Comparative examination of planar K8: K+ waveguide, TE modes, λ = 633 nm.
End-fire mode spectroscopy technique provides reliable measurement of the whole mode spectrum of optical waveguides having arbitrary cross refractive index profile. The method is based on registration of light beams radiated from the abrupt output edge of the waveguide, with each beam corresponding to the individual waveguide mode. Due to different values of mode propagation constants, modes of different orders demonstrate different refraction angles at the output waveguide face when modes reach that face under the same nonzero inclination angle. Just this feature is used in the technique. Mode excitation is performed directly through the input waveguide face, and therefore the technique can be applied to analyze mode spectrum of arbitrary waveguides, including the ones with non-monotonic index profiles (particularly, symmetric step-index profiles or buried graded-index waveguides with any burying depths).
- integrated optics
- mode index
- refractive index
- optical measurements
Optical waveguides are the basic elements of any photonic device, and their parameters define the operating performances of the whole photonic unit. Optimization of those parameters requires performing the choice of appropriate technology conditions. Development of fabrication technology and further designing the waveguide elements having pre-defined properties need performing a control of the characteristics of trial waveguide samples. Furthermore, planar optical waveguides are used intensively in determination of the basic properties of optical materials. And the problem of reliable determination of the main waveguide performances is still actual.
Important part of examination of planar optical waveguides is measurement of the waveguide mode spectrum. Usually this procedure is performed by a well-known m-line spectroscopy technique (e.g., see [1, 2, 3, 4, 5]). The measured set of mode indices can be considered as initial data as for preliminary determination of the device operating performances as for reconstruction of cross refractive index profile in the formed trial sample. Traditional computing techniques allowing reconstruction of that profile are described in Refs. [6, 7]. However, in cases of planar waveguide structures with thick cover layers or so-called buried graded-index waveguides m-line spectroscopy does not provide reliable measurements. Thick cover layers or large burying depths do not allow tunneling the modes to the external prism and forming the corresponding spatial m-lines. In these cases, some modes (first of all, the lower-order modes) may be simply missed in examinations by m-line spectroscopy [8, 9]. The greater the burying depth the fewer number of modes can be measured by this method. To avoid missing the modes, a layer-by-layer etching of the sample surface could be applied [10, 11]. However, that procedure has many chances to cut a part of the refractive index profile occupied by the mode fields, and that should lead to distortion of the original waveguide mode spectrum. The use of nonlinear optical effects like second harmonic generation  can be successful only for limited number of optical materials demonstrating high values of the corresponding coefficients.
Here we describe a measuring technique named the end-fire mode spectroscopy which is suitable for examination of planar waveguides having arbitrary refractive index profiles including the case of buried waveguide structures with any burying depths, and the presented results of examination of buried waveguides prove this advantage of the technique. Furthermore, here we show that this technique allows also conducting direct measurements of another important characteristic – the maximal refractive index in graded-index waveguides, unlike conventional techniques that involve the set of measured mode indices and employ computing of the maximal value in the refractive index profile using different approximations.
2. Method content
2.1. Mode spectrum measuring
Usually waveguide mode spectrum is presented with a kit of mode indices
The content of the end-fire mode spectroscopy is registration of light beams radiated from the abrupt output edge of a planar waveguide, with each beam corresponding to the individual waveguide mode. Due to different values of mode propagation constants, modes of different orders demonstrate different refraction angles at the output sample face if they are directed to that face under nonzero incidence angle into the waveguide. Just this feature is exploited by the technique in procedures of mode spectrum measurements. Both excitation and output of waveguide modes are performed at the sample faces by the end-fire coupling method which allows reliable launching and output of the whole mode spectrum in any planar waveguide. Therefore, the end-fire mode spectroscopy technique can be applied to examination of planar waveguides having arbitrary cross refractive index profiles including symmetric step-index ones and deep-buried graded-index waveguides.
The measuring block-scheme is shown in Figure 2. Collimated light beam is focused on the input waveguide face by the cylindrical lens. The whole mode spectrum can be launched in this manner in few-mode waveguides. Application of the input cylindrical lens provides obtaining collimated (in the sample planform) mode beams propagating into the examined waveguide. In the case of a thick multimode waveguide, a group of modes is excited simultaneously and can be registered. Further scanning the input sample face along the Y axis allows launching and registration of other mode groups until the whole waveguide mode spectrum is measured. Cylindrical lens in the recording block is not necessary for measuring the mode spectrum. That lens should be installed in procedures of complex measuring as described below.
Two scheme variants providing skew incidence of waveguide beams to the sample output face have been proposed . The former one uses the trapezoidal (in planform section) samples having non-parallel opposite (input and output) waveguide faces as it is shown in Figure 3. The latter one allows testing the samples having usual rectangular form with mode launching performed under special procedure by focusing the probe beam on the polished side face of the examined waveguide. Application of a cylindrical lens for mode excitation enables obtaining collimated (in planform XZ section) waveguide beams in both scheme variants. The latter variant is very attractive because of its non-destructive character, but the alternative former scheme is more convenient for conducting measurements.
The optical scheme has been built according to the former measuring variant in our experiments, and Figure 3 demonstrates light ray paths in planform XZ section of the sample. Whereas the directions of simultaneously excited modes slightly differ due to different refraction at the input sample face, the rays of only one mode beam are shown into the waveguide in order to simplify the drawing. Each output light beam is associated with the individual waveguide mode, and the mode orders of the corresponding modes are identified by the inclination of a certain output beam to the output waveguide face: the lower the mode order, the bigger the output angle. The fundamental mode forms the light beam having maximal value of the output angle
Application of the Snell’s law both to input and output sample faces leads to following expression for calculating the mode indices
Evidently, normal incidence of the probe beam to the input waveguide face (i.e., the condition
When graded-index waveguides are examined, the pattern of output beams has a specific view as a set of slightly curved light strips on the cross screen. The simplest way to explain that pattern is application of the known ray approximation of waveguide light propagation. Following to that approach, Figure 4 demonstrates the rays into shallow graded-index planar waveguide. All drawn rays represent the same waveguide mode.
One can see that the ray 3 is radiated being parallel to the sample surface from the output face point with the depth of so-called turning point which corresponds to the depth in the refractive index cross distribution where the mode index is equal to the refractive index value. So, just the direction of that ray in the planform XZ plane should be registered in measuring the waveguide mode spectrum. The ray scheme demonstrates also the rays 2 and 4 radiated from arbitrary point of the output face under equal opposite tilts. The presence of those rays means that the output light beam is symmetric relatively to the ray 3. Furthermore, the rays 1–3 are radiated from the sample points at different depths where the refractive index has different values. Therefore, the projections of those output rays to the planform XZ should have different directions in that plane. Thus the pattern of the output light beam (corresponding to the certain waveguide mode) on the cross screen apart the sample looks like a curved light strip which is symmetric relatively to the waveguide surface as it is shown in Figure 5. As we must register the rays that are analogous to the ray 3, we find those rays at the top of parabolic-like light strip.
Reliability of the results of mode spectrum measuring by the end-fire mode spectroscopy was proved in comparative examinations of graded-index planar waveguides fabricated in optical glasses. The mode spectrum of the same waveguides had been measured independently with the described technique and also by the traditional m-line spectroscopy method. Whereas the main advantage of the end-fire spectroscopy is its capability to analyze buried waveguides, several shallow graded-index samples had been chosen for comparative measuring because the traditional technique provides reliable results only for that type of waveguides.
Figure 6 presents the photo of the typical pattern formed by output light beams on the cross screen apart from the sample in examinations by the end-fire mode spectroscopy.
The whole spectrum of TE modes was launched simultaneously in this experiment, and the light strips really demonstrate some curvature due to the cross graded-index profile in the examined waveguide layer (see Figure 6a). The centers of the parabolic-like light curves were used for measuring the output angles
As an example, Table 1 presents the results of comparative examinations of the planar waveguide fabricated on the substrate of commercial sodium-containing glass K8 by ion exchange in a potassium nitrate melt at 400°C. The probe light of 633 nm wavelength was used, and the bevel angle between the opposite sample faces was measured with the goniometer by the autocollimation method as α = 380 57′ 08′′± 5′′.
A good agreement between the mode index values measured by both techniques is evident. The difference between the results obtained by those methods does not exceed 10−4, which is similar to the errors considered quite acceptable in traditional mode index measurements.
Furthermore, the samples of buried waveguide structures have been tested by the end-fire spectroscopy technique. Planar buried waveguides have been formed in optical glasses by two-staged ion exchange. First, the shallow planar waveguides having the maximal refractive index at the sample surface were fabricated. Then the samples were treated into another melt providing appearance of reverse direction of diffusion process into the sample. That procedure led to decreasing the surface refractive index while the maximum of the cross index distribution was shifted deeper to the sample depth. Performed choice of the stage’s durations resulted in fabrication of buried waveguide structures.
Mode excitation was performed in examinations by focusing the light beam to the input sample face. However, no waveguide modes have been registered in examinations of those structures by traditional m-line spectroscopy while both direct watching and application of 40xand 90x objectives proved the presence of the mode light spots at the output sample face. That means that the obtained burying depths were sufficient for the case when the “tails” of mode field distribution were so weak near the sample surface that their tunneling to the prism did not resulted in appearance of the output light beams which could be registered. Application of the end-fire mode spectroscopy technique allowed analyzing the waveguide structures that supported propagation of single TE mode. The results of performed examinations by the described technique are presented in Table 2.
Thus, the end-fire mode spectroscopy technique has demonstrated successfully its advantageous feature that is capability of examination of planar structures of any type.
2.2. Evaluation of maximal refractive index
Besides mode spectrum measuring, the technique enables evaluating the maximal refractive index in graded-index waveguides. A principle of that procedure can also be explained involving ray approximation of mode propagation. One can conclude from Figure 4 that we should register the ray 1 radiated from the waveguide at the sample point having maximal refractive index in the graded-index layer. Determination of that index is performed using the output angle
However, in our optical scheme the goniometer measures the angles lying in the XZ plane. So, we obtain in our measuring the values of the angle
It should be noted that mentioned collimation of the output beam is needed only in measurements of the maximal refractive index when one must register high-divergent boundary rays. Measurement of the mode spectrum is performed by registering the central parts of the output light beams, and it does not matter is the output cylindrical lens applied or not in that case.
As an example, let us consider the results of evaluation of the maximal refractive index in the K8: K+ waveguide whose mode spectrum is presented above. The photo of the pattern of output light beam obtained in measuring by the described technique is shown in Figure 6c. For comparison, the maximal refractive index had been measured directly by the end-fire mode spectroscopy and also computed according to conventional methods using the measured mode spectrum. The White-Heidrich method  gives the result as
The pattern shown in Figure 6c demonstrates that application of the cylindrical leans in the scheme recording block really does not affect the central parts of light strips and allows conducting measurements of the mode spectrum also in that variant of optical scheme. So, the end-fire mode spectroscopy technique allows performing reliable direct complex measurements of the set of important optical characteristics of arbitrary planar waveguides (the mode spectrum and the maximal refractive index) in a single procedure.
3. Measuring conditions
3.1. Choice of the sample form
For enhancing the technique sensitivity and accuracy, we must consider the conditions providing maximal variation δ
However, when α approaches the value αlim = arcsin(1/
3.2. Requirements to the collimator
Adjustment of the collimator must provide acceptable divergence of the collimated light beam. Let us first consider the axial section of that beam by the plane normal to the waveguide surface (the upright plane YZ in Figure 2). One can conclude from the drawn ray scheme that divergent (in that upright projection) beam causes a mismatch between apertures of waveguide mode and exciting focused spatial light beam. That mismatch results in decreasing the excitation efficiency. However, it does not influence on the registered angular values (they are measured into another planform projection XZ). Now let us consider the affect of beam divergence into that plane XZ (that coincides with the sample surface) on the results of angular measurements. One can conclude from Figure 3 that if a divergence of the incident light beam is small, each output beam acquires a slight angular broadening, but it remains approximately axisymmetric relatively to the direction
Another requirement concerns performances of examined waveguides: the divergence of each output beam must be less than the angles between the output beams corresponding to waveguide modes of adjacent orders. Otherwise, overlapped different beams could not be distinguished and measured. Let us evaluate these angles basing on performances of graded-index waveguides which mostly demonstrate the closer mode indices (and, hence, would form the least beam spatial separation in the considered scheme) for higher-order modes. Considering the presented condition for the bevel angle α, we can deduce following expression from Eq.(1) for adjacent higher-order modes:
Thus we can expect that the source of the main affect on the results could be deviations from the conditions of mode excitation occurring in the launching scheme unit.
3.3. Tolerance of incident beam direction
As Eq. (1) involves the angle of incidence
Let us evaluate those errors. We can deduce from Eq. (2) that
To confirm that unobvious conclusion, we can consider the described sample of K8: K+ waveguide and evaluate numerically the mentioned errors by another manner. In this case we assume that considered mode index error can be defined as Δ
It can be noted that the errors calculated for the modes of different orders are really identical in the most practical cases of small angles of incidence. The Δ
One can also see from Eq. (5) that the choice of the bevel angle α closer to the upper limit value makes it possible not only to increase the sensitivity of the end-fire mode spectroscopy technique but also to reduce the influence of deviation from the condition of normal beam incidence to the input waveguide face.
3.4. Adjustment of input cylindrical lens
Besides the inclination of the incident beam in the XZ plane, occurrence of some turn of the cylindrical lens generatrix relatively to the waveguide plane in the launching scheme block is possible in measuring. Let us consider that case of the lens rotated around its optical axis assuming that the lens axis is directed along the normal to the input sample face. The ray paths in waveguide mode excitation procedure are shown in Figure 9.
Let the lens generatrix be tilted toward the surface of the sample by angle γ. Then the plane of incidence of the focused light beam (that involves the two-sided arrow denoting the lens in the scheme) is turned to the vertical Y axis by the same angle as it is shown in Figure 9. Considering reversible character of light paths in optical systems containing the passive elements only, we can consider our case in the reverse direction as an emission of the waveguide mode from the output waveguide face. That approach allows using the reasons and the results described above.
It is shown that the output mode beam looks like a curved light strip on the cross screen when a skew incidence of collimated beam to the output face is performed into the waveguide, and the strip edges demonstrate maximal inclinations from the longitudinal upright section. Then our studied case can be considered as reversible one – the tilted boundary rays of the incident light beam formed with the turned cylindrical lens excite the mode which is directed at some angle to the normal to the input sample face (see Figure 9) while the paraxial rays of the incident beam still meet the condition of normal incidence. That means excitation of divergent (in the planform XZ plane) waveguide mode beam, and consequently the spatial light beam which is radiated from the opposite output sample face should demonstrate angular broadening into that XZ projection.
If the numerical aperture of the exciting lens, as well as the size and position of the light spot at the input sample face are matched with the corresponding parameters of the excited mode, the output light beam is approximately axisymmetric relatively to the direction of unperturbed output beam, and that produces no additional errors neither in measuring the output beam direction nor in further calculation of the mode index. However, a set of waveguide modes is excited usually with the end-fire technique, and there is a natural wish to use this circumstance by measuring the characteristics of several modes under the single adjustment procedure. For this purpose, one scans the input end with the focused input beam and chooses a beam position that leads to optimizing the visibility of the mode’s set. Then only the part of the shifted incident beam actually excites some individual mode. As the exciting lens is turned in the considered manner, the output light beam is broadened asymmetrically (relatively to the output mode direction that could be in the case of zero lens turn) as can be seen in Figure 9. Just that reason leads to additional errors in measuring. The detailed procedure of determination of dependence Δ
Whereas the considered error Δ
First the tilt of the incident light beam should be registered by watching through the goniometer telescope or with the photoreceiver matrix. Then the reference glass cube (given in the goniometer tool kit) is installed on the goniometer sample mount, and the reflected light beam is registered near the opposite direction according to the scheme in Figure 11. Registered light strip patterns are shown in Figure 12.
If the measuring system is misadjusted in parameter γ, the strips representing direct and reflected beams demonstrate opposite inclinations at the angle of 2γ to each other. Turning the lens around its ax and repeating the procedures one can obtain coincidence of orientations of those light strips. This will be the criterion for correct orientation of the cylindrical lens – the lens generatrix gets right orientation parallel to the sample mount surface. For example: using the micrometer ocular of the goniometer tool kit we were able to adjust the lens orientation with the accuracy of 2 arcmin. It can be concluded from the dependences shown in Figure 10 that the corresponding mode index errors are reduced to an acceptable level. We can also note that our evaluation results in the maximum level of the measurement errors when the cylindrical lens is rotated around the axis, accompanied by the displacement of the input beam as it scans over the end of the waveguide. The mode index errors decrease as the incident beam is shifted toward the position that matches the region of localization of the measured mode, and the range of allowable lens tilts is broadened.
The presented materials prove applicability of the end-fire mode spectroscopy technique to analysis of planar optical waveguides with arbitrary cross refractive index profiles, and performed measurements of the characteristics of buried waveguides highlight this advantage of the technique. Furthermore, the technique allows conducting reliable direct complex measurements of the set of important optical characteristics of arbitrary planar waveguides (the mode spectrum and the maximal refractive index) in a single procedure. End-fire mode spectroscopy has a good potential for wide practical application in examinations of planar structures. Further developments should be aimed at modifying the measuring scheme in order to be able to analyze 3D optical guides. That could allow extending the area of technique applications by involving additional large group of waveguides including optical fibers.
Tien PK, Ulrich R. Theory of prism-film coupler and thin-film light guides. Journal of the Optical Society of America. 1970; 60(10):1325-1337. DOI: 10.1364/JOSA.60.001325
Barnosky MK. Introduction to Integrated Optics. NY, London: Plenum Press; 1974. 515 p. DOI: 10.1007/978-1-4684-2082-1
Wang X, Yin C, Cao Z. Progress in Planar Optical Waveguides. Berlin-Heidelberg: Springer-Verlag; 2016. XI,241 p. DOI: 10.1007/978-3-662-48984-0
Lavchiev VM, Jakoby B, Hedenig U, Grille T, Kirkbride JMR, Ritchie GAD. M-line spectroscopy on mid-infrared Si photonic crystals for fluid sensing and chemical imaging. Optics Express. 2016; 24(1):262-271. DOI: 10.1364/OE.24.000262
Yulianto M, Marzuki A, Suryanti V. Diffusion processes for planar waveguides fabrication in soda-lime glasses. Journal of Physics: Conference Series. 2017; 909(1):012022 (5 pp). DOI: 10.1088/1742-6596/909/1/012022
White JM, Heidrich PF. Optical waveguide refractive index profiles determined from measurement of mode indices: A simple analysis. Applied Optics. 1976; 15(1):151-155. DOI: 10.1364/AO.15.000151
Chiang KS. Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes. Journal of Lightwave Technology. 1985; LT-3(2):385-391. DOI: 10.1109/JLT.1985.1074194
Rogozinski R. Determination of refractive index profiles of planar buried waveguides on the basis of a set of modal propagation constants. Optics Communication. 2003; 219(1):199-214. DOI: 10.1016/S0030-4018(03)01286-0
Marangoni M, Osellame R, Ramponi R, Giorgetti E. Second harmonic generation from radiation to guided modes for the characterization of reverse-proton-exchanged waveguides. Opitcs Express. 2004; 12(2):294-298. DOI: 10.1364/OPEX.12.000294
Glebov LB, Dokuchaev VG, Morozova IS. Simple method for reconstruction of refractive-index profile for planar wave-guides. Optics and Spectroscopy. 1989; 66(5):1110-1114. WOS: A1989AC80700031
Monir M, El-Refaei H, Khalil D. Single-mode refractive index reconstruction using an nm-line technique. Fiber and Integrated Optics. 2006; 25(2):69-74. DOI: 10.1080/01468030500466230
Svistunov DV. End-fire mode spectroscopy technique of examination of planar waveguides. Journal of Optics A: Pure and Applied Optics. 2008; 10(8):085301(4 pp). DOI: 10.1088/1464-4258/10/8/085301
Svistunov DV. New measuring method of examination of planar optical waveguides. In: Proceedings of Progress in Electromagnetics Research Symposium (PIERS 2009 in Beijing); 23-27 March 2009; Beijing. 2009. pp. 1689-1693. DOI: 10.2529/PIERS080904135015
Zolotov EM, Kiselyov VA, Pelekhaty VM. Determination of characteristics of optical diffuse waveguides. Soviet J Quant. Electr. 1978; 8(11):2386-2382. DOI: 10.1070/QE1978v008n11ABEH011261
Svistunov DV. Optimizing the mode-excitation conditions when a planar waveguide is being investigated by means of end-fire mode spectroscopy. Journal of Optical Technology. 2014; 81(1):1-5. DOI: 10.1364/JOT.81.000001