 µm. It is also worth noting that deeper polishing depth allows higher tolerance for the lateral coupling gap. For the same lateral coupling gap (g) of 1 µm, the change in the resonance contrast of the WGMs excited by the LPG in the D-fiber with a polishing depth of 56.5 µm is smaller than that of the WGMs excited by the LPG in the D-fiber with a polishing depth of 48.5 µm, as shown in Fig. 4(f) and Fig. 4(g). To show the change in the resonance more clearly, the spectra shown in Fig. 4(a) and Fig. 4(e) are respectively plotted in Fig. 4(f) and Fig. 4(g) again as the reference.
Fig. 4. Simulated transmission spectrum of the WGM resonator excited by the LPG in the D-fiber with a polishing depth of (a) 56.5 µm, (b) 54.5 µm, (c) 52.5 µm, (d) 50.5 µm, and (e) 48.5 µm. As the lateral coupling gap varies from 0 µm to 1 µm, the spectra of the WGM resonator excited by the LPG in the D-fiber with a polishing depth of (f) 56.5 µm and (g) 48.5 µm.
3. Experimental results and discussion
To fabricate the LPG coupled WGM resonator, a piece of SMF (SMF-28, Corning) is firstly side-polished into a D-fiber. According to the empirical parameters including the axial strain applied to the fiber, the particle size of the polishing tape, and the polishing time, we fabricate a D-fiber with a maximum polish depth of 56 µm [23]. The inset of Fig. 5(a) shows the cross-sectional view of a side-polished D-fiber. Given that the radii of the cladding and core of the original SMF are 62.5 µm and 4 µm, respectively, the cladding thickness between the core and the resonator is calculated to be 2.5 µm. The micrograph of the flat region of a D-fiber polished with polishing tape is shown in Fig. 5(b), where the granularity of the polishing tape is 6 µm.
Fig. 5. (a) Schematic diagram of fabricating LPG in D-fiber with arc discharging, where the inset shows the cross-section of a side-polished D-fiber. (b) and (c) Micrographs of the flat region before and after arc-discharging. (d) Schematic diagram of the experimental setup for measuring the transmission spectrum. (e) Transmission spectrum of the LPG inscribed in D-fiber by arc discharging. (f) Transmission spectra of the LPG coupled spherical WGM resonator under the cases that light travels from left to right and from right to left. (g) Transmission spectrum of the LPG coupled WGM resonator located at another axial point. (h) Detailed spectrum around the dip of the LPG.
Then an LPG is fabricated by arc-discharging with a commercially available fusion splicer (FITEL 100P+), where the polished surface of the D-fiber is placed perpendicularly to the arcs to improve the fabrication efficiency, as schematically shown in Fig. 5(a). The axial movement of the D-fiber and arc-discharging are automatically controlled by the modified program. The micrograph of the flat region after arc discharging is shown in Fig. 5(c). Due to the arc discharging induced surface tension, the original rough surface is slightly smoothened, as shown in the blue dashed rectangular. Figure 5(d) is the schematic diagram of the experimental setup consisting of a supercontinuum source (BBS) and an optical spectrum analyzer (OSA, AQ6370D, YOKOGAWA). The transmission spectrum of the LPG with a period of 450 µm and a length of 7650 µm is shown in Fig. 5(e). The dip of the LPG in the wavelength range from 1400 nm to 1600 nm locates at ∼1490 nm.
A microsphere with a diameter of 321 µm is then fabricated by arc discharging at the end of a piece of SMF. The micrograph of the microsphere with a fiber stem captured by a microscope (VHX-600, KEYENCE) is shown in the inset of Fig. 5(f). Aided with a manual micro-positioner and the microscope, the microsphere is transferred to the grating region of the D-fiber. The blue line in Fig. 5(f) shows the transmission spectrum of the LPG coupled microsphere. By exchanging the light source and the OSA, the same resonances can be obtained as the light travels along the reverse direction, as shown by the red line in Fig. 5(f), verifying the fact that such an LPG based WGM coupler works bidirectionally. To optimize the coupling between the LPG and the microsphere, the microsphere is moved along the axial direction (defined as the z-axis in Fig. 1) but still kept contact with the D-fiber along the x-axis. The transmission spectrum with the maximum resonance contrast is shown in Fig. 5(g). It can be found in both Fig. 5(f) and Fig. 5(g) that maximum resonance contrast is achieved around the resonant dip of the LPG. The detailed spectrum around the resonant dip of the LPG is shown in Fig. 5(h), indicating that the maximum resonance contrast and the FSR are 9.2 dB and 1.53 nm, respectively.
According to the same procedure, another microsphere with a diameter of 316 µm is placed onto the same LPG, the transmission spectrum with maximum resonance contrast is shown in Fig. 6(a). The inset of Fig. 6(a) shows the micrograph of the sphere. The detailed spectrum in Fig. 6(b) shows that a maximum resonance contrast of 6.3 dB can be experimentally achieved. Therefore, such an LPG-based WGM coupler works for different-sized microspheres. Figure 6(c) shows the Lorentzian fitting of the resonance around 1498.26 nm. The full width at half maximum (FWHM) is 0.13 nm, corresponding to a Q-factor of ∼1.15 × 104.
Fig. 6. (a) Transmission spectrum of the LPG coupled spherical resonator with a diameter of 316 µm. (b) Detailed spectrum around 1496 nm. (c) Lorentzian fitting of the resonance around 1498.26 nm.
Another LPG-based WGM coupler working around 1550 nm is fabricated by modifying the grating period and arc-discharging parameters. The period and length of the LPG are respectively 680 µm and 8160 µm. The inset of Fig. 7(a) shows the silica microsphere fabricated at the tip of an SMF. In order to package the WGM cavity and LPG coupler together, the microsphere with a diameter of 242 µm is placed in contact with the D-fiber and coated with a low refractive index polymer. The transmission spectrum of the LPG coupled WGM resonator in the wavelength range from 1545 nm to 1555 nm is shown in Fig. 7(a). The detailed spectrum around the resonant wavelength 1549.444 nm shown in Fig. 7(b) indicates that a maximum resonance contrast of 10.5 dB can be achieved. The FWHM of the resonance is ∼0.088 nm, which corresponds to a Q-factor of ∼1.76 × 104. The Q-factor here is mainly limited by the resolution of the optical spectrum analyzer (0.02 nm), the external coupling loss, and the radiation loss induced by the external low refractive index polymer.
Fig. 7. (a) Transmission spectrum of the LPG coupled WGM resonator. (b) Zoom-in view of the spectrum around the resonant of 1549.444 nm.
4. Conclusions
In conclusion, we have theoretically and experimentally demonstrated a robust and efficient bidirectional fiber coupler for WGM excitation based on the LPG inscribed in D-fiber. A resonance contrast as high as 10.5 dB is achieved in an LPG coupled silica spherical WGM resonator even as the cladding thickness between the core and the resonator is 2.5 µm. In addition, the LPG based fiber coupler can also excite WGM in a selective wavelength band. The long-period D-fiber grating demonstrated here may provide a coupling method for WGM resonator-based signal processing and sensing in long-haul fiber-optic systems, such as add-drop multiplexing and multiparameter sensing.
Funding
National Natural Science Foundation of China (61905028, 61933004); Chongqing Postdoctoral Program for Innovative Talents (CQBX201902); Innovative Research Groups of Chongqing (cstc2020jcyj-cxttX0005); National Science Fund for Distinguished Young Scholars (61825501).
Acknowledgments
We thank Dongmei Huang from The Hong Kong Polytechnic University and Qiang Zhang from Shanxi University for their helpful discussion.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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