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Abstract
Waveguides fabricated in crystals, created by utilizing techniques such as ion implantation, femtosecond laser inscription, and proton exchange, have low refractive index contrast with the crystal substrate, which limits their potential development to create compact passive devices, such as waveguide interferometers. In this work, a new waveguide multi-mode interferometer fabrication strategy based on low-effective-index mode interference is presented. Numerical tools have been used for the analysis of this new guided-wave approach used for the device design. The research has demonstrated that a series of high-order modes with an effective refractive index much lower than the substrate can exist in trench-cladded ridge crystal waveguides that have a tiny index contrast in the vertical direction. Simple trench-cladded tapered waveguide configurations to excite such modes and to realize compact waveguide multi-mode interferometers with lengths of several tens and up to hundreds of micrometers are presented. The waveguide multi-mode interferometer design is compact in size, easy to modulate, and with low insertion loss. Furthermore, refractive index sensing is realized, with a sensitivity of ∼490 nm/RIU for aqueous solution samples. The novel multi-mode interference phenomenon present here offers new possibilities and significant opportunities for waveguide modulation and, thus, the development of compact waveguide refractometers.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical waveguides fabricated in crystals play an important role in the fields of waveguide amplifiers, waveguide lasers and nonlinear frequency converters [1–5]. The benefits seen from the high intensity density in the waveguide core, the laser and the nonlinear conversion efficiency can be greatly improved in the waveguide region used, compared to that in bulk crystals [6–9]. Typical strategies for crystal waveguides fabrication include ion implantation/irradiation, femtosecond laser inscription, proton exchange and metal ion in-diffusion [10–14]. All these methods are based on local refractive index (RI) modulation of the crystals used and therefor will be referred to as Index-Modulated Crystal (IMC) Waveguide in the subsequent discussion.
The waveguide Mach-Zehnder Interferometer (MZI) is one of the basic passive components in many photonic circuits, to provide functions such as filtering and modulation and also they are useful for a range of optical sensing applications [15–19]. However, for the IMC waveguide, as the RI contrast between the waveguide core and the substrate is low (usually at the level of between 10−4 and 10−2, depending on the materials and the fabrication method), it is very challenging to integrate a compact MZI into IMC waveguide circuits [20–23]. One of the difficulties in so doing comes from the large bending radius needed to form the Y-branch, to split the waveguide signal into two arms, due to the low index contrast. As an example, Ajates et al. reported the fabrication of a waveguide Y-branch and MZI structure in a Nd:YAG crystal by using femtosecond laser writing, where the length of the MZI used was ∼8 mm [24]. Another choice that could be used is to implement a MMI-based (MultiMode Interferometer) waveguide splitter. In previous work, we designed and reported on a MMI-based 1 × 2 splitter in an ion implanted LiNbO3 crystal waveguide, with a relatively compact length, of about 330 µm [25]. However, considering the low index contrast, the effective refractive index (ERI) modulation range between the different waveguide arms is very limited: this meaning that a relatively long interference distance is needed to obtain sufficient narrow free spectral range (FSR), similar to what is seen in optical fibers. As can be seen from the work of Lee et al., they have reported a Ti in-diffused LiNbO3 channel waveguide interferometer, based on the MMI effect. The FSR of the device is ∼18 nm and ∼48 nm (for the TM and the TE polarization) in the wavelength range ∼1300 nm: however the size of MMI structure is 33 mm in length, which unfortunately limits its applications [26].
Waveguides with ridge geometries are widely applied in various waveguide devices for the compact size and strong confinement of the field. For example, GaAs/AlGaAs ridge waveguides were designed for mid-infrared sensing applications [27]. The ridge structure of crystalline materials can be processed by several procedures, including precise dicing, ion-beam enhanced etching, and femtosecond laser assisted chemical etching, and close to 90° side-wall angles can be achieved [28–31]. In all these works, only the fundamental mode of the ridge waveguides were studied. In general, the view is taken that the ERI of the waveguide mode should always be higher than that of the surrounding materials. For example, in Ref. [27], the RI of the substrate dielectric (AlGaAs) was taken as the cutoff ERI value for high-order modes. At the same time, little attention was given on the multi-mode phenomenon with mode ERI lower than the substrate in the past.
In the present work, a new waveguide MMI design strategy for an IMC waveguide based on low-ERI mode interference is discussed. It is shown here that for IMC waveguides with ridge geometries, as the RI contrast is quite different at two-transversal dimensions, series of high-order modes can exist, of which the ERI can be much lower than the substrate. A detailed analysis on the characteristics of such low-ERI modes is given for the first time to the best of our knowledge. The huge ERI difference of such modes enables the design of an ultracompact waveguide MMI, of size of several tens of micrometers. This work thus provides new possibilities and important opportunities for the modulation of the IMC waveguide and thus also shows important potential for the development of effective miniaturized waveguide sensors.
2. Characteristics of low-ERI modes in ridge IMC waveguides
A X-cut, Z-propagation LiNbO3 (LN) crystal waveguide forms the object of study in this work. LiNbO3 is one of the most popular crystalline materials as for its outstanding nonlinear, electro and acousto-optical properties, and also an important candidate for photonic circuit construction.
Here, without loss of generality, the waveguide was set to have a uniform RI increase of 0.01 compared to the LN substrate (n0 = 2.213 at 1550 nm wavelength). The basic ridge waveguide structure is shown in Fig. 1, that three sides of the waveguide region are exposed in air while the bottom side is connected with unmodified LN ridge section. Ridge structure of crystalline materials with close to 90° side-wall angles can be achieved by several procedures, including precise dicing, ion-beam enhanced etching, and femtosecond laser assisted chemical etching [28–31].
By applying the Beam Propagation Method (BPM), the mode properties of the LN ridge waveguide was analyzed. The simulation can be implemented by using commercial softwave Rsoft (Host ID: 16850650). During the simulation, the width W and thickness T were both set to be 5 µm, and the height of the unmodified LN ridge D was set to be above 10 µm, with D = 10 µm corresponds to the lower boundary of which the calculation is taken. Steep trench side-walls were used with tilting angle θ to be 0. Several typical TE mode profiles, obtained at a wavelength of 1550 nm are presented in Fig. 2. As can be seen, multi-modes exist in such waveguides. Interestingly, it was found that all the high-order modes have ERI values lower than that of the substrate (2.213). The calculation results were further confirmed by applying a Finite Element Method (FEM) calculation. Further, the difference in the ERI values between these modes is quite large. The TE11 mode has an ERI of ∼2.214 while the high order mode, shown in Fig. 2(d), has an ERI as low as ∼1.465 and a much deeper evanescent field penetration in the horizontal direction. A similar phenomenon was also observed for the TM polarization. The first few modes have negligible propagation loss as presented in Fig. 2(a)-(c). The imaginary part of ERI grows to ∼2.8 × 10−7 for the high-order mode TE11,1 as shown in Fig. 3(d), and leakage of energy into the substrate can be observed. Nevertheless, the corresponding loss is still below 0.1 dB/cm, indicating the leakage is at a negligible level, thus guiding mode property to be confirmed even for modes with high mode orders. The multi-mode behaviors indicate that, by proper exciting different ordered modes, multi-mode interferometers can be constructed in such ridge IMC waveguide platforms. And benefitting from the large ERI contrast of such modes, an interference pattern with a narrow FSR can be obtained, for a much shorter interference length, compared to the current IMC waveguide MMI.
Fig. 2. Several typical TE mode profiles obtained by simulation using the BPM, at wavelength of 1550 nm. In the bracket above each image is the real and imaginary part of ERI of each mode. The color scales are of arbitrary unit.
Fig. 3. (a) The ridge IMC waveguide decomposed firstly into a horizontal planar waveguide and then a vertical planar waveguide; (b) Mode profile of the horizontal waveguide and (c) A typical mode profile of the vertical waveguide. The dashed line in (b) and (c) indicating the waveguide boundaries.
Compared to the guided modes with ERI higher than the substrate, those low-ERI, high-order modes in ridge IMC waveguide have received less attention in past works. One feature of the ridge waveguide studied here is that in the vertical direction, it is weakly guided as the core RI increases only by ∼0.45%, whereas in the horizontal direction, the index contrast is large. Further, by considering the negligible loss, the low-ERI modes presented here show clear “guided mode” properties and therefore, the Effective Index Method (EIM) was implemented for the mode analysis carried out. As shown in Fig. 3(a), the TE mode of the thinned ridge waveguide can be decomposed firstly into the TE mode of the horizontal waveguide sandwiched by air and LN substrate, and then into the TM mode of the vertical waveguide, with a core index of the ERI of the horizontal mode, this surrounded by the trench dielectrics with RI of ns. The mode profile of the first horizontal waveguide is shown in Fig. 3(b), where the ERI is ∼2.2195 (single-mode). A series of modes has been found for the decomposed vertical waveguide where one of these modes is shown in Fig. 3(c), as an example and where the calculation here is made by use of the BPM. Apparently, the ERI value of these modes lie in the ERI range between that of ns and neff1, which represents the RI (between 1 and 2.2195 in this case) of the surrounding medium and the ERI of the horizontal planar waveguide. This implies that the low-ERI modes can be understood as being a series of planar waveguide modes confined by high-contrast interfaces between the LN crystal and the trench dielectrics, which are further perturbed and restricted by the small index contrast in the other dimension.
The ERI values of the first seven TE modes obtained by directly calculating the 3D waveguide structure with the use of the BPM and using EIM analysis, are presented in Table 1. The results obtained agree well with each other, with only minor deviations at the level of 10−5 - 10−4. This confirms that the EIM approximation works well for the low-ERI modes of IMC waveguide, presented here. It is worth noting that the low-ERI mode phenomenon is not limited to LN waveguides. For example, Yashar et al. reported the construction of potassium lithium tantalate niobate (KLTN) crystal ridge waveguide which is side-cladded by air trenches, by a combination of He+ ion implantation and laser ablation procedure. Multi-mode pattern was observed by collecting the near-field image with CCD camera, however detailed analysis of the modal properties was not presented in their study [32]. This novel mode phenomenon offers a new possibility for the modulation of the IMC waveguide, which is traditionally believed to be weakly guided with a very limited ERI modulation range.
Table 1. ERI obtained by directly 3D-BPM calculation and by EIM
The multi-mode property of IMC ridge waveguide was further tested by calculating the electric field evolution in such waveguide with Finite-Difference Time-Domain (FDTD) method. During the calculation, a smaller W of 4 µm is chosen for saving the calculation resources as the self-imaging distance is proportional to W square and all other parameters remained the same as above. A Gaussian beam with waist diameter of 1 µm in width and 4.5 µm in height was input from one side of the ridge waveguide as shown in Fig. 4(a). The absolute value of electric field evolution is shown in Fig. 4(b). Clear multi-mode interference pattern is observed, with the black dashed line indicating the first self-imaging position. The weaker self-imaging spot compared to the input is due to the input coupling loss caused by the mismatch between the input Gaussian spot and the modal profiles. As for comparison, a corresponding two-dimensional field profile is also presented in Fig. 4(c), with the 2D waveguide constructed by the ERI method mentioned above. The self-imaging position of ∼21.5 µm is in good accordance with that of 3D modal (∼21.1 µm) as shown in Fig. 4(b), showing the validity of ERI analysis.
Fig. 4. (a) Schematic view of the in-coupling process, with the red dashed circle indicating the Gaussian beam spot, with the center of the spot at the y = 2 µm plane. (b) The electric field evolution of a Gaussian beam into the ridge LN waveguide at the y = 2 µm plane. The arrow indicating the direction of beam propagation. (c) The field profile in the corresponding 2-dimensional waveguide structure constructed based on ERI results.
The mode performance with limited etching depth of the cladding trenches was also studied. It was found that with reduction of the height D of the ridge section, the propagation loss of the low-ERI modes tend to increase as the evanescent field penetrating into the substrate lost its restriction in the vertical directions. Typical lossy mode profiles are presented in Fig. 5(a) and (b), with ridge height D of 1 µm. Leakage of energies into the substrate can be observed, with the losses of TE11 and TE21 mode determined to be ∼0.37 and ∼57.3 dB/cm respectively.
Fig. 5. The electric field profiles of (a) TE11 and (b) TE21 mode with limited trench depth of D = 1 µm. (c) The TE21 mode propagation loss in relationship with depth D, presented in log scale. (d) The loss curve of different ordered modes TEm1 with fixed D of 3 µm. All results here were resulted from BPM calculations.
The relationship between mode loss and the trench depth D was studied by choosing the same TE21 mode as the example. The result is shown in Fig. 5(c). As can be seen, for D above 6 µm, the loss of the low-ERI TE21 mode is negligible, while it grows dramatically with the decreasing of D. When D drops to 2 µm, the mode loss grows to a level above 10 dB/cm. For a fixed trench depth, the high ordered modes tend to have higher propagation loss compared to the “normal” fundamental mode with ERI larger than the substrate. One such example is shown in Fig. 5(d), in which the depth D is fixed to be 3 µm. The mode loss is close to 0 for the TE11 mode, while with the growth of the mode order m of TEm1 mode to the value of 5, the mode loss is estimated to be ∼5.43 dB/cm.
The influence of tilting trench side-wall on the modal characteristics were also studied by BPM simulation, during which the width of top side of the ridge waveguide was fixed to be 5 µm. It is found that the propagation loss of high-order low ERI modes grows rapidly with increasing of the tilting angle θ, as the modal field tend to be “pushed” down to the substrate direction by the tilting side-walls. For example, at θ of 5°, the loss of TE21 mode grows to ∼10.1 dB/cm at wavelength of 1550 nm. The high-loss fact limits the number of modes supported by the tilting ridge waveguide which can be used for construction of multi-mode interferometers. However, the loss of low ERI modes can be reduced by enhancing the optical restriction in the vertical direction, by increasing either the RI contrast or the thickness of the waveguide region. For example, by increasing the waveguide index contrast to 0.02 and 0.04, the propagation loss of TE31 mode under tilting angle θ=5° and θ=10° is kept to be as low as ∼1.66 and 0.06 dB/cm respectively, with the corresponding mode profiles shown in Fig. 6(a) and (b). The loss problem is not an issue for LN waveguides, as step-like index modulation with magnitude larger than 0.1 and modulation depth of several tens of micrometers can be easily achieved, by for example, swift heavy ion irradiations [33,34].
Fig. 6. TE31 mode profiles of LN ridge waveguide with (a) tilting angle θ of 5° and RI contrast of 0.02 and (b) tilting angle θ of 10° and RI contrast of 0.04. The boundaries of waveguide are indicated by the black solid.
3. MMI design and performance
Waveguide multi-mode interferometer is designed based on MMI effect of the low-ERI modes. The waveguide used here is a LN surface channel waveguide with width and height to be 8 and 5 µm respectively, and with a RI contrast of 0.1 to that of the substrate. A pair of symmetrically arranged trapezoidal-like trenches occupied part of the waveguide core as shown in Fig. 7. The waveguide is thus narrowed by the trench side-walls performing as MMI region, with tapered sections on both sides, with a tapering angle φ of 10°. Such a structure can be built by a combination of lithography assisted ion implantation and selective etching processes. Once the mode energy of the channel waveguide is input, different ordered low-ERI modes are excited as the input waveguide taper is non-adiabatic. The multi-mode energies are then passing through the output waveguide taper and returned back to the single-mode channel waveguide. Interference spectrum is obtained considering the huge ERI difference in-between fundamental and the low-ERI modes in the MMI section.
Fig. 7. (a) The schematic diagram of the trench cladded waveguide MMI, with the arrow indicating the input direction. (b) The top view of the designed waveguide MMI.
FDTD simulations were applied for study of the MMI performance, with a simplified 2D modal based on the ERI method, for faster calculation speed. A mesh grid size of 30 and 50 nm in x and z directions was used, with Perfect Matched Layer (PML) boundary applied. The field distribution with L1 of 50 µm at 1550 nm wavelength is presented in Fig. 8(a). The narrowed ridge section show clear multimode pattern, with only slight energy leakage observed at the input junction. The corresponding transmission spectrum is shown in Fig. 8(b). As can be seen, interference pattern was observed with Free Spectral Range (FSR) of ∼130 nm around wavelength range of 1500 nm. Secondary ripples other than the main interference pattern are observed, especially at shorter wavelength, indicating three or more different modes involved in the interference. The extinction ratio of the peak/dips is above 8 dB at the whole wavelength range and approaches ∼19 dB around 1300 nm, with low average loss below 0.5 dB.
Fig. 8. (a) The Hy field (y component of magnetic field intensity) profile and (b) transmission spectrum of the trench cladded LN wavguide interferometer with MMI length L1 of 50 µm. The transmission spectrum of the MMI with L1 of (c) 90 µm and (d) 200 µm respectively.
The FSR of the MMI can be modulated by changing the length L1 of the MMI region, as shown in Fig. 8(c) and (d). The FSR reduced to ∼89 nm with L1 of 90 µm and to the value of ∼38 nm with L1 of 200 µm around the wavelength of 1500 nm, during which, the length L2 of the tapered section was fixed to be 51 µm. Further, a 3-dimensional FDTD simulation was carried out with L1 = 90 µm, with the channel waveguide mode as the input. The transmission spectrum is shown in Fig. 8(c) with red dashed line. The transmission curve corresponding well with 2D calculation, indicating the accuracy of the 2D-FDTD results.
The designed taper waveguide MMI can be utilized as RI sensor, by immersing the MMI into liquid samples to be tested. Since the low-ERI modes have stronger evanescent interaction with the trench dielectrics as can be seen in Fig. 2, the ERI values of the modes are more sensitive to the surrounding RI change compared with the fundamental mode, which leads to the variation of the transmission curves. The 3D-FDTD simulation was carried out with the same structural parameters as above, with the MMI length L1 fixed to be 90 µm. The variation of transmission curve at different liquid RI is presented in Fig. 9(a). With the increasing of liquid RI from 1.33 to 1.43, the transmission curve shifted to the direction of longer wavelength. By monitoring the transmission dip around 1580 nm, the RI sensitivity is estimated to be ∼490 nm/RIU, and the peak wavelength response to the RI is nearly linear in the range of 1.33 - 1.43, as shown in Fig. 9(b). The sensitivity result is ideal, considering the huge RI difference between LN crystal and the aqueous solution. Higher RI sensitivity is expectable by choosing materials with lower RI as the waveguide MMI platform, or by further optimizing the geometrical parameters of the MMI, which is beyond the scope of this study.
Fig. 9. (a) The transmission curves with surrounding RI of 1.33 - 1.43. (b) The RI sensitivity around 1580 nm.
4. Conclusions
In this work, it has been demonstrated that in index modulated crystal waveguides with a ridge geometry, the high-order modes with an effective refractive index much lower than that of the crystal substrate can exist. These kinds of low-effective-index modes can be understood as a series of planar waveguide modes confined by high-contrast interfaces between the crystal and the groove in the horizontal direction, which are further perturbed and restricted by the small index contrast in the vertical dimension. By using a trench-cladded taper waveguide configuration, the excitation of such high-order modes can readily be achieved. A compact waveguide MMI has been designed by utilizing this approach, with dimensions ranging from several tens to hundreds of micrometers in length. The waveguide MMI present here has advantages such as a compact footprint, a direct and simple geometry, ease of fabrication and modulation of the spectrum, as a result of which only a pair of etched surface cavities is needed, in addition to conventional channel waveguides. The trench-cladded waveguide multi-mode interferometer approach can also be applied in optical sensing. A compact LiNbO3 waveguide interferometer with an interference length of 90 µm has been designed, with a sensitivity of 490 nm/RIU for aqueous solution samples. This work thus offers new possibilities for mode modulation of crystal waveguides and for the development of compact, high-performance waveguide optic sensors.
Funding
National Natural Science Foundation of China (11375081, 12134009); Natural Science Foundation of Shandong Province (ZR2020QF86, ZR2022MF253, ZR2022MF258); Liaocheng University (318051411, 318052199).
Acknowledgments
The authors gratefully acknowledge fruitful discussions with B. M. A. Rahman, and Kenneth T. V. Grattan.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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