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Modal coupling in fiber tapers decorated with metallic surface gratings W. Ding, S. R. Andrews, T. A. Birks, and S. A. Maier Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK Received May 17, 2006; accepted June 14, 2006; posted June 16, 2006 (Doc. ID 71075); published August 9, 2006 An interference-based scheme for fabricating periodic metal gratings on one side of the uniform waist of optical fiber tapers has been developed. Optical characterization of a 5 mm long, 511 nm period gold grating fiber taper with a 10 m diameter reveals backward coupling to both guided and radiation modes that is explained by using an analytical mode-coupling analysis. A refractometer based on this grating taper has a high and constant sensitivity over a large refractive index operating range of 1 to 1.41. © 2006 Optical Society of America OCIS codes: 230.1480, 230.4000, 060.2370.
In a tapered fiber, the reduction of the fiber diameter causes the evanescent tail of the guided mode field to spread out across the outer air-cladding boundary. The fact that a large fraction of the modal field can thus exist in the surrounding medium makes possible many applications such as optical sensing1 and evanescent coupling.2 When longitudinal structure is created on the surface of such waveguides, the overlap of the evanescent field with the surface topography leads to modal coupling along the propagation direction.3,4 In this paper, we report the fabrication of a 5 mm long, 511 nm period gold Bragg grating on the surface of a uniform 10 m diameter fiber taper. The large permittivity contrast between gold and air ensures a large modal coupling coefficient even when transverse field overlap with the grating is small.5 For applications at near-infrared wavelengths, gold is a suitable choice of grating material due to its relatively small absorption coefficient and chemical inertness. We present the spectral characterization of a fiber taper decorated with such a grating and explain the results with analytical theory. We also compare its performance as a refractometer with in-core written fiber Bragg (FBG) grating sensors6,7 and surface plasmon resonance-based fiber sensors.8 A fiber taper with uniform waist was produced by standard tapering of a length of single-mode fiber (Corning, SMF-28, with cutoff wavelength less than 1260 nm).9 Fiber tapers several micrometers in diameter were used in our work to ensure mechanical robustness. The transition regions of the fiber taper satisfied the adiabaticity criterion for low loss.10 A 20 nm thick NiCr layer was deposited on one side of the taper by thermal evaporation. The taper was then dip coated with photoresist, and a grating was exposed by using two interfering 406.7 nm beams from a krypton laser. At this stage, the previously deposited NiCr layer prevents multiple reflection of the exposure beams inside the taper, which would otherwise degrade the fringe quality. After resist development, a solution of cerium ammonium nitrate and acetic acid was used to etch away the NiCr layer through the resist mask. A 3 nm NiCr adhesion layer, followed by 50 nm of gold, was then deposited on the top of the resist grating. Subsequent lift-off in ac0146-9592/06/172556-3/$15.00
etone yielded a gold grating on the taper surface. In the final step, the NiCr between the gold grating strips was removed by using the solution of cerium ammonium nitrate and acetic acid. Figure 1(a) shows a scanning electron micrograph of a typical grating fabricated using this procedure. The taper diameter and grating period, measured with the aid of a calibration standard, were 10.3 m and 511 nm, respectively. Optical characterization was performed by using the experimental setup shown in Fig. 1(b), which comprises an ultrabroadband, unpolarized supercontinuum source based on an endlessly single-mode photonic crystal fiber,11 a fiber-optic circulator, and two optical spectrum analyzers. For experimental convenience, the endlessly single-mode photonic crystal fiber and the input fiber of the circulator were cleaved and butt coupled. Figures 2(a) and 2(b) show the transmission and reflection spectra of the grating taper immersed in air and water, respectively, and measured with a resolution of 1 nm. The transmission minima and reflection maxima close to 1470 nm arise from gratingmediated coupling of the forward fundamental mode to backward-guided modes.5 Among those, only the backward fundamental mode is converted into the core mode of the untapered single-mode fiber and observed in reflection. Other backward-guided modes become cladding modes at the adiabatically tapered transition region and are absorbed by the coating of the untapered fiber.10 By adjusting the resolution to 0.1 nm [Figs. 2(c) and 2(d)], the FWHM of the measured reflection peak in air was found to be 0.4 nm, corresponding to / ⌬ = 3600. The fact that this value
Fig. 1. (a) Scanning electron micrograph of a gold grating fiber taper. (b) Spectral measurement scheme. © 2006 Optical Society of America
September 1, 2006 / Vol. 31, No. 17 / OPTICS LETTERS
R = 关n0共D,R,next兲 + next兴⌳.
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共2兲
To describe the angular selectivity of the backward radiation coupling, we use the formula for the transverse coupling coefficient5 Kljt共z兲 ⬀
Fig. 2. Measured reflectivity and transmittance spectra of the grating taper when immersed in (a) air and (b) water. The grating couples light to backward guided modes at longer wavelengths and to backward radiation modes at short wavelengths. In (c) and (d), the vertical lines mark the calculated resonant wavelengths of the first 19 guided mode couplings.
is less than the number of grating periods 共⬃104兲 means that the effective interaction length for coupling is less than 5 mm. The transmission spectra in Figs. 2(a) and 2(b) change in character at approximately 1250 nm and 1400 nm, respectively. This can be ascribed to the commencement of coupling to the continuum of backward radiation modes. The ⬃20 nm wide transmission dips at these wavelengths arise from radiation coupling enhancement and can be explained by considering the selectivity to radiation angle.12 The transmission dips cannot arise from the coupling to backward surface plasmon modes because the gold grating strips are discontinuous along the taper and prevent the establishment of a well-defined surface mode. The oscillations appearing below 1250 nm and 1400 nm are largely due to an etalon effect associated with the fiber butt coupling. These artifacts could be removed by fusion splicing. The resonant wavelengths for coupling to backward-propagating modes can be calculated by using the phase-matching relation
冕冕
dxdy⌬⑀共x,y,z兲Elt共x,y兲 · Ejt* 共x,y兲. 共3兲
Here, Kljt represents the coupling from mode l to j, ⌬⑀ is the perturbation in permittivity (nonzero only inside the half-ring-shaped gold strips), and Elt, Ejt represent the transverse electric fields of modes l and j, respectively. We approximately model the fundamental mode l with a constant positive electric field distribution over the fiber cross section, and treat the radiation mode j as a plane wave with transverse wave vector kt. Equation (3) is then evaluated across the halfring-shaped gold strips. In order to obtain a substantial integral, the transverse wave vector of the radiation mode must satisfy 兩kt 兩 ⱕ p / D, where D / p is the height of the gold strips. The longitudinal wave vector, kz = 关共nextk0兲2 − kt2兴1/2 has to fulfill the condition nextk0 − p22 / 共2nextk0D2兲 ⱕ kz ⱕ nextk0, where k0 is the vacuum wave vector. Applying the phase-matching condition, the angular selectivity of radiation coupling leads to effective coupling over the range: R关1 − p2⌳R/共8D2next兲兴 ⱕ ⱕ R .
共4兲
共1兲
Outside this region, radiation coupling is suppressed due to the averaging out of the integral in Eq. (3). From the fact that D / p is constrained to be of micrometer magnitude, the radiation coupling enhancement does not occur in infinitesimally thin planar surface relief gratings. To investigate the dependence of the coupling resonances on the external refractive index (RI) next, Fig. 3 shows the measured and calculated radiation coupling wavelengths as a function of next. The error bars denote the bandwidth of the transmission dips. In addition to air and water, standard Cargille optical liquids with RIs between 1.400 and 1.420 were used. Cauchy dispersion equations were used to calculate the RI of the liquids at the experimental wave-
where ⌳ is the grating period and n0 and ni are the effective refractive indices of the fundamental mode and the backward-propagating mode, respectively. The refractive indices depend on taper diameter D, wavelength , and external refractive index next. Figures 2(c) and 2(d) show a magnified view of the transmission spectra in Figs. 2(a) and 2(b). The vertical lines show the calculated resonant wavelengths for coupling to backward modes in the small perturbation limit where the influence of the gold strips on the guided modes is ignored, and assuming D = 10.4 m and ⌳ = 510.4 nm. As apparent, the agreement with the experiment is very good, demonstrating the validity of our interpretations. In a similar way, the upper edge of the radiation coupling continuum can be calculated by replacing ni with next in Eq. (1)12:
Fig. 3. Mode-coupling wavelength as a function of external refractive index. Solid lines show upper and lower boundaries of enhanced radiation-coupling region defined by Eq. (4).
i = 关n0共D,i,next兲 + ni共D,i,next兲兴⌳,
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lengths. The coupling wavelengths for HE11 and HE12 modes are also estimated from the transmission spectra and marked by triangles in Fig. 3. These two resonances have relatively narrow transmission dips in the spectra. In contrast, other transmission dips are broadened by modal degeneration. Figure 3 also shows that the grating-decorated taper has the potential for exploiting the enhanced radiation coupling for refractometric sensing. The field of the radiation mode significantly extends into the external medium so that radiation coupling is more sensitive to the external RI than guided mode coupling. In addition, the overlap of the radiation mode with the external medium is insensitive to the external RI so that the strength and sensitivity of the interaction are independent of the external RI. In our sample, a clearly observed transmission dip from the enhanced radiation coupling exists over the RI range of 1 to 1.41. In contrast, when guided mode coupling is used for refractometric sensing, the excited guided modes will alter their field distributions with changes in the external RI, which limits the external RI range.5 Along the edge of the radiation mode coupling continuum in Fig. 3, the V value of the taper, 2a / ⫻ 共nsilica2 − next2兲1/2, increases as the external RI decreases. When next is less than 1.41, the V value of our sample is large enough for the effective index of the fundamental mode to be nearly constant and very close to the RI of the core material 共ncore兲.13 Equation (3) can then be simplified to R ⬇ 共ncore + next兲⌳.
共5兲
Hence the radiation coupling wavelength has a linear variation with the external RI. Assuming that the measurable resonant wavelength range is limited by the bandwidth of the source and spectral analyzer, Eq. (5) shows the tradeoff between the operating range, 1 ⬍ next ⬍ ncore, and the sensitivity, dR / dnext ⬇ ⌳, of this refractometer. A comparison of the grating-decorated taper with fiber refractometers based on other concepts is shown in Table 1. In-core written FBG refractometers based on etched and side-polished schemes utilize evanescent guided modes for sensing. Their sensitivity and signal strength vary with the mode overlap,6 which limits the operating range. The tilted FBG refractometers employ radiation mode coupling. However, serious mixing with cladding mode coupling hampers their applications.7 As for surface plasmon resonance fiber sensors,8 the large operating range makes our device superior in some applications.14 In conclusion, a gold Bragg grating has been fabricated on the surface of a uniform, 10 m diameter fi-
Table 1. Comparison of Fiber Refractometers Scheme FBG Tilted FBG Surface plasmon resonance Au grating taper
Sensitivity
Q Factor
⌬next (RIUa)
⬍100 共nm/ RIU兲 — ⬃50,000 共nm/ RIU兲
⬃10,000 — ⬃10
5 ⫻ 10−3 1 ⫻ 10−1 2 ⫻ 10−2
⬃500 共nm/ RIU兲
⬃50
4 ⫻ 10−1
a
RIU, refractive index unit.
ber taper by using metal lift-off technology. The measured transmission and reflection spectra can be explained by backward coupling to guided and radiation modes. The resonant wavelength of the enhanced radiation mode coupling has a high and constant sensitivity to the external refractive index over a large range. This characteristic suggests that the gold grating fiber taper might find application in refractometers. We thank P. St. J. Russell for useful discussions. This work was partly supported by the Engineering and Physical Sciences Research Council. W. Ding’s e-mail address is
[email protected]. References 1. J. F. Ding, A. P. Zhang, L. Y. Shao, J. H. Yan, and S. He, IEEE Photon. Technol. Lett. 17, 1247 (2005). 2. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, Opt. Lett. 29, 697 (2004). 3. P. S. J. Russell and R. Ulrich, Opt. Lett. 10, 291 (1985). 4. I. Bennion, D. C. J. Reid, C. J. Rowe, and W. J. Stewart, Electron. Lett. 22, 341 (1986). 5. T. Erdogan, J. Lightwave Technol. 15, 1277 (1997). 6. K. Schroeder, W. Ecke, R. Mueller, R. Willsch, and A. Andreev, Meas. Sci. Technol. 12, 757 (2001). 7. G. Laffont and P. Ferdinand, Meas. Sci. Technol. 12, 765 (2001). 8. A. Diez, M. V. Andres, and J. L. Cruz, Sens. Actuators B 73, 95 (2001). 9. T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992). 10. J. D. Love and W. M. Henry, Electron. Lett. 22, 912 (1986). 11. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St. J. Russell, Opt. Express 12, 299 (2004). 12. T. Erdogan and J. E. Sipe, J. Opt. Soc. Am. A 13, 296 (1996). 13. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983). 14. A. Diez, M. V. Andres, D. O. Culverhouse, and T. A. Birks, Electron. Lett. 32, 1390 (1996).
