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$: Refractive index proﬁling of direct laser written ... · Refractive index proﬁling of direct laser written waveguides: tomographic phase imaging A. Jesacher,1* P. S. Salter,2,4$
Refractive index profiling of direct laserwritten waveguides: tomographic phase

imaging

A. Jesacher,1* P. S. Salter,2,4 and M. J. Booth2,3

1Division of Biomedical Physics, Innsbruck Medical University, Mullerstraße 44, 6020,Innsbruck, Austria

2Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK3Centre for Neural Circuits and Behaviour, University of Oxford, Mansfield Road, Oxford OX1

3SR, UK4 [email protected]

*[email protected]

Abstract: We present a technique to measure the refractive index profileof direct laser written waveguides. This method has the potential forstraightforward implementation in an existing laser fabrication system.Quantitative phase microscopy, based on the Transfer of Intensity equation,is used to analyse waveguides fabricated with an ultrashort pulsed laser em-bedded several hundred micron below the surface of fused silica. It is shownthat the cumulative phase change induced by the waveguide perpendicularto its axis may be monitored in real-time during the fabrication process.Results are verified through comparison with interferometry. Tomographicmeasurements using illumination from a high numerical aperture condenserlens are used to infer the waveguide cross-section. Results are comparedwith measurements of the waveguide cross-section from a third harmonicgeneration microscope.

© 2013 Optical Society of America

OCIS codes: (130.2755) Glass waveguides; (250.5300) Photonic integrated circuits;(120.5050) Phase measurement; (110.6955) Tomographic imaging ; (220.4000) Microstructurefabrication

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#191570 - $15.00 USD Received 31 May 2013; revised 11 Jul 2013; accepted 12 Jul 2013; published 7 Aug 2013(C) 2013 OSA 1 September 2013 | Vol. 3, No. 9 | DOI:10.1364/OME.3.001223 | OPTICAL MATERIALS EXPRESS 1223

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11. A. Roberts, E. Ampem-Lassen, A. Barty, K. A. Nugent, G. W. Baxter, N. M. Dragomir, and S. T. Huntington,“Refractive-index profiling of optical fibers with axial symmetry by use of quantitative phase microscopy,” Opt.Lett. 27, 2061–2063 (2002).

12. T. Allsop, M. Dubov, V. Mezentsev, and I. Bennion, “Inscription and characterization of waveguides written intoborosilicate glass by a high-repetition-rate femtosecond laser at 800nm,” Appl. Opt. 49, 1938–1950 (2010).

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20. D. Liu, Y. Li, R. An, Y. Dou, H. Yang, and Q. Gong, “Influence of focusing depth on the microfabrication ofwaveguides inside silica glass by femtosecond laser direct writing,” Appl. Phys. A 84, (2006), 257–260 (2006).

21. C. Mauclair, A. Mermillod-Blondin, N. Huot, E. Audouard, and R. Stoian, “Ultrafast laser writing of homo-geneous longitudinal waveguides in glasses using dynamic wavefront correction,” Opt. Express 16, 5481–5492(2008).

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25. Y. Cheng, K. Sugioka, K. Midorikawa, M. Masuda, K. Toyoda, M. Kawachi, and K. Shihoyama, “Control of thecross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecondlaser,” Opt. Lett. 28, 55–57 (2003).

26. M. Ams, G. D. Marshall, D. J. Spence, and M. J. Withford, “Slit beam shaping method for femtosecond laserdirect-write fabrication of symmetric waveguides in bulk glasses,” Opt. Express 13, 5676–5681 (2005).

27. P. S. Salter, A. Jesacher, J. B. Spring, B. J. Metcalf, N. Thomas-Peter, R. D. Simmonds, N. K. Langford, I. A.Walmsley, and M. J. Booth, “Adaptive slit beam shaping for direct laser written waveguides,” Opt. Lett. 37,470–472 (2012).

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1. Introduction

Direct laser writing (DLW) with ultrashort pulsed lasers is emerging as a useful tool for machin-ing a variety of structures inside transparent substrates [1]. A particularly interesting applicationinvolves translation of the sample relative to the fabrication beam to create an optical waveg-uide [2, 3]. Knowledge of the refractive index change δn induced by the laser is invaluable inunderstanding the properties of the waveguide, but there still remains to be a well establishedmeasurement method. Previously the δn has been measured at the output facet of the sampleusing a range of techniques, including a refractive index profilometer [4,5], microreflectivity [6]or from analysis of the near field intensity pattern for guided light [7, 8]. Since these methodsare only sensitive to the refractive index profile at the edges of the sample, they are not adequatefor the analysis of more complex circuits where it would be useful to map δn throughout. Someelegant schemes, such as optical coherence tomography (OCT) [9] and digital holographic mi-croscopy (DHM) [10], have been demonstrated that can deliver this information, although theyinvolve complicated experimental systems and heavy data analysis.

Here, drawing inspiration from a technique previously applied to optical fibres [11], we usequantitative phase microscopy to measure the refractive index profile of DLW waveguides [12–14]. The significance of this technique lies in its optical simplicity, allowing incorporation of themeasurement mechanism in an existing laser machining system. Thus, during the fabricationprocess, we could monitor in real-time the induced refractive index change associated with awaveguides at every point in a photonic circuit. Furthermore, since the cross-section of thewaveguides written in a transverse geometry may not be assumed as rotationally symmetricabout the guiding direction, we additionally take tomographic measurements to infer the cross-section of the waveguides.

2. Quantitative phase microscopy: Transport of Intensity Equation

Solving the transport of intensity equation (TIE) represents a non-interferometric method forquantitative phase measurements [15–17]. In contrast to interferometric techniques it does notrequire a phase-stable set-up and the recording of fringe patterns but only two or more inten-sity images of the object that were taken at different values of defocus. The TIE principle isbased upon the fact that phase gradients within a transparent object affect the wavefront of lighttraveling through it. The altered wavefront shape is in turn reflected by the local propagationdirections. From multiple defocused images, one can infer to these local propagation directionsand thus the phase topography of the object. The TIE can be derived from the paraxial waveequation and takes, for a one-dimensional object, the following form:

dI(x)dz

=− λ0

2π nddx

[I(x)

ddx

φ(x)]. (1)

Here, I(x) and φ(x) represent the intensity and phase functions of the object, λ0 the light vac-uum wavelength and n the refractive index of the specimen. dI/dz denotes the gradient of theintensity in axial direction which is in practice approximated by the difference of two slightlydefocused images.

The one-dimensional case described by Eq. (1) can be straightforwardly solved and leads tothe following expression for φ(x):

φ(x) =−2π nλ0

∫ (1

I(x)

∫dI(x)

dzdx

)dx. (2)

The solution is unambiguous except for the two integration constants which define phase offsetand average slope in the final phase profile. Both values however can be set to zero for the


case of inspecting waveguides. We present all our results in terms of the optical path lengthOPL(x) = φ(x) ·λ0/(2π n) rather than the phase, which is the “natural” quantity returned bysolving the TIE.

From Eq. (2) one may conclude that the acquisition of three images should be sufficient tocalculate the phase profile: one image showing the sample in focus (corresponding to I(x))and two symmetrically defocused around the sample to estimate the axial intensity gradient.For transparent objects however showing sufficiently smooth phase profiles, the in-focus imagecan be replaced by a constant, which reduces the number of required images to two. As we willshow later, for the specific case of a direct-laser-written waveguide, even the acquisition of onlya single image allows one to determine the phase profile with good accuracy, which can enablelive quality monitoring during the fabrication process.

3. Results

To confirm the accuracy of the TIE method we performed comparative measurements on DLWwaveguides in fused silica using both an interferometric and the TIE approach.

The TIE measurements were done in an epi-illumination microscope with the sample placedon a mirror. The sample was illuminated under high spatial coherence with light from a fibre-coupled green LED (approx. 532 nm wavelength). The microscope objective (Olympus 20×,0.7 NA) was mounted on a piezo stage which allowed for controlled z-stepping. Each measure-ment comprised the acquisition of three images: one showing the waveguide in focus and twodefocused by ±1.5 μm. Interferometric measurements were performed with a Mach-Zehnderinterferometer, using a laser diode (640 nm wavelength) and the same objective lens. The inter-ferometer was set such that the interferograms showed a high fringe density, which allowed forthe extraction of the phase information without the need for phase stepping. The results of theTIE and interferometric measurements are summarized in Fig. 1.

Figure 1(a) shows the measured integrated optical path lengths across sections through twodifferent waveguides. The reason for the TIE profiles appearing smoother is explained by thedouble-integration (see Eq. (2)) which is required to obtain the phase from the measured data.Figure 1(b) compares peak values and widths (1/e2) of Gaussians that were fitted to nine differ-ent waveguide profiles. Generally, the data delivered by the interferometry and TIE approachesare in good accordance. The error bars for each data point correspond to the standard deviationof five (TIE) and two (interferometry) independent measurements, respectively.

Choosing a suitable value for the defocus distance Δz, i.e. the axial separation between theupper and lower defocused images, represents a trade-off between the signal to noise ratio in theimages and the accuracy of the estimated axial intensity gradient. Too small defoci lead to van-ishing image contrast whereas too large values lead to an inaccurate approximation of dI/dz.We experimentally determined optimal values for Δz by conducting a series of TIE measure-ments on a typical waveguide with varying defocus magnitudes. Five subsequent measurementswere made for each magnitude to estimate the uncertainty caused by noise. Again, Gaussianfits were performed. The obtained peak- and width- parameters of the fitted curves are shownin Fig. 2. The large error bars in both graphs for low values of Δz indicate the presence of sig-nificant noise, whereas the increase of the width parameter for larger Δz values is caused by animprecise estimate of the axial intensity gradient. From the data, an optimal range for Δz canbe defined between two and six micrometers.

The TIE method provides accurate phase measurements as long as the phase gradients withinthe sample fulfill the requirements set by the defocus distance Δz. The value of Δz chosenhere is appropriate for smooth waveguide profiles, and it is worth noting that the presence ofscattering structures, such as nano gratings [18], within the waveguides would lead to corruptedresults. Nevertheless, the TIE method makes no demands on the sample structure in terms of


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nm

(a) Optical path length profiles of waveguides - interferometry vs. TIE

waveguide A waveguide B

(b) Fitted Gaussian peak- and width-values - interferometry vs. TIE

Fig. 1. Comparison of TIE and interferometry. (a) integrated optical path lengths acrosssections through two exemplary waveguides; (b) peak values and widths (1/e2) of Gaus-sians that were fitted to nine different waveguide profiles; the blue lines mark a slope ofone.

its spatial frequency content, and small structures are typically measurable as long as they fallwithin the general limits of imaging with light. Additionally, it would be possible to measurein-plane birefringence of structures by using polarised light for illumination. It is, however,worth mentioning that there exists a class of phase distributions that cannot be measured withpropagation-based techniques such as the TIE method [19]. Such phase distributions are forinstance optical vortices.

4. Live acquisition of phase profiles during fabrication

From an engineering perspective, it would be extremely useful to acquire an estimate of thelocal refractive index contrast for the fabricated waveguides at each point in the network, liveduring the machining process. This would aid quality control during fabrication, allowing moni-toring to ensure uniformity of the waveguides throughout the chip. This is particularly importantwhen manufacturing three dimensional photonic circuits as depth dependent aberrations can af-fect the focal intensity distribution of the fabrication beam [20–22]. It would also enable onlineadjustment of the fabrication procedure to ensure that the waveguide network may display cer-


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�z /µm

peak OPL

optimal range for �z

nm

nm

µm

Dependence of results on defocus parameter z�

width (1/ )e²

Fig. 2. Gaussian fit parameters for a typical waveguide; the TIE measurement was con-ducted for different defocus values Δz. An optimal range for Δz exists between 2 and 6micrometers.

tain desired properties. For example, this would be advantageous when machining evanescentcouplers, since additional passes of the fabrication beam could be executed or other parame-ters adjusted to modify the waveguide index contrast until the appropriate coupling ratios arepredicted.

Calculation of a phase profile via the TIE relies on our knowledge of the axial intensitygradient, requiring at least two images at different defocus planes. However, for weak phaseobjects like the DLW waveguides considered here, an in-focus image may be approximatedby a uniform intensity distribution. Then a single image from a defocus plane allows us to es-timate the axial intensity gradient and hence the transverse phase profile. This can be easilyincorporated into the experimental system for waveguide fabrication, as shown in Fig. 3(a).Since the TIE computation can be done much quicker than the camera frame acquisition, it ispossible to obtain a “live” value for the induced index contrast immediately behind the fabri-cation focus. Kohler epi-illumination is set up using an LED source and coupled through thesame objective lens used for the fabrication by a dichroic mirror. A mirror placed beneath thesample ensures uniform illumination as the sample is scanned. The reflected light is imagedonto a CCD through a 50:50 beamsplitter, with the tube lens ( f = 300 mm) translated axially asmall amount such that the image recorded is defocused by a defined amount Δz with respectto the waveguide axis.

Figure 3(b) and 3(c) show typical images for a DLW waveguide defocussed by Δz = 3μm,and in focus. By inspection of Fig. 3(c) it can be seen that the approximation to a uniformintensity for estimation of the axial intensity gradient is reasonable. Indeed when results arecompared for phase profiles derived from the TIE using a single defocus image as opposed totwo images at defocus plane ±Δz, the residual RMS error is less than 4%. The “live” acqui-sition of phase profiles in this manner allows us, for example, to observe the accumulation ofrefractive index contrast in the waveguide with multiple passes of the fabrication focus alongthe same track, Fig. 3(e).

5. Tomographic imaging of the phase profile

In the preceding section, we measured the accumulated OPL through a waveguide structure.Previously it has been shown that this may be mapped to a radial refractive index distributionfor the waveguide using an inverse Abel transform, on the base assumption that the waveguide


Fig. 3. (a) Experimental setup allowing online acquisition of waveguide phase profiles dur-ing fabrication. (b) An example defocus image captured for the waveguide and, for com-parison, an in focus image (c). Approximating the intensity distribution in (c) as a constant,the phase profile of the waveguide may be estimated (d). The increase in optical path lengthfor the waveguide structure with multiple passes of the fabrication focus (e).

is radially symmetric [11,13]. However, for DLW waveguides there is a strong chance of asym-metry, particularly for those written in the transverse geometry where the sample is translatedperpendicular to the optic axis to trace out a guide. This is related to the natural elongation ofthe focal intensity distribution parallel to the optic axis when focussing with lenses of limitednumerical aperture. Optical techniques such as astigmatic focussing [23], spatio-temporal fo-cussing [24] or slit beam shaping [25–27] may be used to control the waveguide cross-section,although these are still not guaranteed to generate axially symmetric guides due to the potentialfor optical aberrations induced by focussing through a refractive index boundary [28]. Addi-tionally, there are certain scenarios where asymmetry in the refractive index profile is desired;for example in generating form birefringence [29, 30]. Thus we should develop a method forestimation of the refractive index distribution for non-symmetric waveguides.

Quantitative Phase Tomography allows for the measurement of three dimensional phase in-formation, through acquiring a series of images of a sample with light propagating in differentdirections. It has previously been applied to the measurement of refractive index contrast inoptical fibres, where it is straightforward to change the orientation of the sample in the micro-scope [31]. With DLW waveguides in bulk substrates, it is impossible to rotate the sample, butwe may vary the angle of light propagation through selective illumination of a high numericalaperture condenser. The experimental scheme is shown in Fig. 4(a). The LED illumination isfocussed with a tube lens ( f =120 mm) onto the back aperture of a 1.4 NA oil immersion con-denser lens. A rotatable mirror in the back focal plane controls the position of the focus at thecondenser back aperture and, hence, the angle of the illumination through the specimen. Thelight is collected by an objective (Zeiss 1.3 NA 40× oil immersion) and imaged onto a CCD.


Phase profiles for the waveguides are accumulated, using the TIE approach, at a series of illu-mination angles oblique to the waveguide axis. The waveguide cross-section can be estimatedby fitting an appropriate model to the obtained data. If the refractive index profile of a waveg-uide is assumed to be Gaussian, the peak OPL as a function of the illumination angle should beproportional to the radius of an ellipse, i.e., OPL(θ ,e)∝ 1/

√cos(θ)2 + e2 sin(θ)2, where θ de-

notes the illumination angle and e the ellipticity of the guide, i.e. the ratio between the long andshort axes. Likewise, the width of the measured projection should be proportional to the inverseellipse radius. This can be shown using the Fourier projection-slice theorem, which states thatthe one-dimensional Fourier transform of a projection is equal to a slice (taken perpendicularto the projection direction) through the two-dimensional Fourier transform of the profile. It isworth noting that these models are relatively robust against variations in the exact profile shapeas long as the ellipticity is maintained. For instance, numerical simulations showed that Gaus-sian and flat-top profiles with the same ellipticity are not distinguishable from the estimatesdelivered by the fits. Whilst this is advantageous if one is only interested in producing waveg-uides with a certain axis ratio, it also means that the method is not suitable for reconstructingquantitative refractive index profiles of waveguides. This task would require more elaboratedata analysis as for instance used in X-ray computed tomography.

Fig. 4. (a) Experimental schematic for tomographic phase imaging of DLW waveguides.(b) Sample retrieved plots of the OPL for waveguides A and B for illumination at differentincident angles. Measurements of the characteristic waveguide width σ (c) and peak OPL(d) as a function of the illumination direction. Fits to the data are shown as dashed redcurves providing a measure of waveguide ellipticity e (as denoted in the caption). (e) Thewaveguide cross-sections estimated from the tomographic measurements and measuredusing a third harmonic generation (THG) microscope.

DLW Waveguides were fabricated in a transverse geometry in fused silica using an amplifiedTi:Sapphire laser (λ = 790 nm and pulse repetition rate 1 kHz). An adaptive slit beam shapingmethod [27] was used to control the cross-section of the waveguide by varying both the widthand length of the slit illumination in the back aperture of the fabrication objective. The slit widthgoverns the broadening of the intensity distribution within the focal plane, while the length ofthe slit essentially controls the numerical aperture (NA) of the objective and, hence, the depthof focus. Two differing waveguides were written with slit width w and effective numerical


aperture NAeff. Guide A was designed to have circular cross-section with w = 0.9 mm andNAeff = 0.5. The parameters used for Guide B were chosen to generate an elliptical cross-section by decreasing the numerical aperture NAeff = 0.4 to stretch the structure along thefabrication optical axis and widening the slit w = 1.6 mm to reduce the transverse dimension.

Measurements of the three dimensional structural properties of the two waveguides weremade by Quantitative Phase Tomography. Defocus images were taken for a range of illumi-nation angles up to 36◦. Images at higher illumination angles became too highly distorted byoff-axis aberrations in the system to be included. Five measurements were taken for each illumi-nation angle. Care needs to be taken in estimating the axial intensity gradient from the defocusimages, since the off-axis illumination introduces an additional lateral translation of the imagewith defocus. The results are shown in Fig. 4(b), where we display for the two waveguidessome examples of the calculated OPL for different incident illumination angles. These resultsare quantified in Figs. 4(c) and 4(d), where we display for the two waveguides a characteris-tic width σ and the peak OPL from the measured phase profiles. Error bars take into accountdifferences between measurements and uncertainty arising from the data processing.

With incident illumination normal to the substrate our results predict the waveguides to besimilar in transverse dimension but that Guide B has a significantly greater OPL. As the illumi-nation angle is increased, both the OPL and transverse size remain approximately constant forGuide A as to be expected for a circular waveguide cross-section. In contrast, the OPL dropssteadily and the transverse dimension increases for Guide B at higher illumination angles, con-sistent with a highly elliptical waveguide cross-section. The red dashed lines in Figs. 4(c) and4(d) are the fitted curves for the data. By assuming an elliptical description of the waveguidecross-section, the fit to the tomographic width data (Fig. 4(c)) provides estimated ellipticities of2.04±0.14 and 3.85±0.10 for guides A and B, respectively. The corresponding estimates fromfitting the peak OPL data (Fig. 4(d)) are 0.62±0.17 and 3.04±0.30. Both fits reveal waveguideB to be significantly more elliptic than waveguide A, although the ellipticity estimates from thewidth data generally show higher values than those from the peak OPL data. This discrepancyis probably caused by the afore-mentioned image distortions at high illumination angles, whicheffectively broaden the image (and hence increase the width) of the waveguide. An initial cali-bration measurement [32], done with a waveguide of known circular cross-section, might allowthe derivation of more accurate predictions from the tomographic data.

Sketches of the waveguide profiles estimated from the tomographic measurements are shownin Fig. 4(e) (dashed lines indicate the one sigma confidence intervals). The sketches highlightthe discrepancy in the expected profiles obtained from the different fits to the tomographic data.This discrepancy is particularly pronounced for waveguide A, where the expected ellipticity isreversed dependent on whether we use the peak OPL data or the characteristic width of the OPLmeasurement. In order to ascertain the true nature of the waveguide cross-sections, we imagedthe sample in a third harmonic generation (THG) microscope [33]. The THG microscope issensitive to non-uniformity in the third order susceptibility (χ(3)), which typically coincideswith regions where there is a gradient in the local refractive index. The nature of the THGprocess dictates that the signal is only generated at the focus of the excitation beam, and hencegives a direct measurement of the waveguide structure with three dimensional resolution.

The cross section images obtained with the THG microscope for waveguides A and B areshown in Fig. 4(e), in addition to the cross-sections inferred by tomography. The THG cross-section for both waveguides is hollow, indicating that the refractive index change has a stepnature, with a vanishing gradient in the middle of the guide. The THG data confirms our con-clusions from the tomographic data that waveguide B is more elliptical than waveguide A.The ellipticity of the measured THG cross-sections are also found to coincide well with thewaveguide profiles estimated from the characteristic width in the retrieved tomographic OPL


measurements. However, it should be noted that due to the diffraction limited shape of the prob-ing laser spot, the PSF of the THG microscope is elongated along the optic axis. This causesasymmetric blurring of the image and the appearance of greater elongation along the optic axis,which is particularly apparent at the small length scales considered here. As a consequence, thewaveguide ellipticity displayed by the THG microscope corresponds more closely to an averageof the elipticities predicted from the two tomographic fits.

6. Summary

The extraction of the refractive index (RI) profile for DLW waveguides represents a difficulttask, yet is incredibly important for a clear understanding the properties of photonic circuits.We use quantitative phase microscopy, via the TIE method, as an optically simple approach togain indirect information about the waveguide RI. The technique requires no specialist equip-ment, can be easily performed at any point within a 3D waveguide network and is not com-putationally expensive. An obvious engineering advantage is gained from the incorporation ofthe TIE measurement into a laser machining system to allow real-time monitoring of a waveg-uide RI during fabrication. However, since waveguides formed by DLW are not guaranteed tobe rotationally symmetric about the guiding axis, for the TIE measurement to provide an ac-curate inference of the waveguide properties, we require some further information about thewaveguide cross-section. A tomographic implementation of the TIE method, as demonstratedhere, is useful in gaining an estimate of the waveguide ellipticity and is also simple enough topotentially be included within the fabrication experimental system. It is apparent that some ofthe estimates of individual waveguide characteristics, such as the cross-section profile, basedupon TIE measurements are subject to large uncertainties. However, the combination of suchmeasurements with a priori information about the expected waveguide properties would lead tomore accurate estimates. Such in situ measurement will be a valuable addition to the technologyof DLW waveguide fabrication.

Acknowledgments

The authors gratefully acknowledge financial support from the Innsbruck Medical University(A.J., scholarship AS-2012-3-2), the John Fell Oxford University Press (OUP) Research Fund(P.S.) and grant EP/E055818/1 from the Engineering and Physical Sciences Research CouncilUK (M.B).


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