1. Introduction

Scanning near field optical microscopy (SNOM) has been use in by several research groups in recent years for the characterization of various nano photonic structures, in particular photonic crystal based waveguides and cavities [1–11]. The ability to map the near field distribution of a nano photonic structure using SNOM is hampered however since the tiny SNOM tip affects the field distribution [2,3,5–8]. The disturbance induced by the SNOM tip is particularly severe in nano cavities where the position, size and type of a SNOM tip have been used to actually tune cavity resonances in a controllable manner [7]. A theoretical calculation that assumes small perturbations by the tip affecting the resonance frequency and the cavity-Q [3] has been confirmed in experiments with a photonic crystal cavity placed along a defect waveguide which use both bare (uncoated) [7,9] and metal coated [5] SNOM tips.

In this paper we describe a series of SNOM measurements characterizing the wavelength and polarization dependences of the field distribution in a GaAs photonic crystal cavity placed near and coupled to a defect waveguide. These cavities have extremely high Q-values [12] and as such are important for many quantum optics experiments. Side coupling of such cavities to waveguides enables complex arrangements of multi cavity systems which will be imperative in quantum processing and computing applications. Near field imaging and examination of the polarization properties are crucial for a full understanding of these complex systems. The evanescent and scattered field distributions of the waveguide are also observed. The SNOM system employs a cantilever type metal coated fiber tip [13,14] with apertures of 100-200 nm.

We calculate the effect of this metal coated tip on the resonance characteristics and the field distribution using full pledged finite difference time domain (FDTD) simulations which are found to be consistent with the measurements. These simulations support the calculations based on perturbation techniques [3]; both predict small red shifts in the resonance wavelength and some change in the modal field distributions due to the SNOM probe.

2. Photonic crystal structure

An atomic force microscope (AFM) image of the GaAs based photonic crystal structure we used is shown in Fig. 1(a) . The structure consists of a two dimensional hexagonal lattice of finite height. The basic period is $a=420nm$, the air holes radius is nominally $r=0.29a$ and the height of the slab is $h=265nm$. The waveguide is obtained by removing one row of air holes with an additional shift of about$0.07a$. The cavity is placed to the side of the waveguide at a distance of three rows of air holes. The cavity is a so called optimized extractor modified L5 type which is formed by a line of 5 missing air holes [12].

 

Fig. 1 (a) AFM image of the waveguide and cavity, (b) Simulated distribution of $E_y$at resonance, (c) Measured off-plane emission from the cavity (blue) with a Lorenzian fit (red).

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The spatial distribution of the fields in the cavity was calculated using high resolution, three dimensional FDTD simulations of the electric and magnetic field distributions. The simulation used a non uniform grid with 16 to 20 slices per period in the plain of the photonic crystal and a 20 to 40 nm spacing in the perpendicular direction. The effect of the metal could not be calculated properly in the present model. The tip was modeled therefore as a dielectric cylinder. Since the calculations match the experiments well, we conclude that the losses introduced by the metal coating do not affect the resonance frequency and their impact on the Q-value is small. The experiments were performed in contact mode so the simulations assumed zero distance between the tip and the surface. The boundary conditions were perfectly matched layers.

An exemplary distribution of E_y, the near field in plane component is shown in Fig. 1(b). The distribution was calculated for resonance excitation without the presence of the SNOM tip. This near field distribution differs very little from that of a conventional L5 cavity. Nevertheless, the far field is significantly modified as described in [12]. A high quality factor,Q, is obtained by displacing the end-holes of the cavity from their original position by a small amount of about $0.18a$.

Far field spectral measurements reveal typically Lorenzian shaped spectra. Figure 1(c) shows a measured spectrum for the cavity we describe hereon with a resonance wavelength of the fundamental mode of $\lambda =1598.15nm$ and a Q of$\sim 22,400$.

3. Near field imaging

The experimental system we employed is shown schematically in Fig. 2 . It consists of a collection-mode SNOM which uses a metal coated monomode optical fiber tip with an aperture of 100-200 nm. The near field is coupled to the guided mode of the fiber. The collected signal is then detected by an InGaAs femtowatt photoreceiver. The photonic crystal waveguide is fed by a piezo electrically controlled tapered fiber which is placed at the waveguide input (perpendicular to the SNOM tip). The system allows for easy exchange between the SNOM head and a far field measurement set up. Far field imaging is used for the input alignment prior to each SNOM scan. The SNOM probe was positioned at a contact with the surface using position sensitive detection for normal and lateral force sensing feedback. The system yields simultaneous acquisitions of the topography via AFM and the SNOM optical information.

 

Fig. 2 Experimental schematic of (a) the far field and (b) the SNOM imaging system.

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First we address the propagation of light along the waveguide. Figure 3 shows an AFM image (Fig. 3(a)) together with polarization resolved images (Fig. 3(b) and 3(c)) that include also line scans (Fig. 3(d) and 3(e)). Under the condition of an off resonance excitation, we scanned a portion of the waveguide which is far from the input port (to avoid imaging of radiative modes) and from the cavity to avoid recording any waveguide - cavity interaction. The input polarization is set to be either TE (in the plane of the photonic crystal membrane) or TM.

 

Fig. 3 (a) AFM image of the waveguide. Near field images of propagation along the waveguide and line scans for TE input (b, d, respectively) and for TM input (c, e, respectively).

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Scans along the waveguide when it is fed at a wavelength of $\lambda =\text{1590}nm$ are presented in Fig. 3(b) for the TE polarization and in Fig. 3(c) for TM. The light propagates from left to right. Also shown, in Fig. 3(a0, is an AFM image of the structure.

The SNOM tip collects, in principle, a combination of an evanescent field and some scattered light. For the TE polarization (Fig. 3(b)) a clear periodic signal is detected. The line scan through the center of the waveguide (Fig. 3(d)) reveals an intensity pattern with a periodicity of the propagating Bloch mode which is further modulated (with a longer period) due to an interference of Fabry Perot modes (defined by the waveguide end facets), the propagating mode itself and the mode of the SNOM tip [4]. For the TM polarization (Fig. 3(c)), the only detectable signal is from the region outside the defect line (along the holes). The dynamic range of the detection system prohibits detection of any scattered TM light along the waveguide itself. A line scan along the region outside the waveguide (Fig. 3(e)) reveals an intensity periodicity similar to the distance between holes which extends, in the direction perpendicular to the defect line, for a distance of about three holes, consistent with theoretical predictions [15].

Near field intensity distributions of the coupled waveguide-cavity system were recorded at various excitation wavelengths in the TE polarization. The cavity cannot be excited in the TM polarization. The presence of the probe modifies the resonance conditions of the cavity such that the resonance frequency is always red shifted compared to the case with no tip [3,6–9] with the shift depending on the exact probe location. This is shown in Fig. 4 which is a calculation of the resonance spectra for different placements of a 200 nm tip as seen schematically in Fig. 4(b). Figure 4(a) shows calculated spectra for the condition of no tip (blue trace), an uncoated tip placed at the cavity center where the undisturbed intensity (Fig. 1(b)) in maximum (black trace), the same tip placed 1 μm from the center along the x axis where the undisturbed distribution exhibits a moderate intensity (red trace) and finally the tip placed off axis: 1 μm from the center along the x axis and 0.72 μm above the center line. Here the intensity for the case with no tip is rather low (see Fig. 1(b)). The effect of the tip on the resonance frequency is expected to be smaller in this off-axis location since the intensity is low and hence the interaction with the tip is reduced.

 

Fig. 4 (a) Simulated spectra for different tip locations shown schematically (in corresponding colors) in (b). The blue trace is the spectrum with no tip.

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The calculation shows that indeed, the tip red shifts the resonance frequency while the Q value changes in a minor way. The red shift increases as the tip is placed where the unperturbed intensity is large (see Fig. 1(b)). Resonant wavelength shifts similar to the ones shown in Fig. 4 have also been calculated by a perturbation technique [3]. The two calculations are consistent with each other but the simulation enables, naturally, more accurate results for more general conditions.

Typical measured wavelength dependent near field images of the cavity are shown in Fig. 5 together with an AFM image. Each SNOM pattern corresponds to an excitation wavelength which is red shifted by δ from $\lambda =1598.15nm$ - the cavity resonance wavelength obtained in a far field measurement.

 

Fig. 5 AFM and SNOM images for different excitation wavelengths. All traces shown have the same intensity scale.

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For $\delta =0$, the light is distributed outside the cavity in an elliptical shape pattern, similar to [8]. The elliptical like cavity pattern shrinks as δ increases. The cavity reaches resonance at$\delta =1.1nm$ when a clear bright spot (surrounded by four lighter spots) is detected in the SNOM image at the center of the cavity. A similar red shift of the resonance was observed experimentally for uncoated and metallic tips. For longer wavelengths, $\delta =1.3nm$, the cavity is dark as the cavity is totally out of resonance.

The evolution of the wavelength dependent patterns in Fig. 5 is easily explainable using the simulation results of Fig. 4. Explanation of the evolution requires knowledge of the shift in resonance frequency with the tip position. While the simulations in Fig. 4 do not describe a metal coated tip, they are sufficient since the metal has but a minor effect on the shift in resonance frequency and on the Q-value. For an excitation wavelength of $1599.25nm$ ( $\delta =1.1nm$) and the tip placed at the center of the cavity, the simulation predicts, and the experiments confirm, that the cavity is in resonance. As the tip scans to other locations, the resonance wavelength changes (see Fig. 4) and since the excitation wavelength is fixed, other regions, which are all out of resonance, do not contribute to the detected signal and the pattern consists of only the bright spot at the center. Moreover, as the SNOM tip scans the cavity with other excitation wavelengths, the SNOM signal maps the regions where the intensity is large for that particular excitation wavelength resulting in the various patterns shown in Fig. 5.

4. Summary

To summarize, we described SNOM studies of a photonic crystal waveguide which is side-coupled to a high Q nano cavity. Polarization resolved SNOM measurements of the waveguide reveal the expected TE polarization of the propagating mode. The SNOM tip has a severe effect on the cavity. It perturbs the modal field distribution and red shifts the resonance wavelength. The effect of the tip was modeled using high resolution FDTD simulations. The simulated results fit well to the experiments and also support earlier calculations based on perturbation techniques. The results shed light on the emission and polarization properties of this important class of devices [12] whose full understanding is crucial for its use in quantum processing and computation applications.