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Excitation of cladding modes has been achieved using long-period (LPGs) inscribed in an endlessly single-mode photonic crystal fiber (ESM PCF) by CO2 laser irradiation. Core-cladding mode coupling and recoupling has resulted in marked improvement in the evanescent field overlap throughout the cladding air channels in the PCF-LPG, compared to the PCF alone. Our numerical simulation has shown that design optimization of the PCF-LPG configuration can lead to a field power overlap as high as 22% with a confinement loss of less than 1 dB/m in the cladding mode.
©2010 Optical Society of America
1. Introduction
Compared to their conventional all-solid fiber counterpart, photonic crystal fibers (PCFs) [1] are a particularly attractive sensing platform [2,3] since they are both a waveguide and a gas/liquid transmission cell, permitting light-analyte interaction over long path length without the removal of fiber cladding. Solid-core PCFs utilize the fundamental core mode for evanescent field-based absorption spectroscopy. While this sensing modality has demonstrated its potential for sub-monolayer measurements, there exist two inherent limitations. First, the evanescent field extends only a small distance (~wavelength λ/3) from the guiding core to the surrounding PCF cladding air channels, restricting the probing of an analyte only in the inner most ring of the cladding air channels. Second, the fundamental core mode is localized mostly in the PCF core and, in fact, for most PCF designs, less than 1% power of the core mode [4,5] overlaps with the surrounding air channels thus affording weak light-analyte interactions for absorption spectroscopic interrogation. The potential of PCF evanescent field sensors can be significantly advanced if the light-analyte interaction can be extended through the entire cladding air channels with stronger field overlap.
Forward-propagating cladding modes can be excited by the HE11 core mode via periodic perturbation along the transmission axis of an optical fiber. Long-period gratings (LPGs) [6] induced in PCFs have been investigated primarily to probe the modes of PCF structures [7–9], as symmetric cladding modes can be excited individually by the HE11 core mode. LPGs in both conventional fibers and PCFs have also been explored for telecommunications components [10] as well as sensors [11–13]. The effective coupling of the core mode to the cladding mode allows field overlap throughout the cladding air channels. The subsequent recoupling of the cladding mode back to the core mode enables low-loss forward transmission along the core. Core-cladding mode coupling and recoupling offers a potentially robust means of evanescent field sensing that fully utilizes all of the cladding air channels with strong field overlap in PCF.
We report here the use of a LPG to realize the core-cladding mode coupling and recoupling in an endlessly single-mode PCF (ESM PCF) [14]. Marked increase in the field power overlap with the cladding air channels was achieved. Our numerical simulation further suggests that the field overlap can be as high as 22.3% by design optimization of the PCF-LPG configuration. The mode coupling and recoupling strategy represents a new paradigm in exploring and exploiting the PCF evanescent field sensing platform.
2. Core-cladding mode coupling and recoupling in PCF
The operating principle of core mode and cladding mode coupling and recoupling is based upon coupled-mode theory and phase-matching condition. An LPG can be induced in the PCF to couple the HE11 core mode to a series of cladding modes in order to probe and identify cladding mode structure. The coupling between two modes propagating in the same direction in the PCF-LPG is a function of detuning ratio δ/km, where δ is the detuning parameter [15,16], which depends on λ in the phase-matching condition, and km is the m th cladding mode coupling coefficient, which is related to the index change and the overlap integral between the HE11 core mode and the m th cladding mode and can be written as
where ηm is the overlap integral and Δn is the average cross-section index modulation of PCF core and/or cladding. The HE11 core mode is coupled forward to the HE12-like cladding mode with initial grating periods written. The resonant peak of the HE11 core mode transmission varies in intensity that corresponds to the amount of power transferred to the coupled cladding mode at the resonant wavelength, which is dictated by the number of periods inscribed. The forward-propagating cladding mode is recoupled to the HE11 core mode after the resonance reaches its maximum intensity in the HE12-like cladding mode. The minimum transmission can be expressed bywhere k HE12 is the coupling coefficient of the HE12-like cladding mode as defined in Eq. (1), and L is the grating length. When k HE12 L in Eq. (2) equals π/2, the light is completely coupled to the HE12-like cladding mode, and the power distribution is expanded around many more air channels in the cladding region, giving arise to a significant increase in the overlap of evanescent field with cladding air channels. Illustrated in Fig. 1 is the schematic diagram for core-cladding mode coupling and recoupling in a PCF-LPG structure, in which the coupled cladding mode is recoupled to the HE11 core mode of the PCF at the resonant wavelength and the spectral change in the cladding mode is recorded through the HE11 core mode.
Fig. 1 Schematic illustration of core-cladding mode coupling and recoupling in the ESM PCF-LPG (bottom) with progression of transmission spectra (top) indicating the power intensity of mode coupling and recoupling as the number of grating period increases.
3. Experimental results
We used the ESM PCF-LPG for realization of both core-cladding mode coupling and recoupling. The ESM PCF is comprised of 4 ring of hexagonally arrayed air channels with an air channel diameter of d = 3.7 μm and air filling of d/Λ = 0.41, where Λ is the distance between adjacent air channels. In our study, the excitation of cladding modes was enabled by LPG inscription in the ESM PCF using a CO2 laser that induces refractive index modulation through relaxation of residual stress in the fiber. The power of the CO2 laser was carefully chosen to cause no deformation or collapse to the air channel. Details of the LPG fabrication method have been reported elsewhere [17]. The lowest-order cladding mode, denoted as the HE12-like mode, was selected for coupling with the HE11 core mode. The HE11 and HE12-like modes have the same symmetry and polarization, which maximizes their coupling strength. Shown in inset of Fig. 2(a) is an optical micrograph of the ESM PCF. Complete power transformation from the HE11 core mode to the HE12-like cladding mode was achieved at an LPG periodicity of 860 μm with total number of 40 periods. Shown in Fig. 2(a) is the evolution of transmission spectra of forward core-cladding mode in the LPG with the 0th - 40th periods located at 1545 nm. The strongest resonance is about −17 dB that includes an insertion loss about −1 dB caused mainly by non-uniform perturbation of refractive index due to power fluctuation of the CO2 laser. The cladding-core mode recoupling of HE12-like to HE11 mode occurs immediately after all power of the core mode is transferred to the cladding mode at the resonant wavelength. Figure 2(b) plots the evolution of transmission spectra of cladding-core mode recoupling by the LPG at 40th – 80th periods, which represents the completion of one cycle of beating-length oscillation. The gain in the ESM PCF-LPG between coupling and recoupling is about 12 dB. When k HE12 L = π, T min = 1. The HE12-like cladding mode is recoupled back into the HE11 core mode, with a minor loss peak in its transmission spectrum.
Fig. 2 Transmission spectra of core-cladding mode coupling and recoupling with the number of grating period in steps of 10 periods as parameter: (a) forward core-cladding mode coupling in the ESM PCF-LPG and (b) cladding-core mode recoupling in the ESM PCF-LPG. Inset, optical micrograph of a cleaved facet of the ESM PCF.
4. Numerical simulation and optimization
We have numerically analyzed ESM-PCF used in the core-cladding mode coupling and recoupling experiment using a full-vectorial mode solver based on the finite element method (FEM). According to our simulation, the field overlap of the HE12-like cladding mode with air channels is 0.075%, whereas the field overlap of HE11 core mode with air channels is 0.013% at a wavelength of 1550 nm. While an increase in the field overlap by about six folds can be achieved by coupling the core mode with the cladding mode through LPG fabrication, the overall field overlap is very low with a high confinement loss of ~351 dB/m for the ESM PCF used in the investigation. Our simulation further showed that much higher field overlap is possible with design optimization of the PCF-LPG configuration. For our numerical optimization, we employed the FEM in a combination with the Nelder-Mead simplex method [18]. We reduced the computational window to one-quarter of the fiber cross-section with a perfect electric and magnetic conductor boundary condition applied along symmetric planes [19], taking into account the PCF symmetry of hexagonally arrayed air channels. Anisotropic perfectly-matched layers were positioned outside the outmost ring of air channels in order to further reduce the simulated waveguide cross section and to evaluate the PCF mode’s confinement loss.
Our simulations have shown that the overlap depends strongly on LPG periodicity and the PCF microstructure. The cladding mode with a lower effective refractive index extends its mode profile to a larger area in contrast to the cladding mode with a higher effective refractive index that restricts itself around the core. Thus, for a cladding mode with a lower effective refractive index, a shorter LPG period is needed to maintain the same resonance wavelength, according to phase-matching conditions and assuming that the effective refractive core modes are basically constant at different periodicity values. The lower bound of the periodicity used in our simulation is determined in accordance with what can be realistically achieved using a typical laser source (e.g., CO2 laser or femtosecond laser) for LPG fabrication. Two types of PCFs optimized for given analytes and LPGs written by CO2 laser (setting the shortest periodicity of LPG to 180 μm) were obtained: FIBER1 for gas analyte with d1(a) = 1.00 μm in inner 4 rings, d1(b) = 2.06 μm in outer 5th ring, and Λ1 = 2.75 μm and FIBER2 for aqueous analyte with d2(a) = 2.50 μm in inner 4 rings, d2(b) = 3.50 μm in outer 5th ring, and Λ2 = 4.37 μm. The power flow (z-component of the Poynting vector) of HE11 core mode and HE12-like cladding mode are plotted respectively in Fig. 3(a) and 3(b) for FIBER1, and in Fig. 3(c) and 3(d) for FIBER2. For an LPG resonant wavelength of 1550 nm and an LPG periodicity of 180 μm, the cladding mode field overlaps with air channels are 1.83% for gas (n ~1) in FIBER1 and 6.06% for liquid (n ~1.33) in FIBER2, whereas the field overlaps of HE11 core mode with air channels are 0.6% in FIBER1 and 1.1% in FIBER2 respectively. As shorter periodicity of an LPG can efficiently improve the field overlap of HE12-like cladding mode with air channels, we further designed another two types of PCFs (denoted as FIBER3 and FIBER4) for LPG with periodicity of 50 μm that could be written by femtosecond laser [20]. The optimized fiber geometries are d3(a) = 1.08 μm in inner 4 rings and d3(b) = 1.72 μm in outer 5th ring as well as Λ3 = 1.91 μm for FIBER3, while the parameters of FIBER4 are d4(a) = 3.31 μm in inner 4 rings and d4(b) = 3.75 μm in outer 5th ring as well as Λ4 = 4.16 μm. The power flows of HE11 core mode and HE12-like cladding mode are shown respectively in Fig. 4(a) and 4(b) for FIBER3 and in Fig. 4(c) and 4(d) for FIBER4. The cladding mode field overlaps of HE12-like cladding mode with air channels are 8.05% for gas in FIBER3 and 22.3% for liquid in FIBER4, which is close to the field overlap of the core mode with air channels in a tapered steering-wheel PCF (SW-PCF) [21]. The field overlap of HE11 core mode with air channels is 1.8% both in FIBER3 and FIBER4. Compared to the defected-core PCF [22], our PCF-LPG approach has the advantages of easy fabrication and tunability of resonant wavelength for versatile applications. By enlarging the air channels in the 5th rings the HE12-like cladding mode confinement loss was reduced (by ~3 orders of magnitude) to less than 1 dB/m, making it possible to increase the HE12-like cladding mode-analyte interaction path length. These results will be of significant value in guiding design optimization of PCF-LPGs.
Fig. 3 Calculated power flow of optimized PCFs for HE11-HE12 mode coupling for a LPG resonant wavelength of 1550 nm and a periodicity of 180 μm: (a) HE11 core mode in FIBER1, (b) HE12-like cladding mode in FIBER1, (c) HE11 core mode in FIBER2, (d) HE12-like cladding mode in FIBER2.
Fig. 4 Calculated power flow of optimized PCFs for HE11-HE12 mode coupling for a LPG resonant wavelength of 1550 nm and a periodicity of 50 μm: (a) HE11 core mode in FIBER3, (b) HE12-like cladding in FIBER3, (c) HE11 core mode in FIBER4, (d) HE12-like cladding mode in FIBER4.
5. Conclusions
In summary, we have performed numerical optimization of PCF-LPGs in terms of HE12-like cladding mode overlap with the air channels. It has been shown that design optimization of the PCF-LPG configuration can yield substantially enhanced evanescent field overlap (up to ~22%) with the air channels throughout the cladding structure. The approach of core-cladding mode coupling and recoupling using the PCF-LPG scheme thus has the potential to emerge as a new evanescent field sensing paradigm due to greatly strengthened field overlap and vastly expanded light-analyte interaction over all of the PCF cladding air channels.
Acknowledgments
The authors would like to thank Dr. Dennis J. Trevor of OFS for providing us with the ESM PCF. This work is partially supported by the US National Science Foundation under grant number ECS-0404002 and by the Czech Science Foundation under grant number 102-08-1719.
Yinian Zhu’s current address: Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA.
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