Abstract

Abstract: Photonic splitters and couplers are one of the fundamental elements in integrated optical circuits. As such, over the past decade significant research efforts have been dedicated to the development of low loss, wide bandwidth devices. While silica-based devices have clear advantages in terms of bandwidth, silicon and silicon nitride devices have lead the field in terms of ease of integration. In the present work, we provide design parameters for a novel splitter based on a suspended silica device. Unlike previous coupler devices which have smooth transition regions, the proposed device has a small defect which enables coupling across a large membrane. The designs are based on 3D FDTD models, and incorporate wavelength, refractive index and polarization dependence. The model is experimentally verified at select wavelengths from the visible through the near-IR. For comparison, we have also modeled the splitting ratio for several materials which are commonly used as waveguiding devices.

© 2013 OSA

1. Introduction

Influenced by strong demands for integrated optical systems, there is an ever-increasing interest in developing optical devices with improved performance. For example, complex computational systems require increased data processing speed, and optical sensors are less affected by electrical noise [15]. One of the fundamental components in any integrated optical circuit is the power splitter. This ubiquitous structure is used in a wide range of applications, including routing light within the circuit and monitoring the circuit [68]. Given the wide variety of potential applications of optical systems, there are numerous splitter designs and splitting mechanisms. The two most commonly used mechanisms are the evanescent coupler/splitter and the Y-branch splitter [912].

Recently, a new type of suspended silica waveguide splitter was developed (Fig. 1 ) [8]. Like many splitters, the device demonstrated both power independent and wavelength independent splitting behavior [8]. However, the device also demonstrated a nearly 50% splitting ratio with over 20 microns between the adjacent waveguides. Coupling over this distance is simply not possible by evanescent coupling mechanism. Therefore, although its basic structure is reminiscent of an evanescent coupler, its fundamental operational behavior was quite different. Therefore, the device seemed to be neither a Y-splitter nor an evanescent splitter.

 

Fig. 1 Suspended silica splitter. a) Rendering of suspended silica splitter, path of optical field indicated in red. b) Scanning electron microscopy image of the device. Inset: Optical microscopy image of insertion region, with protrusion indicated with arrows.

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One of the unique features of the structure is the slight protrusion at the beginning of the input waveguide which changes the injection angle of the optical field into the coupling/splitting region of the device (Fig. 1(b), inset). This change in curvature is lithographically patterned, and as such, appears in all devices. As a silica-based device, it has significant potential in the field of biodetection. Therefore, developing a robust theoretical model is of significant interest. In the present work, a 3D finite difference time domain (FDTD) model is developed for this structure. Using this model, the dependence of the splitting ratio on the insertion angle, wavelength (visible through near-IR), polarization and waveguide material are systematically studied. Complementary experimental investigations using silica-based devices operating from the visible through the near-IR are performed to verify the model.

2. Experimental methods and modeling

2.1. Finite differential time domain simulations

To accurately model the device behavior, a 3D finite difference time domain (FDTD) model is designed in Lumerical. The design parameters are selected to match experimentally realizable values and to enable investigations of several of the different variables of this system. Specifically, the relationship between the splitting ratio and the insertion angle, wavelength, polarization and waveguide material are studied. An overview of the simulations is contained in Table 1 .

Tables Icon

Table 1. Overview of Simulations Performed

A schematic of the model is shown in Fig. 2 , with the relevant variables indicated. The silica waveguide diameter is 5μm. There are two silica membranes in the device structure. Before the coupling region, the membrane is 900nm (T1, light gray); in the coupling region, the membrane is 2μm (T2, dark gray). As shown in previous experimental and theoretical work, the thin silica membrane isolates the optical field from the high index silicon pillar, enabling confinement in the cylindrical waveguide.

 

Fig. 2 Schematic of the device. a) T1 = 900nm and T2 = 2µm represent thin and thick regions respectively. The black line is the waveguide and the red line indicates the direction of optical field insertion. b) Protrusion region defined by two pieces, R1 and R2, and the insertion angle, ϕ.

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For the case of silica coupler with 10 degrees of insertion angle, the protrusion is comprised of three major parts with R1 = R2≈200μm. In addition, in all of the simulations, R3 = R4 = 250μm, L = 160μm and L = 155μm. After propagating the length Lp≈L’/cos(ϕ) where Lp is the transition length and ϕ is the insertion angle, the light enters the rectangular coupling region, comprised of the two cylindrical waveguides separated by the 2μm thick membrane. The separation distance is 22μm, and is selected based on previous research. Finally, the optical power is split by a Y-branch.

We chose to hold R2, W, L and L constant for all of the simulations and focused on varying ϕ, calculating the coupling ratios for several angles ranging from 5 to 15 degrees. As can be observed in Table 1, R1 is also held constant, except for the first simulation where the effect of no protrusion is compared with the presence of a protrusion. For the simulations in which the wavelength was varied, wavelength increments of 0.68nm are used. All of the simulations have been run in vacuum (n = 1). The refractive index of silicon dioxide was set to 1.445 at 1550 nm [13]. For comparison, we also modeled the coupling ratios and field distribution if the device was fabricated from Silicon Nitride (n = 2), Er-doped sol-gel (n = 1.493) and titanium butoxide doped silica sol-gel (1.5895) [1416].

To calculate the power splitting ratio, we placed power monitors at the positions indicated in Fig. 2(a). The monitors extend out of the boundaries of the waveguides to include the evanescent field associated with the propagating mode inside the waveguides. As a result, a negligible amount of power is coupled into the monitor directly from the source from outside of the waveguide. However, since this extension is approximately 400nm, we have neglected the direct coupled power from the source in our calculations.

In our simulations, the mechanisms that contribute to the loss of the device are: Loss = Lic + Lrad + LTr + LY, where Lic, Lrad, LTr, and LY are input coupling loss, radiation loss, mode transition loss and Y-branch loss respectively. Clearly, the actual value of the input loss is higher than the calculated value and is affected by other factors such as the input waveguide end-cut, input fiber misalignment and lensed fiber quality. However, our purpose is to find the total effect of radiation, transition and Y-branch loss, and previous work demonstrated that the suspended silica waveguide has nearly constant loss from the visible through the near-IR [17,18]. As such, we are not including propagation loss in our calculations, and this loss is assumed to be a constant offset.

2.2. Device fabrication

The suspended silica waveguides are fabricated from 2μm of thermal oxide on silicon wafers using a previously detailed procedure, which involves a double photolithography and double buffered oxide etching steps and XeF2 etching, followed by a CO2 laser reflow step [8]. An overview of the process is shown in Fig. 3 . As measured using optical microscopy and with small variations across devices, in the present work, the silica waveguide diameter is 5 µm, the silica membrane thickness is 2 µm, the splitting region (L) is 160 µm, and the splitting width (W) is 22µm.

 

Fig. 3 Fabrication outline of splitter device. a) A pair of photolithographic and BOE etching steps define the bowtie shape and thin and thick membranes. b) A XeF2 etch undercuts the oxide, isolating the low index silica from the high index silicon. c) A CO2 laser reflow step forms the cylindrical waveguides and the coupling region.

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The motivation for the double lithography process is to create a thin membrane between the waveguide and high index pillar, yet maintain a thick membrane (2μm) in the coupling region. The membrane thickness is determined by the wavelength of light being confined and the diameter of the cylindrical waveguide [17,18]. If the membrane is too thick, light will not be efficiently confined in the waveguide; however, if it is too thin, it is unable to support the weight of the waveguide. However, this thinning down process has another, initially unintended, effect. The pair of photolithographic masks do not match up perfectly, resulting in a small defect at the transition region between the thin membrane and the coupling region. Because this is a defect in the masks, it is present in all devices.

However, it is important to note that in all of the experiments the input waveguides have a diameter of 5 µm and they have no cladding layer (air-clad) [17]. As a result, the waveguides are multimode at all wavelengths tested and have a normalized frequency greater than 2.405 (V-number>2.405) [19]. Complementary research is ongoing to reduce the core-cladding refractive index contrast by coating the device with alternative materials in order to realize single mode input waveguides.

2.3. Experimental setup

We used a single mode (at 1550nm) lensed fiber (OZ Optics) to couple the light from a series of tunable lasers (Newport, Velocity series) into the input waveguide. The spot size for the lensed fiber was 2.5 µm with a working distance of 12 ± 4 µm. A fixed wavelength diode laser at 658nm is used for the initial alignment of the setup. The lensed fiber is mounted on a nanometer resolution XYZ motorized stage (Newport) for precise alignment. The output light from the waveguide is directly focused into an optical beam profiler by an aspheric lens which is part of a Beam Quality Analysis system (InGasAs detector, Thor Labs). The output power from each port is measured and spatially integrated to calculate the output coupling ratio.

3. Modeling and experimental results

The three modeling studies will be discussed individually, and when appropriate, the complementary experimental results will be presented in parallel. For reference, all numerical parameters for the models are contained in Table 1.

3.1. Effect of protrusion on splitting ratio

The first study focuses on exploring the basic effect of the protrusion on the splitting. Therefore, it begins by modeling the case of no protrusion (R1>300μm). The field profile from this simulation is shown in Figs. 4(a) , and 4(c). Because the transition and the radiation losses are minimal, nearly all of the power is coupled into and confined within the waveguide and negligible power is coupled into the membrane or the cross port (< 4%). Although the thickness of the membrane (2μm) in the coupling region is larger than the wavelength (1550nm) inside the medium, due to the orthogonality of the modes inside the structure, the field is strongly confined within the waveguide [20]. Given that the experimental results showed a nearly 50/50 splitting ratio, a model without a protrusion clearly does not accurately capture the behavior of the device.

 

Fig. 4 Field profile at the input region (a, b) and in the membrane region (c,d) of a waveguide without (a, c) and with (b, d) a protrusion. In this model a 10° insertion angle was used. As can be seen by comparing parts a) and b), the presence of the protrusion clearly alters the path of the optical field. This deviation results in the splitting of the optical field between the through and the cross ports (part d), which does not occur without the protrusion (part c). e) Coupling percentage for cross and through output waveguides as a function of the input waveguide angle.

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When a protrusion is incorporated (R1 = 200μm), a controlled amount of the field is directed into the membrane where it excites propagating modes which subsequently couple into either the cross or bar port (Figs. 4(b), 4(d)). In this scenario, two loss mechanisms are dominant at the protrusion region [21]:

  • 1) Waveguide transition loss: Since the propagating light inside the straight waveguide could not be fully expanded in terms of the modes of the curved waveguide, a fraction of light cannot propagate in this region and leaks out.
  • 2) Radiation loss: At a bend in the waveguide, the incident angle of rays is greater than the critical angle of the waveguide. Therefore, using a ray optics approach, in a bent waveguide, the leaky modes are supported; however, they are continuously losing power.

Therefore, by controlling the amount of loss at the protrusion, we can achieve the desired coupling ratio.

To further explore the effect of the insertion angle ϕ on the coupling ratio of the silica structures, additional simulations are performed. Figure 4(e) contains these results, showing the effect of input waveguide angle on coupling ratio. From this graph, it is straightforward to conclude that coupling ratio is almost 50/50 at 13°. This behavior is related to the increased loss of the device at the protrusion region which reduces the amount of power in the through port and as a result, the two output powers approach to equal values.

3.2. Dependence of splitting ratio on wavelength and polarization

Typically, the splitting ratio is dependent on the wavelength and polarization of the input light. However, one unique feature of the suspended silica splitter was that the splitting ratio was nearly constant across a wide range of wavelengths, making this device a good candidate for broadband applications.

Figure 5 shows the experimental results and the complementary simulation results for both TE and TM input polarizations. In both, the coupling ratio remains nearly constant. In addition, the maximum polarization dependent difference in coupling ratio is around 10% for 1550nm range which shows the operation of this device is slightly polarization dependent. At other wavelengths, the dependence is significantly less.

 

Fig. 5 a)/b)/c)/d) Theoretical and e)/f)/g)/h) experimental Bar and Cross coupling ratio as a function of wavelength for TE and TM polarizations. It can be seen that coupling ratio remains almost constant for a wide range of wavelengths.

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While there is very good qualitative agreement between the experimental and modeling results, some discrepancies are observed which could be related to fabrication defects, imperfections in the end faces of the devices or minor alignment errors. In addition it should be noted that since the lensed fiber that was used is not AR-coated a parasitic Fabry-Perot might be generated between the input end face and the fiber or the defects in the input waveguide and the input end face. This cavity could result in the observation of the periodic fluctuations in experimental transmission graphs.

In order to explain the slight difference in the coupling ratios for two output ports, the total loss for the two outputs for each polarization is calculated by simply taking the logarithm of the total normalized output power. The results from this calculation are in Fig. 6 .

 

Fig. 6 Total excess loss from through and cross outputs of the device for both TE and TM input polarizations at all wavelengths. The total TE loss is slightly higher than the total TM loss.

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As can be observed from the results in Fig. 6, the total loss for TM polarization is slightly less than that of TE polarization across all wavelengths. This slight difference in the total loss is primarily the result of the difference in mode mismatch and radiation loss at the bent waveguides for TE and TM polarizations.

3.3. Dependence of splitting ratio on material

In the final series of simulations, we explored the splitting behavior and loss for other materials which are frequently used in a wide range of applications, including non-linear optics, telecommunications and biodetection. As mentioned in Table 1, all other parameters are held constant. Figure 7 shows four simulations of the device, and the results are quantitatively summarized in Table 2 .

 

Fig. 7 Field distributions for four different materials. a) Silica (n = 1.445) b) Er-doped Silica (1.493), c) Sol-gel Silica with Titania dopant (1.5895), d) Silicon Nitride (n = 2.00)

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Tables Icon

Table 2. Simulation results for three different materials

Across the entire refractive index range modeled, the protrusion enabled power splitting. However, the splitting ratio varied slightly with refractive index. The main component of loss is the input coupling loss which ranges from 2.18 to 3.51 dB for the different cases.

Although we have analyzed the cases where the splitting ratio was 50/50 or very close to this value, it is possible to have other splitting ratios by changing various factors including:

  • 1) Protrusion length: By increasing the length of the curved region and therefore increasing the radius of curvature, the radiation loss decreases.
  • 2) Material: By using a different waveguiding material or adding a cladding layer, both the radiation loss and the transition loss are altered.

4. Conclusion

In conclusion, we have developed and experimentally verified a 3D FDTD model which accurately predicts the splitting behavior of a novel suspended silica device which contains a lithographically patterned protrusion. This device uses transition loss to split the incoming light. The precise splitting ratio is governed by the insertion angle and radius of curvature of the protrusion. Additionally, we have shown that the coupling ratio is almost wavelength independent and has a slight polarization dependence. Due to its large surface area, low optical loss and wide bandwidth, this device can have a variety of applications in the telecommunications and biodetection communities as well as being used in fundamental non-linear and quantum optics investigations [2227].

Acknowledgments

The authors thank Xiaomin Zhang and Mark Harrison (University of Southern California) for helpful discussions on suspended splitter experimental parameters, and Prof. William Steier (University of Southern California) for helpful discussions on mode mismatch loss and field distribution. This work is supported by the Office of Naval Research (N00014-11-1-0910).

References and links

1. T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of Silicon-, Germanium-, and Silica-based optical devices for telecommunications applications,” IEEE J. Sel. Top. Quantum Electron. 17(3), 516–525 (2011). [CrossRef]  

2. M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater. 11(2), 148–154 (2011). [CrossRef]   [PubMed]  

3. P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6(1), 45–49 (2011). [CrossRef]  

4. D. Q. Yang, H. P. Tian, and Y. F. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun. 285(18), 3752–3757 (2012). [CrossRef]  

5. P. W. Nugent, J. A. Shaw, and S. Piazzolla, “Infrared cloud imaging in support of Earth-space optical communication,” Opt. Express 17(10), 7862–7872 (2009). [CrossRef]   [PubMed]  

6. Y. H. Fei, S. W. Chen, L. B. Zhang, and T. T. Cao, “Design and analysis of polarization splitter based on a horizontal slotted waveguide,” Opt. Eng. 51(5), 054601 (2012). [CrossRef]  

7. L. L. Zhang, Q. Li, and Q. Wang, “1-to-N beam splitter based on photonic crystal branched waveguide structure,” Opt. Laser Technol. 43(7), 1325–1330 (2011). [CrossRef]  

8. X. M. Zhang and A. M. Armani, “Suspended bridge-like silica 2×2 beam splitter on Silicon,” Opt. Lett. 36(15), 3012–3014 (2011). [CrossRef]   [PubMed]  

9. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 2007).

10. K. Thyagarajan, A. Kumar, and I. C. Goyal, “Exact analysis of the evanescent coupling between two indiffused optical waveguides,” Appl. Opt. 20(10), 1821–1824 (1981). [CrossRef]   [PubMed]  

11. A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. B 62(11), 1267–1277 (1972). [CrossRef]  

12. H. Sasaki and N. Mikoshiba, “Normalized power transmission in single mode optical brancing waveguides,” Elec Lett 17(3), 136–138 (1981). [CrossRef]  

13. E. Palik, Handbook of Optical Constants of Solids (Elsevier 1998).

14. A. Martínez, F. Cuesta-Soto, J. M. J. García, N. V. Sochinskii, M. Abellan, J. R. Fernández, A. M. S. Mengali, C. Corsi, I. Reid, M. Robertson, S. Neretina, R. A. Hughes, J. Wojcik, J. S. Preston, and P. Mascher, “Cadmium Telluride: a Silicon-compatible optical material as an alternative technology for building all-optical photonic devices,” in SPIE: Silicon Photonics and Photonic Integrated Circuits (SPIE, 2008).

15. E. M. Yeatman, M. M. Ahmad, O. McCarthy, A. Martucci, and M. Guglielmi, “Sol-gel fabrication of rare-earth doped photonic components,” J. Sol-Gel Sci. Technol. 19(1/3), 231–236 (2000). [CrossRef]  

16. B. A. Rose, A. J. Maker, and A. M. Armani, “Characterization of thermo-optic coefficient and material loss of high refractive index silica sol-gel films in the visible and near-IR,” Opt. Mater. Express 2(5), 671–681 (2012). [CrossRef]  

17. A. J. Maker and A. M. Armani, “Low-loss silica-on-silicon waveguides,” Opt. Lett. 36(19), 3729–3731 (2011). [CrossRef]   [PubMed]  

18. X. Zhang, M. Harrison, A. Harker, and A. M. Armani, “Serpentine low loss trapezoidal silica waveguides on silicon,” Opt. Express 20(20), 22298–22307 (2012). [CrossRef]   [PubMed]  

19. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Springer, London, 1984).

20. R. Sammut and A. W. Snyder, “Leaky modes on a dielectric waveguide: orthogonality and excitation,” Appl. Opt. 15(4), 1040–1044 (1976). [CrossRef]   [PubMed]  

21. I. Papakonstantinou, K. Wang, D. R. Selviah, and F. A. Fernández, “Transition, radiation and propagation loss in polymer multimode waveguide bends,” Opt. Express 15(2), 669–679 (2007). [CrossRef]   [PubMed]  

22. C. R. Murthy and A. M. Armani, “Mass transport effects in suspended waveguide biosensors integrated in microfluidic channels,” Sensors (Basel) 12(12), 14327–14343 (2012). [CrossRef]   [PubMed]  

23. B. Chen, L. Huang, Y. Li, C. Liu, and G. Liu, “Flexible optical waveguide beam splitters based on directional coupling,” J. Opt. Soc. Am. B 28(11), 2680–2684 (2011). [CrossRef]  

24. W. C. Chiu, C. Y. Lu, and M. C. M. Lee, “Monolithic integration of 2-D multimode interference couplers and Silicon photonic wires,” IEEE J. Sel. Top. Quantum Electron. 17(3), 540–545 (2011). [CrossRef]  

25. A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun 2, 566 (2011). [CrossRef]   [PubMed]  

26. J. H. Zhu, X. G. Huang, and X. Mei, “Improved models for plasmonic waveguide splitters and demultiplexers at the telecommunication wavelengths,” IEEE Trans. NanoTechnol. 10(5), 1166–1171 (2011). [CrossRef]  

27. J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun 3, 1075 (2012). [CrossRef]   [PubMed]  

References

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  1. T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of Silicon-, Germanium-, and Silica-based optical devices for telecommunications applications,” IEEE J. Sel. Top. Quantum Electron.17(3), 516–525 (2011).
    [CrossRef]
  2. M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
    [CrossRef] [PubMed]
  3. P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
    [CrossRef]
  4. D. Q. Yang, H. P. Tian, and Y. F. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun.285(18), 3752–3757 (2012).
    [CrossRef]
  5. P. W. Nugent, J. A. Shaw, and S. Piazzolla, “Infrared cloud imaging in support of Earth-space optical communication,” Opt. Express17(10), 7862–7872 (2009).
    [CrossRef] [PubMed]
  6. Y. H. Fei, S. W. Chen, L. B. Zhang, and T. T. Cao, “Design and analysis of polarization splitter based on a horizontal slotted waveguide,” Opt. Eng.51(5), 054601 (2012).
    [CrossRef]
  7. L. L. Zhang, Q. Li, and Q. Wang, “1-to-N beam splitter based on photonic crystal branched waveguide structure,” Opt. Laser Technol.43(7), 1325–1330 (2011).
    [CrossRef]
  8. X. M. Zhang and A. M. Armani, “Suspended bridge-like silica 2×2 beam splitter on Silicon,” Opt. Lett.36(15), 3012–3014 (2011).
    [CrossRef] [PubMed]
  9. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 2007).
  10. K. Thyagarajan, A. Kumar, and I. C. Goyal, “Exact analysis of the evanescent coupling between two indiffused optical waveguides,” Appl. Opt.20(10), 1821–1824 (1981).
    [CrossRef] [PubMed]
  11. A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. B62(11), 1267–1277 (1972).
    [CrossRef]
  12. H. Sasaki and N. Mikoshiba, “Normalized power transmission in single mode optical brancing waveguides,” Elec Lett17(3), 136–138 (1981).
    [CrossRef]
  13. E. Palik, Handbook of Optical Constants of Solids (Elsevier 1998).
  14. A. Martínez, F. Cuesta-Soto, J. M. J. García, N. V. Sochinskii, M. Abellan, J. R. Fernández, A. M. S. Mengali, C. Corsi, I. Reid, M. Robertson, S. Neretina, R. A. Hughes, J. Wojcik, J. S. Preston, and P. Mascher, “Cadmium Telluride: a Silicon-compatible optical material as an alternative technology for building all-optical photonic devices,” in SPIE: Silicon Photonics and Photonic Integrated Circuits (SPIE, 2008).
  15. E. M. Yeatman, M. M. Ahmad, O. McCarthy, A. Martucci, and M. Guglielmi, “Sol-gel fabrication of rare-earth doped photonic components,” J. Sol-Gel Sci. Technol.19(1/3), 231–236 (2000).
    [CrossRef]
  16. B. A. Rose, A. J. Maker, and A. M. Armani, “Characterization of thermo-optic coefficient and material loss of high refractive index silica sol-gel films in the visible and near-IR,” Opt. Mater. Express2(5), 671–681 (2012).
    [CrossRef]
  17. A. J. Maker and A. M. Armani, “Low-loss silica-on-silicon waveguides,” Opt. Lett.36(19), 3729–3731 (2011).
    [CrossRef] [PubMed]
  18. X. Zhang, M. Harrison, A. Harker, and A. M. Armani, “Serpentine low loss trapezoidal silica waveguides on silicon,” Opt. Express20(20), 22298–22307 (2012).
    [CrossRef] [PubMed]
  19. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Springer, London, 1984).
  20. R. Sammut and A. W. Snyder, “Leaky modes on a dielectric waveguide: orthogonality and excitation,” Appl. Opt.15(4), 1040–1044 (1976).
    [CrossRef] [PubMed]
  21. I. Papakonstantinou, K. Wang, D. R. Selviah, and F. A. Fernández, “Transition, radiation and propagation loss in polymer multimode waveguide bends,” Opt. Express15(2), 669–679 (2007).
    [CrossRef] [PubMed]
  22. C. R. Murthy and A. M. Armani, “Mass transport effects in suspended waveguide biosensors integrated in microfluidic channels,” Sensors (Basel)12(12), 14327–14343 (2012).
    [CrossRef] [PubMed]
  23. B. Chen, L. Huang, Y. Li, C. Liu, and G. Liu, “Flexible optical waveguide beam splitters based on directional coupling,” J. Opt. Soc. Am. B28(11), 2680–2684 (2011).
    [CrossRef]
  24. W. C. Chiu, C. Y. Lu, and M. C. M. Lee, “Monolithic integration of 2-D multimode interference couplers and Silicon photonic wires,” IEEE J. Sel. Top. Quantum Electron.17(3), 540–545 (2011).
    [CrossRef]
  25. A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
    [CrossRef] [PubMed]
  26. J. H. Zhu, X. G. Huang, and X. Mei, “Improved models for plasmonic waveguide splitters and demultiplexers at the telecommunication wavelengths,” IEEE Trans. NanoTechnol.10(5), 1166–1171 (2011).
    [CrossRef]
  27. J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
    [CrossRef] [PubMed]

2012

D. Q. Yang, H. P. Tian, and Y. F. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun.285(18), 3752–3757 (2012).
[CrossRef]

Y. H. Fei, S. W. Chen, L. B. Zhang, and T. T. Cao, “Design and analysis of polarization splitter based on a horizontal slotted waveguide,” Opt. Eng.51(5), 054601 (2012).
[CrossRef]

B. A. Rose, A. J. Maker, and A. M. Armani, “Characterization of thermo-optic coefficient and material loss of high refractive index silica sol-gel films in the visible and near-IR,” Opt. Mater. Express2(5), 671–681 (2012).
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C. R. Murthy and A. M. Armani, “Mass transport effects in suspended waveguide biosensors integrated in microfluidic channels,” Sensors (Basel)12(12), 14327–14343 (2012).
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X. Zhang, M. Harrison, A. Harker, and A. M. Armani, “Serpentine low loss trapezoidal silica waveguides on silicon,” Opt. Express20(20), 22298–22307 (2012).
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J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
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2011

B. Chen, L. Huang, Y. Li, C. Liu, and G. Liu, “Flexible optical waveguide beam splitters based on directional coupling,” J. Opt. Soc. Am. B28(11), 2680–2684 (2011).
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W. C. Chiu, C. Y. Lu, and M. C. M. Lee, “Monolithic integration of 2-D multimode interference couplers and Silicon photonic wires,” IEEE J. Sel. Top. Quantum Electron.17(3), 540–545 (2011).
[CrossRef]

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
[CrossRef] [PubMed]

J. H. Zhu, X. G. Huang, and X. Mei, “Improved models for plasmonic waveguide splitters and demultiplexers at the telecommunication wavelengths,” IEEE Trans. NanoTechnol.10(5), 1166–1171 (2011).
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A. J. Maker and A. M. Armani, “Low-loss silica-on-silicon waveguides,” Opt. Lett.36(19), 3729–3731 (2011).
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L. L. Zhang, Q. Li, and Q. Wang, “1-to-N beam splitter based on photonic crystal branched waveguide structure,” Opt. Laser Technol.43(7), 1325–1330 (2011).
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X. M. Zhang and A. M. Armani, “Suspended bridge-like silica 2×2 beam splitter on Silicon,” Opt. Lett.36(15), 3012–3014 (2011).
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T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of Silicon-, Germanium-, and Silica-based optical devices for telecommunications applications,” IEEE J. Sel. Top. Quantum Electron.17(3), 516–525 (2011).
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M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

2009

2007

2000

E. M. Yeatman, M. M. Ahmad, O. McCarthy, A. Martucci, and M. Guglielmi, “Sol-gel fabrication of rare-earth doped photonic components,” J. Sol-Gel Sci. Technol.19(1/3), 231–236 (2000).
[CrossRef]

1981

H. Sasaki and N. Mikoshiba, “Normalized power transmission in single mode optical brancing waveguides,” Elec Lett17(3), 136–138 (1981).
[CrossRef]

K. Thyagarajan, A. Kumar, and I. C. Goyal, “Exact analysis of the evanescent coupling between two indiffused optical waveguides,” Appl. Opt.20(10), 1821–1824 (1981).
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1976

1972

A. W. Snyder, “Coupled-mode theory for optical fibers,” J. Opt. Soc. Am. B62(11), 1267–1277 (1972).
[CrossRef]

Ahmad, M. M.

E. M. Yeatman, M. M. Ahmad, O. McCarthy, A. Martucci, and M. Guglielmi, “Sol-gel fabrication of rare-earth doped photonic components,” J. Sol-Gel Sci. Technol.19(1/3), 231–236 (2000).
[CrossRef]

Armani, A. M.

Bianco, F.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Bongioanni, I.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
[CrossRef] [PubMed]

Borga, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Bourderionnet, J.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Cao, T. T.

Y. H. Fei, S. W. Chen, L. B. Zhang, and T. T. Cao, “Design and analysis of polarization splitter based on a horizontal slotted waveguide,” Opt. Eng.51(5), 054601 (2012).
[CrossRef]

Capmany, J.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Cazzanelli, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Chen, B.

Chen, S. W.

Y. H. Fei, S. W. Chen, L. B. Zhang, and T. T. Cao, “Design and analysis of polarization splitter based on a horizontal slotted waveguide,” Opt. Eng.51(5), 054601 (2012).
[CrossRef]

Chiu, W. C.

W. C. Chiu, C. Y. Lu, and M. C. M. Lee, “Monolithic integration of 2-D multimode interference couplers and Silicon photonic wires,” IEEE J. Sel. Top. Quantum Electron.17(3), 540–545 (2011).
[CrossRef]

Colman, P.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Combrié, S.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Crespi, A.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
[CrossRef] [PubMed]

De Rossi, A.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Degoli, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Dolfi, D.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Fei, Y. H.

Y. H. Fei, S. W. Chen, L. B. Zhang, and T. T. Cao, “Design and analysis of polarization splitter based on a horizontal slotted waveguide,” Opt. Eng.51(5), 054601 (2012).
[CrossRef]

Fernández, F. A.

Gasulla, I.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Ghulinyan, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Goyal, I. C.

Guglielmi, M.

E. M. Yeatman, M. M. Ahmad, O. McCarthy, A. Martucci, and M. Guglielmi, “Sol-gel fabrication of rare-earth doped photonic components,” J. Sol-Gel Sci. Technol.19(1/3), 231–236 (2000).
[CrossRef]

Harker, A.

Harrison, M.

Huang, L.

Huang, X. G.

J. H. Zhu, X. G. Huang, and X. Mei, “Improved models for plasmonic waveguide splitters and demultiplexers at the telecommunication wavelengths,” IEEE Trans. NanoTechnol.10(5), 1166–1171 (2011).
[CrossRef]

Itabashi, S.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of Silicon-, Germanium-, and Silica-based optical devices for telecommunications applications,” IEEE J. Sel. Top. Quantum Electron.17(3), 516–525 (2011).
[CrossRef]

Ji, Y. F.

D. Q. Yang, H. P. Tian, and Y. F. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun.285(18), 3752–3757 (2012).
[CrossRef]

Kou, R.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of Silicon-, Germanium-, and Silica-based optical devices for telecommunications applications,” IEEE J. Sel. Top. Quantum Electron.17(3), 516–525 (2011).
[CrossRef]

Kumar, A.

Laing, A.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

Lee, M. C. M.

W. C. Chiu, C. Y. Lu, and M. C. M. Lee, “Monolithic integration of 2-D multimode interference couplers and Silicon photonic wires,” IEEE J. Sel. Top. Quantum Electron.17(3), 540–545 (2011).
[CrossRef]

Lehoucq, G.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Li, Q.

L. L. Zhang, Q. Li, and Q. Wang, “1-to-N beam splitter based on photonic crystal branched waveguide structure,” Opt. Laser Technol.43(7), 1325–1330 (2011).
[CrossRef]

Li, Y.

Liu, C.

Liu, G.

Lloret, J.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Lobino, M.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

Lu, C. Y.

W. C. Chiu, C. Y. Lu, and M. C. M. Lee, “Monolithic integration of 2-D multimode interference couplers and Silicon photonic wires,” IEEE J. Sel. Top. Quantum Electron.17(3), 540–545 (2011).
[CrossRef]

Luppi, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Maker, A. J.

Martucci, A.

E. M. Yeatman, M. M. Ahmad, O. McCarthy, A. Martucci, and M. Guglielmi, “Sol-gel fabrication of rare-earth doped photonic components,” J. Sol-Gel Sci. Technol.19(1/3), 231–236 (2000).
[CrossRef]

Mataloni, P.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
[CrossRef] [PubMed]

Matthews, J. C. F.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

McCarthy, O.

E. M. Yeatman, M. M. Ahmad, O. McCarthy, A. Martucci, and M. Guglielmi, “Sol-gel fabrication of rare-earth doped photonic components,” J. Sol-Gel Sci. Technol.19(1/3), 231–236 (2000).
[CrossRef]

Mei, X.

J. H. Zhu, X. G. Huang, and X. Mei, “Improved models for plasmonic waveguide splitters and demultiplexers at the telecommunication wavelengths,” IEEE Trans. NanoTechnol.10(5), 1166–1171 (2011).
[CrossRef]

Mikoshiba, N.

H. Sasaki and N. Mikoshiba, “Normalized power transmission in single mode optical brancing waveguides,” Elec Lett17(3), 136–138 (1981).
[CrossRef]

Modotto, D.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Murthy, C. R.

C. R. Murthy and A. M. Armani, “Mass transport effects in suspended waveguide biosensors integrated in microfluidic channels,” Sensors (Basel)12(12), 14327–14343 (2012).
[CrossRef] [PubMed]

Nishi, H.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of Silicon-, Germanium-, and Silica-based optical devices for telecommunications applications,” IEEE J. Sel. Top. Quantum Electron.17(3), 516–525 (2011).
[CrossRef]

Nugent, P. W.

O'Brien, J. L.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

Osellame, R.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
[CrossRef] [PubMed]

Ossicini, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Papakonstantinou, I.

Park, S.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of Silicon-, Germanium-, and Silica-based optical devices for telecommunications applications,” IEEE J. Sel. Top. Quantum Electron.17(3), 516–525 (2011).
[CrossRef]

Pavesi, L.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Peruzzo, A.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

Piazzolla, S.

Pierobon, R.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Politi, A.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

Pucker, G.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Ramponi, R.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
[CrossRef] [PubMed]

Rose, B. A.

Sales, S.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Sammut, R.

Sancho, J.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat Commun3, 1075 (2012).
[CrossRef] [PubMed]

Sansoni, L.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
[CrossRef] [PubMed]

Sasaki, H.

H. Sasaki and N. Mikoshiba, “Normalized power transmission in single mode optical brancing waveguides,” Elec Lett17(3), 136–138 (1981).
[CrossRef]

Sciarrino, F.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
[CrossRef] [PubMed]

Selviah, D. R.

Shadbolt, P. J.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

Shaw, J. A.

Shinojima, H.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of Silicon-, Germanium-, and Silica-based optical devices for telecommunications applications,” IEEE J. Sel. Top. Quantum Electron.17(3), 516–525 (2011).
[CrossRef]

Snyder, A. W.

Thompson, M. G.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

Thyagarajan, K.

Tian, H. P.

D. Q. Yang, H. P. Tian, and Y. F. Ji, “High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends,” Opt. Commun.285(18), 3752–3757 (2012).
[CrossRef]

Tsuchizawa, T.

T. Tsuchizawa, K. Yamada, T. Watanabe, S. Park, H. Nishi, R. Kou, H. Shinojima, and S. Itabashi, “Monolithic integration of Silicon-, Germanium-, and Silica-based optical devices for telecommunications applications,” IEEE J. Sel. Top. Quantum Electron.17(3), 516–525 (2011).
[CrossRef]

Vallone, G.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat Commun2, 566 (2011).
[CrossRef] [PubMed]

Véniard, V.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Verde, M. R.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O'Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6(1), 45–49 (2011).
[CrossRef]

Wabnitz, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by Silicon Nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Wang, K.

Wang, Q.

L. L. Zhang, Q. Li, and Q. Wang, “1-to-N beam splitter based on photonic crystal branched waveguide structure,” Opt. Laser Technol.43(7), 1325–1330 (2011).
[CrossRef]

Watanabe, T.

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Figures (7)

Fig. 1
Fig. 1

Suspended silica splitter. a) Rendering of suspended silica splitter, path of optical field indicated in red. b) Scanning electron microscopy image of the device. Inset: Optical microscopy image of insertion region, with protrusion indicated with arrows.

Fig. 2
Fig. 2

Schematic of the device. a) T1 = 900nm and T2 = 2µm represent thin and thick regions respectively. The black line is the waveguide and the red line indicates the direction of optical field insertion. b) Protrusion region defined by two pieces, R1 and R2, and the insertion angle, ϕ.

Fig. 3
Fig. 3

Fabrication outline of splitter device. a) A pair of photolithographic and BOE etching steps define the bowtie shape and thin and thick membranes. b) A XeF2 etch undercuts the oxide, isolating the low index silica from the high index silicon. c) A CO2 laser reflow step forms the cylindrical waveguides and the coupling region.

Fig. 4
Fig. 4

Field profile at the input region (a, b) and in the membrane region (c,d) of a waveguide without (a, c) and with (b, d) a protrusion. In this model a 10° insertion angle was used. As can be seen by comparing parts a) and b), the presence of the protrusion clearly alters the path of the optical field. This deviation results in the splitting of the optical field between the through and the cross ports (part d), which does not occur without the protrusion (part c). e) Coupling percentage for cross and through output waveguides as a function of the input waveguide angle.

Fig. 5
Fig. 5

a)/b)/c)/d) Theoretical and e)/f)/g)/h) experimental Bar and Cross coupling ratio as a function of wavelength for TE and TM polarizations. It can be seen that coupling ratio remains almost constant for a wide range of wavelengths.

Fig. 6
Fig. 6

Total excess loss from through and cross outputs of the device for both TE and TM input polarizations at all wavelengths. The total TE loss is slightly higher than the total TM loss.

Fig. 7
Fig. 7

Field distributions for four different materials. a) Silica (n = 1.445) b) Er-doped Silica (1.493), c) Sol-gel Silica with Titania dopant (1.5895), d) Silicon Nitride (n = 2.00)

Tables (2)

Tables Icon

Table 1 Overview of Simulations Performed

Tables Icon

Table 2 Simulation results for three different materials

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