Diameter measurement of optical nanofibers using a ... - OSA Publishing

4122

Letter

Vol. 40, No. 17 / September 1 2015 / Optics Letters

Diameter measurement of optical nanofibers using a composite photonic crystal cavity JAMEESH KELOTH,1 MARK SADGROVE,2 RAMACHANDRARAO YALLA,1

AND

KOHZO HAKUTA1,*

1

Center for Photonic Innovations, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan Research Institute of Electrical Communication, Tohoku University, Aoba-ku, Sendai, Miyagi 980-8577, Japan *Corresponding author: [email protected]

2

Received 7 July 2015; revised 10 August 2015; accepted 10 August 2015; posted 11 August 2015 (Doc. ID 245517); published 28 August 2015

We demonstrate a method for making precise measurements of the diameter of a tapered optical fiber with a sub-wavelength diameter waist (an optical nanofiber). The essence of the method is to create a composite photonic crystal cavity by mounting a defect-mode grating on an optical nanofiber. The resultant cavity has a resonance wavelength that is sensitive to the nanofiber’s diameter, allowing the diameter to be inferred from optical measurements. This method offers a precise, nondestructive, and in situ way to characterize the nanofiber diameter. © 2015 Optical Society of America OCIS codes: (350.4238) Nanophotonics and photonic crystals; (130.5296) Photonic crystal waveguides. http://dx.doi.org/10.1364/OL.40.004122

Optical fiber tapers with sub-wavelength diameter waist regions, known as optical nanofibers (ONFs), offer an important and growing platform for nanophotonics. Examples of their applications include quantum optics with laser-cooled atoms [1–5], fiber-coupled solid-state quantum light sources [6–9], and sensing [10,11]. Very recently, the realization of the cavity-enhanced coupling of quantum emitters to an ONF was achieved using a composite photonic crystal cavity (CPCC) [12,13] by combining an ONF with a nanofabricated grating. Other methods of creating photonic crystal cavities in ONFs by fabricating them on the nanofiber’s surface have also been developed [14,15]. In all of these cases, accurate knowledge of the ONF diameter is essential. Although these diameter measurements have typically been performed by a scanning electron microscope (SEM), ONF diameter measurement methods using whispering gallery modes [16,17] and second harmonic generation [18] have recently been published. Nonuniformities in the diameter of an ONF have also been measured by sliding a regular optical fiber along the ONF [19]. However, these methods typically require significant post-processing of the data in order to find the ONF diameter. In this Letter, we propose a method of in situ measurement that provides an immediate indication of the ONF diameter via a one-to-one mapping between the cavity resonance of the ONF guided mode and the diameter. This method uses a 0146-9592/15/174122-04$15/0$15.00 © 2015 Optical Society of America

technique introduced in [13], where a CPCC is formed by combining an ONF and a defect-mode grating. The concept is shown in Fig. 1(a). In the region where the ONF and the grating make contact, the effective refractive index experienced by the ONF guided mode is strongly modulated by the grating, creating a photonic stopband. The defect at the center of the grating gives rise to a single-cavity mode inside the stopband. The cavity resonance wavelength λres is sensitive to the exact ONF diameter D. This allows the use of spectral measurements of the CPCC to determine D. We simulated the behavior of the CPCC device using the finite-difference time-domain (FDTD) method. The grating parameters used in the simulations were similar to those used in [13]. The grating had N 150 slats, with a period of Λg 320 nm. The grating slats had a rectangular shape and extended d 2 μm from the substrate, with a duty cycle of α 12%. In the center of the grating pattern, a defect with a width of 3Λg ∕2 480 nm was introduced between the slats on either side. The nanofiber was positioned so that it lay flat on the tips of the grating slats in all cases. Figure 1(b) shows D plotted against λres for a range of D 400–600 nm. The trend may be seen to be approximately linear, with a gradient of ΔD∕Δλres 2.93. The insets show the simulated reflection spectra for D 400 and 600 nm. The full width at half maximum (FWHM) of the resonance dip is seen to vary from 0.96 nm at D 400 nm (λres 727 nm) to 2.9 nm at D 600 nm (λres 795 nm). Over the same diameter range, the visibility of the resonance dip varies from 52% to almost 100%. The experimental setup is illustrated in Fig. 2. First, we fabricated an ONF using a heat-and-pull technique [20]. We used an oxygen–hydrogen flame from a 250 μm diameter burner nozzle along with two motorized translation stages, which simultaneously scanned the fiber through the flame and pulled it, creating a symmetrical taper. The typical diameter of the ONF produced was around 500 nm. After fabrication of the ONF, optical measurements were performed in situ (i.e., with the nanofiber still attached to the pulling rig) by mounting the ONF on a nanofabricated grating. The grating parameters were Λg 320 nm, α 10%, with a central defect width of 3Λg ∕2. We used two gratings with N 350 and 400, corresponding to a total grating length of 112 and 128 μm, respectively. We observed that the value of λres was independent of the

Letter

Fig. 1. (a) Experimental concept: a nanofabricated grating containing a central defect is mounted on an ONF, creating a photonic crystal cavity. (b) FDTD simulation results showing the dependence of D on λres along with a linear fit to the data (black line). The upper left and lower right insets show the simulated reflection spectra for D 400 and 600 nm, respectively.

value of N . The grating pattern was fabricated on a 25 mm × 10 mm × 2 mm silica substrate that was glued to an optically flat, round silica base. This base was attached to an xyzθϕstage, where the x, y, and z directions are defined as seen in the inset of Fig. 2. The ϕ and θ degrees of freedom rotate the grating in the x–z and y–z planes, respectively. The grating was introduced from below the ONF and raised using a picomotor-controlled x-translation stage (Newfocus, 9064).

Fig. 2. Optical setup of the experiment used to perform diameter measurements as explained in the text. The inset shows the mechanical setup used to produce the ONF and to mount the grating on the ONF for diameter measurements.


4123

Next, we introduced broadband light with a wavelength ranging from 650 to 1000 nm from a super continuum source (SC)(NKT Photonics, SuperKEXR15) into the ONF using an optical setup, as shown in Fig. 2. The polarization angle of the input light was controlled by an in-line polarizer (Oz Optics, PFPC-11). The light was then coupled to a 3 dB fiber coupler at port (1). Coupler output (4) was connected to the ONF by a mechanical splice, with an index-matching gel used to reduce reflections from the fiber ends. Light reflected at the fibergrating interface was collected at port (3) and sent to two spectrum analyzers. One spectrum analyzer was an optical multichannel analyzer (OMA) (Ocean Optics, QE65000) with a resolution of 2 nm and an update rate of ∼125 Hz. The OMA was used to monitor the mounting condition of the ONF and the grating in quasi-real time due to its faster update rate. The other spectrum analyzer was a Fourier transform spectrum analyzer (FTSA) (Thermo Fisher, Scientific Nicolet 8700) with a resolution of 0.01 nm and an update rate of ∼0.25 Hz. The FTSA was used to take detailed measurements of the reflection spectrum. Before mounting the grating, we aligned the grating surface plane parallel to the ONF axis using the ϕ-stage. We monitored the mounting process by observing the light scattered at the ONF-grating interface with a digital microscope (Dino-Lite, Basic AM2111), along with Bragg reflected light detected by the OMA. Under such conditions, the reflection spectrum showed a dip at the center due to the existence of a single-cavity mode created by the defect at the grating center [13]. To ensure that the mounting angle was the same for each nanofiber measured, we mounted the grating over a range of angles. The angle that gives the shortest λres corresponds to the grating slats being perpendicular to the nanofiber. By observing the cavity reflection spectrum on the OMA, we adjusted λres to a minimum within 1 nm, corresponding to an angle of 90 5° between the grating slats and the nanofiber. It should be noted that when the grating comes sufficiently close to the nanofiber, the nanofiber and the grating effectively “stick” together. To unmount the nanofiber, it is necessary to lower the grating by several micrometers before the nanofiber detaches from the grating. Due to this effect, along with the uniformity of light scattering at the fiber-grating interface and the good agreement seen between the experiments and simulations, the gap between the nanofiber and the grating in our experiments was assumed to be zero. We experimentally measured the reflection spectrum at several different values of D using the FTSA by mounting the grating at various positions along the fiber taper using the z-stage. λres was obtained by fitting a Gaussian function to the resonance dip of the reflection spectrum. It should be noted that neither mounting nor unmounting of the grating causes any permanent change to the transmission of the nanofiber. For this reason, the technique can be considered to be nondestructive. We also measured the diameter using a scanning electron microscope (KEYENCE, VE-9800). Figure 3 shows the measured values of λres and D. The inset shows a typical reflection spectrum at the waist region of the tapered optical fiber. This resonance dip has a FWHM of 1.5 nm and a visibility of 90% relative to the Bragg reflection peak. We measured λres and D in the waist region as well as in the tapered region. The CPCC method reproduced the behavior of the diameter profile given by the SEM. We note that in the

4124


Fig. 3. Experimentally measured values of λres (blue points) and D (red points) for an ONF. The points have been joined with straight lines to guide the eye. The inset shows an experimentally measured reflection spectrum at a diameter of D ∼ 500 nm.

CPCC method, λres depends on the average value of D over the effective grating length. In the waist region, the fluctuation in D over the length of the grating was 5 nm, as given by the SEM measurement. However, in the tapered region, the variation in D was ∼30 nm over the length of the grating. Such a diameter variation leads to the broadening of the cavity resonance dip, compared to that obtained by mounting in the waist region for the same average D. As a result, the systematic uncertainty of the measurement in the tapered region is larger than that of the measurements made in the uniform waist region, and the uncertainty increases with the tapering angle. For this reason, we used only CPCC measurements made in the waist region for our calibration. In order to calibrate the dependence of λres on D, we measured ONFs with different diameters ranging from 350 to 600 nm in the waist region of the ONF, using both the CPCC method and the SEM. Figure 4 summarizes the calibration results. The top left and bottom right insets show the measured values of D and λres for D ∼ 335 and 570 nm, respectively. The error bars in the measured D-values were derived from the standard deviation of several diameter measurements over a ∼2 μm length of the nanofiber waist. The error bars for the measurements of λres show the FWHM of the cavity mode. Each data point in the calibration curve is obtained by averaging the λres and D values over all the measured points in a ∼2 mm section of the ONF waist where the nominal diameter is constant. The error bars for the measured points in the calibration curve show the standard errors of the measurements in the waist region of the ONF. The average errors in the values of D and λres were 5 and 1 nm, respectively. The relationship between D and λres is seen to be well described by a linear function. The estimated gradient of the fitted line is 2.61 0.07. It should be noted that the linear behavior predicted by the simulations is well reproduced in the experiment. Moreover, the experimentally estimated gradient of the calibration curve is close to the value predicted by the FDTD simulations. Using the calibration curve shown in Fig. 4, diameter measurements for nanofibers within the calibrated diameter range may be performed by simply measuring the cavity resonance wavelength.

Letter

Fig. 4. Experimentally measured dependency of D on λres . The upper left and lower right insets show D (red points) and λres (blue points) at D ∼ 335 and 570 nm, respectively. The error bars for the λres axis lie inside the plotted point in all cases. In the main figure, red circles show the measured value of λres corresponding to various measured D values. A linear function (black line) was fitted to the data with parameters as given in the main text.

Furthermore, the range of measurable diameters may be adjusted by optimizing the parameters for the defect-mode grating over the required diameter range. Fabricating gratings with a range of different parameters on a single substrate would allow great flexibility for measuring nanofiber diameters over a large range of values. We estimate that the precision of the current method is 10 nm, based on the errors in the parameters of the fitted curve. We note that the precision of the present calibration is limited by the SEM used to measure the diameter. A more precise calibration can be achieved by using a higherprecision SEM. The ultimate limitation to the precision of the method is the cavity linewidth, which can be improved by optimizing the design of the grating [13]. The cavity linewidth can be narrowed by increasing either the number of slats or the duty cycle of the grating. Additionally, we note that for the detection of nonuniformities in the nanofiber diameter, e.g., determining whether two points on a nanofiber have the same diameter, the calibration procedure is not necessary and the accuracy of the method is only limited by the cavity linewidth. In this case, we can distinguish between nanofiber diameters that differ by as little as ∼2 nm, assuming the present narrowest FWHM of 0.75 nm. This value is similar to the accuracy achieved in [19]. In summary, we have demonstrated a precise, nondestructive, and in situ method to measure the diameter of ONFs by mounting them on a grating nanostructure. By using a grating with a central defect and observing the cavity resonance of the associated cavity mode, we were able to achieve a measurement precision as high as 10 nm for our diameter measurements. The current method can, in principle, be used to measure the transverse dimension of any waveguide with a sub-wavelength cross section and has the advantage that the dimension may simply be read from the wavelength of the cavity resonance using the calibration curve. We anticipate that the method of diameter measurement that we present here will provide a

Letter convenient and accurate way to measure the dimensions of nanowaveguides in a variety of experimental contexts, and thus will prove to be a useful tool in the growing field of nanowaveguide quantum optics. Funding. Japan Science and Technology Agency (JST); Japan Society for the Promotion of Science (JSPS) (15K13544); Ministry of Education, Culture, Sports, Science, and Technology (MEXT). Acknowledgment. We thank K. P. Nayak for discussions and suggestions. This work was supported by the Japan Science and Technology Agency (JST) as one of the strategic innovation projects. J. K. acknowledges a Japanese government scholarship (MEXT). M. S. acknowledges support from a grant-in-aid for scientific research from the Japan Society for the Promotion of Science (JSPS), grant number 15K13544. REFERENCES 1. F. Le Kien and K. Hakuta, Phys. Rev. A 80, 053826 (2009). 2. K. P. Nayak, P. N. Melentiev, M. Morinaga, F. Le Kien, V. I. Balykin, and K. Hakuta, Opt. Express 15, 5431 (2007). 3. K. P. Nayak and K. Hakuta, New J. Phys. 10, 053003 (2008). 4. E. Vetsch, D. Reitz, G. Sague, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, Phys. Rev. Lett. 104, 203603 (2010).


4125

5. A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroute, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev Lett. 109, 033603 (2012). 6. R. Yalla, K. P. Nayak, and K. Hakuta, Opt. Express 20, 2932 (2012). 7. R. Yalla, F. Le Kien, M. Morinaga, and K. Hakuta, Phys. Rev. Lett. 109, 063602 (2012). 8. T. Schroeder, M. Fujiwara, T. Noda, H. Zhao, O. Benson, and S. Takeuchi, Opt. Express 20, 10490 (2012). 9. L. Liebermeister, F. Petersen, A. V. Munchow, D. Burchardt, J. Hermelbracht, T. Tashima, A. W. Schell, O. Benson, T. Meinhardt, A. Krueger, A. Stiebeiner, A. Rauschenbeutel, H. Weinfurter, and M. Weber, Appl. Phys. Lett. 104, 031101 (2014). 10. M. J. Morrissey, K. Deasy, M. Frawley, R. Kumar, E. Prel, L. Russell, V. G. Truong, and S. N. Chormaic, Sensors 13, 10449 (2013). 11. J. Lou, Y. Wang, and L. Tong, Sensors 14, 5823 (2014). 12. M. Sadgrove, R. Yalla, K. P. Nayak, and K. Hakuta, Opt. Lett. 38, 2542 (2013). 13. R. Yalla, M. Sadgrove, K. P. Nayak, and K. Hakuta, Phys. Rev. Lett. 113, 143601 (2014). 14. K. P. Nayak, F. Le Kien, Y. Kawai, K. Hakuta, K. Nakajima, H. T. Miyazaki, and Y. Sugimoto, Opt. Express 19, 14040 (2011). 15. K. P. Nayak and K. Hakuta, Opt. Express 21, 2480 (2013). 16. T. A. Birks, J. C. Knight, and T. E. Dimmick, IEEE Photon. Technol. Lett. 12, 182 (2000). 17. M. Sumetsky and Y. Dulashko, Opt. Lett. 35, 4006 (2010). 18. U. Wiedemann, K. Karapetyan, C. Dan, D. Pritzkau, W. Alt, S. Irsen, and D. Meschede, Opt. Express 18, 7693 (2010). 19. M. Sumetsky, Y. Dulashko, J. M. Fini, A. Hale, and J. W. Nicholson, Opt. Lett. 31, 2393 (2006). 20. J. M. Ward, A. Maimaiti, V. H. Le, and S. N. Chormaic, Rev. Sci. Instrum. 85, 111501 (2014).