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Efficient post-process suppression is demonstrated of spurious Fabry-Pérot oscillations, introduced by multiple cavity effects in transmission spectra measurements of various Bragg grating devices. These devices were fabricated within access waveguides and terminated with cleaved facets. The tool, based on a curve-fitting to an equivalent scattering matrix model, is shown to extract transmission spectra of devices, without a-priori knowledge of their properties. Simple and complex grating structure spectra are successfully extracted and compare well with simulated results. The technique exhibits robust behaviour for varying facet conditions and device geometries, outperforming classical averaging techniques.
©2009 Optical Society of America
1. Introduction
With the reduction of propagation losses in integrated optical platforms[1, 2] increasing levels of integration of individual components are becoming possible. However, it is still necessary to characterise these integrated optical components individually before inclusion in larger systems. One method of measuring the wavelength dependent scattering coefficients of devices is to include them in a simple waveguide structure. In this manner light, emitted by a tunable laser or white light source, may be coupled to the Device Under Test (DUT) by means of microscope objectives and access waveguides fabricated with the device of interest. However, this arrangement places a Fabry-Pérot (FP) cavity around the DUT, with partially reflecting mirrors formed by the test bar facets. These FP cavities necessarily introduce a coupled effect with the scattering characteristics of the DUT. With cleaved facet reflectivities of ~30% (common for high confinement waveguides e.g. in GaAs and Silicon-on-Insulator) the associated FP fringes may significantly mask the spectral features of the device. Possible solutions to this problem include application of anti-reflection (AR) coatings to the facets, cleaving facets at a non-orthogonal angle to the propagating mode direction [3] or out coupling from the waveguides by means of surface grating devices [4]. The use of AR coatings and surface gratings require extra fabrication steps, and in the latter system the surface grating spectral response will have an effect on the out-coupled light. For both the surface gratings and angled facet devices, a more complex coupling rig is required that allows alignment of lensed fibres for coupling light in and out of the test bar.
A less practically involved technique that may be used to overcome the effects of the external FP cavity is to subject the measured data to a post-processing tool. Simple filters or shifting window (SW) averaging methods may be used to enhance the spectral features of interest, in cases where they are significantly detuned from the major FP oscillation frequency. However, the amount of distortion introduced into the processed data, and the normalization needed, is not usually trivially known. A curve-fitting of the measured data to a known model of the DUT characteristics may also be implemented, though this necessitates a model of the response of the DUT in the first place. An alternative scheme was proposed by Gnan et al. [5], who show that with knowledge of the access waveguide properties and facet conditions, an equivalent Transfer Matrix Method (TMM) model of the whole system may be constructed, considering the DUT as a black-box element with unknown, complex, reflectivities and transmittivity. The advantage of this technique is that it does not need a-priori knowledge of the device characteristics; by creating a system with no recourse to knowledge of the DUT this method may be used even with complex devices where equivalent models may be very difficult to construct. Also, the processed data is normalised and distorted according to theoretically known relations [5]. To complete the previous study where the technique was investigated mainly theoretically, in this paper the performance of the method is demonstrated in a variety of experimental cases, and by comparing its results with a SW averaging technique and simulated data. The transmission spectra analysed have diverse shapes, characteristic of Bragg grating devices with non-linear chirp and apodisation profiles. The consistency of the FP fringe removal is also tested, through post-processing of transmission of nominally identical devices that have only different facet reflectance, fabricated by means of AR coatings.
The paper is organised as follows: in section 2 details of the post-processing methods, both the TMM and SW averaging techniques, are exposed. In section 3 details on the device fabrication are given. In section 4 the comparison is performed by studying Bragg gratings with transmission spectra having increasing degrees of complexity. The results of both post processing techniques are compared with the experimental spectra of devices with and without AR facet coatings, and with their simulated responses.
2. Post-processing recovery algorithms
In this section, the post-processing algorithms used in the paper, TMMand SW, are described. A more detailed description of the TMM method is published elsewhere [5]. The block diagram of a fabricated test bar is given in Fig. 1. It includes the elements of a DUT having access waveguides. Given the usual matrix elements for simple waveguides and reflectors, the complex transmission coefficient of the entire system may be written as (1).
where r f1,r f2,t f1 and t f2 are the facet reflectivities and transmitivities, L 1, L 2 and α 1, α 2 are the access waveguide lengths and losses respectively, t bb is the black-box transmitivity and r and r bb-n are the directionally dependent DUT reflectivities. This model, by providing a black-box description of the DUT in terms of complex reflectivities and transmittivity, requires no foundation on any particular device models and can be applied to any DUT that may be fabricated within the two access waveguide geometry. Considering the fabricated test bar as being placed within a measurement system comprising, for example, a light source feeding facet 1, and a detector collecting power from facet 2, the total detected power may be written as in (2).
Where I 0 is the input power, A 1 and A 2 are the attenuation coefficients associated with the coupling from the light source to the test bar and from the test bar to the detector respectively and D is the detector characteristic. T=|tsys|2 is the characteristic of the fabricated test bar. Finally, A is defined as the normalisation coefficient of the system and can be assumed to vary slowly with wavelength.
In this paper the transmission spectra of the DUTs is focussed on, given that experimentally, these are easily measured using the endfire rig setup previously described. The goal of the post-processing tool is therefore to extract the DUT transmission coefficient (tbb) from the experimental measurements. For the extraction to be as reliable as possible, all parameters in equation (1) should be known. The first set of parameters that may be obtained are those pertaining to the facets. It is assumed that they are identical - if the access waveguides terminating at these surfaces are geometrically similar - and so the reflectivity and transmittivity are easily obtained by recourse to mode solver packages. For example, the material structure and waveguide geometry, as defined in section 3, may be rendered in a Finite Difference Time Domain (FDTD) mesh. Solutions for the guided modes of the waveguide are found, with FDTD mesh dimensions set by convergence of the mode solution. The transmission and reflectivity may be directly simulated by propagating the mode through a facet defined in the simulation, measuring both the transmitted and back-reflected modes. In turn, the waveguide losses may be extracted from the transmission spectra of simple waveguides fabricated on the sample alongside the devices, using the Fabry-Pérot fringe measurement [6], and given the facet reflectivities. Also, if AR coatings are applied to the test bar, the reflectivities of these treated facets may be calculated given values already calculated for the waveguide losses using the untreated facet reflectivities. By careful fabrication, the access waveguide lengths may be directly measured by inspection of the cleaved test bar. The uncertainty of these calculated and measured values for facet and access waveguide conditions has been explicitly dealt with in [5], and the TMM method is shown to tolerate these by solving for estimated DUT parameters, which contain the true DUT parameters and the uncertainty on the input variables. The theoretical accuracy of this fitting method, including the uncertainty of the input parameters is dealt with in [5].
Finally, the TMM model becomes a function of the unknown reflectivities and transmittivity, and of the normalisation coefficient, A. So, once the transmission spectrum of the device is obtained and the accessible parameters of the total system extracted, the transmission and reflection coefficients of the DUT may be extracted using a curve-fitting method of the transmission spectrum to the TMM representation outlined above, with the parameters of interest remaining free. In this work the curve-fitting was carried out using the least squares curve-fitting method in Matlab. In this routine the least squares distance between the measured transmission and TMM model is minimised in an iterative manner from some initial guess taken as an input. Thus, the DUT transmission and reflection coefficients may be defined free of the effects of the enclosing system, with normalisation of the resultant spectra coming from the fitting of A from (2).
The SW averaging is implemented in a point by point manner. The window length is defined with the point of interest at its centre. In general there is a trade-off in the window length chosen between averaging out of the FP fringes and the loss of detail of the spectra of interest. The more points within the window, the better the smoothing of the FP fringes, if they have constant period and amplitude. However, since the fringes are superimposed on the DUT spectrum, too wide a window also smooths out the features of interest. It was found that a window length of approximately five times the unmodulated FP free spectral range was a sufficient compromise. The corrected point is then taken as the mean value of the measurement data over the window, for that wavelength. Both post-processing tools operate on TD, however, since the SW method has no means by which to extract A, the post-processed data have to be normalised. To facilitate the comparison of the data, in the following, when the results of the two tools are compared, the data extracted by SW averaging is rescaled by the A found with the curve-fitting tool.
3. Test devices and measurement setup
In this paper the devices used as the DUTs are Bragg gratings fabricated on AlxGa 1-xAs. Where, x=75% : 25% : 75% for uppercladding : core : undercladding depths of 0.3 : 0.5 : 4.2µm. The gratings were written into Hydrogen Silsesquioxane (HSQ) resist using electron beam lithography. The resulting patterns were etched 1.1µm into the lower cladding using SiCl 4 reactive ion etching.
A scanning electron micrograph (SEM) image of one of the grating devices is shown in Fig. 2. The access waveguides were 2#x000B5;m wide, and the average length of the test bars was 1.5mm. The AR coatings used on some of the cleaved access waveguides ends were fabricated as a quarter-wavelength layer of Zirconium oxide deposited using an electron-beam evaporation tool.
The transmission spectra of the devices were taken with a tunable laser source coupled through a mechanical chopper and microscope objective to the test bar. The out-coupled light from a second microscope objective was detected using a Germanium photodiode and lock-in amplifier. Finally, given the design parameters of the gratings, their transmission spectra may be calculated using a TMM model [7], and these then compared with the retrieved spectra from the measurements. It is worth reiterating that although the DUTs are known before the post-processing technique is applied, none of the design parameters are used in the recovery algorithm.
4. Results
Fig. 3 illustrates the measured transmission spectrum of a Bragg grating device (green line), 450µm in length with waveguide width and grating recess depth of W=2µm and d=117nm respectively. The FP fringes from the cavity formed by the facets are clearly identifiable. After processing with the post-processing tools, the recovered transmission spectra are also given in Fig. 3a (blue and red lines), where a reduction of the FP effect is clearly visible. The normalisation of the measured data was relative to its maximum value, the normalisation of the curve-fitted spectrum came from the extracted A parameter, and this value of A was used to normalise the shifting window averaging spectrum also. Fig. 3b shows the simulated and recovered reflection spectra from the TMM tool. The reflection spectrum is recovered by the TMM algorithm from the transmission measurement - and is therefore only compared with simulation, since no reflection measurements could be made with our test-rig. The recovered transmission and reflection spectra exhibit an adequate matching with the simulated grating response. In the high gradient edges of the grating stopband, and the highly transmissive portions of the spectra, the SW averaging does not perform so well. In particular, in the full transmission regions the SW averaging produces a signal following the average of the FP oscillations rather than the full transmission of the DUT.
The results presented in Fig. 3 are for a device with untreated, cleaved facets giving ~30% reflectivity. Devices were also fabricated with one or two coated facets, where the AR coating reduced the facet reflectivity to ~2%. The reduction of the facet reflectivity results in a smaller spurious FP effect, so that the measured signal becomes more similar to the transmittance of the isolated DUT. The relevant conditions were then used in the curve fitting algorithm to retrieve the spectra for these devices. Fig. 4 shows the recovered spectra for devices with all three various facet conditions using (a) the TMM curve-fitting method and (b) a shifting window averaging. Regarding the former method (Fig. 4a), there is good agreement between the recovered spectra of all of the devices and the simulated grating response, showing that the algorithm produces consistent results despite the varying facet conditions. In the case of the SW averaging (Fig. 4b), as the reflectivity of the external cavity to the DUT is reduced, the measured, and so the recovered spectra, tend to converge towards the simulated response. As before, the regions of the response most poorly represented are the areas of large gradient or high transmission. Note that also in this case, the SW averaging normalisation has been carried out using the normalization parameters extracted from the curve-fitting tool.
Fig. 3: (a) Measured, recovered, simulated and shifting window averaging processed transmission spectra, and (b) measured and simulated reflection spectra of an integrated Bragg grating device.
Fig. 4: Recovered transmission spectra of Bragg grating devices, with untreated and AR coated facets, using (a) the TMM curve-fitting method and (b) a shifting window averaging.
To provide further insight into the quality of the results, the recovered spectra were curve-fitted further, using a least-squares method, to a model of the Bragg grating characteristic, leaving as free parameters, the Bragg wavelength and the coupling coefficient. A range of gratings were fabricated with varying grating recess depths, that necessarily vary their coupling coefficient and Bragg condition as described elsewhere [8]. In addition these variations were subject to the same facet conditions outlined above. Fig. 5 shows the variation of Bragg wavelength and coupling coefficient with recess depth for all facet conditions. The small standard deviation of 0.13nm in Bragg condition and 3cm -1 in κ, of the recovered parameters with varying facet conditions, are comparable in magnitude to random fabrication variations and therefore show robust behaviour of the post processing tool. In comparison to the curve-fitting technique, the SW averaging performs as well with regards to the Bragg condition extracted, but cannot provide the coupling coefficient figure because it does not reconstruct the normalization coefficient. Considering the data shown in figure Fig. 4b, normalised making use of the results of the curve fitting method, the variation in the recovered coupling coefficient is up to 15cm -1, which is not useful for any practical measurement of κ.
Fig. 5: Bragg wavelength and grating coupling coefficients as functions of grating recess depth, with varying facet conditions.
The simple Bragg grating devices examined so far have transmission characteristics with a single broad feature. In order to characterise further the algorithms’ capabilities, devices with more complex spectra were subsequently fabricated. A grating device, initially developed for ultrafast pulse shaping applications [9], was fabricated as a complex apodisation profile where individual grating sections were written as in Fig. 6. In addition to having a complex internal structure, the grating also exhibits a lower peak reflectivity than the simple Bragg gratings, thus making the transmission spectrum more prone to being masked by the coupled-cavity effect of the external FP cavity. Fig. 6c shows the relevant measured, recovered and simulated spectra of the pulse shaping grating, along with the SW averaging response. Again the curve-fitting algorithm has significantly suppressed the FP oscillations on the measured spectra and the recovered transmission characteristics match well with the simulated response. In addition, the SW averaging shows the same offset problems in areas of large gradient and high transmission as before, failing to recover well the sharp spectral features of the DUT spectrum. Finally, a non-linearly chirped and apodised grating device with peak reflectivity of around 50% was measured and the transmission spectrum recovered. The non-linear chirp and apodisation of the grating present a more complex device characteristic than the uniform period grating, in both amplitude and phase. Also, in this case the FP fringes greatly obscure the device characteristics. However, the recovered spectrum can be seen to match well with the simulated model, giving confidence in the post-processing tool as a method for the recovery of arbitrary device characteristics.
Fig. 6: Schematics of (a) a multi-grating pulse shaping DUT and (b) Non-linearly chirped and apodised grating. (c) Measured, recovered and simulated spectra for the multi-grating DUT and (d) a non-linearly chirped and apodised Bragg grating device.
5. Conclusions
The post-processing tool based on TMM curve fitting, previously proposed for application with measurement systems including external cavity effects to a DUT, was used with experimental measurements of the transmission spectra of various Bragg grating devices.
The tool exhibited excellent suppression of the FP fringes and produced spectra matching well with simulated results, for the wide range of grating devices fabricated here. In particular, the algorithm dealt markedly better with spectral features of large gradient, than the SW averaging method, which tended to smooth these features.
In addition, by providing normalised data, the curve-fitting tool allowed faithful recovery of device parameters, something not possible with the SW averaging where absence of normalisation appeared a significant limitation. The curve fitting post-processing was also tested against devices having varying facet reflectivity, producing consistent results over all cases, and giving improvement even to measurement data from devices with AR coatings on both cleaved facets. In conclusion, it was demonstrated that the tool can handle many types of spectra consistently and can be used as a valid alternative to simple averaging post-processing techniques for fast and accurate initial device characterisation.
Acknowledgments
The authors would like to thank the staff of the James Watt Nanofabrication Centre at Glasgow University, B. Ward for his support with the laser facilities and P. Bassi for invaluable help. Part of this work was funded by the ProMiNER Project for Micro and Nano Technologies in Emilia-Romagna, Italy.
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