Complete determination of the orientation of NV centers with radially polarized beams Philip R. Dolan, Xiangping Li, Jelle Storteboom, and Min Gu* Centre for Micro-Photonics, Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia * [email protected]
Abstract: In this paper, we report on the precise determination of the orientation of NV centers by imaging with a radially polarized beam. Vectorial Debye theory is applied to the field in the focus of radially polarized beams to generate emission profiles of two orthogonal optical dipoles. By comparing features of the measured emission intensity patterns with simulated results, complete orientation determination of the NV axis is achieved. Results are corroborated by using established methods requiring the polarization rotation of a linearly polarized excitation source, and by analysis of optically detected magnetic resonance spectra. These results lay new ground for any application where the knowledge of the orientation of the NV centers is prerequisite. ©2014 Optical Society of America OCIS codes: (260.0260) Physical optics; (260.2510) Fluorescence; (260.5430) Polarization.
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#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4379
14. D. A. Simpson, E. Ampem-Lassen, B. C. Gibson, S. Trpkovski, F. M. Hossain, S. T. Huntington, A. D. Greentree, L. C. L. Hollenberg, and S. Prawer, “A highly efficient two level diamond based single photon source,” Appl. Phys. Lett. 94(20), 203107 (2009). 15. P. Neumann, J. Beck, M. Steiner, F. Rempp, H. Fedder, P. R. Hemmer, J. Wrachtrup, and F. Jelezko, “Singleshot readout of a single nuclear spin,” Science 329(5991), 542–544 (2010). 16. L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science 314(5797), 281–285 (2006). 17. S. Barrett and P. Kok, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. A 71(6), 060310 (2005). 18. G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J. Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hemmer, A. Krueger, T. Hanke, A. Leitenstorfer, R. Bratschitsch, F. 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Chang, “Polarization modulation spectroscopy of single fluorescent nanodiamonds with multiple nitrogen vacancy centers,” J. Phys. Chem. A 115(10), 1878–1884 (2011). 27. F. Grazioso, B. R. Patton, P. Delaney, M. L. Markham, D. J. Twitchen, and J. M. Smith, “Measurement of the full stress tensor in a crystal using photoluminescence from point defects: The example of nitrogen vacancy centers in diamond,” Appl. Phys. Lett. 103(10), 101905 (2013). 28. E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262(5138), 1422–1425 (1993). 29. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001). 30. B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000). 31. M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B 21(6), 1210 (2004). 32. A. V. Failla, H. Qian, H. Qian, A. Hartschuh, and A. J. Meixner, “Orientational imaging of subwavelength Au particles with higher order laser modes,” Nano Lett. 6(7), 1374–1378 (2006). 33. P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009). 34. X. Li, T. H. Lan, C. H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat Commun 3, 998 (2012). 35. F. Wackenhut, A. V. Failla, T. Züchner, M. Steiner, and A. J. Meixner, “Three-dimensional photoluminescence mapping and emission anisotropy of single gold nanorods,” Appl. Phys. Lett. 100(26), 263102 (2012). 36. L. M. Pham, N. Bar-Gill, D. Le Sage, C. Belthangady, A. Stacey, M. Markham, D. J. Twitchen, M. D. Lukin, and R. L. 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#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4380
1. Introduction Nitrogen vacancy (NV) centers, particularly in the negative charge state have attracted considerable interest from several areas of science [1]. As a biological marker, the possibility of monitoring both its location and orientation allows optical microscopy to identify subcellular functionality in entirely new ways [2–6]. The capacity of the host crystal to be functionalised [7] and the center’s nonlinear properties [8] suggest that it is yet to be fully exploited for these applications. In addition the electron’s long coherence time makes it one of the most exciting candidates for a role in quantum information processing, also possessing a microwave transition in the ground state of a spin polarizing optical transition [9–14]. This accommodates the possibility of measurement based entanglement schemes, as well as coherent coupling to proximal nuclear spins [15–17]. In particular, the optically detected magnetic resonance (ODMR) it exhibits has been shown to be a promising magnetic field sensor, with the Zeeman splitting allowing for external magnetic fields to be sensed and imaged with exquisite accuracy, as well as being used as nanoscale thermometers [18–23]. The attention garnered by the center, and the disparate nature of its numerous potential applications indicate the impact it stands to have in various technologies. Without exception, every major potential application of the defect relies in some way on the optical interrogation of the NV centers. Therefore, orientation determination is a crucial step when one attempts to utilize the NV centers for many of its applications, which are often based on the response of the center to local changes in the environment and therefore rely on its complete characterisation. Analysis of ODMR spectra, involving the application of external magnetic fields has been used for highly precise and rapid determination of the orientation of the axis of symmetry of the NV center [3]. Since the photoluminescence of the NV centers is associated with two orthogonal dipoles arranged in a plane perpendicular to the NV defect symmetry axis, it is possible to determine the orientation of NV centers with an optical microscope [24–27]. However these methods involve time consuming linear polarization rotations to determine the photoluminescence anisotropy and are sensitive to both background and particle drift. Considering the wealth of applications that the NV centers can potentially impact, alternative methods of orientation determination may prove invaluable. Orientation determination has been performed for individual molecules with single dipoles in the near field [28], using longitudinal modes of cylindrically polarized light [29], annular illumination [30], and by direct emission pattern imaging [31]. In addition, tightly focusing cylindrically polarized beams have enabled the determination of the orientation of single gold nanoparticles [32–35]. These methods establish the capacity of structured illumination to determine the orientation of single optical dipoles although they are yet to be applied to sources containing multiple dipoles. In this paper it is shown that by accurately detailing the interaction of two orthogonal optical dipoles with the field components of a tightly focussed radially polarized beam, the precise orientation of the NV centers can be determined. This method demonstrates the application of radially polarized imaging to the problem of NV center orientation determination, opening a new avenue for ascertaining its orientation, which may prove vital for many of the applications listed above. 2. Experimental details Samples of high pressure high temperature nanodiamonds (NDs) nominally 100 nm in size were prepared with an acid clean and centrifuged before being drop cast on a coverslip. Atomic force microscopy revealed the processing to have reduced the mean size to be centered on 60 nm. Microwaves were delivered for ODMR by either running a 25 µm diameter wire along the substrate surface or patterning a 25 nm Cr plus 75 nm Au conductive channel directly onto the surface of the coverslip. This variety in microwave delivery did not
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4381
impart any relevant change to the observed spectra. A homebuilt stage scanning confocal microscope was used to acquire images with the 532 nm excitation beam focussed onto the sample through a 1.4 NA oil immersion lens. The photo-luminescence (PL) was imaged onto a multimode fibre and detected with a single photon avalanche diode (SPAD). The radially polarized beam was generated by passing the linearly polarized excitation source through an Arcoptix radial polarization converter (RPC, Fig. 1(a)). This particular converter did not have the functionality to switch easily between azimuthally and radially polarized, although this capability has been shown to improve results [33]. The Fluorescence was either focussed onto a fibre and either coupled straight to a SPAD for imaging and ODMR experiments or passed through a fibre beam splitter and coupled to two separate SPADs, which were used in conjunction with a time correlated single photon counting card to obtain the correlation data.
Fig. 1. (a) Schematic of the optical set up used to image single NV centers with radially polarized beam generated by a radial polarization converter (RPC). Microwaves were delivered though a conductive path on the coverslip. The conical expansion depicts the deposited nanodiamonds with a variety of possible orientations of NV axes. (b) Coordinate system used to label the NV axis orientation, with the optical dipoles in the orthogonal plane labelled d1 & d2. The inset shows the NV axis with respect to a unit cell in the diamond host matrix.
For bulk diamond samples knowledge of the crystalline facet under consideration allows one to limit the orientation of the center to four possibilities [36]. Much of the utility of the center comes from its existence in nanocrystaline diamond, for which no facet knowledge is available. For considering the orientation, the polar angle (θ) and the azimuthal angle (φ) that the NV axis makes with the laboratory frame of reference need to be determined as depicted in Fig. 1(b). The inset of Fig. 1(b) establishes the NV axis as the vector joining the nitrogen and vacancy in the diamond lattice. The plane which the NV axis is normal to contains the two orthogonal optical dipoles responsible for the photoluminescence, labelled d1 and d2. The samples are scanned in the transverse x-y and the optical axis is parallel to the z axis. Initially regions drop-cast with a suitable concentration of ND solution were imaged with a linearly polarized excitation source, subsequent to drying. Although agglomerations and NDs containing multiple NV centers were not uncommon, it was straight forward to find regions with several distinct, well-spaced emitters. Figure 2(a) shows a scan with several such emitters. By inserting a beam splitter and an extra SPAD into the collected fluorescence optical path, it is possible to conduct Hanbury-Brown Twiss (HBT) experiments, where the correlation of the intensities recorded show the characteristic anti-bunching dip for a single emitter. As is evidenced by Fig. 2(b), four of the emitters showed strong anti-bunching dips and were selected for further study.
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4382
Fig. 2. (a) Scanning confocal image of a sample with linearly polarized light (directionality indicated by upper left arrow). (b) HBT data indicating singularity of NV centers labelled 1-4. Count rates dropping to below half the 0 ns delay value indicates a positive result. (c) The same region as imaged in (a), but with a radially polarized beam (indicated by the arrows in upper left). Four NV centers are highlighted and labelled for further analysis.
Once a region containing several good candidates for optical analysis was identified, a radial polarization converter was inserted into the excitation path. Figure 2(c) shows the same region imaged for a second time with a radially polarized beam at the same power. A clear difference in the emission patterns was observed upon switching polarization of the incident light. When imaging with a linearly polarized beam, each of the single NV centers has a Gaussian distribution with a diffraction-limited extent. However, the image gains distinguishable lobe structures when switched to imaging with a radially polarized beam. These differences can be attributed to the richer distribution of focal electric field components owing to the depolarization effect when focusing the radially polarized beam with a high numerical aperture [37]. 2. Modeling details In order to model the effect the polarization of the excitation light has on the PL observed, a full description of the field distribution at the focus is required. By making use of the vectorial Debye integrals shown in Eqs. (1) and (2) the field distributions can be computed [38]. These are algebraically most convenient to write in terms of the field contribution in the longitudinal (Ez) and radial directions (Eρ), although these can be mapped onto Cartesian or cylindrical coordinate systems as required. E z ( ρ ) = 2iE0
α
0
E z ( ρ ) = E0
α
0
cos(θ ) sin 2 (θ ) J 0 ( k ρ sin(θ ))eik cos(θ ) dθ .
cos(θ ) sin(2θ ) J 1 ( k ρ sin(θ ))eik cos(θ ) dθ .
(1) (2)
Here the integral is performed over the polar angle (θ) with an upper bound determined by the NA of the objective lens. The field strength at the pupil aperture is E0 , J n refers to the nth order Bessel function of the first kind and k is the wave vector of the light in the medium (taken as immersion oil, with refractive index n = 1.514). In this way a field vector can be attributed to every point in the focal plane. In order to ascertain the emission pattern from scanning an NV center through this field distribution, it is necessary to consider the contributions of two orthogonal dipoles lying in the plane which the NV center axis is normal to. Programmatically this is achieved by first defining the NV axis and the two optical dipoles ( d1 and d 2 ) as unit vectors lying parallel to the z, y and x axes respectively. All three vectors were then rotated appropriately by amounts θ and φ. The emission rate of the specifically
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4383
oriented NV center is calculated by the product of the projection of each dipole on the x-y plane with the electric field is then calculated for each location with the expression as follows, 2
I ( x, y ) = ( d1 E ( x, y )) + ( d2 E ( x, y )) .
(3)
Here the intensity I is the intensity at the point ( x, y ) in the focal plane, d1 and d 2 are the optical dipoles and E ( x, y ) is the given by the Debye equations. Programmatically a script was developed which allowed for the emission patterns of an arbitrarily orientated NV center axis to be quickly displayed. As one would expect these patterns are invariant for rotations about the NV center axis itself.
Fig. 3. A range of simulated far-field emission patterns for a range of NV center orientations. The orientation of the pattern is determined by φ whilst the structure of the pattern is due to the polar angle, θ. For values of θ = 0 there is no coupling to the central z field, however as θ → 90 the component of the dipoles lying parallel to the optical axis ultimately dominates the farfield emission pattern. Each image plotted corresponds to a focal region of 1x1 µm.
Figure 3 shows a range of emission patterns for several different values of θ and φ. The orientation has a distinct effect on the emission patterns detected when scanning the NV centers through such a focal field distribution. For values of θ = 0° both optical dipoles d1 and d 2 lie in the plane. With this arrangement, both dipoles couple equally well to the transverse field and the distinctive annulus pattern is observed. As the value of θ is increased the dipoles begin to have a component lying parallel to the optical axis. This component couples to the central longitudinal lobe of the focused radially polarized beam. For non-zero values of θ, the value of φ can be ascertained from the line connecting the intensity maximum to the local minimum of the emission pattern. In this way the azimuthal angle is identified without the ambiguity of a 180° rotation around the optical axis, as the emission pattern is not symmetric under a 180° rotation. The same cannot be said of the alternative optical method of orientation determination, by rotating linearly polarized light. Admittedly this ambiguity returns once the NV center axis has been rotated to lie completely in the focal plane (θ = 90°), as the final column now has such rotational symmetry. Here the coupling to the central longitudinal lobe
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4384
of the field dominates the emission pattern, and the imaging benefits from the sharp focal spot as previously reported [37]. 3. Results and discussion
The results of the model were then used to determine the orientation of the four single emitters identified in Fig. 2. Values of φ and θ were varied until a visual match was obtained with the higher resolution experimental images shown in Fig. 4(a). Although this fitting method was performed manually, it would be straightforward to develop an algorithmic approach with suitable image processing software.
Fig. 4. (a) Higher resolution far-field images of the 4 centers identified in Fig. 2. Scale bar 500 nm. (b) Depiction of the orientation of each of the NV center determined by radial imaging. (c) Fluorescence dependence of each center on the orientation of the linearly polarized excitation source. For NV1 the strongest fluctuation in fluorescence is observed, corresponding to a large polar angle. NV4 exhibits very little fluctuation suggesting both optical dipoles lie almost parallel to the focal plane. Two possible values of φ are given by the location of the minima. Values for θ are calculated using Eq. (4). (d) ODMR peak splitting plotted against the orientation of the (B) field in the focal plane. The location of the maximum indicates alignment of (B) field and the projection of the NV axis on the transverse plane and is equal to φ.
The orientation inferred from the modelling is depicted in Fig. 4(b). Clearly the emission pattern for NV 4 closely resembles the annular distribution of the transverse component of the focussed radially polarized beam, and therefore possesses a small angle of θ. The slight disparity in the intensities is enough to infer a value for φ, although this value loses relevance as θ tends to 0.
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4385
In order to corroborate these values of θ and φ two established alternative methods were employed. The first of these is the Fluorescence variation with the polarization angle of a linearly polarized excitation source. In these plots the value of φ is given directly by the location of the minimum, although as mentioned previously it is ambiguous to 180° rotations. In each of the four centers one of the minima agrees with the value suggested by the image analysis. The value for θ can be calculated using Eq. (4), the results for both values are tabulated in the third major column of Table 1, and are discussed further at a later stage.
θ = cos−1
I min . I max
(4)
The final experimental method for determining the orientation of the centers takes advantage of the ODMR response of the center. Here a static magnetic field, B is arranged to lie in the focal plane. The resultant resonance splitting is dependent on the projection of the B field onto the NV center axis defined previously. Figure 4(d) shows the frequency splitting of the ODMR response as the field in the plane was rotated by 180°. In this case it is the maximum which corresponds to the value of φ, as the field causes maximum splitting when aligned to be parallel with the projection of the NV center axis on the focal plane. Determination of the polar angle from the ODMR spectra is possible with precise knowledge of the strength of the magnetic field in the focal plane, but the agreement already displayed was judged sufficient to establish the credibility of the radially polarized imaging approach. Table 1. Orientation of NV centers
Radial imaging (deg.)
Linear polarization rotation (deg.) Azimuthal Polar angle angle (φ) (θ)
ODMR (deg.) Azimuthal angle (φ)
NV center
Azimuthal angle (φ)
Polar angle (θ)
1
345±4
80±5
349.2±4.2
58.2±1.2
342.5±1.2
2
30±4
42±5
31.6±1.5
40.6±1.1
30.1±1.5
3
175±4
50±5
172±1.7
51.8±1.2
173.4±1.6
4
340±4
20±5
345.1±4.2
25.8±2.3
337.1±1.4
The first important feature to note in comparing the first and second major columns of the table is the disagreement for the NV center with a dipole lying out of the focal plane (NV 1). When calculating θ from the linear polarization rotation, it is assumed that the Fluorescence drops to zero as θ approaches 90° and when the polarization is parallel to φ. Whilst this is true as long at the NV center is located precisely at the center of the linearly focused beam, depolarization effects of the high NA lens generate an appreciable field in the longitudinal direction that would couple well to an NV with θ ≈90°. For the case of NDs it is also difficult to quantify precisely background counts which should be subtracted when determining fluorescence levels. For these reasons, it is suggested that the rotation of linearly polarized light is not a robust method for ascertaining an accurate value of θ as it approaches 90°. When a radially polarized beam is used this is not the case. A second point to note about characterization using the rotation of linearly polarized light is that it is inherently ambiguous for rotations of 180°. Specifically in the depiction given in Fig. 1, this method cannot distinguish between an NV center with azimuthal angles of φ or φ + 180°, whilst the radial imaging only suffers such ambiguity when θ equals precisely 0° or 90°. The values of φ listed in the table for the linear rotation have been shifted by 180° where
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4386
appropriate to facilitate the comparison with the radially polarized approach. The final major column of Table 1 contains results obtained by rotating the angle of a magnetic field in the xy plane. Without information about the precise field strength at the location of the NV center, it was not possible to obtain reliable values for the polar angle, however the angles ascertained for the azimuthal angle are in good agreement with the two other approaches. 4. Conclusions
In this paper we have presented a precise method for determining the orientation of NV centers in NDs. This feature is achieved by imaging the two orthogonal optical dipoles of NV centers with a radially polarized beam. The demonstrated technique paves the way for polarization microscopy to control the light-matter interaction, for example, for single molecule/particle detection [23] and polarization-sensitive optical data storage [33,34]. Acknowledgments
We would like to acknowledge S. Castelletto for the provision of the NDs and D. Simpson for his helpful advice on details of ODMR. This work was supported by the Australian Research Council Laureate Fellowship project (FL100100099).
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4387
Abstract: In this paper, we report on the precise determination of the orientation of NV centers by imaging with a radially polarized beam. Vectorial Debye theory is applied to the field in the focus of radially polarized beams to generate emission profiles of two orthogonal optical dipoles. By comparing features of the measured emission intensity patterns with simulated results, complete orientation determination of the NV axis is achieved. Results are corroborated by using established methods requiring the polarization rotation of a linearly polarized excitation source, and by analysis of optically detected magnetic resonance spectra. These results lay new ground for any application where the knowledge of the orientation of the NV centers is prerequisite. ©2014 Optical Society of America OCIS codes: (260.0260) Physical optics; (260.2510) Fluorescence; (260.5430) Polarization.
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#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4380
1. Introduction Nitrogen vacancy (NV) centers, particularly in the negative charge state have attracted considerable interest from several areas of science [1]. As a biological marker, the possibility of monitoring both its location and orientation allows optical microscopy to identify subcellular functionality in entirely new ways [2–6]. The capacity of the host crystal to be functionalised [7] and the center’s nonlinear properties [8] suggest that it is yet to be fully exploited for these applications. In addition the electron’s long coherence time makes it one of the most exciting candidates for a role in quantum information processing, also possessing a microwave transition in the ground state of a spin polarizing optical transition [9–14]. This accommodates the possibility of measurement based entanglement schemes, as well as coherent coupling to proximal nuclear spins [15–17]. In particular, the optically detected magnetic resonance (ODMR) it exhibits has been shown to be a promising magnetic field sensor, with the Zeeman splitting allowing for external magnetic fields to be sensed and imaged with exquisite accuracy, as well as being used as nanoscale thermometers [18–23]. The attention garnered by the center, and the disparate nature of its numerous potential applications indicate the impact it stands to have in various technologies. Without exception, every major potential application of the defect relies in some way on the optical interrogation of the NV centers. Therefore, orientation determination is a crucial step when one attempts to utilize the NV centers for many of its applications, which are often based on the response of the center to local changes in the environment and therefore rely on its complete characterisation. Analysis of ODMR spectra, involving the application of external magnetic fields has been used for highly precise and rapid determination of the orientation of the axis of symmetry of the NV center [3]. Since the photoluminescence of the NV centers is associated with two orthogonal dipoles arranged in a plane perpendicular to the NV defect symmetry axis, it is possible to determine the orientation of NV centers with an optical microscope [24–27]. However these methods involve time consuming linear polarization rotations to determine the photoluminescence anisotropy and are sensitive to both background and particle drift. Considering the wealth of applications that the NV centers can potentially impact, alternative methods of orientation determination may prove invaluable. Orientation determination has been performed for individual molecules with single dipoles in the near field [28], using longitudinal modes of cylindrically polarized light [29], annular illumination [30], and by direct emission pattern imaging [31]. In addition, tightly focusing cylindrically polarized beams have enabled the determination of the orientation of single gold nanoparticles [32–35]. These methods establish the capacity of structured illumination to determine the orientation of single optical dipoles although they are yet to be applied to sources containing multiple dipoles. In this paper it is shown that by accurately detailing the interaction of two orthogonal optical dipoles with the field components of a tightly focussed radially polarized beam, the precise orientation of the NV centers can be determined. This method demonstrates the application of radially polarized imaging to the problem of NV center orientation determination, opening a new avenue for ascertaining its orientation, which may prove vital for many of the applications listed above. 2. Experimental details Samples of high pressure high temperature nanodiamonds (NDs) nominally 100 nm in size were prepared with an acid clean and centrifuged before being drop cast on a coverslip. Atomic force microscopy revealed the processing to have reduced the mean size to be centered on 60 nm. Microwaves were delivered for ODMR by either running a 25 µm diameter wire along the substrate surface or patterning a 25 nm Cr plus 75 nm Au conductive channel directly onto the surface of the coverslip. This variety in microwave delivery did not
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4381
impart any relevant change to the observed spectra. A homebuilt stage scanning confocal microscope was used to acquire images with the 532 nm excitation beam focussed onto the sample through a 1.4 NA oil immersion lens. The photo-luminescence (PL) was imaged onto a multimode fibre and detected with a single photon avalanche diode (SPAD). The radially polarized beam was generated by passing the linearly polarized excitation source through an Arcoptix radial polarization converter (RPC, Fig. 1(a)). This particular converter did not have the functionality to switch easily between azimuthally and radially polarized, although this capability has been shown to improve results [33]. The Fluorescence was either focussed onto a fibre and either coupled straight to a SPAD for imaging and ODMR experiments or passed through a fibre beam splitter and coupled to two separate SPADs, which were used in conjunction with a time correlated single photon counting card to obtain the correlation data.
Fig. 1. (a) Schematic of the optical set up used to image single NV centers with radially polarized beam generated by a radial polarization converter (RPC). Microwaves were delivered though a conductive path on the coverslip. The conical expansion depicts the deposited nanodiamonds with a variety of possible orientations of NV axes. (b) Coordinate system used to label the NV axis orientation, with the optical dipoles in the orthogonal plane labelled d1 & d2. The inset shows the NV axis with respect to a unit cell in the diamond host matrix.
For bulk diamond samples knowledge of the crystalline facet under consideration allows one to limit the orientation of the center to four possibilities [36]. Much of the utility of the center comes from its existence in nanocrystaline diamond, for which no facet knowledge is available. For considering the orientation, the polar angle (θ) and the azimuthal angle (φ) that the NV axis makes with the laboratory frame of reference need to be determined as depicted in Fig. 1(b). The inset of Fig. 1(b) establishes the NV axis as the vector joining the nitrogen and vacancy in the diamond lattice. The plane which the NV axis is normal to contains the two orthogonal optical dipoles responsible for the photoluminescence, labelled d1 and d2. The samples are scanned in the transverse x-y and the optical axis is parallel to the z axis. Initially regions drop-cast with a suitable concentration of ND solution were imaged with a linearly polarized excitation source, subsequent to drying. Although agglomerations and NDs containing multiple NV centers were not uncommon, it was straight forward to find regions with several distinct, well-spaced emitters. Figure 2(a) shows a scan with several such emitters. By inserting a beam splitter and an extra SPAD into the collected fluorescence optical path, it is possible to conduct Hanbury-Brown Twiss (HBT) experiments, where the correlation of the intensities recorded show the characteristic anti-bunching dip for a single emitter. As is evidenced by Fig. 2(b), four of the emitters showed strong anti-bunching dips and were selected for further study.
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4382
Fig. 2. (a) Scanning confocal image of a sample with linearly polarized light (directionality indicated by upper left arrow). (b) HBT data indicating singularity of NV centers labelled 1-4. Count rates dropping to below half the 0 ns delay value indicates a positive result. (c) The same region as imaged in (a), but with a radially polarized beam (indicated by the arrows in upper left). Four NV centers are highlighted and labelled for further analysis.
Once a region containing several good candidates for optical analysis was identified, a radial polarization converter was inserted into the excitation path. Figure 2(c) shows the same region imaged for a second time with a radially polarized beam at the same power. A clear difference in the emission patterns was observed upon switching polarization of the incident light. When imaging with a linearly polarized beam, each of the single NV centers has a Gaussian distribution with a diffraction-limited extent. However, the image gains distinguishable lobe structures when switched to imaging with a radially polarized beam. These differences can be attributed to the richer distribution of focal electric field components owing to the depolarization effect when focusing the radially polarized beam with a high numerical aperture [37]. 2. Modeling details In order to model the effect the polarization of the excitation light has on the PL observed, a full description of the field distribution at the focus is required. By making use of the vectorial Debye integrals shown in Eqs. (1) and (2) the field distributions can be computed [38]. These are algebraically most convenient to write in terms of the field contribution in the longitudinal (Ez) and radial directions (Eρ), although these can be mapped onto Cartesian or cylindrical coordinate systems as required. E z ( ρ ) = 2iE0
α
0
E z ( ρ ) = E0
α
0
cos(θ ) sin 2 (θ ) J 0 ( k ρ sin(θ ))eik cos(θ ) dθ .
cos(θ ) sin(2θ ) J 1 ( k ρ sin(θ ))eik cos(θ ) dθ .
(1) (2)
Here the integral is performed over the polar angle (θ) with an upper bound determined by the NA of the objective lens. The field strength at the pupil aperture is E0 , J n refers to the nth order Bessel function of the first kind and k is the wave vector of the light in the medium (taken as immersion oil, with refractive index n = 1.514). In this way a field vector can be attributed to every point in the focal plane. In order to ascertain the emission pattern from scanning an NV center through this field distribution, it is necessary to consider the contributions of two orthogonal dipoles lying in the plane which the NV center axis is normal to. Programmatically this is achieved by first defining the NV axis and the two optical dipoles ( d1 and d 2 ) as unit vectors lying parallel to the z, y and x axes respectively. All three vectors were then rotated appropriately by amounts θ and φ. The emission rate of the specifically
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4383
oriented NV center is calculated by the product of the projection of each dipole on the x-y plane with the electric field is then calculated for each location with the expression as follows, 2
I ( x, y ) = ( d1 E ( x, y )) + ( d2 E ( x, y )) .
(3)
Here the intensity I is the intensity at the point ( x, y ) in the focal plane, d1 and d 2 are the optical dipoles and E ( x, y ) is the given by the Debye equations. Programmatically a script was developed which allowed for the emission patterns of an arbitrarily orientated NV center axis to be quickly displayed. As one would expect these patterns are invariant for rotations about the NV center axis itself.
Fig. 3. A range of simulated far-field emission patterns for a range of NV center orientations. The orientation of the pattern is determined by φ whilst the structure of the pattern is due to the polar angle, θ. For values of θ = 0 there is no coupling to the central z field, however as θ → 90 the component of the dipoles lying parallel to the optical axis ultimately dominates the farfield emission pattern. Each image plotted corresponds to a focal region of 1x1 µm.
Figure 3 shows a range of emission patterns for several different values of θ and φ. The orientation has a distinct effect on the emission patterns detected when scanning the NV centers through such a focal field distribution. For values of θ = 0° both optical dipoles d1 and d 2 lie in the plane. With this arrangement, both dipoles couple equally well to the transverse field and the distinctive annulus pattern is observed. As the value of θ is increased the dipoles begin to have a component lying parallel to the optical axis. This component couples to the central longitudinal lobe of the focused radially polarized beam. For non-zero values of θ, the value of φ can be ascertained from the line connecting the intensity maximum to the local minimum of the emission pattern. In this way the azimuthal angle is identified without the ambiguity of a 180° rotation around the optical axis, as the emission pattern is not symmetric under a 180° rotation. The same cannot be said of the alternative optical method of orientation determination, by rotating linearly polarized light. Admittedly this ambiguity returns once the NV center axis has been rotated to lie completely in the focal plane (θ = 90°), as the final column now has such rotational symmetry. Here the coupling to the central longitudinal lobe
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4384
of the field dominates the emission pattern, and the imaging benefits from the sharp focal spot as previously reported [37]. 3. Results and discussion
The results of the model were then used to determine the orientation of the four single emitters identified in Fig. 2. Values of φ and θ were varied until a visual match was obtained with the higher resolution experimental images shown in Fig. 4(a). Although this fitting method was performed manually, it would be straightforward to develop an algorithmic approach with suitable image processing software.
Fig. 4. (a) Higher resolution far-field images of the 4 centers identified in Fig. 2. Scale bar 500 nm. (b) Depiction of the orientation of each of the NV center determined by radial imaging. (c) Fluorescence dependence of each center on the orientation of the linearly polarized excitation source. For NV1 the strongest fluctuation in fluorescence is observed, corresponding to a large polar angle. NV4 exhibits very little fluctuation suggesting both optical dipoles lie almost parallel to the focal plane. Two possible values of φ are given by the location of the minima. Values for θ are calculated using Eq. (4). (d) ODMR peak splitting plotted against the orientation of the (B) field in the focal plane. The location of the maximum indicates alignment of (B) field and the projection of the NV axis on the transverse plane and is equal to φ.
The orientation inferred from the modelling is depicted in Fig. 4(b). Clearly the emission pattern for NV 4 closely resembles the annular distribution of the transverse component of the focussed radially polarized beam, and therefore possesses a small angle of θ. The slight disparity in the intensities is enough to infer a value for φ, although this value loses relevance as θ tends to 0.
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4385
In order to corroborate these values of θ and φ two established alternative methods were employed. The first of these is the Fluorescence variation with the polarization angle of a linearly polarized excitation source. In these plots the value of φ is given directly by the location of the minimum, although as mentioned previously it is ambiguous to 180° rotations. In each of the four centers one of the minima agrees with the value suggested by the image analysis. The value for θ can be calculated using Eq. (4), the results for both values are tabulated in the third major column of Table 1, and are discussed further at a later stage.
θ = cos−1
I min . I max
(4)
The final experimental method for determining the orientation of the centers takes advantage of the ODMR response of the center. Here a static magnetic field, B is arranged to lie in the focal plane. The resultant resonance splitting is dependent on the projection of the B field onto the NV center axis defined previously. Figure 4(d) shows the frequency splitting of the ODMR response as the field in the plane was rotated by 180°. In this case it is the maximum which corresponds to the value of φ, as the field causes maximum splitting when aligned to be parallel with the projection of the NV center axis on the focal plane. Determination of the polar angle from the ODMR spectra is possible with precise knowledge of the strength of the magnetic field in the focal plane, but the agreement already displayed was judged sufficient to establish the credibility of the radially polarized imaging approach. Table 1. Orientation of NV centers
Radial imaging (deg.)
Linear polarization rotation (deg.) Azimuthal Polar angle angle (φ) (θ)
ODMR (deg.) Azimuthal angle (φ)
NV center
Azimuthal angle (φ)
Polar angle (θ)
1
345±4
80±5
349.2±4.2
58.2±1.2
342.5±1.2
2
30±4
42±5
31.6±1.5
40.6±1.1
30.1±1.5
3
175±4
50±5
172±1.7
51.8±1.2
173.4±1.6
4
340±4
20±5
345.1±4.2
25.8±2.3
337.1±1.4
The first important feature to note in comparing the first and second major columns of the table is the disagreement for the NV center with a dipole lying out of the focal plane (NV 1). When calculating θ from the linear polarization rotation, it is assumed that the Fluorescence drops to zero as θ approaches 90° and when the polarization is parallel to φ. Whilst this is true as long at the NV center is located precisely at the center of the linearly focused beam, depolarization effects of the high NA lens generate an appreciable field in the longitudinal direction that would couple well to an NV with θ ≈90°. For the case of NDs it is also difficult to quantify precisely background counts which should be subtracted when determining fluorescence levels. For these reasons, it is suggested that the rotation of linearly polarized light is not a robust method for ascertaining an accurate value of θ as it approaches 90°. When a radially polarized beam is used this is not the case. A second point to note about characterization using the rotation of linearly polarized light is that it is inherently ambiguous for rotations of 180°. Specifically in the depiction given in Fig. 1, this method cannot distinguish between an NV center with azimuthal angles of φ or φ + 180°, whilst the radial imaging only suffers such ambiguity when θ equals precisely 0° or 90°. The values of φ listed in the table for the linear rotation have been shifted by 180° where
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4386
appropriate to facilitate the comparison with the radially polarized approach. The final major column of Table 1 contains results obtained by rotating the angle of a magnetic field in the xy plane. Without information about the precise field strength at the location of the NV center, it was not possible to obtain reliable values for the polar angle, however the angles ascertained for the azimuthal angle are in good agreement with the two other approaches. 4. Conclusions
In this paper we have presented a precise method for determining the orientation of NV centers in NDs. This feature is achieved by imaging the two orthogonal optical dipoles of NV centers with a radially polarized beam. The demonstrated technique paves the way for polarization microscopy to control the light-matter interaction, for example, for single molecule/particle detection [23] and polarization-sensitive optical data storage [33,34]. Acknowledgments
We would like to acknowledge S. Castelletto for the provision of the NDs and D. Simpson for his helpful advice on details of ODMR. This work was supported by the Australian Research Council Laureate Fellowship project (FL100100099).
#201175 - $15.00 USD Received 13 Nov 2013; accepted 7 Jan 2014; published 19 Feb 2014 (C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.004379 | OPTICS EXPRESS 4387
