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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26742–26761
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Mode control and mode conversion in nonlinear aluminum nitride waveguides

Matthias Stegmaier and Wolfram H.P. Pernice  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26742-26761 (2013)
http://dx.doi.org/10.1364/OE.21.026742


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Abstract

While single-mode waveguides are commonly used in integrated photonic circuits, emerging applications in nonlinear and quantum optics rely fundamentally on interactions between modes of different order. Here we propose several methods to evaluate the modal composition of both externally and device-internally excited guided waves and discuss a technique for efficient excitation of arbitrary modes. The applicability of these methods is verified in photonic circuits based on aluminum nitride. We control modal excitation through suitably engineered grating couplers and are able to perform a detailed study of waveguide-internal second harmonic generation. Efficient and broadband power conversion between orthogonal polarizations is realized within an asymmetric directional coupler to demonstrate selective excitation of arbitrary higher-order modes. Our approach holds promise for applications in nonlinear optics and frequency up/down-mixing in a chipscale framework.

© 2013 Optical Society of America

1. Introduction

2. Optical modes in AlN-ridge waveguides

The number of modes and the respective field profiles of an optical waveguide are determined by its specific geometry and the considered wavelength. The methods for identification of excited modes presented here for ridge waveguides are nevertheless directly transferable to other waveguide geometries since they rely on general properties, such as the effective mode indices, which can be derived from the propagation constant for any waveguide mode.

2.1 Device fabrication and experimental setup

Here, we study AOI based ridge-waveguide structures as schematically depicted in Fig. 1(a)
Fig. 1 (a) Basic structure of the studied AOI based ridge-type waveguides. The AlN film of height hAlN = 500 nm is fully etched down to the underlying silica layer while the remaining e-beam resist HSQ of approximately hHSQ = 140 nm is left on top. Resulting from the fabrication, sloped sidewalls with θ = 12° are observed. (b) Optical micrograph of a fabricated device with evanescently coupled ring resonator for evaluation of the group index from measured free spectral ranges (FSRs). Light is coupled into the structure by the grating coupler on the lower left and out by the one on the lower right. The ring resonator is separated from the waveguide of width ww = 650 nm by a small gap g = 550 nm.
. The used wafer stack consists of a highly c-axis oriented polycrystalline AlN film of height h = 500 nm, which is sputter deposited onto a silicon substrate with a buried oxide layer of 2.0 μm thickness. Nanophotonic circuits are defined with electron-beam lithography using a Jeol 5300 50 kV system and Fox 15 negative tone e-beam resist (HSQ). Subsequently, the developed samples are etched in Cl2/SiCl4/Ar inductively coupled plasma using an Oxford 100 system. The resulting waveguide structures are connected to focusing grating couplers for out-of-plane optical access. Fabricated photonic circuits exhibit in the telecoms C-band low insertion loss down to 11 dB, corresponding to an overall transmission of up to 8%. The insertion loss consists of 5 dB input and output coupling losses and propagation loss of approximately 3.5 dB/cm, respectively. The performance of the fabricated devices is characterized using transmission measurements. For that, light is coupled in and out of the integrated circuits with focusing grating couplers, whose central coupling wavelengths are suitable adjusted to be in the required spectral regimes [18

18. P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol 4, 300–305 (2013). [CrossRef] [PubMed]

, 19

19. S. Ghosh, C. R. Doerr, and G. Piazza, “Aluminum nitride grating couplers,” Appl. Opt. 51(17), 3763–3767 (2012). [CrossRef] [PubMed]

]. Besides their convenience for quick and reliable measurement, these gratings benefit from being mode sensitive due to their dependence on the effective grating index [20

20. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006). [CrossRef]

]. Between λ = 1500 nm and λ = 1630 nm, the tunable lasers New Focus TLB-6600 and Santec TSL-510 are used in combination with a low-noise photodetector (New Focus 2117). In the measurement setup an additionally employed fibre polarization rotator enables control of the polarization of the light sent to the chip. In contrast, for measurements outside of the spectral band covered by the tunable laser sources, unpolarized light from a supercontinuum source (Leukos SM-30-UV) with a broad spectral output between 350 nm and 1750 nm is employed. In this case, the transmitted signal is analyzed with two spectrometers (ANDO AQ-6315A or Ocean Optics JAZ), depending on the spectral regime and the intensity of the light to detect.

2.2 Finite-element simulations

In order to design suitable AOI photonic circuits numerical simulations are performed initially. Besides their importance for the design of new devices, accurate simulations are also important for the interpretation of experimental data. In particular in case of multimode waveguides, good knowledge of the properties of the guided modes is essential, especially given the complexity of the system. Therefore, we used finite-element analysis with COMSOL® to predict the number of guided modes of the considered ridge-waveguides and their respective properties. Since different modes can exhibit similar properties, e.g. only slightly differing values of the group index ng, accuracy of the simulation is an important issue to identify an excited mode unambiguously. Hence, the used input parameters for the FEM-simulation have to be chosen as accurate as possible. For this purpose, the geometrical quantities like width, heights and sidewall angle were extracted from high-resolution SEM-micrographs. Furthermore, fused silica is accurately described by the refractive index nSiO2 = 1.444 while in case of HSQ nHSQ = 1.4 is adequate. Here, the exact refractive index of HSQ is not known as it depends on various parameters like the concentration and the processing technique [21

21. C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) films produced by thermal curing,” J. Mater. Chem. 12(4), 1138–1141 (2002). [CrossRef]

] but due to the small width of the remaining layer, deviations do not change the simulation results considerably. In contrast, the optical properties of AlN itself determine sensitively the properties of the waveguide. We expect that the used polycrystalline AlN film still exhibits birefringence like its crystalline counterpart due to its columnar micrograin structure with strong c-axis orientation. Hence, in the simulation the ordinary nAlN,o and extraordinary nAlN,e refractive indices were taken into account separately. However, these refractive indices deviate from the reported values of crystalline AlN [22

22. Handbook of Optics (McGraw-Hill, 1994).

] which effect cannot be neglected due to its high influence on the simulation results. Therefore, we performed series of experimental studies to derive more precise refractive index values for wavelengths around λ = 1550 nm.

2.3 Adjustment of the ordinary and extraordinary refractive index of AlN

3. Experimental identification of excited modes

In principle, any one of these presented methods is sufficient to determine the nature of an excited mode. However, as discussed in section 2 the employed simulations depend sensitively on various geometrical and physical input parameters which suffer from small but non-negligible inaccuracies. This results in unavoidable deviations between experimental and simulation results which complicate an unambiguous identification of a mode, in particular in systems where several modes exhibit similar values of the considered property. Therefore, several independent criteria are in general required for a clear distinction between such modes and a final identification.

In the following subsections, the discussed criteria are applied to exemplary cases of externally and internally excited modes. Since these two cases differ fundamentally in the way how the considered modes are exited they require different approaches. First, the mode excitation characteristic of the used grating couplers is studied since good control over the initial mode composition is essential for further studies of internal processes. Subsequently, second harmonic generation (SHG) in an integrated AlN circuit is discussed [17

17. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012). [CrossRef]

]. Here, the nature of the phase-matched mode at the 2nd harmonic is identified.

3.1 Externally excited modes by a grating coupler

As long as external light sources and detectors are used, controlled coupling of light between the integrated photonic circuits and the external fibres is of major importance for optical device characterization. Besides sufficient high coupling efficiencies, good knowledge on the mode excitation characteristic of the used technique is essential to improve device performance and analyze internal processes. Here, we use focusing grating couplers which are inherently mode sensitive [20

20. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006). [CrossRef]

]. In contrast to the design in [18

18. P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol 4, 300–305 (2013). [CrossRef] [PubMed]

], we use an apodized grating to suppress internal back-reflections at the coupler [24

24. X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22(15), 1156–1158 (2010). [CrossRef]

]. For that, additional 10 bars are included at the taper with linearly increasing fill factor from 75% to 85%. To study their mode excitation characteristic, simple devices like the one presented in Fig. 1(b) are used. The grating couplers are adjusted to couple light around λ = 1550 nm. In Fig. 3(a)
Fig. 3 (a) FEM-simulation of the geometric dispersion at λ = 1550 nm and field profiles (|(E)|) of the respective guided modes. For widths ww between 0.4 µm and 1.2 µm, the waveguide supports the fundamental TE- and TM-like mode only. (b) Measured transmission of an apodized grating coupler for different polarizations of the incident light. Two clearly separated coupling curves corresponding to the TE- and TM- like mode are observed while the resonance peaks result from a coupled ring resonator. The excitation of different modes is confirmed by the observation of different types of resonances (different resonance wavelengths and FSRs) in dependence on the incident polarization.
, the respective simulated geometric dispersion of the given waveguide geometry is plotted. While a singlemode waveguide is only obtained for narrow widths of 300 nm < ww < 400 nm, both the fundamental TE- and TM-like modes are supported for widths between 0.4 μm and 1.2 μm.

Exemplary transmission curves for different polarizations of the incident fibre mode are presented in Fig. 3(b). Clearly, two separated coupling curves are observed which correspond to the excitation of the TM-like (left) and TE-like (right) mode. This assessment is supported by the fact that the respective peaks can be shifted against each other by rotating the incident polarization using the polarization controller. Additionally, this excitation of two different modes is confirmed by the observation of two types of resonances in the evanescently coupled ring resonators, cf. inset of Fig. 3(b). Around λ = 1590 nm, clearly distinct resonance wavelengths corresponding to the TE- and TM-like mode are obtained by rotating the polarization. In contrast, around λ = 1520 nm only the TE- and not the TM-resonances can be suppressed by properly adjusting the incident light. This, as well as the impossibility to suppress one of the two coupling curves completely, is most likely caused the deviations of the mode profiles from the ideal TE- and TM-cases since these make it impossible to polarize the incident light perpendicular to the waveguide modes.

Next, the cut-off waveguide widths of the guided modes are considered. According to the simulated geometric dispersion in Fig. 3(a), the TE-like mode is expected not to be guided anymore for a waveguide width below ww = 400 nm. This is confirmed by the measured transmission curves presented in Fig. 4(b). While at ww = 600 nm both the TE- and TM-like coupling curves can be observed in the transmission, the TE (right) one vanishes by going to ww = 400 nm. The intensity decrease of the TM coupling curve is most likely caused by the fact that ww = 400 nm is close to the critical waveguide width of the TM-like mode as well which results in an increased propagation loss.

3.2 Internally excited higher-order mode by second-harmonic generation (SHG)

In waveguide structures phase matching can conveniently be achieved by adjusting the waveguide width ww properly [25

25. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007). [CrossRef] [PubMed]

] as shown in Fig. 5(a)
Fig. 5 (a) Calculated geometric dispersion of both the fundamental modes at λ = 1550 nm and the 2nd-harmonic modes at λ = 775 nm. The higher-order modes are numbered according to their critical waveguide widths, i.e. their first guidance while gradually increasing ww. Nine phase matching points are observed within the presented waveguide width regime. (b) Measured geometric dispersion of the phase matching wavelength λPM around ww = 1000 nm. A linear decrease is observed which represents the discussed anomalous behaviour. Inset: The respective extracted proportionalities CFIT(λ) for various devices with different waveguide widths. (c) Exemplary higher-order mode profiles (|(E)|).
. Here, the simulated geometric dispersion for both λ = 1550 nm and the second harmonic λ = 775 nm are plotted in the same graph. The marked intersection points correspond to the waveguide widths at which phase matching is achieved. However, deviations between these predictions and experimental conditions have to be expected due to small uncertainties in the simulation parameters. In particular, slightly deviating values of the refractive indices can lead to considerable shifts or even result in more or less phase-matching points. This complicates the identification of the internally excited higher-order mode.

However, this knowledge is essential to study and optimize the efficiency of the wavelength conversion. The actual properties of this internal process are superimposed by the characteristics of the grating couplers. Since the coupling efficiency of the grating coupler varies from mode to mode, both the nature of the involved mode at the 2nd harmonic and its coupling curve have to be known in order to deduce the actual characteristics of the SHG. In addition, as mentioned above the implementation of the reverse process of SPDC on a chip requires the selective and efficient excitation of this phase-matched mode. Hence, besides a technique for selective excitation, cf. section 4, the participating modes must be clearly known.

3.2.1 Experimental investigation of SHG in AlN

In this work SHG is realized in devices with long, meander-like shaped waveguides analogous to the ones used in [17

17. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012). [CrossRef]

]. Within the varied waveguide width regime (0.8 μmww 1.1 μm)two phase-matching points are observed around ww = 800 nm and ww = 1000 nm. By applying different input powers at the fundamental frequency ω, the theoretically expected quadratic increase of the generated power at the second harmonic 2ω was confirmed.
Pwg=ω2|C|2(Pω,0wg)2L2sinc2(ΔβL/2)=C¯(Pω,0wg)2.
(2)
Here, Pω,0wg denotes the waveguide internal power at ω, P2ωwg the waveguide internal generated power at 2ω, Δβ the phase-mismatch, L the length of the waveguide and C the coupling coefficient between the two participating modes. However, in the experiment not the waveguide internal powersPwgbut the powersPoutoutside of the integrated circuit are measured, i.e. the contributions of the respective grating coupler efficiencies η(λ) have to be taken into account. Therefore, by plotting P2ωoutversus(Pω,0out)2a straight line with the following slope is expected:
CFIT=2ηηω2C¯.
(3)
Hence, as long as the coupling curve η(λ) of the higher-order mode is not known, neither the total generated powerP2ωwg nor the coupling coefficient C can be derived.

The first step for identification of the generated higher-order mode is the controlled excitation of the TE- or TM-like mode only. Here, this is most conveniently achieved by properly adjusting the grating couplers as shown in section 3.1. In case of both observed phase-matching points, the TM-like mode was excited exclusively which reduces the number of possible modes considerably. Taking possible small deviations of the simulation into account, in the phase-matching around ww = 800 nm the modes 6, 7 and 8 and around ww = 1000 nm the modes 7, 8 and 9 come into consideration, cf. Figure 5(a).

In the following, the nature of these two higher-order modes is studied in more detail. First, the focus is set on criteria which rely specifically on SHG. Here, the coupling coefficient which governs the strength of the nonlinear coupling and the dispersion of the phase-matching point are employed to successively exclude mode by mode. Though these considered properties are specific for SHG, the presented methods rely on properties which have similar counterparts in other circuit internal inter-mode couplings and are thus transferable. Eventually, the coupling length Lc in directional couplers is taken into account for the final identification.

3.2.2 Nonlinear coupling coefficient

Besides the phase-mismatch Δβ, the nonlinear interaction in SHG is governed by the respective coupling coefficient C which depends on a certain overlap of the participating modes and the 2nd-order nonlinear susceptibility tensor dAlN. Theoretically, C can be expressed in terms of the normalized mode profiles ω and 2ωand the AlN-specific form of dAlN as follows [26

26. J.-M. Liu, Photonic Devices (Cambridge University, 2009).

]:
C=4ε022ω*d(2ω=ω+ω):ωωdxdyd31C31+d33C33.
(4)
Here, for convenience the mode overlapsC31andC33are defined because they are independent of the strength of the nonlinear coupling. Furthermore, it has been reported that in AlN d310.04d33 [27

27. Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett. 31(12), 815–816 (1977). [CrossRef]

] holds, i.e. the tensor-element d31 is much smaller than d33. This is in good agreement with the observed SHG since d33 determines the coupling between TM-like modes. Therefore, only the interactions of the TM-like mode at λ = 1550 nm are discussed. Since it holdsC31C33in cases in which a TM-like mode is involved in the coupling andd31d33, the contributions of C31are neglected in the following. The various values forC33are derived by using the respective mode profiles obtained from COMSOL® and calculating the integral in Eq. (4) directly by numerical quadrature. The results for the still possible modes are summarized in Table 1

Table 1. Calculated nonlinear coupling coefficients of SHG in AlN ridge-waveguide structures between the TM-mode at λ = 1550 nm and various higher-order modes at λ = 775 nm according to Eq. (4).

table-icon
View This Table
.

In contrast, C could be experimentally derived from Eq. (3) if the coupling efficiency η was known. Even though in our case this is not directly possible, from the measured powers a lower limit of C can be estimated. In the experiment, output powers of up to P2ωwg=10nW have been observed at input powers of Pω,0out=1mW.While the coupling efficiency at the fundamental frequency was found to be approximately ηω = 0.2, the respective efficiency of the mode at the second harmonic can be estimated upward by the maximal achieved transmission in identical reference devices, i.e. η2ω0.06.By using all this and d338pm/V [27

27. Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett. 31(12), 815–816 (1977). [CrossRef]

], the following lower boundary can be found:|C33|2108s2/(m4A).Hence, by comparing the calculated values with this lower boundary it can be deduced that mode 8 and mode 9 are too weakly coupled to be one of the searched modes. Since due to the effective refractive index simulations for the SHG around ww = 1000 nm only the modes 7, 8 and 9 come into consideration, from this follows that here the 7th mode is excited.

3.2.3 Geometric dispersion of the phase-matching point

Another possible criterion to identify the excited higher-order mode is the geometric dispersion of the phase matching point, i.e. how the phase matched wavelength λPM changes if the waveguide width ww is altered. Most conveniently, this relation is expressed in terms of its underlying properties, i.e. the wavelength dependence and geometric dispersion of the effective refractive indices. By doing so, different behaviours can instructively be explained in terms of these underlying properties and hypothetical dispersions of not phase-matched modes can be estimated. To do so, the effective refractive indices are considered as functions of λ and ww. Then, the respective relation can be derived by setting the total derivatived[Δneff]of the phase mismatch between mode 1 at the fundamental frequency λ and mode 2 at the 2nd-harmonic to zero.
ΔλPM=neff1ww(λ) neff2ww(λ/2)neff1λ(λ) 12neff2(λ/2)(λ/2)Δww.
(5)
As long as this linear approximation is valid, the slope of this relation can be predicted with COMSOL® by calculating the required derivatives with linear extrapolation. However, the absolute numbers will sensitively depend on the precise input parameter as well. Fortunately, another typical distinguishing feature can be extracted from this formula: the sign of the slope. While in general the denominator is always smaller than zero, the sign of the numerator depends on the mode combination. The former is true since the dispersion decreases rapidly with increasing wavelength. The latter can be clearly read from Fig. 5(a): while in most cases the mode at λ = 775 nm exhibits a higher slope at a phase matching point compared with the respective mode at λ = 1550 nm (“it crosses from below”), there are some cases where it is the other way around. In the first case, the dispersion of the phase matching point shows a positive slope while in the second (anomalous) case a negative slope is observed. Now, this criterion is used to confirm independently that the 7th mode is excited by the observed SHG around ww = 1000 nm. From the discussion above and Fig. 5(a), normal dispersion in case of mode 8 and 9 and anomalous dispersion for mode 7 are expected. Hence, from the measured anomalous dispersion presented in Fig. 5(b) it can be deduced that mode 7 is the searched mode. In addition, the experimentally measured slope m = −0.77 is in reasonable agreement with the calculated value m = - 0.55. Here, the presented phase-matching points for various waveguide widths are obtained as follows: First, the coupling coefficients CFIT(λ) are derived from linear fits ofP2ωoutversus(Pω,0out)2. The results shown in the inset of Fig. 5(b) exhibit narrow peaks. According to Eq. (2), at the phase-matching pointC¯(λ)reaches its maximal value. Since the widths of the involved coupling curves η(λ) are much broader than the nonlinear resonance, it can be assumed that at phase-matching CFIT(λ) reaches its maximum as well. Therefore, λPM is taken to be the wavelength at which CFIT(λ) reaches its maximum.

3.2.4 Coupling length Lc in co-directional couplers

In the following the focus is set on the SHG point at ww = 800 nm. By considering the simulated effective refractive indices and the expected coupling coefficients, the selection of the possible modes is reduced to mode 6 and mode 7. Since in accordance with the experiment in both cases an increase of λPM(ww) is expected, this criterion cannot be used to distinguish between these modes. Therefore, another method to identify the generated mode is needed. For that purpose, photonic circuits as shown in Fig. 6(a)
Fig. 6 (a) Optical micrograph of a photonic circuit designed for measuring the coupling length of visible light generated by SHG. While the waveguide width ww is designed to achieve phase matching and generate visible light, the width ww’ = ww + 30 nm is chosen sufficiently off- resonance in order to prevent further SHG within and behind the directional coupler. (b) Pictures of visible scattered light for devices with different interaction lengths L. The pictures were taken with a CCD-camera by using a sufficiently long integration time. (c) Measured conversion efficiencies in the directional coupler in case of the phase matching point at ww = 800 nm.
were fabricated to measure the coupling length within directional couplers. Light at the fundamental frequency is coupled into the circuit at the second grating coupler from the left. The subsequent Y-splitter and grating coupler on the very left are inserted as a reference for alignment. In contrast, the two output grating couplers on the right are designed to couple light around λ = 775 nm. The waveguide width ww before the directional coupler is suitably adjusted to achieve phase-matching. Since, however, further generation of visible light within and behind the directional coupler are not desired for the determination of Lc, the width ww’ is increased by 30 nm. In order to perturb the system as little as possible, the transition is facilitated by a taper right in front of the directional coupler which adiabatically increases the waveguide width over a length of 100 μm. Pictures taken with the CCD-camera of devices with various interaction lengths L and waveguide width ww = 800 nm are shown in Fig. 6(b). Depending on L, most of the light is transferred to the upper port (L = 20 μm), is approximately split 50/50 (L = 40 μm) or exits the device at the lower port (L = 60 μm). The significant brightness decrease behind the directional coupler is a result of propagation loss. The coupling lengths Lc were now determined by evaluating several devices with varying interaction length L in the same way as in [28

28. M. Stegmaier and W. H. P. Pernice, “Broadband directional coupling in aluminum nitride nanophotonic circuits,” Opt. Express 21(6), 7304–7315 (2013). [CrossRef] [PubMed]

]. The results are presented in Fig. 6(c). Though the expected sinusoidal behaviour cannot be clearly seen, the results are sufficient to identify the excited mode. The obtained coupling length of 53.5 µm is in good agreement with the simulated value Lc = 50 μm of the 7th mode. In contrast, the simulated coupling length Lc = 10 μm of the 6th mode is much smaller. Therefore, this criterion clearly allows to distinguish between these two possibilities and to identify the excited mode as mode 7.

4. Selective excitation of guided modes

4.1 Concept of mode conversion in an asymmetric directional coupler

We discuss and successfully test a general method for coupling between arbitrary modes based on a co-directional structure which has also been used for polarization rotation on the SOI platform [30

30. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express 19(13), 12646–12651 (2011). [CrossRef] [PubMed]

]. Here, using the AOI platform power conversion between the fundamental TE- and TM-like mode around λ = 1550 nm is exemplary realized due to the highly selective coupling of these modes by the used grating couplers, cf. section 3.1. Therefore, in the following the discussion is limited to this system. However, the general approach can be easily transferred to any other pair of modes in contrast to other schemes specifically designed for integrated polarization rotation [31

31. M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett. 30(2), 138–140 (2005). [CrossRef] [PubMed]

, 32

32. J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 53–60 (2010). [CrossRef]

].

The geometry of the studied mode converter is schematically depicted in Fig. 7(a)
Fig. 7 (a) Cross-sectional sketch of an asymmetric co-directional waveguide structure. Two parallel waveguides with different widths ww and ww’ are separated by a gap g. (b) Calculated geometric dispersion of an asymmetric directional coupler with a gap of 200 nm. Here, the right waveguide width was kept constant at ww = 1060 nm while the left one was varied. Due to the evanescent coupling, the degeneracy of neff at the phase matching point is lifted. The presented field profiles (|(E)|2) of the supermodes at phase matching show the characteristic superposition of the coupled single-waveguide modes. (c) Calculated coupling efficiency of the studied system for various waveguide widths around the phase matching point at ww’ = 830 nm. η was derived from the simulated geometric dispersion by using Eq. (6).
. It is an asymmetric co-directional structure which consists of two parallel waveguides with widths ww and ww’. Due to the small gap g, the evanescent fields of the single-waveguide modes overlap which leads to the desired coupling. However, power is only efficiently converted if the coupled modes are phase-matched. This is achieved by properly adjusting the waveguide widths. Considering Fig. 3(a), it can be seen that the TM-like mode at ww = 1060 nm exhibits the same effective refractive index as the TE-like mode at ww’810 nm. Therefore, by adjusting the waveguide widths of the asymmetric structure accordingly, phase-matching between the TE- and TM-like mode is expected. This is confirmed by the simulation presented in Fig. 7(b). Here, the supermodes of the asymmetric directional coupler are analyzed. While the width of the right waveguide is left constant at ww = 1060 nm, the other width is varied around the expected phase-matching point of ww’ = 810 nm. Due to the evanescent coupling between the TE- and TM-like modes, the degeneracy of neff at the phase-matching point is lifted, i.e. an anticrosssing is observed. The observed small shift of the phase matching point to a broader waveguide width ww’ is expected to be the result of unequal self-coupling coefficients.

Though in the system at hand two unequal modes are coupled, the same relations as in the case of a symmetric directional coupler are adequate to describe the energy transfer [26

26. J.-M. Liu, Photonic Devices (Cambridge University, 2009).

]. Hence, a sinusoidal energy transfer between the TE- and TM-like modes with oscillation period 2Lc is expected. Here, the coupling length Lc can be calculated from the simulated phase-difference Δneff between the two supermodes [26

26. J.-M. Liu, Photonic Devices (Cambridge University, 2009).

]. At phase-matching, the simulation yields that complete power transfer is achieved at Lc,max = 474 μm. In addition, from this the maximal conversion efficiency ηmax can be derived as follows:
ηmax(Δneff)=(Lc(Δneff)Lc,max)2.
(6)
The associated results are plotted in Fig. 7(c). A narrow resonance with a FWHM of approximately 10 nm is observed. This and the relatively high coupling length Lc result from the weakness of the interaction between the almost orthogonal TE- and TM-like modes.

4.2 Experimental TE-TM mode conversion

An exemplary photonic circuit for the realization of a TE-TM mode converter in AlN is presented in Fig. 8(a)
Fig. 8 (a) Optical micrograph of a photonic circuit for efficient TE-TM mode conversion. The power transfer takes place in the central asymmetric directional coupler of interaction length L if the two different waveguide widths ww and ww’ are chosen properly. In order to be able to measure the mode conversion, the grating couplers 2 and 3 were designed to excite exclusively the TM-like and the grating couplers 1 and 4 the TE-like mode around λ = 1520 nm. Hence, measured signals between the ports 1/3 or 2/4 can only result from converted powers between TE and TM. (b) Measured transmission curves of two reference grating couplers identical to the ones used for the mode converter and fabricated on the same chip. Clearly, two distinct coupling curves corresponding to the TM- (left) and TE-like (right) mode (cf. section 3.1) are observed. As intended, the TE-coupling curve of the 1/4 port lies at the same position as the TM-coupling curve of the 2/3 port.
. Note, that the photonic circuit consists of two separated parts with different waveguide widths ww and ww’ which connect the ports 2/3 (lower part) and 1/4 (upper part), respectively. Here, the actual mode converter device is the asymmetric directional structure of interaction length L in the center. As discussed in section 3.1, the TE- and TM-like modes are coupled differently by the employed grating couplers. Most importantly, the corresponding transmission curves are well separated in wavelength from each other. On the one hand, this has to be taken into account to be able to detect any converted power. But on the other hand, this allows the clear distinction of converted TE-like and TM-like light. Therefore, the four grating couplers were designed in such a way that the ports 1/4 exhibit the TE-coupling curve at the same spectral position at which the ports 2/3 exhibit the TM-coupling curve. This is demonstrated in Fig. 8(b) where transmission measurements of identical reference couplers are summarized. Both grating couplers clearly exhibit a TE- and TM-like coupling curve, even if in case of the port 2/3 coupler the TE-like mode is much less efficiently excited as the TM-like mode. As intended, the grating coupler for port 2/3 exhibits the TM coupling curve at almost the same wavelength (λ = 1520 nm) as the grating coupler for port 1/4 exhibits the TE coupling curve. Hence, due to the overlap of the two coupling curves only TE-TM converted light could be transmitted if the two shown grating couplers were operated in a row. In addition, a ring resonator with radius R = 50 μm is attached to port 1 to be able to measure the FSR and thus the group index of converted light. However, though measured values for converted light T1-3 lie in the same region as values for reference TE-light T4-1 the results scatter too much to be able to distinguish between TE- and TM-like light. This scattering is most likely caused by small power fluctuations which result from the conversion within the directional coupler.

In the presented photonic circuit, four ports were used for two reasons. First of all, they allow the TETM and TMTE conversion in all possible directions, i.e. 13 and 24. However, the main reason is the possibility to normalize the measured transmissions from the superimposed grating coupler curves more accurately. Though these curves are well known by studying reference couplers, the exact shape depends sensitively on the exact alignment of the external fibres above the gratings and varies slightly from device to device. Therefore, here a calibration procedure which does not suffer from these problems is used.

First, the alignment is carried out for optimal transmission T1-4 since these ports are farthest apart and therefore are most sensitive on the precise alignment. Then, the transmissions T4-1 and T2-3 are recorded. Denoting the coupling efficiencies of the respective grating couplers as η4-1 and η3-2 and the mode conversion efficiency of the directional coupler as ηTE-TM, these transmissions can be expressed as follows:
T41=η41(1ηTE-TM)η41          T32=η3-2(1-ηTM-TE)η3-2.
(7)
Therefore, by rearranging these two equations the ratio of coupling efficiencies can be expressed in terms of the measured transmissions:
ηTEηTM=η4-1η3-2=(T41T32)1/2.
(8)
This relation proves useful in calculating the obtained mode conversion efficiency since in contrast to a symmetric directional coupler the transmitted and converted light is coupled by two different grating couplers. Therefore, the different coupling efficiencies of the TE- and TM-like mode have to be taken into account:
ηTMTE=PconvertedwgPtransmittedwg+Pconvertedwg=(1+PtransmittedwgPconvertedwg)1=(1+PtransmittedoutPconvertedoutηconvertedηtransmitted)1.
(9)
Here, Pwg and Pout denote the powers within and outside of the waveguide structure, respectively. Note that the expressions Eq. (7) and thus the determination of the coupling ratio according to Eq. (8) require an optimal polarization of the incident light which is discussed in more detail below.

In order to study the TE-TM power conversion, devices of the previously presented type with fixed ww = 1060 nm and 600 nmww’900 nm were fabricated. Considerable power conversion is only observed at waveguide widths around ww’ = 780 nm, where mode conversion with an efficiency of up to 75% within an interaction length of L = 360 μm was achieved. To demonstrate the observed power transfer, in Fig. 9(a)
Fig. 9 Experimental results for mode converter devices with phase-matched waveguide width ww’ = 780 nm. The measurements were carried out with the white light source. (a) The TM-like light in T3→2 decreases gradually with increasing interaction length L until almost no power is transmitted anymore at L = 360 µm (b) With increasing L, more and more TE-like light is measured at port 1 which indicates that more and more power is converted.
and 9(b) measured transmissions T3-2 and T3-1 for various interaction lengths L are shown. It can be observed that the transmitted TM power P3-2 decreases drastically from a small interaction length of 40 μm to L = 360 μm where almost no TM-power is transmitted anymore. At the same time, the measured TE-power at port 3 increases with increasing interaction length. Hence, if the interaction length L is increased from 40 μm to 360 μm more and more power is converted from the TM-like to the TE-like mode. Note, that the sum of transmitted TM and TE power decreases considerably with L which is mainly a result of the fact that the coupling efficiency ηTE of port 1 is much smaller than ηTM of port 2.

The resulting conversion efficiency, calculated with Eq. (9) and Eq. (10), is presented in Fig. 10
Fig. 10 TE-TM conversion efficiencies derived from the measured data, Eq. (9) and Eq. (10). Over a bandwidth of 30 nm and 120 nm, conversion efficiencies of over 70% and 50% are achieved, respectively. For clarity, error bars (average variance of 5.1% within the shown wavelength interval) are suppressed.
. Here, the presented TE-TM power conversion exhibits efficiencies exceeding 70% and 50% within bandwidths of 30 nm and 120 nm, respectively. Furthermore, the highest conversion efficiency of (75±5.4)%is achieved at λ = 1540 nm. In this derivation, the most dominant error source is the implicit assumption that equally designed grating couplers exhibit the same coupling characteristics. Due to slightly different grating coupler/ fibre alignments and fabrication variations, this is not perfectly true. To estimate this error, we derived the conversion efficiencies η1-3, η4-2 (TETM) and η2-4, η3-1 (TMTE). Averaging the respective efficiencies yields an average error of 5.1% within the presented wavelength interval with maximal error of 7.6% at λ1560 nm.

The observed phase-matched waveguide width ww’ = 780 nm is in good agreement with the simulated value of ww’ = 830 nm. In contrast, the obtained interaction length L = 360 μm deviates clearly from the expected coupling length Lc = 474 μm. This results from the fact that the almost orthogonal TE- and TM-like modes deviate from the ideal TE- and TM-polarization only in the vicinity of the waveguide boundary and in particular its edges. Therefore, the coupling is governed by the profile overlaps in these regions and is thus sensitive on the actual surface morphology which is not adequately mapped by the used simple geometry in Fig. 7(a).

Though an initial increase of converted power with increasing interaction length L is obtained, the expected characteristic sinusoidal behaviour of the power conversion is not observed. Most certainly, this results from the weakness and thus an increased sensitivity on perturbations of the coupling. As presented in Fig. 7(c), the predicted resonance with a FWHM of approximately 10 nm is quite narrow. Hence, random fluctuations as due to surface roughness of the waveguide width ww of a few nanometer are comparable to the width of the resonance and are thus most likely affecting the functionality of the studied devices. Additionally, deviations from coupled mode theory due to the small gap g = 200 nm required for efficient coupling will also contribute. In particular, this strong perturbation to the single-waveguide modes causes enhanced coupling to radiation modes and thus additional loss. In order to estimate this loss, the transmissions T1-4 and T2-3 were recorded in several devices with varying interaction length L and with waveguide widths ww = 680 nm sufficiently off-resonance. Plotting the obtained transmissions logarithmically versus L, a linear decrease is observed. From linear fits, coupling losses of 2 dB/mm and 4.5 dB/mm for the thick and the thin waveguide are obtained, respectively.

4.3 Discussion

Most importantly in the context of this work, the design can be transferred to the conversion between arbitrary modes. Here, the interaction can be much stronger if the two coupled modes are not orthogonally polarized. Hence, in such cases less sensitivity on geometric fluctuations, higher control of the transfer characteristics and shorter coupling lengths Lc are expected.

5. Conclusions

Using the approaches described above we have gained sufficient control to efficiently and selectively excite either the TE- or TM-like mode. In combination with the discussed mode converter, this enables the reversible transfer of high powers into any required waveguide mode. Furthermore, choosing an adequate pair of coupled modes potentially reduces the coupling length considerably, allowing for both efficient and compact power transfer. In addition, in AlN active control over the power transfer via the Pockels effect enables both modulation and fine-tuning for phase-matching. Due to its wide bandgap, the presented schemes can straightforwardly be transferred to applications in the visible regime. Taking all together, we pave the way towards the on-chip realization of SPDC where the correctly phase-matched higher-order mode at the second harmonic has to be efficiently excited to initiate the frequency doubling. Potential applications of our work include integrated nonlinear optics, optomechanics and frequency up/down-mixing in a chipscale framework.

The expressions Eq. (7) and thus the determination of the coupling ratio according to Eq. (8) require an optimal polarization of the incident light. This can be understood in terms of Fig. 3(b) where the dependence of the overall transmission T on this polarization is demonstrated. Due to this and the fact that the coupling at the output does not depend on the input light, it is clear that the coupling efficiencies of the input and output grating coupler are in general not the same. Therefore, the coupling efficiencies ηTE and ηTM are conveniently defined with respect to accordingly polarized light because in this case holds ηinput = ηoutput. Then, the input coupling efficiency is given by ηTETM times the ratio of suitably polarized light. Hence, in general Eq. (7) and Eq. (8) have to be corrected by these polarization dependent factors.

If a linearly polarized light source and a fibre polarization rotator are used, the incident light can be suitably adjusted and this problem does not arise. Here, however, we use the unpolarized white light source due to its broader spectral output. Fortunately, the problem that these factors are not known can be circumvented by measuring both the mode conversion efficiency from TE-like to TM-like mode and vice versa. Resulting from theory [26

26. J.-M. Liu, Photonic Devices (Cambridge University, 2009).

], at phase-matching these two efficiencies are expected to be the same, i.e. ηTE-TM = ηTM-TE. In addition, according to (9) they depend differently on the ratio of coupling efficiency and thus on the polarization dependent factors. Hence, these relations can be used to derive the dependence of the actual mode conversion efficiency ηTE↔TM on the measured efficiencies ηTE-TM and ηTM-TE:

ηTMTE=(1+(1ηTMTEmeasured)(1ηTETMmeasured)ηTMTEmeasuredηTMTEmeasured)1.
(10)

Acknowledgments

W.H.P. Pernice acknowledges support by DFG grants PE 1832/1-1 and PE 1832/1-2. We also acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) and the State of Baden-Württemberg through the DFG-Center for Functional Nanostructures (CFN) within subproject A6.4. The authors further wish to thank Silvia Diewald for assistance in device fabrication. We acknowledge support by the Deutsche Forschungsgemeinschaft and Open Access Publishing Fund of Karlsruhe Institute of Technology.

References and links

1.

G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress [Invited],” J. Opt. Soc. Am. B 28(12), A1–A10 (2011). [CrossRef]

2.

A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1673–1684 (2009). [CrossRef]

3.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008). [CrossRef] [PubMed]

4.

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O'Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst. 5(2), 94–102 (2011). [CrossRef]

5.

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express 19(11), 10462–10470 (2011). [CrossRef] [PubMed]

6.

S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A-Pure. Appl. Opt. 6, 569 (2004).

7.

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ² microring resonators,” Opt. Express 20(7), 7526–7543 (2012). [CrossRef] [PubMed]

8.

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011). [CrossRef] [PubMed]

9.

M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A 66(2), 023815 (2002). [CrossRef]

10.

K. Banaszek, A. B. U’ren, and I. A. Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett. 26(17), 1367–1369 (2001). [CrossRef] [PubMed]

11.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995). [CrossRef] [PubMed]

12.

J. L. O’Brien, “Optical quantum computing,” Science 318(5856), 1567–1570 (2007). [CrossRef] [PubMed]

13.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009). [CrossRef] [PubMed]

14.

T. P. M. Alegre, A. Safavi-Naeini, M. Winger, and O. Painter, “Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap,” Opt. Express 19(6), 5658–5669 (2011). [CrossRef] [PubMed]

15.

C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. 14(9), 095014 (2012). [CrossRef]

16.

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett. 100(9), 091105 (2012). [CrossRef]

17.

W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012). [CrossRef]

18.

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol 4, 300–305 (2013). [CrossRef] [PubMed]

19.

S. Ghosh, C. R. Doerr, and G. Piazza, “Aluminum nitride grating couplers,” Appl. Opt. 51(17), 3763–3767 (2012). [CrossRef] [PubMed]

20.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006). [CrossRef]

21.

C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) films produced by thermal curing,” J. Mater. Chem. 12(4), 1138–1141 (2002). [CrossRef]

22.

Handbook of Optics (McGraw-Hill, 1994).

23.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).

24.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22(15), 1156–1158 (2010). [CrossRef]

25.

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007). [CrossRef] [PubMed]

26.

J.-M. Liu, Photonic Devices (Cambridge University, 2009).

27.

Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett. 31(12), 815–816 (1977). [CrossRef]

28.

M. Stegmaier and W. H. P. Pernice, “Broadband directional coupling in aluminum nitride nanophotonic circuits,” Opt. Express 21(6), 7304–7315 (2013). [CrossRef] [PubMed]

29.

H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S.-i. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express 16(7), 4872–4880 (2008). [CrossRef] [PubMed]

30.

L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express 19(13), 12646–12651 (2011). [CrossRef] [PubMed]

31.

M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett. 30(2), 138–140 (2005). [CrossRef] [PubMed]

32.

J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron. 16(1), 53–60 (2010). [CrossRef]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(130.3130) Integrated optics : Integrated optics materials
(160.6000) Materials : Semiconductor materials
(230.5750) Optical devices : Resonators

ToC Category:
Integrated Optics

History
Original Manuscript: September 6, 2013
Revised Manuscript: October 19, 2013
Manuscript Accepted: October 22, 2013
Published: October 29, 2013

Citation
Matthias Stegmaier and Wolfram H.P. Pernice, "Mode control and mode conversion in nonlinear aluminum nitride waveguides," Opt. Express 21, 26742-26761 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26742


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References

  1. G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress [Invited],” J. Opt. Soc. Am. B28(12), A1–A10 (2011). [CrossRef]
  2. A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009). [CrossRef]
  3. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320(5876), 646–649 (2008). [CrossRef] [PubMed]
  4. M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O'Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011). [CrossRef]
  5. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express19(11), 10462–10470 (2011). [CrossRef] [PubMed]
  6. S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A-Pure. Appl. Opt.6, 569 (2004).
  7. Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ² microring resonators,” Opt. Express20(7), 7526–7543 (2012). [CrossRef] [PubMed]
  8. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express19(12), 11415–11421 (2011). [CrossRef] [PubMed]
  9. M. C. Booth, M. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Counterpropagating entangled photons from a waveguide with periodic nonlinearity,” Phys. Rev. A66(2), 023815 (2002). [CrossRef]
  10. K. Banaszek, A. B. U’ren, and I. A. Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett.26(17), 1367–1369 (2001). [CrossRef] [PubMed]
  11. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett.75(24), 4337–4341 (1995). [CrossRef] [PubMed]
  12. J. L. O’Brien, “Optical quantum computing,” Science318(5856), 1567–1570 (2007). [CrossRef] [PubMed]
  13. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462(7269), 78–82 (2009). [CrossRef] [PubMed]
  14. T. P. M. Alegre, A. Safavi-Naeini, M. Winger, and O. Painter, “Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap,” Opt. Express19(6), 5658–5669 (2011). [CrossRef] [PubMed]
  15. C. Xiong, W. H. P. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012). [CrossRef]
  16. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “High-Q aluminum nitride photonic crystal nanobeam cavities,” Appl. Phys. Lett.100(9), 091105 (2012). [CrossRef]
  17. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett.100(22), 223501 (2012). [CrossRef]
  18. P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Grating-assisted coupling to nanophotonic circuits in microcrystalline diamond thin films,” Beilstein J Nanotechnol4, 300–305 (2013). [CrossRef] [PubMed]
  19. S. Ghosh, C. R. Doerr, and G. Piazza, “Aluminum nitride grating couplers,” Appl. Opt.51(17), 3763–3767 (2012). [CrossRef] [PubMed]
  20. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006). [CrossRef]
  21. C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) films produced by thermal curing,” J. Mater. Chem.12(4), 1138–1141 (2002). [CrossRef]
  22. Handbook of Optics (McGraw-Hill, 1994).
  23. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).
  24. X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010). [CrossRef]
  25. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express15(20), 12949–12958 (2007). [CrossRef] [PubMed]
  26. J.-M. Liu, Photonic Devices (Cambridge University, 2009).
  27. Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett.31(12), 815–816 (1977). [CrossRef]
  28. M. Stegmaier and W. H. P. Pernice, “Broadband directional coupling in aluminum nitride nanophotonic circuits,” Opt. Express21(6), 7304–7315 (2013). [CrossRef] [PubMed]
  29. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S.-i. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express16(7), 4872–4880 (2008). [CrossRef] [PubMed]
  30. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express19(13), 12646–12651 (2011). [CrossRef] [PubMed]
  31. M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett.30(2), 138–140 (2005). [CrossRef] [PubMed]
  32. J. Zhang, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon-waveguide-based mode evolution polarization rotator,” IEEE J. Sel. Top. Quantum Electron.16(1), 53–60 (2010). [CrossRef]

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