Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: Dependence of tip apex angle

Optics Communications 267 (2006) 264–270 www.elsevier.com/locate/optcom

Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: Dependence of tip apex angle Young-Jun Yu a, Haneol Noh a, Mun-Heon Hong a, Heung-Ryoul Noh b, Yasuhiko Arakawa c, Wonho Jhe a,* b

a School of Physics and Astronomy, Seoul National University, Seoul 151-747, Republic of Korea Department of Physics and Institute of Opto-Electronic Science and Technology, Chonnam National University, Gwangju 500-757, Republic of Korea c Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

Received 26 November 2005; received in revised form 28 April 2006; accepted 7 June 2006

Abstract We fabricated axicon microlenses on a single-mode bare optical fiber by using selective chemical etching technique. By varying the concentration and mixture ratios of etching solutions, we could make axicon microlenses with different apex angles (118, 107 and 90). We measured the illumination and collection efficiency of these microlenses by both objective-lens imaging and near-field photoluminescence (PL) spectroscopy of semiconductor quantum dots with respect to the distance between the sample and the axicon lens probe. We found that axicons with 118 and 107 [90] apex angle tend to exhibit the laser focusing spot sizes of about 406 and 478 nm [382 nm] and maintain the high [slightly low] collection PL intensity with the distance between the sample and the axicon probe.  2006 Elsevier B.V. All rights reserved. PACS: 42.81.Bm; 42.79.Bh; 78.55.m; 78.67.Hc Keywords: Axicon lens; Optical fiber; Near-field; Photoluminescence; Quantum dots

1. Introduction An axicon lens [1] has many applications such as selftrapping of intense Bessel beams in plasma channels [2], optical pumping of plasma [3], annular focusing in laser machining [4], doughnut-like blue-detuned laser beam for trapping atoms in a dark spatial region [5], harmonics generation [6], and optical tweezers system [7]. To date the axicon lens has been fabricated by using various methods such as vapor deposition of dielectric layers through shadow masks [8], structure transfer into substrate by reactive-ion etching [9] or electron-beam lithography [10]. In case of etched optical fiber probes, it also has axicon shape with various apex angles under various etching conditions. It *

Corresponding author. E-mail addresses: [email protected] (Y.-J. Yu), whjhe@snu. ac.kr (W. Jhe). 0030-4018/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.06.044

can be used for low-loss coupling of single mode injection lasers into single mode fibers [7,11] or detecting the weak near-field signal from optical nanostructure [12]. In micro axicon lens, the focusing and collecting efficiency of the light depend on its apex angle of the optical fiber probe. In previous works, there have been studies of the nondiffracting focused Bessel beams at a long distance from the axicon lens [10,13]. In this article, we perform a quantitative study of the optical properties of micro axicon lens fabricated on optical bare fiber probes without making the metallic apertures. We fabricated three kinds of the axicon microlens with different apex angles of the optical fiber probes using selective chemical etching method. We also investigated their optical properties by measuring the beam profile of light emanating from the axicon microlens by objective lens imaging as well as near-field photoluminescence (PL) spectroscopy of semiconductor quantum dots (QDs). From this

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study one can obtain the illumination and collection efficiency as a function of the distance between the tip end of a microlens and the sample for optimized near-field spectroscopy. 2. Fabrication and focusing performance of axicon microlens with different apex angles A fiber can be sharpened by utilizing the difference in etching rate between its core and cladding when immersed in an etching solution of buffered hydrofluoric acid (BHF), a mixture of 50% weight hydrofluoric acid (HF) and 40% aqueous solution of ammonium fluoride (NH4F) [11,13]. To make different types of axicon lenses, we prepared three different etching solutions. They are mixtures of NH4F versus HF by volume ratio of 1:1, 2:1 and 3:1. The Teflon beaker filled with BHF is warmed in a double boiler to a temperature of 30 C. A cleaved fiber is immersed in the 1:1, 2:1 and 3:1 BHF etching solution for 50, 75 and 140 min, respectively. Then each axicon microlens with different apex angle is formed at the cleaved fiber. Fabricated axicons have apex angles of 118, 107, and 90 for 1:1, 2:1 and 3:1 solutions, respectively (see Fig. 1). As the concentration of NH4F increased, the axicon angle decreased. We used the objective lens imaging method to measure the beam profile with a 780 nm laser light source, a trans-

Fig. 2. Experimental schematic of detecting the field distribution at an etched fiber end for axicons.

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lation stage with 0.5 lm division, and a charge-coupled device (CCD) camera with adjustable shutter speed. The 780 nm laser coupled to the axicon microlens fiber tip was placed on the translation stage facing toward the objective lens and the CCD camera acting as a screen was placed in line with the fiber and the objective lens. We observed the image of the laser beam on the object plane of the monitor, which was connected to the CCD camera at various points on the tip by moving the fiber tip as shown in Fig. 2. Typical beam images measured by the objective lens imaging method with increased distance from the axicon microlens are shown in Fig. 3. They are two dimensional intensity profiles of each axicon surface. Due to the Bessel beam property of the axicon, there are several rings in the beam passed through the axicon microlens, especially 118 axicon probe. However, the central spot is dominant enough to make the others disappear in the captured images of 107 and 90 in Fig. 3.

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3. Numerical calculation

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Fig. 1. SEM images of optical fiber axicon microlens. We can control the apex angle of the axicon microlens by adjusting the volume ratio of the etching solutions. The volume ratio of NH4F:HF is (a) 1:1 (b) 2:1 (c) 3:1 and the apex angles are (a) 118 (b) 107 (c) 90, respectively.

We compare the experimental results with the theoretical ones by calculating the diffracted laser fields. The diffracted laser field from the axicon microlens can be calculated by the Rayleigh–Sommerfeld diffraction integral [17]   ikq I 1 1 e Eð~ rÞ ¼  ik cos ð~ q  ^nÞdS 0 ; E0 ð~ r0 Þ ð1Þ 2p S 0 q q where ~ r0 denotes a point at the surface of the axicon lens or at the facet of the fiber, ~ r is the considered point in the space, qð¼ j~ qj ¼ j~ r ~ r0 jÞ is the distance between these two points, k = 2p/k is the wave vector, ^n is the unit vector normal to the surface, and E0 ð~ r0 Þ is the electric field at the end of the axicon fiber. In Eq. (1), the integration should be performed over whole area including the axicon surface and the remained fiber facet. Since the surface for the dif-

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Fig. 3. CCD camera images of field distribution at the etched fiber end for 118, 107 and 90 axicons. Each figure has 8.6 · 8.6 lm2 scale.

fraction calculation is not a simple plane, we approximate these situations by dividing the surface into a lot of infinitesimal circular rings which are planes microscopically, so that we might apply Rayleigh–Sommerfeld diffraction integral for the curved surface. As can be observed in Fig. 1, the apex of the axicon is not sharp but round, which is taken into account in the diffraction calculation by assuming that the apex has a curvature of radius q. The approximate value of q is obtained to q = 0.1a  0.2a from Fig. 1. We adopt q = 0.1a by comparison of the experimental and calculation results. When the additional phase shifts for r0 < a are considered, the electric field for the fundamental HE11 mode at the surface is given by

pffiffiffiffiffiffiffiffiffi 8 ikn ðatan aq sec aþ q2 r20 Þ > ; ðr0 < q sin aÞ; < AJ 0 ðk T r0 Þe 1 E0 ðr0 ; h0 Þ ¼ AJ 0 ðk T r0 Þeikn1 ðar0 Þtan a ; ðqsin a 6 r0 < aÞ; > : BK 0 ðcr0 Þ; ðr0 P aÞ; ð2Þ

where a is the radius of the core and also the radius of an axicon, a = (p  b)/2 is the base angle, n1(nq is the refrac2)ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tive q index of the core (cladding), and k T ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

c¼

n21 k 2  b2 and

b2  n22 k 2 with the propagation constant b.

Note that we approximated that the radius of axicon was same as that of fiber core, though the real radius of axicon is smaller than that of fiber core. Because the real radius of axicon and fiber core could not be distinguished with SEM image and we consider that the difference between radius of axicon and fiber core is not large for affecting the calculating results. The constant b and the coefficients A, B in Eq. (2) can be easily obtained from the secular equations [18]. Also the

obliquity q  n^Þ can be replaced by ðz þ q sec a  pffiffiffiffiffiffiffiffiffiffiffiffiffiffi factor cosð~ q2  r20 Þ=q, (z + r0 tan a)/q and (z + a tan a)/q for r < q sin a, q sin a 6 r0 < a and r P a, respectively. We note that, since the apex of the axicon is at the point z = 0, q should be carefully determined for three different cases. The numerically calculated results are shown with measured results in Fig. 4. The several side Bessel peaks (marked by arrows) of both calculated and measured results in Fig. 4(a) could be observed, although the measured results are not clearly matched with calculated results. Fig. 4(b) and (c) show that the first Bessel rings (marked by arrows) from center Gaussian beam are observed at both calculated and measured results. However, the other side rings in calculated results could not be observed in measured results for large distance from the axicon lens, over 2 lm distance in Fig. 4(b) and (c). Note that there exists Bessel beam in measured results. However the intensity of this Bessel beams is much smaller than center Gaussian peaks and our CCD camera sensitivity is poor for observing these side rings. Thus we could not observe these in measured results of Fig. 4. From these properties of diffracted beams in Fig. 4, we consider that the apex shape of the axicon lens is not suitable for making sharp peak of Bessel beams similar to the calculated results. But we found that the measured center Gaussian beams in Fig. 4 are clearly matched with calculated results. The spot size of center Gaussian beams is sub-micrometer (400 nm) in this figure, where the spot size is defined by the full width at the position of e1/2 times the peak intensity. The center Gaussian spot sizes in Fig. 4 are about 406[718], 478[631] and 382[655] nm for 118, 107 and 90

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Fig. 4. The comparison between calculated (black solid line) and measured results (red circle and solid line) of (a) 118, (b) 107 and (c) 90 with various distance between a tip and a sample. The dotted lines in (c) denote the calculated Gaussian beam profiles of fiber probe without the axicon lens.

axicons at 0.5 lm [4 lm], respectively. Note that the calculated Gaussian beam profiles of a lensless single mode fiber with increasing distance was plotted in Fig. 4(c) [dotted line]. However the width of Gaussian beam profile [5 lm] is not changed with increasing distance. Thus, we could confirm that the optical fiber axicon microlens probe has laser focusing performance better than the cleaved lensless single mode fiber. From these results, it could be known that the focusing beams of the 118 [107, 90] axicon lens dominate side Bessel beam [center Gaussian beams] in the vicinity of the axicon lens (<1 lm). Thus, we confirm that the 107 and 90 axicon lenses are more useful than 118 axicon lens for submicrometer beam focusing. 4. Collection performance of axicon microlens with different apex angles In case of performing at restricted experimental environment (e.g. ultra high vacuum (UHV) or low-temperature condition at chamber), it is used with illumination and collection mode (I–C mode) [14,15]. We also want to observe the possibility of I–C mode with using axicon microlens probe at these restricted experimental environments. Thus in this section, we try the measure the collection efficiency of axicon microlens having different apex angles with low-temperature NSOM experiment.

In order to measure the collection efficiency of each axicon microlens, we observed near-field PL images of QDs from several hundred nanometer apertures using three kinds of optical fiber axicon microlens probes. Fig. 5 shows the experimental schematic for near-field spectroscopy of InAs QDs with an optical fiber axicon microlens probe and a 100 nm apertured shadow mask. The self-assembled InAs QDs were grown on a GaAs substrate by molecularbeam epitaxy, having a lateral dimension of 20 nm, a height of 2 nm, and a density of >100 lm2, with deposiOptical fiber axicon lens probe Core

Laser focusing

PL

Cladding

Apertued shadow mask GaAs cap layer

GaAs buffer layer

InAs QDs

GaAs substrate Fig. 5. Experimental schematic for near-field spectroscopy of InAs QDs with optical fiber axicon microlens probe and 100 nm apertured shadow mask.

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tion thickness of about two monolayers. The QDs were capped by a 50 nm thick GaAs layer to reduce the contribution from diffused carriers in the barrier layer as shown in Fig. 5 [16]. In order to fabricate 100 nm aperture on the sample, we masked the sample by thin metallic apertures. Such apertures are fabricated by first dispersing 100 nm diameter polystyrene spheres, then depositing 70 nm aluminum film, and finally removing the spheres by sonication [14]. For optical pumping of QDs, a Ti:sapphire laser operating at a photon energy of 1.65 eV was coupled to the optical fiber axicon lens probe. The resulting PL signal was collected using the same fiber probe. Both the sample and the fiber probe were enclosed in a gas-flow-type cryostat and kept at 77 K. The PL signal was dispersed by a 0.3 m single monochromator with a spectral resolution of 0.3 meV and detected by a liquid-nitrogen-cooled CCD camera to accomplish high signal-to-noise ratio.

Fig. 6 shows the PL spectra and spatial PL images of InAs QDs from 100 nm apertures using three axicon microlens probes at various distances between samples and the axicon microlens probes (from 0.1 to 3 lm) at 77 K. Here the PL spectrum was observed on center of each PL image. The scan area of PL images and excitation power are 1 · 1 lm2 and about 1 lW, respectively. The data acquisition (DAQ) process is as follows: (i) The probe is located on a selected sample position (as shown in Fig. 5) and PL spectrum is taken in the entire spectral range with a nitrogen-cooled CCD camera during 1 s as shown in Fig. 6(a). Then collective entire PL spectrum are integrated from 1.18 to 1.33 eV. (ii) This DAQ process is repeated sequentially in all other 11 · 11 pixels of the scanning area.

Fig. 6. (a) Time-integrated PL spectra and spatial PL images using; (b) 118, (c) 107 and (d) 90 axicon microlens probes of QDs with 100-nm apertured shadow mask, collected during 1 s at 77 K with various distance between sample and probe from 0.1 to 3 lm. Scanning range is 1 · 1 lm2 where the excitation power is 1 lW.

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(iii) Then, each PL image at an integrated energy spectrum from the 121 data files is processed to obtain the corresponding spatial spectrum of the InAs QDs [15]. (iv) These PL images were obtained at various distances between the sample and axicon microlenses (from 0.1 to 3 lm). Thus the PL images in Fig. 6(b)–(d) are spatial transmission distribution of integrated PL spectrum in Fig. 6(a) of InAs QDs through the about 100 nm apertured shadow mask. For a quantitative understanding of the various PL images presented in Fig. 6, we present the intensity and the width of the PL images as a function of the distance between the sample and axicon microlens probes in Fig. 7. The widths of PL images in Fig. 7(a)–(c) were 360, 280, and 340 nm at 500 nm distance, respectively, and increased as increasing the distance between sample and axicon microlens probe. Note that, where the width of PL image

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size is defined by the full width at the position of e1/2 times the PL image center intensity. From this fact, We found out that all probes could distinguish a several hundred nm spatial resolution. The collective intensity of PL image of 118 and 107 axicon microlens in Fig. 7(a) and (b) could also collect the PL signal at large distance between sample and probe (3 lm). However, the intensity of PL image of 90 axicon microlens in Fig. 7(c) decrease rapidly above 1 lm distance between sample and probe. Note that the far-field dominate and the near-field decrease rapidly at tip-surface distance above 1 lm. Thus the PL images at <0.1 lm and above 1 lm at Fig. 6 correspond to near-field and far-field PL images, respectively. Finally, the image of 90 axicon microlens could not observe PL signal above 2 lm distance in Fig. 6(d). Note that the intensity and width above 2 lm distance between sample and probe in Fig. 7(c) were background value (about 100, where maximum intensity is about 930) and scanning size (1 lm), respectively. The solid angle of the axicon lens decrease with decreasing apex angle. Then the light collection performance decrease with decreasing solid angle of axicon microlens. Thus we could know that the light collection performance of the large apex angle (118 and 107) axicon microlens is good with large distance between sample and probe in Figs. 6 and 7. From the results in Figs. 3–7 we found the relationship between illumination, collection efficiency and the apex angle of axicon lens. 5. Conclusion

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We controlled the apex angles of an axicon microlens by adjusting the mixture volume ratio of etching solution. The volume ratio of NH4F:HF and the resulting apex angles are as follows: 1:1 for 118, 2:1 for 107, and 3:1 for 90. We also studied the laser beam profiles emanating from the axicon lens by objective-lens imaging experiments. The smallest central spot size is about 382 nm with 780 nm wavelength light-source and the spot size increases linearly with the distance but is less diffractive than the lensless ones. We also compared the relative collection efficiency among the axicon microlenses by near-field spectroscopy experiments. The experimental results may be useful for researchers fabricating the axicon lenses with bare optical fibers for several purposes such as optical-fiber-based integrated circuits or near-field nano optics and spectroscopy. Acknowledgement This work was supported by the Korean Ministry of Science and Technology through the Creative Research Initiatives program. References

Fig. 7. The intensity (dash line) and the width (solid line) of the spatial PL images in Fig. 4 with various distance between sample and axicon microlens probe. (a) 118, (b) 107 and (c) 90 axicon microlens.

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