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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 17 — Aug. 17, 2009
  • pp: 15128–15133
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Hybrid integration of Ca0.28Ba0.72Nb2O6 thin film electro-optic waveguides with silica/silicon substrates

Paul F. Ndione, Marcello Ferrera, David Duchesne, Luca Razzari, Mounir Gaidi, Mohamed Chaker, and Roberto Morandotti  »View Author Affiliations


Optics Express, Vol. 17, Issue 17, pp. 15128-15133 (2009)
http://dx.doi.org/10.1364/OE.17.015128


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Abstract

Ca0.28Ba0.72Nb2O6 (CBN-28) waveguides based on thin film technology were fabricated on SiO2/(100) Si substrates. By using X-ray diffraction, we confirmed the preferential c-axis orientation of the CBN structures. An effective unclamped electro-optic r33 coefficient of 12 pm/V was measured in CBN thin films by using an ellipsometric technique in reflection geometry. In addition, by means of a Fabry-Perot technique, the propagation losses of our strip loaded waveguides were estimated to be as low as 4.8 dB/cm and 6.5 dB/cm at telecommunication wavelengths for the fundamental TE and TM modes, respectively.

© 2009 Optical Society of America

1. Introduction

The development of integrated optical devices has become increasingly important for future photonic telecommunication networks. This in turn has stimulated a substantial interest towards optical thin films for photonic waveguide applications [1

1. F. J. Walker and R. A. McKee, “Thin-film perovskites-ferroelectric materials for integrated optics,” Nanostruct. Mater. 7, 221–227 (1996). [CrossRef]

,2

2. B. W. Wessels, “Ferroelectric epitaxial thin films for integrated optics,” Annu. Rev. Mater. Res. 37, 659–679 (2007). [CrossRef]

]. Thin films based on ferroelectric perovskites such as BaTiO3, PbTiO3, (Pb,La)(Zr,Ti)O3, SrTiO3, SrxBa1-xNb2O6 (strontium barium niobate-SBN) and CaxBa1-xNb2O6 (calcium barium niobate-CBN) are promising for integrated optical devices as a result of their high optical transparency and important electro-optical properties [1

1. F. J. Walker and R. A. McKee, “Thin-film perovskites-ferroelectric materials for integrated optics,” Nanostruct. Mater. 7, 221–227 (1996). [CrossRef]

4

4. M. Eßer, M. Burianek, D. Klimm, and M. Mühlberg, “Single crystal growth of the tetragonal tungsten bronze CaxBa1-xNb2O6 (x=0.28; CBN-28),” J. Cryst. Growth 240, 1–5 (2002). [CrossRef]

]. Specifically, strontium barium niobate has proved to posses the highest electro-optical response amongst the other materials of its class [5

5. R. A. Vasquez, M. D. Ewbank, and P. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991). [CrossRef]

7

7. A. M. Glass, “Investigation of the electrical properties of Sr1-xBaxNb2O6 with special reference to pyroelectric detection,” J. Appl. Phys. 40, 4699–4713 (1969). [CrossRef]

]. However, SBN suffers from a very low Curie temperature which may prevent high speed applications such as ultrafast optical integrated waveguides modulators where elevated temperatures can be generated by the propagation of extremely dense optical information packets [7

7. A. M. Glass, “Investigation of the electrical properties of Sr1-xBaxNb2O6 with special reference to pyroelectric detection,” J. Appl. Phys. 40, 4699–4713 (1969). [CrossRef]

]. In turn, research has been geared towards alternative materials possessing both a high Curie temperature and a large electro-optic response. Of particular importance, CBN has recently shown to be such a material, and possesses a Curie temperature greater than 250°C [3

3. R. Helsten, L. Razzari, M. Ferrera, P. F. Ndione, M. Gaidi, C. Durand, M. Chaker, and R. Morandotti, “Pockels response in calcium barium niobate thin films,” Appl. Phys. Lett. 91, 261101 (2007). [CrossRef]

]. The growth of CBN thin films has traditionally been carried out by using oxide single crystal substrates (such as MgO and SrTiO3

3. R. Helsten, L. Razzari, M. Ferrera, P. F. Ndione, M. Gaidi, C. Durand, M. Chaker, and R. Morandotti, “Pockels response in calcium barium niobate thin films,” Appl. Phys. Lett. 91, 261101 (2007). [CrossRef]

, for example [8

8. P. F. Ndione, M. Gaidi, C. Durand, R. Morandotti, and M. Chaker, “Epitaxial CBN growth for fast electro-optic tunable devices,” Proc. SPIE 5970, 597011 (2005). [CrossRef]

,9

9. P. F. Ndione, M. Gaidi, C. Durand, M. Chaker, R. Morandotti, and G. Rioux, “Structural and optical properties of epitaxial CaxBa1-xNb2O6 thin films grown on MgO by pulsed laser deposition,” J. Appl. Phys. 103, 033510 (2008). [CrossRef]

]). From a commercial and technological point of view, the growth of high quality CBN thin films on SiO2

2. B. W. Wessels, “Ferroelectric epitaxial thin films for integrated optics,” Annu. Rev. Mater. Res. 37, 659–679 (2007). [CrossRef]

/Si substrates can be particularly interesting for the fabrication of optical waveguides. It could remarkably improve today’s integrated hybrid systems and offer an alternative route for fabricating integrated modulators and ultrafast tunable devices on a silicon platform [10

10. G. T. Reed, “The optical age of silicon,” Nature 427, 595–596 (2004). [CrossRef] [PubMed]

,11

11. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2003). [CrossRef]

]. Surprisingly, no attempt to fabricate 2D confining waveguides based on CBN or even SrxBa1-xNb2O6 thin films directly deposited on a SiO2/silicon wafer have been reported to date.

In this work, we report the fabrication of CBN thin film waveguides grown on (100) Si substrates via pulsed laser deposition technique (PLD) with an intermediate SiO2 buffer layer. First, we have studied the unclamped electro-optic (EO) response of CBN thin films grown on p-type (100) Si substrates. Subsequently, we have determined the propagation losses of strip-loaded waveguides fabricated in a similar set of CBN thin films grown on an undoped (100) Si substrate. The auspicious results reported in this paper may pave the way to new and attractive alternatives for hybrid electro-optic waveguide modulators and other electro-optically controlled devices operating at ultra high speeds. However, we wish to mention that the design and fabrication of a CBN based device certainly requires further fundamental investigations such as the study of the unclamped coefficient at high frequency (in progress) and the research of the best design and location for the necessary electrodes required to trigger the electro-optic effect, depending on the specific applications.

2. Material growth and characterization

2.1 Growth

2.2 Structural characterization

The crystalline structure of the deposited layers was investigated by X-ray diffraction (XRD) while the thicknesses of CBN were evaluated by spectroscopic ellipsometry, scanning electron microscopy and profilometric techniques. Figure 1 compares the XRD patterns in logarithmic scale for the CBN thin films grown on SiO2/p-type Si and SiO2/Si substrates after annealing. The presence of a (00l) texture in the XRD pattern can clearly be observed. In order to determine the degree of orientation achieved in the films, Lotgering factors f(00l) [13

13. F. K. Lotgering, “Topotactical reactions with ferrimagnetic oxides having hexagonal crystal structures-I,” J. Inorg. Nucl. Chem. 9, 113–123 (1959). [CrossRef]

] were calculated using the XRD patterns, where f(00l)=(P-P0)/(1-P0), P=∑I(00l)/∑I(hkl) and P0 is the P-value for a non-oriented specimen. P0 was calculated from the XRD of CBN powder taken from the target used for the ablation. For example, the f(002) value was found to be 0.68 and 0.61 for CBN thin films grown on SiO2/p-type Si and SiO2/Si substrates respectively. Hence, both films demonstrate a preferred c-axis orientation which in turn, is expected to enhance the effective electro-optic activity of our thin films.

Fig. 1. XRD pattern in logarithmic scale of a CBN thin film deposited on (a) a p-type (100) Si substrate and (b) an undoped SiO2/(100) Si multilayer structure (the measurements were performed after the sample was annealed at 650 °C).

2.3 Electro-optic properties

In order to evaluate the electro-optic properties, a 110 nm thick layer of transparent ITO was deposited on top of the CBN/SiO2/p-type Si multi-stack structure to form the upper electrode (note that no waveguides were patterned in this case). The p-type (100) Si substrate was used as the bottom electrode. The effective r33 coefficient was extracted by analyzing the polarization change in the reflection of a 633 nm linearly polarized CW laser beam incident on the CBN thin film; further details can be found elsewhere [3

3. R. Helsten, L. Razzari, M. Ferrera, P. F. Ndione, M. Gaidi, C. Durand, M. Chaker, and R. Morandotti, “Pockels response in calcium barium niobate thin films,” Appl. Phys. Lett. 91, 261101 (2007). [CrossRef]

].

Fig. 2. Modulated and normalized signal intensity as a function of the incidence angle. The modulation is performed around three different biasing points: A, B and O, as defined in ref. [16]. For more details about the electro-optical characterization procedure, see ref. [3].

Figure 2 shows the experimentally obtained modulated and normalized electro-optic response induced by a sinusoidal 1 kHz electric field as a function of the incident angle. The fitting to this data was performed according to:

ΔII0=1(rs+rp)2[rs2+rp22rsrpcos(Ψsp)rs'2rp'2+2rs'rp'cos(Ψsp')E0]
(1)

Where Ψsp is the phase difference between the s and the p waves, rs and rp are the Fresnel reflection coefficients of the entire stack for the s and p polarization states respectively, and the primed quantities (rs rp and Ψsp) indicate the presence of the externally applied electric field. This model is formally equivalent to that developed by Levy et al. [16

16. Y. Levy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Mol. Cryst. Liq. Cryst. Sci. Technol. B 4, 1–19 (1993).

]. In addition, the SiO2 layer, below the CBN, reduces the effective applied voltage across the film. This effect was taken into account in the modified model by considering the voltage partitor formed by the impedances of the two adjacent layers of CBN and SiO2 in series. Under these assumptions, a fit between Eq. (1) and the experimental data was performed and an unclamped effective electro-optical coefficient r33 of 12 pm/V was measured in our samples (more details about the EO measurements are reported in [3

3. R. Helsten, L. Razzari, M. Ferrera, P. F. Ndione, M. Gaidi, C. Durand, M. Chaker, and R. Morandotti, “Pockels response in calcium barium niobate thin films,” Appl. Phys. Lett. 91, 261101 (2007). [CrossRef]

]). This value is quantitatively important for thin films grown on silicon, especially if compared to other compound such as LiNbO3 which, despite being the most used electro-optic substrate for fabricating standard EO modulators, can achieve a comparable EO performance only in its bulk form (r33=30.9 pm/V) [17

17. A. Yariv and P. Yeh, Photonics (Oxford University Press, 2007), Chap. 9.1.

].

3. CBN strip-loaded waveguides

To demonstrate the feasibility of hybrid integration of optical devices with prefabricated CBN-based devices on silicon substrates, strip-loaded CBN waveguides were fabricated on the SiO2/Si substrates by using photolithography and reactive ion etching. The waveguide structure, shown in Fig. 3 (a), had an overall etch depth of 0.9 µm, a CBN core thickness of 0.6 µm and a ridge width of 5 µm, as determined using scanning electron microscopy (SEM).

Fig. 3. (a) Cross-sectional scanning electron microscopy view of the fabricated waveguide. (b) Schematic illustration of the strip-loaded waveguide geometry used in the simulations.

After having cleaved the facets, light from a continuous-wave tunable fiber laser source was end-fire coupled into the 8.2 mm long waveguide via a single mode tapered fiber. An inline polarization controller was used at the input to control the polarization state. The beam was then collected at the waveguide output by means of a 20X microscope objective and imaged on a Vidicon camera while the power was measured using an InGaAs based photodetector. The Fabry-Perot loss measurements were carried out by continuously tuning the wavelength of the light coupled into the waveguide while maintaining a fixed input power.

Fig. 4. Experimental Fabry-Perot fringe patterns for the fundamental TE (a) and TM (b) modes.

The experimentally obtained Fabry-Perot fringe patterns are shown in Fig. 4, where the normalized output power is plotted as a function of the wavelength for both TE and TM modes. The Fabry-Perot technique is well-suited for the analysis of low loss waveguides [18

18. L. S. Yu, Q. Z. Liu, S. A. Pappert, P. K. L. Yu, and S. S. Lau, “Laser spectral linewidth dependence on waveguide loss measurements using the Fabry-Perot method,” Appl. Phys. Lett. 64, 536–538 (1994). [CrossRef]

,19

19. D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, “Group-index birefringence and loss measurements in silicon-on-insulator photonic wire waveguides,” Opt. Eng. 46, 104602 (2007). [CrossRef]

], this is in part due to the high sensitivity and independence on the coupling efficiency, which can require significant additional effort to be determined experimentally. In particular, from the data shown in Fig. 4, the propagation losses were estimated to be ~4.9 and ~6.2 dB/cm for the TE and TM modes respectively. These losses were determined using [19

19. D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, “Group-index birefringence and loss measurements in silicon-on-insulator photonic wire waveguides,” Opt. Eng. 46, 104602 (2007). [CrossRef]

]:

α=1Lln[Rγ+1γ+1]
(2)

Where L is the length of the waveguide, R is the power reflectivity that can be estimated by assuming normal incidence upon reflections, γ=(Imax/Imin)1/2 where Imax and Imin are the maximum and the minimum intensity of the Fabry-Perot interference, respectively (see Fig. 4). Atomic force microscopy revealed a residual surface roughness of approximately 4.3 nm rms for the CBN layer, measured before the SiO2 deposition. However, the dominant source of losses is probably not the above mentioned roughness, but more likely the scattering from the coarse polycrystalline structure of the CBN film, which could further be improved by refining the deposition technique. Note that experimental systematic errors such as the finite line width of the laser source, some defects in the facets, and/or the existence of higher order modes will also result in an overestimation of the losses [18

18. L. S. Yu, Q. Z. Liu, S. A. Pappert, P. K. L. Yu, and S. S. Lau, “Laser spectral linewidth dependence on waveguide loss measurements using the Fabry-Perot method,” Appl. Phys. Lett. 64, 536–538 (1994). [CrossRef]

].

Fig. 5. Simulated (a, b) and experimental (c, d) near field images of the fundamental modes of the waveguide at a wavelength of 1550 nm; (a, c) TE modes and (b, d) TM modes. Note the scale on the experimental images is larger due to diffraction limitations of the imaging system.

4. Conclusion

References and links

1.

F. J. Walker and R. A. McKee, “Thin-film perovskites-ferroelectric materials for integrated optics,” Nanostruct. Mater. 7, 221–227 (1996). [CrossRef]

2.

B. W. Wessels, “Ferroelectric epitaxial thin films for integrated optics,” Annu. Rev. Mater. Res. 37, 659–679 (2007). [CrossRef]

3.

R. Helsten, L. Razzari, M. Ferrera, P. F. Ndione, M. Gaidi, C. Durand, M. Chaker, and R. Morandotti, “Pockels response in calcium barium niobate thin films,” Appl. Phys. Lett. 91, 261101 (2007). [CrossRef]

4.

M. Eßer, M. Burianek, D. Klimm, and M. Mühlberg, “Single crystal growth of the tetragonal tungsten bronze CaxBa1-xNb2O6 (x=0.28; CBN-28),” J. Cryst. Growth 240, 1–5 (2002). [CrossRef]

5.

R. A. Vasquez, M. D. Ewbank, and P. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991). [CrossRef]

6.

P. Tayebati, D. Trivedi, and M. Tabat, “Pulsed laser deposition of SBN:75 thin films with electro-optic coefficient of 844 pm/V,” Appl. Phys. Lett. 69, 1023–1025 (1996). [CrossRef]

7.

A. M. Glass, “Investigation of the electrical properties of Sr1-xBaxNb2O6 with special reference to pyroelectric detection,” J. Appl. Phys. 40, 4699–4713 (1969). [CrossRef]

8.

P. F. Ndione, M. Gaidi, C. Durand, R. Morandotti, and M. Chaker, “Epitaxial CBN growth for fast electro-optic tunable devices,” Proc. SPIE 5970, 597011 (2005). [CrossRef]

9.

P. F. Ndione, M. Gaidi, C. Durand, M. Chaker, R. Morandotti, and G. Rioux, “Structural and optical properties of epitaxial CaxBa1-xNb2O6 thin films grown on MgO by pulsed laser deposition,” J. Appl. Phys. 103, 033510 (2008). [CrossRef]

10.

G. T. Reed, “The optical age of silicon,” Nature 427, 595–596 (2004). [CrossRef] [PubMed]

11.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2003). [CrossRef]

12.

M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder, and M. Mühlberg, “Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x=0.28; CBN-28),” Cryst. Res. Technol. 38, 457–464 (2003). [CrossRef]

13.

F. K. Lotgering, “Topotactical reactions with ferrimagnetic oxides having hexagonal crystal structures-I,” J. Inorg. Nucl. Chem. 9, 113–123 (1959). [CrossRef]

14.

H.-F. Cheng, “Structural and optical properties of laser deposited ferroelectric (Sr0.2Ba0.8)TiO3 thin films,” J. Appl. Phys. 79, 7965–7971 (1996). [CrossRef]

15.

A. Bardal, Th. Matthee, J. Weaker, and K. Samwer, “Initial stages of epitaxial growth of Y-stabilized ZrO2 thin films on a-SiOx/Si(001) substrates,” J. Appl. Phys. 75, 2902–2910 (1994). [CrossRef]

16.

Y. Levy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret, and F. Kajzar, “Reflection method for electro-optical coefficient determination in stratified thin film structures,” Mol. Cryst. Liq. Cryst. Sci. Technol. B 4, 1–19 (1993).

17.

A. Yariv and P. Yeh, Photonics (Oxford University Press, 2007), Chap. 9.1.

18.

L. S. Yu, Q. Z. Liu, S. A. Pappert, P. K. L. Yu, and S. S. Lau, “Laser spectral linewidth dependence on waveguide loss measurements using the Fabry-Perot method,” Appl. Phys. Lett. 64, 536–538 (1994). [CrossRef]

19.

D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, “Group-index birefringence and loss measurements in silicon-on-insulator photonic wire waveguides,” Opt. Eng. 46, 104602 (2007). [CrossRef]

OCIS Codes
(230.7370) Optical devices : Waveguides
(260.2130) Physical optics : Ellipsometry and polarimetry
(310.6845) Thin films : Thin film devices and applications
(250.4110) Optoelectronics : Modulators

ToC Category:
Optical Devices

History
Original Manuscript: June 1, 2009
Revised Manuscript: July 10, 2009
Manuscript Accepted: August 5, 2009
Published: August 11, 2009

Citation
Paul F. Ndione, Marcello Ferrera, David Duchesne, Luca Razzari, Mounir Gaidi, Mohamed Chaker, and Roberto Morandotti, "Hybrid integration of Ca0.28Ba0.72Nb2O6 thin film electro-optic waveguides with silica/silicon substrates," Opt. Express 17, 15128-15133 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-15128


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References

  1. F. J. Walker and R. A. McKee, "Thin-film perovskites-ferroelectric materials for integrated optics," Nanostruct. Mater. 7, 221-227 (1996). [CrossRef]
  2. B. W. Wessels, "Ferroelectric epitaxial thin films for integrated optics," Annu. Rev. Mater. Res. 37, 659-679 (2007). [CrossRef]
  3. R. Helsten, L. Razzari, M. Ferrera, P. F. Ndione, M. Gaidi, C. Durand, M. Chaker and R. Morandotti, "Pockels response in calcium barium niobate thin films," Appl. Phys. Lett. 91, 261101 (2007). [CrossRef]
  4. M. Eßer, M. Burianek, D. Klimm and M. Mühlberg, "Single crystal growth of the tetragonal tungsten bronze CaxBa1?xNb2O6 (x=0.28; CBN-28)," J. Cryst. Growth 240, 1-5 (2002). [CrossRef]
  5. R. A. Vasquez, M. D. Ewbank and P. R. Neurgaonkar, "Photorefractive properties of doped strontium-barium niobate," Opt. Commun. 80, 253-258 (1991). [CrossRef]
  6. P. Tayebati, D. Trivedi and M. Tabat, "Pulsed laser deposition of SBN:75 thin films with electro-optic coefficient of 844 pm/V," Appl. Phys. Lett. 69, 1023-1025 (1996). [CrossRef]
  7. A. M. Glass, "Investigation of the electrical properties of Sr1?xBaxNb2O6 with special reference to pyroelectric detection," J. Appl. Phys. 40, 4699-4713 (1969). [CrossRef]
  8. P. F. Ndione, M. Gaidi, C. Durand, R. Morandotti and M. Chaker, "Epitaxial CBN growth for fast electro-optic tunable devices," Proc. SPIE 5970, 597011 (2005). [CrossRef]
  9. P. F. Ndione, M. Gaidi, C. Durand, M. Chaker, R. Morandotti and G. Rioux, "Structural and optical properties of epitaxial CaxBa1?xNb2O6 thin films grown on MgO by pulsed laser deposition," J. Appl. Phys. 103, 033510 (2008). [CrossRef]
  10. G. T. Reed, "The optical age of silicon," Nature 427, 595-596 (2004). [CrossRef] [PubMed]
  11. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu and M. Paniccia, "A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor," Nature 427, 615-618 (2003). [CrossRef]
  12. M. Eßer, M. Burianek, P. Held, J. Stade, S. Bulut, C. Wickleder and M. Mühlberg, "Optical characterization and crystal structure of the novel bronze type CaxBa1-xNb2O6 (x = 0.28; CBN-28)," Cryst. Res. Technol. 38, 457-464 (2003). [CrossRef]
  13. F. K. Lotgering, "Topotactical reactions with ferrimagnetic oxides having hexagonal crystal structures-I," J. Inorg. Nucl. Chem. 9, 113-123 (1959). [CrossRef]
  14. H.-F. Cheng, "Structural and optical properties of laser deposited ferroelectric (Sr0.2Ba0.8)TiO3 thin films," J. Appl. Phys. 79, 7965-7971 (1996). [CrossRef]
  15. A. Bardal, Th. Matthee, J. Weaker and K. Samwer, "Initial stages of epitaxial growth of Y-stabilized ZrO2 thin films on a-SiOx/Si(001) substrates," J. Appl. Phys. 75, 2902-2910 (1994). [CrossRef]
  16. Y. Levy, M. Dumont, E. Chastaing, P. Robin, P.-A. Chollet, G. Gadret and F. Kajzar, "Reflection method for electro-optical coefficient determination in stratified thin film structures," Mol. Cryst. Liq. Cryst. Sci. Technol. B 4, 1-19 (1993).
  17. A. Yariv and P. Yeh, Photonics (Oxford University Press, 2007), Chap. 9.1.
  18. L. S. Yu, Q. Z. Liu, S. A. Pappert, P. K. L. Yu and S. S. Lau, "Laser spectral linewidth dependence on waveguide loss measurements using the Fabry-Perot method," Appl. Phys. Lett. 64, 536-538 (1994). [CrossRef]
  19. D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz and D. Christodoulides, "Group-index birefringence and loss measurements in silicon-on-insulator photonic wire waveguides," Opt. Eng. 46, 104602 (2007). [CrossRef]

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