Near-field imaging and frequency tuning of a high-Q photonic crystal membrane microcavity
S. Mujumdar, A. F. Koenderink, T. Suenner, B. C. Buchler, M. Kamp, A. Forchel, V. Sandoghdar
aa r X i v : . [ c ond - m a t . o t h e r] S e p Near-field imaging and frequency tuning ofa high- Q photonic crystal membrane microcavity S. Mujumdar, ∗ A. F. Koenderink, † T. S¨unner, B. C.Buchler, ‡ M. Kamp, A. Forchel, and V. Sandoghdar Laboratory of Physical Chemistry and optETH, ETH Zurich, CH-8093 Zurich, Switzerland Technische Physik, Universit¨at W¨urzburg, Am Hubland, D-97074 W¨urzburg, Germany (Dated: November 15, 2018)
Abstract
We discuss experimental studies of the interaction between a nanoscopic object and a photoniccrystal membrane resonator of quality factor Q =55000. By controlled actuation of a glass fibertip in the near field of the photonic crystal, we constructed a complete spatio-spectral map of theresonator mode and its coupling with the fiber tip. On the one hand, our findings demonstrate thatscanning probes can profoundly influence the optical characteristics and the near-field images ofphotonic devices. On the other hand, we show that the introduction of a nanoscopic object providesa low loss method for on-command tuning of a photonic crystal resonator frequency. Our resultsare in a very good agreement with the predictions of a combined numerical/analytical theory. ∗ Present address: Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400 005, India † Present address: Center for Nanophotonics, FOM Institute AMOLF, Kruislaan 407, NL-1098SJ Amster-dam, The Netherlands ‡ Present address: ARC Centre of Excellence for Quantum Atom Optics, Department of Physics, The Aus-tralian National University, Canberra, Australia Q . Our results have important implicationsfor SNOM imaging, controlled tuning of high- Q photonic devices and optical sensing.Microcavities have stimulated a great deal of activity in design and fabrication of newoptical systems [7]. For most applications in quantum optics, integrated optics and opticalsensing it is desirable to increase Q and decrease the mode volume V . As the microcavitiesbecome smaller though, the Q often begins to degrade either because of the relative im-portance of surfaces or because of diffraction losses. Resonators based on photonic crystal(PC) structures offer a good compromise [8, 9, 10, 11]. By controlling the subwavelengthfeatures of PC structures, scientists have demonstrated their potential for molding the flowof light [12, 13]. However, the intrinsic sensitivity of a PC performance to its nanoscopicfeatures also imposes stringent demands on its fabrication accuracy. Considering that to-day’s control in nanofabrication is still not sufficient to produce PCs with the exact designparameters, it is imperative to 1) characterize the end product and 2) fine tune its propertiesafter manufacturing. In this work, we address both of these issues in the near field.In the past few years, several groups have demonstrated the power of SNOM and relatedtechniques for imaging light propagation and confinement in PC structures [14, 15, 16,17, 18, 19, 20]. Recently, we theoretically analyzed the influence of a nano-object on thespectral resonance and the intensity distribution of a PC microresonator with Q = 13000.We concluded that depending on the polarizability of the tip, its influence might no longerbe negligible for cavities of low V and high Q [21]. We found that in general, the tip couldintroduce a frequency shift and a broadening in the resonance of the PC mode. However,we also showed that the effect of the tip could be exploited to one’s advantage for tuningthe microcavity resonance by a large amount without inflicting a significant broadening [21].Indeed, the promise of this technique has been already recognized and the first experimentalattempts along this line have been pursued by applying silicon tips to PC cavities with low2 IG. 1: Scanning electron micrograph of the heterostructure. The yellow lines mark regionswith different lattice constants. a =410 nm, a = 400 nm. (b) Schematics of the experimentalarrangement. (c) The unperturbed cavity resonance as measured in the far field. The red curveis a Lorentzian fit to the measured data (black circles). (d) The calculated (FDTD) intensitydistribution on resonance in the region marked by the white rectangle in Fig. (a). Q s of the order of 500 [22, 23]. However, the observed frequency shifts were accompaniedby substantial broadenings of the cavity resonances. While these results are of interest forswitching purposes, the large induced loss would suggest that they are not suitable for tuninghigh- Q systems.The design of high- Q PC resonators has witnessed a tremendous progress in the lastfive years [24, 25]. Nevertheless, structures with Q & Q values beyond 10 [11], but GaAs based structures have been more difficult tomaster [10, 26]. As depicted in Fig. 1(a), we have used a line-defect heterostructure cavitydesign [9] realized by connecting crystals with lattice parameters a = 410 nm, a = 400nm and r/a = 0 .
23 in a 221 nm thick GaAs membrane ( ǫ = 11 .
39) [27]. A collinear W1waveguide throughout the two lattices resulted in a mode gap in the transmission banddiagram of the structure, confining light in the longitudinal direction, while the photonicbandgap confined light in the transverse direction. Two heterostructures were further createdon either side of the cavity to facilitate incoupling and outcoupling of light. The details ofthe fabrication procedure are reported in Ref. [10].3inearly polarized laser light from a grating-tunable diode laser (linewidth <
300 KHz,tuning range 1550 nm - 1630 nm) was focussed onto one end facet of the membrane using alarge numerical aperture lens (NA = 0.68). To facilitate the incoupling, the W1 waveguideof the cavity was gradually enlarged to a W3 waveguide at the input facet of the fabricatedmembrane. As sketched in Fig. 1(b), a small fraction of light is typically scattered fromthe surface of a PC resonator. This light was detected using a lens system and was sent toa sensitive InGaAs camera or avalanche photodiode (APD) to perform spectroscopy on thepassive resonator. Figure 1(c) displays an experimental spectrum centered at λ =1565.38and a Lorentzian fit, yielding a linewidth of 28 pm corresponding to Q = 55000. We pointout that over the months that our measurements were made, the Q remained the same,but the cavity resonance frequency shifted, possibly due to environmental changes. Asa result, the exact resonance frequencies discussed in what follows might differ from onestudy to the next although they were all performed on the same PC resonator. Figure1(d) shows the light intensity distribution within the cavity on resonance calculated usingthe three-dimensional finite difference time domain (FDTD) method [28, 29]. We employedLiao absorbing boundary conditions with grid spacings a/
14 in the lateral and a/
28 in thevertical dimensions and used volume averaging of epsilon to improve the resolution [30].As depicted in Fig. 1(b), we employed a SNOM setup to access the cavity mode in thenear field. We used a sharp uncoated heat-pulled fiber tip (diameter ∼
100 nm) glued ontoa quartz tuning fork. Shear-force tip-sample distance stabilization was used to maintain thetip at a distance of about 10 nm from the membrane and to image the sample topography.The optical fiber tip detected the evanescent light intensity above the surface using theInGaAs APD at a typical resolution of 100 nm. Figure 2 shows tiles of recorded imagesillustrating the near-field intensity distribution recorded at various fixed wavelengths closeto the cavity resonance. At λ = 1565 . λ = 1565 .
16 nm, the light intensity begins to enterthe cavity region, but it also leaks into the PC structure (tiles B & C). At λ = 1565 . λ = 1565 .
22 nm − . IG. 2: Tiles A through M represent SNOM images of the intensity distribution in the PC structureat different wavelengths indicated in each image. Each image is normalized independently accordingto the color scale shown. waveguide light is overwhelmed in images D-K. These measurements show the first near-fieldmeasurements of light distribution in a high- Q PC cavity. They also reveal a drastic spatial variation of the intensity distribution within a very narrow wavelength range. The deviationof the images D-K from that of Fig. 1(d) hints to the influence of the tip. In other words,at each wavelength the structure admits light only for a specific locus of the tip positions.In order to verify our experimental findings and their interpretation, one could performcomputationally intensive FDTD calculations for each tip position. However, a faster andmore instructive check could be achieved by applying the perturbative treatment describedin Ref. [21]. The frequency detuning ∆ ω induced by the tip, or in general a nanoscopicperturber, is given by, ∆ ωω = − α eff | E ( r k ) | R ǫ ( r ) | E | d r exp( − z p /d ) (1)where α eff = 3 V eff ( ǫ p − / ( ǫ p + 2) is the perturber’s effective polarizability, z p is its sepa-ration from the sample, and d is the interaction length of the evanescent part of the cavitymode, found to be 50 nm in FDTD calculations [21]. We used the results of the 3D FDTD5 IG. 3: Calculated intensity distribution at different wavelengths, based on 3D FDTD simulationssupplemented with first-order perturbation calculations to take into account the impact of the fibertip. At each wavelength, the structure is resonant with the incident laser for selected locationsof the tip. The calculation only considered the cavity mode without the waveguide mode. Eachimage is normalized independently according to the color scale shown. calculations for | E | shown in Fig. 1(d), the typical value of r p = 50 nm for an uncoatedSNOM tip, and the perturber effective volume V eff = πr p d to compute the resonance fre-quency detuning ∆ ω at each pixel. Next, we took into account a Lorentzian profile witha full width at half-maximum of 28 pm (see Fig. 1(c)) for the cavity spectrum and thencalculated the intensity of light at a wavelength of interest. A selection of the results corre-sponding to or very close to the wavelengths of the experimental images in Fig. 2D-M arepresented in Fig. 3A-J. We remark that since the FDTD calculations did not consider thewaveguide mode, the theoretical images in Fig. 3 do not reproduce Figs. 2A-C or Figs. 2L-M. In fact, Figs. 3I-J indicate that the experimental images of Figs. 2L-M are dominatedby the waveguide mode. The theoretical and experimental results show a very good semi-quantitative agreement and confirm that the tip influences the cavity resonance frequencyin a subwavelength position dependent manner.Next, we analyzed the complete perturbation landscape by recording SNOM spectra fortip positions in the x-y plane. At each tip position, the laser wavelength was scanned,6 IG. 4: a) The peak wavelengths of the detuned cavity resonance as a function of tip location. b)Four examples of the local resonance spectra measured through the SNOM tip at the indicatedlocations A-D in part (a). giving results such as those shown in Fig. 4(b). The wavelength of peak intensity for eachtip position is plotted in Fig 4(a) to give a detailed map of the change in cavity frequencyinduced by the tip. Over subwavelength displacements (e.g. see the points ‘A’ to ‘D’), theresonance shifts by more than 3 linewidths. As predicted in Ref. [21], the spatial variationof the tip-induced resonance frequency shift resembles the distribution of the intensity inthe unperturbed cavity shown in Fig. 1(d). Figure 4(b) plots examples of spectra recordedat points A-D, revealing that the resonance lines could deviate from a Lorentzian shape,making it difficult to assess a quantitative measure of the Q degradation. However, the dataclearly show that the tip-induced broadening is negligible compared to the frequency shift.In conclusion, we have used a scanning near-field probe to study the spatio-spectralfeatures of light in a photonic crystal membrane cavity of Q =55000. The data in Figs. 1, 2,and 3 show that at any given laser frequency, the resonator admits light only if the probe7s positioned with subwavelength accuracy on a specific locus of points. We expect similarresults also for other cavities with high- Q s and small volumes. The extreme spectral andspatial sensitivities of such structures to the presence of a subwavelength object such asa tip means that SNOM images of photonic structures would have to be interpreted withcare. On the other hand, these sensitivities offer opportunities for a number of applications.In particular, we have demonstrated that the resonance spectrum of a microcavity can bemanipulated at will by actuating a nanoscopic object without a notable sacrifice in theresonator Q . Such a nanomechanical actuation could be exploited in compact devices suchas high- Q filters or routers. Furthermore, our findings indicate that a nanoparticle or ananoscopic flow of fluid would result in the spectral modification of the cavity and could beused for sensing. High- Q cavities are advantageous for these applications because one cankeep the nano-object of interest at fairly large distances of several tens of nanometers.We are grateful to C. M. Soukoulis, M. Kafesaki and M. 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