1. Introduction

In 1994 Zhong and Inniss discovered that weak chemical etching in hydrofluoric acid (HF) of a cleaved germanosilicate fiber, followed by atomic force microscopy (AFM) to measure the resulting topography, could be used to deduce the fiber’s index of refraction profile [1]. The index profile could be measured with a spatial resolution of 20 nm, some 20 to 30 times better than what could be achieved with conventional optical indexing techniques [2, 3] that are restricted by the diffraction limit of light. It is possible to improve the spatial resolution to beyond the diffraction limit of light using reflection Near-Field Scanning Optical Microscopy (R-NSOM). However, R-NSOM experiments are difficult to perform and it is not straightforward to transform the reflection data into meaningful index data [4]. The AFM etch technique successfully mapped out the refractive index profile, because it was shown experimentally that i) for Ge doped fibers the core etches faster than the cladding and ii) the differential etch rate of the core versus the cladding in HF was linearly dependent on the core dopant concentration [1]. Since the index of refraction of the core was also linearly dependent on the dopant concentration, the inverted etch profile represented the index of refraction profile of the fiber. It should be noted that the etch depth cannot be used to give the absolute value for the index change, Δn, but it can provide a relative measure, allowing one to compare index changes of germanosilicate fibers with different dopant concentrations. The linear relationship between etch rate and dopant concentration was not obvious since the chemistry of etching pure silica never mind doped silica is very complicated [5]. The high spatial resolution of the technique has proved useful over the years for obtaining accurate index profiles of small core GeO₂ doped fibers [6].

There is presently a need for such high spatial resolution index profiling to map out induced index changes in dielectrics such as glass produced, for example, by VUV (157 nm) laser radiation [7] as well as produced by high intensity femtosecond laser (800 nm) radiation [8]. However, there is no a priori reason to expect that the AFM/etch technique can be applied to these cases. In fact, the formation mechanisms responsible for both these laser induced index changes are not well known [7, 8] and they clearly differ from the doped fiber case mentioned above. In reference [7], we used high resolution (400 nm) microreflectivity measurements of the type described in [9, 10] to confirm the validity of using the AFM technique to map out a very narrow (1/e width = 800 nm) region of VUV induced index change at the core cladding interface of hydrogen loaded Corning SMF-28 telecom fibers.

In this paper, we show that the combined use of selective chemical etching and AFM can also be used to predict the index profiles produced when Ti:Sapphire femtosecond laser radiation at a wavelength of 800 nm is focussed into a block of silica to form waveguide structures. The modification process is highly non-linear and some of the induced index changes have feature sizes as small as 50 nm, which cannot be measured with standard optically based index profiling techniques. Detailed knowledge of these fine structures has very recently allowed us to fabricate sub-micron holes and channels in silica [11]. In other research on femtosecond laser modification of dielectrics scanning electron microscopy [12], third harmonic generation microscopy [13] and transmission electron microscopy [14] have been used to image the modified structures with sub-micron resolution. However, none of these techniques are able to measure the index of refraction profile which is key to assessing the potential of a modified structure for waveguide applications. We also show in this paper that the AFM/etch technique is particularly well suited to measuring index profiles of arrays of waveguides.

2. Experimental

A regeneratively amplified Ti:Sapphire laser operating at λ=800 nm over a repetition rate range of 10–250 kHz and with a maximum average power of 270 mW measured after a spatial filter was used in the experiments. The laser pulse duration was nominally 40 fs. A 40×, NA=0.65 microscope objective was used to focus the laser radiation transverse to a polished block of high grade fused silica at a depth of approximately 100 µm. Waveguides were written by translating the sample with scan rates in the range of 10–200 µm/s.

The use of the NA=0.65 microscope objective results in a focal volume that is significantly stretched in the direction of light propagation. We have found that the insertion of a long focal length (40 cm) cylindrical lens before the objective to produce a line focus at an angle to the sample scan direction can be used to decrease the ellipticity of the focal volume [15]. Waveguides with more circular cross-sections were produced in this way for index profiling analysis. We also used reflective optics to write waveguide structures longitudinally (i.e., sample translation is in the direction of the laser beam). Here the laser beam was brought through the work-piece and reflected back into it using a 50 mm focal length mirror with an effective aperture of 8 mm.

After laser writing the waveguides the silica block was cut into two pieces perpendicular to the scan direction and the two inside surfaces were polished for index profiling analysis using a standard pitch polishing technique. The two inside surfaces were chosen for analysis to eliminate the problem of laser damage, which often occurred on the outside surface. Furthermore, focussing light transversely through the edge of a block results in distortions within a few microns of the natural ends of the waveguide. We have verified that the uniformity of the waveguides down the length of the block of silica was excellent so that the same index profile could be obtained independent of exactly where the block was cut and polished.

To validate the AFM/etching technique and to obtain the absolute value Δn, microreflectivity was performed on one of the two non etched polished inside surfaces. The sample was glued onto a probe holder at the base of a scanning probe microscopy (SPM) head of a Digital Instruments Dimension 3000 AFM. The AFM has been modified to permit a tethered mode of operation allowing the SPM head to be decoupled from its vertical position in the main microscope body and deployed horizontally to scan the sample [16]. A 50x, NA=0.8 microscope objective focussed unpolarized He-Ne light (633nm) to a near-diffraction limited spot on the sample. Light reflected from this surface returned through the lens and was directed by a cube beamsplitter onto a Newport model 1830-C powermeter for detection. Blockage of the laser beam before the lens provided a reference signal to estimate the core/cladding index difference using the Fresnel equations for an air/glass reflection [10]. Blocking the light after the lens verified that backreflection and backscattering from the lens was negligible. The back surfaces of the waveguides were terminated with a bead of index matching epoxy to ensure that negligible back reflected light returned to the front surface. The microreflection technique could detect index changes as small as 1×10^-4 with a lateral spatial resolution of approximately 400 nm.

The second piece of silica block was used for the AFM/etch analysis. The AFM was operated in the contact mode with silicon nitride probes. Prior to etching we confirmed that polishing did not produce any significant topography (≤ 1 nm) change over the waveguide region. Etching took place in a room temperature bath of 1% by volume hydrofluoric acid (HF) for typically 3 to 6 minutes. The sample was rinsed in distilled water then cleaned in isopropanol, dried and mounted and placed under the AFM. The etching generally produced a structure approximately 20–40 nm deep. The lateral resolution of the AFM image is determined by the sharpness of the probe tips, estimated to be between 15 nm and 20 nm. The vertical resolution is generally sub-nm although for very large image scans (≥40 µm) the vertical accuracy was a few nm.

3. Results

Figure 1 shows an inverted image of the AFM topography profile of an etched longitudinally written waveguide. It is the claim of this paper that the inverted AFM image represents the index of refraction profile. The waveguide is circular with a diameter of only 1.7 µm much less than the estimated diameter (8 µm) of the focussed laser beam waist. Similar observations have been made in references [12–14]. We have performed a preliminary theoretical analysis which suggests that at laser pulse energies of ≈ 40 nJ (peak power of ≈1MW) there is a sudden onset of a six photon absorption process (based upon the femtosecond laser photon energy of 1.4 eV and an ≈ 8 eV band-gap for silica) which compensates for self-focussing to prevent catastrophic collapse of the modified zone resulting in the uniform circular structure shown in Fig. 1.

Figure 1 demonstrates the importance of using an ultra-high resolution index profiling technique. The AFM image shows that there is a very sharp (100 nm) transition to the induced index change again indicative of highly non-linear processes being responsible for the material modification. There is also an immediate transition to a flat-topped index profile suggesting saturation in the magnitude of the induced index change. A section analysis through the center of the inverted AFM image is shown in Fig. 2. Normalized index data obtained from microreflectivity measurements on the sample before etching are also shown for comparison. Considering the poorer resolution of the microreflectivity technique (400 nm) the agreement between the two index profiles shown in Fig. 2 is good providing validation for the AFM etch technique.

 

Fig. 1. Inverted cross-sectional AFM image of a chemically etched longitudinally written waveguide. The laser was operated at a repetition rate of 250 kHz and an average power of 175 mW. The scan rate was 100 µm/s. The width of the flat-topped region is ≈ 1.7 µm.

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Fig. 2. Index of refraction profiles (arbitrary units) across the longitudinally written waveguide shown in Fig.1 and obtained using the chemical etching/AFM and microreflectivity techniques.

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We have verified for a number of different experimental conditions that the etch depth (1% HF) for both longitudinally and transversely written waveguides depends linearly on etch time at least up to etch depths of 100 nm. We have also observed that the shape of the etched profile is invariant with etch time showing no change for a five times increase in etch duration. There is an optimum etch time for a given etch concentration. If the etch time is too short then a shallow trench is formed which results in a poorer signal to noise ratio on the AFM image. If the etch time is too long then deep (>100 nm) trenches are formed. In this case the AFM probe tip does not accurately track the topography of such narrow deep trenches. An etch depth range of 20–60 nm gives the most reliable results.

In Fig. 3, the average etch depth across a waveguide is plotted as a function of induced index of refraction obtained from microreflectivity measurements for five waveguides that were written in the same block of silica using the aspherical lens (microscope objective plus cylindrical lens). Measurements were made for three different angles (6°, 10° and 15°) between the line focus produced with the cylindrical lens and the sample scan direction and at two different scan rates (50 µm/s and 100 µm/s). The laser power was 250 mW before the lens combination for each waveguide. The lower scan rate results in a times two higher dosage of laser energy per micron of scan travel leading to a higher index change. The higher values for the induced index of refraction with the lower laser writing angles is the result of narrower but more highly modified waveguide structures. Figure 3 clearly demonstrates that the etch depth for a fixed HF etch concentration and etch time scales approximately linearly with the induced index of refraction change. Consequently the inverted topographic profiles of the weakly etched waveguides represent the induced index of refraction profiles produced by the femtosecond laser pulses.

 

Fig. 3. Average AFM etch depth (1%HF,6 minutes) as a function of induced index change measured using microreflectivity averaged across the width of five waveguides written with an aspherical lens using a femtosecond laser power of 250mW and under the following conditions: (◆) 15°, 100µm/s, (■) 15°,50µm/s, (▲) 10°,100µm/s, (▪) 10°, 50 µm/s and (●) 6°, 50µm/s. The line shown in the figure is the best line visually through the data and the origin. The error bars indicate the experimental uncertainty on the AFM and microreflectivity data, which is higher for the lower index changes.

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The potential of the AFM/etch technique for high resolution index mapping is demonstrated in Fig.4, which shows an inverted AFM image of a chemically etched transversely written (lens NA=0.65) conical tapered structure. The structure is highly tapered in the direction of the focussed light from ≈ 1 µm to a very sharp tip of only ≈ 100 nm width. The high resolution (20 nm) of the AFM/etch technique revealed for the first time the sharpness of the tip region (100 nm); the steepness (150 nm) of the transition from the unmodified to a flat-topped modified region and the uniformity of the index change throughout the conical structure. This information led to the fabrication of sub-micron holes and channels in silica [11]. Microreflectivity data supports the AFM /etch data. Similar shaped conical tapered structures were observed in the microreflectivity images.

 

Fig. 4. Inverted AFM image of the cross-section of an etched tapered conical structure in a silica glass sample. The etch depth (before inversion) was ≈ 40 nm over the entire conical structure. The structure was produced by focussing (NA=0.65) a 30 mW, 100 kHz laser beam ≈ 150 µm below the top surface and translating the sample perpendicular to the laser beam at a scan rate of 25 µm/s. The sample was then cut in two pieces transverse to the scan direction. One of the inside surfaces was polished then etched (1% HF for 3 min) and placed under the AFM. The focussed femtosecond laser light entered from the top of the image.

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We have performed numerous microreflectivity experiments to measure the index of refraction profiles of femtosecond laser written waveguides in amorphous silica. The data consistently confirmed the index profiles predicted by the AFM/etching technique. Furthermore, the results of Fig. 3 how that the etch depths (for a given concentration of acid and etch time) of the modified regions created with different laser parameters provide a relative measure of the magnitude of the index changes. The AFM technique is very straightforward to use and since all the waveguides written into a block of silica are etched simultaneously it is possible to obtain index data on tens of waveguides in a few hours. The technique is simpler to perform and is less sensitive to sample surface quality (i.e., dust, scratches) than microreflectivity. The technique is essentially non-invasive since etching produces topography changes of less than 100 nm, which shouldn’t effect the ability to couple light out of the waveguide.

4. Discussion

In this paper, we show that the etch rate of femtosecond laser modified silica structures is approximately linearly dependent on the induced index of refraction change at least up to index changes of ≈ 0.01. The linear relationship between etch depth and index may only apply to fused-silica and could be completely different for multi-component glasses.

The mechanism, which accounts for the formation of positive index regions in silica glass using focussed femtosecond laser radiation is not completely clear [8]. The dimensions of some of the highly tapered modified regions such as shown in Fig. 4 are much smaller than what would be predicted from just multiphoton absorption. The etched structures reveal a complex response of the material that develops over a number of laser shots. It is believed that near the power threshold for material modification changes occur in the silica bond structure affecting how the bonds pack together. For example, there appears to be an increase in the number of 3 and 4 member silica ring structures at the expense of 5 or 7 member rings [17]. The reordering into smaller ring member structures reduces the bridging bond angle [17,18]. This process is often referred to as “densification” and is believed to be the primary mechanism for UV writing of strong Bragg gratings in Ge-doped silica fibers [19].

If the modified structure corresponds to a region of densification then there should also be a surrounding region of lower density. This region might correspond to the much larger focal volume prior to the non-linear collapse to form the modified structure. We have used both microreflectivity and the AFM/etch technique to search for the low density region. In the case of the AFM technique we highly over-etched the modified structure to produce ≈ 2 µm deep holes hoping to pick-up a weak topography transition at larger dimensions between the nonirradiated silica and a lower density region. To date we have had no success finding such a low density region.

Marcinkevicius et. al. have suggested that the decrease in bridging bond angle in densified silica increases the reactivity of the oxygen atoms due to the deformed configuration of their valence electrons [20]. The increase in reactivity results in greater etching in the modified zones with respect to the unmodified zones. It is also possible that there is an increase in the number of non-bridging oxygen atoms due to bond breaking which can enhance the chemical activity.

More research is required to understand the relationship between the etching activity, densification, index of refraction and the decrease in the bridging bond angle.

5. Conclusions

In this paper, we have shown that selective chemical etching and atomic force microscopy can be used to measure the index of refraction profiles of femtosecond laser induced structures in silica glass. The technique is simple to use and provides ultra-high spatial resolution (20 nm). The high resolution has been used to reveal new information on the shape and size of the index modifications.