Abstract

Subwavelength grating (SWG) structures are an essential tool in silicon photonics, enabling the synthesis of metamaterials with a controllable refractive index. Here we propose, for the first time to the best of our knowledge, tilting the grating elements to gain control over the anisotropy of the metamaterial. Rigorous finite difference time domain simulations demonstrate that a 45° tilt results in an effective index variation on the fundamental TE mode of 0.23 refractive index units, whereas the change in the TM mode is 20 times smaller. Our simulation predictions are corroborated by experimental results. We furthermore propose an accurate theoretical model for designing tilted SWG structures based on rotated uniaxial crystals that is functional over a wide wavelength range and for both the fundamental and higher order modes. The proposed control over anisotropy opens promising venues in polarization management devices and transformation optics in silicon photonics.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Periodic laminar structures with a period (Λ) much smaller than the wavelength (λ) of propagating light behave, with respect to the average electromagnetic field, as homogeneous metamaterials [1]. This homogenized metamaterial is frequently characterized as an isotropic medium with a different equivalent refractive index for each polarization, or more generally, as a form birefringent anisotropic medium [2]. These approaches have long been studied in free-space optics [3,4], enabling, for example, the design of half-wave and quarter-wave plates [5,6].

More recently, metamaterial nanostructures have been incorporated into silicon-on-insulator (SOI) waveguides, in the form of subwavelength gratings (SWGs) [79]. In SWG devices, a controllable refractive index is synthesized by adjusting the relative amount of silicon per period, i.e., the duty cycle (DC). By approximating the SWG as an isotropic homogeneous material, a wide range of high-performance integrated devices has been demonstrated, including fiber-to-chip grating couplers [1012], edge couplers [7,13,14], waveguide couplers [15,16], Bragg filters [17,18], multimode bends based on transformation optics [19], and evanescent field waveguide sensors [20,21]. Simple anisotropic models have enabled further applications of SWG waveguides, such as ultra-broadband devices [22,23], polarization management [24,25], or evanescent field confinement [26,27]. However, by changing the duty cycle, both polarizations are affected and can also hamper device fabrication due to aspect ratio dependent etching and proximity effects [28].

In this work, we propose, analyze, and experimentally demonstrate a technique to control the anisotropy of an SWG structure. We show that tilting the silicon segments, as shown in Fig. 1, mainly affects the in-plane (TE) modes, with little impact on the out-of-plane (TM) modes, while maintaining a constant duty cycle and minimum feature size. Therefore, the practical advantages of tilted SWG structures are apparent for applications in on-chip polarization management, where controlling waveguide birefringence is of fundamental importance. We envision that the proposed technique will enable development of nonbirefringent waveguides and novel polarization management devices (e.g., polarization beam splitters based on phase matching).

 figure: Fig. 1.

Fig. 1. Scanning electron microscope (SEM) image of a tilted SWG waveguide. The waveguide parameters (width, period, duty cycle, and tilt angle) are wc=1μm, Λ=0.25μm, DC=0.5, θ=45°. The device was fabricated in 220 nm thick Si layer on a 3 μm thick layer of buried oxide (BOX). A 3 μm thick upper SiO2 cladding was deposited by plasma-enhanced chemical vapor deposition after the SEM image was taken.

Download Full Size | PPT Slide | PDF

To gain insight into the physics of tilted SWG structures, let us first revisit the properties of a laminar periodic structure. Specifically, consider a periodic structure with period Λ, composed of two transversally infinite materials with refractive indexes n1 and n2, and thicknesses a=DC·Λ and b=(1DC)·Λ, respectively [see Fig. 2(a)]. For the purpose of illustration, typical values for SWG waveguides in the SOI platform are considered, i.e., Λ=0.2μm, DC=0.5, n1=3.476, n2=1.444, and λ0=1.55μm. A plane wave propagating along this structure with an angle ϕ with respect to the z axis is described by its k vector k(ϕ)=kxx^+kzz^, where ϕ=atan(kx/kz) and kx, kz are related via the dispersion equation [29]

cos(kzΛ)=cos(k1xa)cos(k2xb)Δsin(k1xa)sin(k2xb),
where kix=(k0ni)2kx2, k0=2π/λ0 and Δ is a polarization-dependent factor. Defining as TE polarization the plane waves with the electric field polarized in the xz plane, and as TM polarization the y-polarized waves, we have the following:
ΔTE=12(n22n12k1xk2x+n12n22k2xk1x)andΔTM=12(k1xk2x+k2xk1x).
The normalized magnitude of the k vector, |k(ϕ)|/k0, is shown with solid lines in Fig. 2(c) for both polarizations. The pairs (kx, kz) were obtained giving suitable values to kx and then applying the above expressions to calculate kz. Note that kz can be easily isolated from Eq. (1), so this calculation is straightforward. For a TM (y-polarized) plane wave, the magnitude of the k vector is practically independent of the angle ϕ (red solid curve), because its electric field is orientated parallel to the periodic interfaces. However, for a TE plane wave, it strongly depends on the angle ϕ (blue solid curve), because the electric field orientation changes from parallel to the interfaces when propagating along the z axis, to normal to the interfaces when the propagation is along the x direction. Hence, the normalized k vector in a TE plane wave changes from nxx=|k(0)|/k0 to nzz=|k(90)|/k0 when the propagation direction changes from z to x.

 figure: Fig. 2.

Fig. 2. (a) Laminar periodic structure comprising two materials with refractive indexes n1 and n2 and thicknesses a=DC·Λ and b=(1DC)·Λ. (b) Anisotropic material described by the tensor ϵ=diag[nxx2,nyy2,nzz2], which characterizes the propagation properties of a laminar periodic structure. (c) Comparison of the k vector of a laminar structure and an anisotropic homogeneous metamaterial for n1=3.476, n2=1.444, Λ=0.2μm, DC=0.5, and λ0=1.55μm.

Download Full Size | PPT Slide | PDF

This behavior is closely related to that of a homogeneous but anisotropic uniaxial medium described by the dielectric permittivity tensor ϵ=diag[nxx2,nyy2,nzz2], illustrated in Fig. 2(b). For the aforementioned parameters typical for silicon SWG waveguides, we obtain nxx=2.79 and nzz=1.94, where nxx=nyy from symmetry considerations. The k vector of a plane wave propagating through such a homogeneous anisotropic uniaxial medium can be calculated using the well-known dispersion equations

(kznxx)2+(kxnzz)2=k02and(kznyy)2+(kxnyy)2=k02,
for TE and TM polarization, respectively [29]. From Fig. 2(c) it is clear that this anisotropic homogenization, shown with dashed lines, provides an excellent approximation of the laminar periodic structure. In other words, the laminar periodic structure [Fig. 2(a)] works as a uniaxial crystal [Fig. 2(b)].

We will now show that this behavior can be extended to SWG waveguides, where the periodic structure is finite in the transversal directions [Fig. 3(a)]. Note that when tilting the segments in the SWG waveguide, the period along the propagation direction (Λz) is given by Λz=Λ/cos(θ). Extending the equivalence between a periodic structure and a uniaxial crystal, we model the tilted SWG waveguide [Fig. 3(a)] as an anisotropic homogeneous waveguide [Fig. 3(b)]. With the coordinate system set by the light propagation along the waveguide (z direction), the tilt angle θ of the SWG segments results in a rotation of the diagonal permittivity tensor, yielding the nondiagonal tensor ϵ˜ [30],

ϵ˜(θ)=T1(θ)ϵT(θ)=[ϵ˜xx(θ)0ϵ˜xz(θ)0ϵ˜yy0ϵ˜xz(θ)0ϵ˜zz(θ)],
where T is the rotation matrix in the xz plane and the different elements of the tensor ϵ˜ are given by
ϵ˜xx=nxx2cos2(θ)+nzz2sin2(θ),ϵ˜yy=nyy2,ϵ˜zz=nxx2sin2(θ)+nzz2cos2(θ),ϵ˜xz=(nzz2nxx2)cos(θ)sin(θ).
To validate this model, we compare the modes guided by the structures shown in Figs. 3(a) and 3(b) for a multimode waveguide (wc=3.25μm, Λ=0.2μm, DC=0.5) in a standard 220 nm thick silicon waveguide. First, we compare, in Figs. 3(c) and 3(d), the electric fields of the fundamental TE and TM modes propagating through the periodic and homogeneous waveguide for a tilt angle θ=30°. As expected, the average electric field is very similar in both cases. Note that tilting the SWG segments implies a phase front tilt, which is predicted by the uniaxial crystal model [30]. We then calculate the effective indexes (neff) of the fundamental TE and TM modes of the anisotropic homogeneous waveguide for tilt angles ranging from θ=0° to θ=45°. In Fig. 3(e) we compare these results to rigorous finite difference time domain (FDTD) simulations of the effective indices of the Floquet modes of the tilted SWG waveguide calculated as outlined in Ref. [20]. From this comparison we obtain two of the main results reported in this Letter. First, the effective index of the TE mode changes significantly with the tilt angle, achieving a refractive index variation of ΔneffTE0.25 for θ=45°, whereas the effective index of the TM mode remains practically constant (ΔneffTM0.02). This enables engineering of the metamaterial anisotropy and the effective refractive index while maintaining a constant duty cycle and minimum feature size. Second, the anisotropic homogeneous model exhibits the same behavior as the periodic structure when tilting the SWG segments, providing a quick yet accurate tool to perform preliminary designs.

 figure: Fig. 3.

Fig. 3. (a) Schematic of a tilted SWG multimode waveguide and (b) the corresponding homogeneous anisotropic model. The SiO2 upper cladding is not shown. (c) Real part of the main component of the fundamental TE (Ex) and TM (Ey) modes propagating along an SWG waveguide with a θ=30° tilt angle. (d) Real part of the main component of the fundamental TE (Ex) and TM (Ey) modes propagating along the homogeneous anisotropic waveguide. (e) Effective index of the fundamental TE and TM modes of the tilted SWG waveguide and the anisotropic homogeneous waveguide at λ0=1.55μm.

Download Full Size | PPT Slide | PDF

From Eq. (1) we observe that the laminar periodic structure is dispersive even if the constituent materials are not. If this structural dispersion is taken into account, the model also predicts the wavelength dependence of the periodic structure, as shown in Fig. 4(a) for an example of θ=30°. Examining this wavelength behavior reveals the intrinsic limitation of any homogenization model: although the anisotropic model is very accurate for long wavelengths (small Λ/λ ratios), it becomes less accurate when approaching the Bragg regime (λBragg1.3μm). Finally, Fig. 4(b) shows the effective indexes of the guided TE and TM modes for different tilt angles, revealing that the anisotropic model also provides a good estimation for the higher order modes.

 figure: Fig. 4.

Fig. 4. (a) Effective index dispersion of the fundamental TE and TM mode of the θ=30° tilted SWG waveguide. (b) Effective indices of guided modes in the multimode SWG waveguide, for both polarization and different tilt angles (λ0=1.55μm).

Download Full Size | PPT Slide | PDF

To experimentally validate the proposed structures, a set of tilted SWG waveguides was fabricated in a 220 nm SOI platform with 3 μm buried oxide (BOX). A 3 μm thick upper SiO2 cladding was deposited by plasma-enhanced chemical vapor deposition (PECVD). The test structure was a Mach–Zehnder interferometer (MZI) where a tilted SWG waveguide was placed in one arm and a reference straight SWG waveguide was placed in the other arm [Fig. 5(a)]. This architecture allows us to easily measure the group index difference between these two types of SWG waveguides. The tapers between the homogeneous and SWG waveguides in the MZI arms were 30 μm long to avoid transition losses, and the SWG waveguides were 600 μm long to accurately characterize the group index variation; a period of Λ=0.25μm was used. To reduce the influence of fabrication jitter, narrow single-mode SWG waveguides are preferred [31], so a width of wc=1μm was chosen. Highly efficient input and output SWG edge couplers [7,13] were used to couple light in and out of the chip with a lensed polarization maintaining fiber (PMF).The PMF is mounted on a rotatory mount, allowing us to control the input polarization (TE—horizontal or TM—vertical) by using a Glan–Thompson polarizer. The transmission spectrum of each MZI [Fig. 5(b), inset] was measured by sweeping the wavelength of a tunable laser while measuring output power. From the measured transmittance function the group index difference (Δng) is calculated using the procedure described in Ref. [32]. A comparison to the FDTD simulation results [Fig. 5(b)] shows an excellent agreement for both polarization. By simulating the relation between the group index and effective index in both waveguides, the effective index difference can be estimated from the measured group index difference. In particular, for the fabricated single-mode 45° tilt SWG waveguide we find an effective index variation of ΔneffTE0.23 for the TE mode and only ΔneffTM0.01 for the TM mode.

 figure: Fig. 5.

Fig. 5. (a) Schematic of the MZI used for the characterization of the tilted SWG waveguides. Insets: SEM images of the SWG tapers and waveguides. (b) Measured and simulated group index difference between the waveguides in the MZI arms. Inset: MZI transmittance measurement for a θ=37° tilt angle.

Download Full Size | PPT Slide | PDF

In conclusion, we have shown through both simulation and experiments that tilted SWG structures enable engineering of the effective metamaterial anisotropy in nanophotonics waveguides. Tilting the SWG segments strongly affects both fundamental and higher order TE modes, while this effect is significantly less prominent for TM modes. This approach provides a new degree of freedom to engineer the refractive index in silicon waveguides, while circumventing small variable duty cycles that hamper fabrication. Furthermore, a simple yet accurate homogenization model, based on Eqs. (1)–(5), has been developed and used to characterize and design these structures. The control over metamaterial anisotropy provided by this approach offers promising prospects for advanced polarization management devices and the implementation of metamaterials for transformation optics.

Funding

Universidad de Málaga (UMA); Ministerio de Economía y Competitividad (MINECO) (IJCI-2016-30484, TEC2015-71127-C2-R, TEC2016-80718-R); Ministerio de Educación, Cultura y Deporte (MECD) (FPU16/06762); European Regional Development Fund (ERDF); Comunidad de Madrid (SINFOTON-CM S2013/MIT-2790); European Association of National Metrology Institutes (EURAMET) (H2020-MSCA-RISE-2015:SENSIBLE, JRP-i22 14IND13 Photind).

Acknowledgment

We would like to thank Jean Lapointe for the e-beam processing.

REFERENCES

1. S. M. Rytov, Sov. Phys. J. Exp. Theor. Phys. 2, 466 (1956).

2. M. Born and E. Wolf, Principles of Optics (Cambridge University, 2013), Chap. 14.

3. H. Kikuta, H. Yoshida, and K. Iwata, Opt. Rev. 2, 92 (1995). [CrossRef]  

4. P. Lalanne and D. Lemercier-Lalanne, J. Mod. Opt. 43, 2063 (1996). [CrossRef]  

5. D. C. Flanders, Appl. Phys. Lett. 42, 492 (1983). [CrossRef]  

6. H. Kikuta, Y. Ohira, and K. Iwata, Appl. Opt. 36, 1566 (1997). [CrossRef]  

7. P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006). [CrossRef]  

8. R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014). [CrossRef]  

9. R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018). [CrossRef]  

10. X. Chen and H. K. Tsang, Opt. Lett. 36, 796 (2011). [CrossRef]  

11. Y. Wang, W. Shi, X. Wang, Z. Lu, M. Caverley, R. Bojko, L. Chrostowski, and N. A. F. Jaeger, Opt. Lett. 40, 4647 (2015). [CrossRef]  

12. A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016). [CrossRef]  

13. P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015). [CrossRef]  

14. T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016). [CrossRef]  

15. A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013). [CrossRef]  

16. B. Naghdi and L. R. Chen, Opt. Express 25, 25310 (2017). [CrossRef]  

17. D. Pérez-Galacho, C. Alonso-Ramos, F. Mazeas, X. L. Roux, D. Oser, W. Zhang, D. Marris-Morini, L. Labonté, S. Tanzilli, É. Cassan, and L. Vivien, Opt. Lett. 42, 1468 (2017). [CrossRef]  

18. J. Čtyroký, J. G. Wangüemert-Pérez, P. Kwiecien, I. Richter, J. Litvik, J. H. Schmid, Í. Molina-Fernández, A. Ortega-Moñux, M. Dado, and P. Cheben, Opt. Express 26, 179 (2018). [CrossRef]  

19. H. Xu and Y. Shi, Laser Photon. Rev. 12, 1700240 (2018). [CrossRef]  

20. J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014). [CrossRef]  

21. J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, Opt. Express 24, 15672 (2016). [CrossRef]  

22. R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016). [CrossRef]  

23. D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018). [CrossRef]  

24. H. Nikkhah, M. Hasan, and T. Hall, Appl. Phys. A 124, 106 (2018). [CrossRef]  

25. L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018). [CrossRef]  

26. S. Jahani and Z. Jacob, Optica 1, 96 (2014). [CrossRef]  

27. S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018). [CrossRef]  

28. Y. Tang, Z. Wang, L. Wosinski, U. Westergren, and S. He, Opt. Lett. 35, 1290 (2010). [CrossRef]  

29. P. Yeh, A. Yariv, and C.-S. Hong, J. Opt. Soc. Am. 67, 423 (1977). [CrossRef]  

30. D. Marcuse, IEEE J. Quantum Electron. 14, 736 (1978). [CrossRef]  

31. A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, Opt. Express 25, 12222 (2017). [CrossRef]  

32. J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016). [CrossRef]  

References

  • View by:

  1. S. M. Rytov, Sov. Phys. J. Exp. Theor. Phys. 2, 466 (1956).
  2. M. Born and E. Wolf, Principles of Optics (Cambridge University, 2013), Chap. 14.
  3. H. Kikuta, H. Yoshida, and K. Iwata, Opt. Rev. 2, 92 (1995).
    [Crossref]
  4. P. Lalanne and D. Lemercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
    [Crossref]
  5. D. C. Flanders, Appl. Phys. Lett. 42, 492 (1983).
    [Crossref]
  6. H. Kikuta, Y. Ohira, and K. Iwata, Appl. Opt. 36, 1566 (1997).
    [Crossref]
  7. P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006).
    [Crossref]
  8. R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
    [Crossref]
  9. R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
    [Crossref]
  10. X. Chen and H. K. Tsang, Opt. Lett. 36, 796 (2011).
    [Crossref]
  11. Y. Wang, W. Shi, X. Wang, Z. Lu, M. Caverley, R. Bojko, L. Chrostowski, and N. A. F. Jaeger, Opt. Lett. 40, 4647 (2015).
    [Crossref]
  12. A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016).
    [Crossref]
  13. P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
    [Crossref]
  14. T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
    [Crossref]
  15. A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
    [Crossref]
  16. B. Naghdi and L. R. Chen, Opt. Express 25, 25310 (2017).
    [Crossref]
  17. D. Pérez-Galacho, C. Alonso-Ramos, F. Mazeas, X. L. Roux, D. Oser, W. Zhang, D. Marris-Morini, L. Labonté, S. Tanzilli, É. Cassan, and L. Vivien, Opt. Lett. 42, 1468 (2017).
    [Crossref]
  18. J. Čtyroký, J. G. Wangüemert-Pérez, P. Kwiecien, I. Richter, J. Litvik, J. H. Schmid, Í. Molina-Fernández, A. Ortega-Moñux, M. Dado, and P. Cheben, Opt. Express 26, 179 (2018).
    [Crossref]
  19. H. Xu and Y. Shi, Laser Photon. Rev. 12, 1700240 (2018).
    [Crossref]
  20. J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
    [Crossref]
  21. J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, Opt. Express 24, 15672 (2016).
    [Crossref]
  22. R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
    [Crossref]
  23. D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
    [Crossref]
  24. H. Nikkhah, M. Hasan, and T. Hall, Appl. Phys. A 124, 106 (2018).
    [Crossref]
  25. L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
    [Crossref]
  26. S. Jahani and Z. Jacob, Optica 1, 96 (2014).
    [Crossref]
  27. S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
    [Crossref]
  28. Y. Tang, Z. Wang, L. Wosinski, U. Westergren, and S. He, Opt. Lett. 35, 1290 (2010).
    [Crossref]
  29. P. Yeh, A. Yariv, and C.-S. Hong, J. Opt. Soc. Am. 67, 423 (1977).
    [Crossref]
  30. D. Marcuse, IEEE J. Quantum Electron. 14, 736 (1978).
    [Crossref]
  31. A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, Opt. Express 25, 12222 (2017).
    [Crossref]
  32. J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016).
    [Crossref]

2018 (7)

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

J. Čtyroký, J. G. Wangüemert-Pérez, P. Kwiecien, I. Richter, J. Litvik, J. H. Schmid, Í. Molina-Fernández, A. Ortega-Moñux, M. Dado, and P. Cheben, Opt. Express 26, 179 (2018).
[Crossref]

H. Xu and Y. Shi, Laser Photon. Rev. 12, 1700240 (2018).
[Crossref]

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

H. Nikkhah, M. Hasan, and T. Hall, Appl. Phys. A 124, 106 (2018).
[Crossref]

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

2017 (3)

2016 (5)

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016).
[Crossref]

J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, Opt. Express 24, 15672 (2016).
[Crossref]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

2015 (2)

2014 (3)

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
[Crossref]

S. Jahani and Z. Jacob, Optica 1, 96 (2014).
[Crossref]

2013 (1)

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

2011 (1)

2010 (1)

2006 (1)

1997 (1)

1996 (1)

P. Lalanne and D. Lemercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
[Crossref]

1995 (1)

H. Kikuta, H. Yoshida, and K. Iwata, Opt. Rev. 2, 92 (1995).
[Crossref]

1983 (1)

D. C. Flanders, Appl. Phys. Lett. 42, 492 (1983).
[Crossref]

1978 (1)

D. Marcuse, IEEE J. Quantum Electron. 14, 736 (1978).
[Crossref]

1977 (1)

1956 (1)

S. M. Rytov, Sov. Phys. J. Exp. Theor. Phys. 2, 466 (1956).

Alonso-Ramos, C.

D. Pérez-Galacho, C. Alonso-Ramos, F. Mazeas, X. L. Roux, D. Oser, W. Zhang, D. Marris-Morini, L. Labonté, S. Tanzilli, É. Cassan, and L. Vivien, Opt. Lett. 42, 1468 (2017).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Alonso-Ramos, C. A.

Atkinson, J.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Barwicz, T.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Benedikovic, D.

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

Bock, P. J.

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

Bojko, R.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2013), Chap. 14.

Boyer, N.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Cassan, É.

Caverley, M.

Cheben, P.

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

J. Čtyroký, J. G. Wangüemert-Pérez, P. Kwiecien, I. Richter, J. Litvik, J. H. Schmid, Í. Molina-Fernández, A. Ortega-Moñux, M. Dado, and P. Cheben, Opt. Express 26, 179 (2018).
[Crossref]

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, Opt. Express 25, 12222 (2017).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016).
[Crossref]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006).
[Crossref]

Chen, L. R.

Chen, X.

Cheung, K. C.

Chrostowski, L.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, Opt. Express 24, 15672 (2016).
[Crossref]

Y. Wang, W. Shi, X. Wang, Z. Lu, M. Caverley, R. Bojko, L. Chrostowski, and N. A. F. Jaeger, Opt. Lett. 40, 4647 (2015).
[Crossref]

Ctyroký, J.

Dado, M.

DeCorby, R. G.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Densmore, A.

Donzella, V.

Durán-Valdeiglesias, E.

El-Fiky, E.

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

Engelmann, S.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Fédéli, J.-M.

Flanders, D. C.

D. C. Flanders, Appl. Phys. Lett. 42, 492 (1983).
[Crossref]

Flueckiger, J.

Fortier, P.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

González-Andrade, D.

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

Halir, R.

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, Opt. Express 25, 12222 (2017).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016).
[Crossref]

A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016).
[Crossref]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Hall, T.

H. Nikkhah, M. Hasan, and T. Hall, Appl. Phys. A 124, 106 (2018).
[Crossref]

Han, K.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Hasan, M.

H. Nikkhah, M. Hasan, and T. Hall, Appl. Phys. A 124, 106 (2018).
[Crossref]

He, S.

Herrero-Bermello, A.

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

Hong, C.-S.

Iwata, K.

H. Kikuta, Y. Ohira, and K. Iwata, Appl. Opt. 36, 1566 (1997).
[Crossref]

H. Kikuta, H. Yoshida, and K. Iwata, Opt. Rev. 2, 92 (1995).
[Crossref]

Jacob, Z.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

S. Jahani and Z. Jacob, Optica 1, 96 (2014).
[Crossref]

Jaeger, N. A. F.

Jahani, S.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

S. Jahani and Z. Jacob, Optica 1, 96 (2014).
[Crossref]

Janta-Polczynski, A.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Janz, S.

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006).
[Crossref]

Kalhor, F.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Kamlapurkar, S.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Khater, M. H.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Kikuta, H.

H. Kikuta, Y. Ohira, and K. Iwata, Appl. Opt. 36, 1566 (1997).
[Crossref]

H. Kikuta, H. Yoshida, and K. Iwata, Opt. Rev. 2, 92 (1995).
[Crossref]

Kim, S.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Kimbrell, E. L.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Kumar, A.

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

Kwiecien, P.

Labonté, L.

Lalanne, P.

P. Lalanne and D. Lemercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
[Crossref]

Lapointe, J.

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Leidy, R.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Lemercier-Lalanne, D.

P. Lalanne and D. Lemercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
[Crossref]

Li, R.

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

Lichoulas, T. W.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Litvik, J.

Lu, Z.

Luque-González, J. M.

A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016).
[Crossref]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

Maese-Novo, A.

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Marcuse, D.

D. Marcuse, IEEE J. Quantum Electron. 14, 736 (1978).
[Crossref]

Marris-Morini, D.

Martin, Y.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Mashanovich, G. Z.

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

Mazeas, F.

Molina-Fernández, I.

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
[Crossref]

Molina-Fernández, Í.

J. Čtyroký, J. G. Wangüemert-Pérez, P. Kwiecien, I. Richter, J. Litvik, J. H. Schmid, Í. Molina-Fernández, A. Ortega-Moñux, M. Dado, and P. Cheben, Opt. Express 26, 179 (2018).
[Crossref]

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, Opt. Express 25, 12222 (2017).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016).
[Crossref]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Naghdi, B.

Nah, J. W.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Newman, W. D.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Nikkhah, H.

H. Nikkhah, M. Hasan, and T. Hall, Appl. Phys. A 124, 106 (2018).
[Crossref]

Noman, A. A.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Numata, H.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Ohira, Y.

Ortega-Moñux, A.

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

J. Čtyroký, J. G. Wangüemert-Pérez, P. Kwiecien, I. Richter, J. Litvik, J. H. Schmid, Í. Molina-Fernández, A. Ortega-Moñux, M. Dado, and P. Cheben, Opt. Express 26, 179 (2018).
[Crossref]

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, Opt. Express 25, 12222 (2017).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016).
[Crossref]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Oser, D.

Painchaud, Y.

Patel, D.

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

Pérez-Galacho, D.

Picard, M.-J.

Plant, D. V.

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

Qi, M.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Ratner, D. M.

Richter, I.

Roux, X. L.

Rytov, S. M.

S. M. Rytov, Sov. Phys. J. Exp. Theor. Phys. 2, 466 (1956).

Sánchez-Postigo, A.

Sarmiento-Merenguel, J. D.

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016).
[Crossref]

Schmid, J. H.

J. Čtyroký, J. G. Wangüemert-Pérez, P. Kwiecien, I. Richter, J. Litvik, J. H. Schmid, Í. Molina-Fernández, A. Ortega-Moñux, M. Dado, and P. Cheben, Opt. Express 26, 179 (2018).
[Crossref]

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, Opt. Express 25, 12222 (2017).
[Crossref]

A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016).
[Crossref]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Schmidt, S.

Shekhar, P.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Sherwali, A.

Shi, W.

Shi, Y.

H. Xu and Y. Shi, Laser Photon. Rev. 12, 1700240 (2018).
[Crossref]

Taira, Y.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Takenobu, S.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Tang, Y.

Tanzilli, S.

Tsang, H. K.

Vachon, M.

Van, V.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Velasco, A. V.

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

Vivien, L.

Vlasov, Y. A.

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

Wang, S.

A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, Opt. Express 25, 12222 (2017).
[Crossref]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

Wang, X.

Wang, Y.

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

Y. Wang, W. Shi, X. Wang, Z. Lu, M. Caverley, R. Bojko, L. Chrostowski, and N. A. F. Jaeger, Opt. Lett. 40, 4647 (2015).
[Crossref]

Wang, Z.

Wangüemert-Pérez, G.

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

Wangüemert-Pérez, J. G.

J. Čtyroký, J. G. Wangüemert-Pérez, P. Kwiecien, I. Richter, J. Litvik, J. H. Schmid, Í. Molina-Fernández, A. Ortega-Moñux, M. Dado, and P. Cheben, Opt. Express 26, 179 (2018).
[Crossref]

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

J. D. Sarmiento-Merenguel, A. Ortega-Moñux, J.-M. Fédéli, J. G. Wangüemert-Pérez, C. Alonso-Ramos, E. Durán-Valdeiglesias, P. Cheben, Í. Molina-Fernández, and R. Halir, Opt. Lett. 41, 3443 (2016).
[Crossref]

A. Sánchez-Postigo, J. G. Wangüemert-Pérez, J. M. Luque-González, Í. Molina-Fernández, P. Cheben, C. A. Alonso-Ramos, R. Halir, J. H. Schmid, and A. Ortega-Moñux, Opt. Lett. 41, 3013 (2016).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Westergren, U.

Wirth, J. C.

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2013), Chap. 14.

Wosinski, L.

Xing, Z.

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

Xu, D.

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Xu, D.-X.

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, Opt. Lett. 39, 4442 (2014).
[Crossref]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006).
[Crossref]

Xu, H.

H. Xu and Y. Shi, Laser Photon. Rev. 12, 1700240 (2018).
[Crossref]

Xu, L.

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

Yariv, A.

Yeh, P.

Yoshida, H.

H. Kikuta, H. Yoshida, and K. Iwata, Opt. Rev. 2, 92 (1995).
[Crossref]

Zavargo-Peche, L.

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Zhang, W.

Appl. Opt. (1)

Appl. Phys. A (1)

H. Nikkhah, M. Hasan, and T. Hall, Appl. Phys. A 124, 106 (2018).
[Crossref]

Appl. Phys. Lett. (1)

D. C. Flanders, Appl. Phys. Lett. 42, 492 (1983).
[Crossref]

IEEE J. Quantum Electron. (1)

D. Marcuse, IEEE J. Quantum Electron. 14, 736 (1978).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

T. Barwicz, Y. Taira, T. W. Lichoulas, N. Boyer, Y. Martin, H. Numata, J. W. Nah, S. Takenobu, A. Janta-Polczynski, E. L. Kimbrell, R. Leidy, M. H. Khater, S. Kamlapurkar, S. Engelmann, Y. A. Vlasov, and P. Fortier, IEEE J. Sel. Top. Quantum Electron. 22, 455 (2016).
[Crossref]

IEEE Photon. J. (1)

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

IEEE Photon. Technol. Lett. (1)

L. Xu, Y. Wang, A. Kumar, D. Patel, E. El-Fiky, Z. Xing, R. Li, and D. V. Plant, IEEE Photon. Technol. Lett. 30, 403 (2018).
[Crossref]

J. Mod. Opt. (1)

P. Lalanne and D. Lemercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
[Crossref]

J. Opt. Soc. Am. (1)

Laser Photon. Rev. (4)

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, Laser Photon. Rev. 10, 1039 (2016).
[Crossref]

H. Xu and Y. Shi, Laser Photon. Rev. 12, 1700240 (2018).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, Laser Photon. Rev. 9, 25 (2014).
[Crossref]

A. Ortega-Moñux, C. Alonso-Ramos, A. Maese-Novo, R. Halir, L. Zavargo-Peche, D. Pérez-Galacho, Í. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, J. H. Schmid, J. Lapointe, D. Xu, and S. Janz, Laser Photon. Rev. 7, L12 (2013).
[Crossref]

Nat. Commun. (1)

S. Jahani, S. Kim, J. Atkinson, J. C. Wirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, Nat. Commun. 9, 1893 (2018).
[Crossref]

Opt. Express (6)

Opt. Lett. (7)

Opt. Rev. (1)

H. Kikuta, H. Yoshida, and K. Iwata, Opt. Rev. 2, 92 (1995).
[Crossref]

Optica (1)

Proc. IEEE (1)

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, Proc. IEEE PP, 1 (2018).
[Crossref]

Sov. Phys. J. Exp. Theor. Phys. (1)

S. M. Rytov, Sov. Phys. J. Exp. Theor. Phys. 2, 466 (1956).

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2013), Chap. 14.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. Scanning electron microscope (SEM) image of a tilted SWG waveguide. The waveguide parameters (width, period, duty cycle, and tilt angle) are w c = 1 μm , Λ = 0.25 μm , DC = 0.5 , θ = 45 ° . The device was fabricated in 220 nm thick Si layer on a 3 μm thick layer of buried oxide (BOX). A 3 μm thick upper SiO 2 cladding was deposited by plasma-enhanced chemical vapor deposition after the SEM image was taken.
Fig. 2.
Fig. 2. (a) Laminar periodic structure comprising two materials with refractive indexes n 1 and n 2 and thicknesses a = DC · Λ and b = ( 1 DC ) · Λ . (b) Anisotropic material described by the tensor ϵ = diag [ n x x 2 , n y y 2 , n z z 2 ] , which characterizes the propagation properties of a laminar periodic structure. (c) Comparison of the k vector of a laminar structure and an anisotropic homogeneous metamaterial for n 1 = 3.476 , n 2 = 1.444 , Λ = 0.2 μm , DC = 0.5 , and λ 0 = 1.55 μm .
Fig. 3.
Fig. 3. (a) Schematic of a tilted SWG multimode waveguide and (b) the corresponding homogeneous anisotropic model. The SiO 2 upper cladding is not shown. (c) Real part of the main component of the fundamental TE ( E x ) and TM ( E y ) modes propagating along an SWG waveguide with a θ = 30 ° tilt angle. (d) Real part of the main component of the fundamental TE ( E x ) and TM ( E y ) modes propagating along the homogeneous anisotropic waveguide. (e) Effective index of the fundamental TE and TM modes of the tilted SWG waveguide and the anisotropic homogeneous waveguide at λ 0 = 1.55 μm .
Fig. 4.
Fig. 4. (a) Effective index dispersion of the fundamental TE and TM mode of the θ = 30 ° tilted SWG waveguide. (b) Effective indices of guided modes in the multimode SWG waveguide, for both polarization and different tilt angles ( λ 0 = 1.55 μm ) .
Fig. 5.
Fig. 5. (a) Schematic of the MZI used for the characterization of the tilted SWG waveguides. Insets: SEM images of the SWG tapers and waveguides. (b) Measured and simulated group index difference between the waveguides in the MZI arms. Inset: MZI transmittance measurement for a θ = 37 ° tilt angle.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

cos ( k z Λ ) = cos ( k 1 x a ) cos ( k 2 x b ) Δ sin ( k 1 x a ) sin ( k 2 x b ) ,
Δ TE = 1 2 ( n 2 2 n 1 2 k 1 x k 2 x + n 1 2 n 2 2 k 2 x k 1 x ) and Δ TM = 1 2 ( k 1 x k 2 x + k 2 x k 1 x ) .
( k z n x x ) 2 + ( k x n z z ) 2 = k 0 2 and ( k z n y y ) 2 + ( k x n y y ) 2 = k 0 2 ,
ϵ ˜ ( θ ) = T 1 ( θ ) ϵ T ( θ ) = [ ϵ ˜ x x ( θ ) 0 ϵ ˜ x z ( θ ) 0 ϵ ˜ y y 0 ϵ ˜ x z ( θ ) 0 ϵ ˜ z z ( θ ) ] ,
ϵ ˜ x x = n x x 2 cos 2 ( θ ) + n z z 2 sin 2 ( θ ) , ϵ ˜ y y = n y y 2 , ϵ ˜ z z = n x x 2 sin 2 ( θ ) + n z z 2 cos 2 ( θ ) , ϵ ˜ x z = ( n z z 2 n x x 2 ) cos ( θ ) sin ( θ ) .

Metrics