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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 23 — Nov. 10, 2008
  • pp: 18675–18683
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Silicon optical fiber

J. Ballato, T. Hawkins, P. Foy, R. Stolen, B. Kokuoz, M. Ellison, C. McMillen, J. Reppert, A. M. Rao, M. Daw, S. Sharma, R. Shori, O. Stafsudd, R. R. Rice, and D. R. Powers  »View Author Affiliations


Optics Express, Vol. 16, Issue 23, pp. 18675-18683 (2008)
http://dx.doi.org/10.1364/OE.16.018675


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Abstract

Described herein are initial experimental details and properties of a silicon core, silica glass-clad optical fiber fabricated using conventional optical fiber draw methods. Such semiconductor core fibers have potential to greatly influence the fields of nonlinear fiber optics, infrared and THz power delivery. More specifically, x-ray diffraction and Raman spectroscopy showed the core to be highly crystalline silicon. The measured propagation losses were 4.3 dB/m at 2.936 µm, which likely are caused by either microcracks in the core arising from the large thermal expansion mismatch with the cladding or to SiO2 precipitates formed from oxygen dissolved in the silicon melt. Suggestions for enhancing the performance of these semiconductor core fibers are provided. Here we show that lengths of an optical fiber containing a highly crystalline semiconducting core can be produced using scalable fiber fabrication techniques.

© 2008 Optical Society of America

1. Introduction

Over the past few years, silicon photonics has become an active field as waveguides have been included for transmission and processing of signals on large semiconductor integrated circuits. Of particular interest is the use of Stimulated Raman Scattering (SRS) to demonstrate Raman waveguide lasers on chips in the near infrared (NIR)[1

1. B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, “Raman-based silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 412–421 (2006). [CrossRef]

], and even for an image amplifier in the mid-wave infrared (MWIR).[2

2. V. Raghunathan, D. Borlaug, R. Rice, and B. Jalali, “Demonstration of a mid-infrared silicon Raman amplifier,” Opt. Express 15, 14355–14362 (2007). [CrossRef] [PubMed]

] The extension of silicon waveguide technology to optical fibers would be a significant complement to this emerging field, and would enable additional capabilities. The high thermal conductivity, the high optical damage threshold, and the low loss transmission between ~1.2–6.6 µm of crystalline silicon are particularly beneficial features. Hence, fibers with crystalline silicon cores are highly attractive for MWIR power delivery and nonlinear applications. Initial attempts at fabricating a silicon core optical fiber have been made with limited success.[3

3. B. Jackson, P. Sazio, and J. Badding, “Single-Crystal semiconductor wires integrated into microstructured optical fibers,” Adv. Mater. 20, 1135–1140 (2008). [CrossRef]

]

One interesting application of a silicon optical fiber is Raman beam cleanup [4

4. T. Russell, S. Willis, M. Crookston, and W. Roh, “Stimulated Raman scattering in multi- mode fibers and its application to beam cleanup and combining,” J. Nonlinear Opt. Phys. Mater. 11, 301–316 (2002). [CrossRef]

,5

5. S. Baek and W. Roh, “Single mode Raman laser based on multimode fiber,” Opt. Lett. 29, 153–155 (2004). [CrossRef] [PubMed]

] in which the goal has been to use SRS in long fibers to generate a high quality Stokes-shifted output beam using many low brightness pump sources. Significant improvement in Stokes beam quality has already been achieved using multimode fibers, though long propagation lengths are generally required because of the small value for the Raman gain coefficient of typical silicate glass fibers. The Raman gain coefficient in single crystal silicon is three-to-four orders of magnitude higher than that in glass fibers, and this high gain can be exploited in device applications without free carrier losses for pump wavelengths longer than ~2.3 µm (the two-photon absorption edge).

2. Experimental procedures

2.1 Fiber fabrication

Three tubes of optical quality silica were sleeved concentrically to yield an overall cladding with outer diameter about 50 mm and inner diameter of 3.5 mm. A section of bulk silica rod was joined to one end of this tube assembly to act as a seal for the silicon core, which would be molten during the draw. This approach to layering of concentric tubes was utilized since a single glass tube of those dimensions was not commercially available. Such a thick-walled cladding tube was chosen to mitigate potential issue with the weight of the molten silicon leaking out or otherwise deforming the softened cladding glass during the draw.

A rod of silicon measuring about 3 mm in diameter by about 40 mm in length, which had been core drilled out of a Czochralski-grown single crystal boule, was sleeved into this end-sealed silica tube assembly.

Fibers were drawn at Clemson University using the Heathway draw tower at temperatures conventionally used for fabricating telecommunications-grade silica fiber (approximately 1950 °C). At these temperatures, the silicon core is well above its melting point and the melt is then encapsulated by the viscous silica cladding. The fabrication of fibers involving the melting of the core material during the draw process was originally developed over a decade ago [6

6. J. Ballato and E. Snitzer, “Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications,” Appl. Opt. 34, 6848–6854 (1995). [CrossRef] [PubMed]

]. The fibers were thick enough to be characterized as ‘cane’ and were drawn at a rate of 2.7 m/min using a cane tracker on the draw tower. Several sizes of cane were fabricated for comparison; generally in the range of 1 to 2 mm in diameter yielding core diameters of between approximately 60 and 120 µm, respectively. These diameters, which yielded lengths that were strong but not overly flexible, were simply chosen to be large enough to visually see if the core remained black during the draw process. Approximately 30 m of fiber was drawn, though, due to its relatively thick diameter, fibers were scribed off in approximately 1.5 m lengths. The bubble density was high but we were able to select several approximately 5 cm bubble-free lengths for optical transmission measurements.

2.2 Electron microscopy characterization

Microscopic characterization of the fibers was performed using back-scattered electron microscopy (BSEI). Prior to examination the fiber ends were mechanically polished with 600 grit silicon carbide (SiC) bonded paper. Un-coated samples were investigated with a Hitachi 3400N scanning electron microscope (SEM). Energy Dispersive X-ray Spectroscopy (EDX) was performed to examine the distribution of Si and O elements across the fiber core. Elemental compositions were measured at several locations along a line traversing the core. The microscope was operated at 20 or 30 kV and 10 mm working distance under variable pressure. The EDX measurements are not surface sensitive and penetrate approximately 1 micron into the sample.

2.3 Powder and single crystal x-ray diffraction analysis

Powder x-ray diffraction was performed on well-ground samples of the cane using a Scintag XDS 2000-2 powder diffractometer with Cu Kα radiation (λ=1.5418 Å) and a solid-state Ge detector. The samples contained material from both the silicon core and the silica cladding. Diffraction patterns were collected in 0.03° steps (15 seconds per step) from 5–65° in 2-theta. A 0.5×0.3×0.3 mm length of fiber was separately mounted for analysis by single crystal xray diffraction using a Rigaku AFC8 diffractometer equipped with graphite monochromated Mo Kα radiation (λ=0.71073 Å) and a Mercury CCD area detector. A total of 480 diffraction images were collected and used for subsequent structure determination and refinement using the SHELXTL software package.[7

7. G. M. Sheldrick, “SHELXTL version 6.1, Program for Crystal Structure Refinement,” University of Gottingen: Germany, 2000.

]

2.4 Micro-Raman analysis

Room temperature micro-Raman measurements were carried out in reflection off the polished fiber end using the 514.5 nm excitation of an Ar-ion laser. The ISA Triax 550 spectrometer had a typical resolution of 1.0 cm-1 in a backscattering geometry and the Raman signal was detected using a liquid nitrogen cooled charge-coupled device (CCD).

2.5 Optical transparency measurements

In order to establish the intrinsic loss of the silicon core material the cane sample was replaced with a 3.27 cm rod core-drilled from the silicon boule. Measured transmission through the bulk rod was 0.46 at 1306 nm and 0.49 at 1532 nm. Reflection loss is 0.465 and 0.481 at 1306 and 1532 nm.[8] Side scattered light was examined with the infrared viewer.

The transmission measurements at 2.936 µm were made by focusing the output from a 2.936 µm Er:YAG laser onto the Si core of a polished 50 mm long cane of 50 µm core diameter. The pulse duration and the pulse energy of the Er:YAG laser were 380 µs (FWHM) and 50 +/- 1 mJ. The spatial profile of the laser output beam was highly multi-moded. The focal length of the lens was 25 mm. When the incident beam was misaligned so as to propagate via the cladding, the measured transmission through the silica was measured to be almost identical to the transmission through Si core. However, the similarity of the two values is coincidental as the silica is absorptive at this wavelength. Furthermore, transmission measurements taken using a shorter cane (~4 cm length) yielded higher transmission which further supports this notion. All measurements were performed at room temperature.

3. Results and discussion

Figure 1 provides an electron microscopy image of the cross-section of the Si core, silica-clad optical fiber. The core exhibits a degree of ovality, which possibly from a direct and indirect few sources. Firstly, from inspection of the polishing marks the electron micrograph was taken at a slight tilt which facilitates the appearance of added ovality. Secondly, the ovality could result from slight gaps between the three concentric silica tubes that comprised the cladding. As the preform consolidates down during the draw the tubes can adhere to one slide of its neighboring tube causing a non-uniform reduction. This can be corrected in future draws through tighter tolerances between all silica cladding tubes or by using a single cladding tube of proper outer diameter to inner diameter ratio to yield the desired core/clad ratio. Since the silicon is significantly above its melting point (Tmelt ~1414 °C) at the draw temperature (1950 °C) the core is a fluent liquid and inevitably conforms to the inner geometry of the cladding tube.

Fig. 1. Scanning electron micrograph of the core region of the silicon core, silica-clad optical fiber.

3.1 Phase purity, crystallinity, and effects of diffusion

X-ray diffraction analysis (XRD) of the fibers was used to study the phase purity and degree of crystallinity of the silicon core within the amorphous silica glass cladding. It was not expected that the core be single crystalline due to the rapid quenching conditions (~2000K/s) that the core melt experiences upon drawing into fiber. However, the powder x-ray diffraction results shown in Figure 2 clearly prove that the core is crystalline silicon with no other phases apparent. Further, the narrowness of the peak width implies a high degree of crystallinity.

In order to evaluate the degree of single crystallinity of the silicon core, the silica cladding glass was partially removed from the silicon core by etching in diluted hydrofluoric acid. The resulting silicon core sample was analyzed using single crystal x-ray diffraction. The structure was determined to be in the Fd-3m space group with a lattice parameter of a=5.4366(6) Å and 8 formula units per unit cell. The resulting r-factor of 0.0189 is very low, indicating good agreement between the diffraction data and assigned atomic position and a correct, well-refined solution. This result also indicates that the sample is indeed highly single crystalline. Twinned crystals typically do not produce r-factors this low because the twinned portion also diffracts the x-rays and leads to extra refined data that do not fit the known structure well. These x-ray results do not confirm that the Si core is truly single crystalline; however, they do strongly suggest that the grain size is sufficiently large that the Si core behaves effectively as a single crystal experimentally.

Fig. 2. X ray diffraction spectrum for the Si core optical fiber (black lines) relative to that for a bulk single crystal (blue line). The crystallographic indices are specified and match perfectly those of crystalline silicon.

The unit cell parameter of 5.4366(6)Å is slightly high in the 3rd decimal place compared to structure determinations reported in the literature.[9

9. B. N. Dutta, “Lattice constants and thermal expansion of silicon up to 900 C,” Phys. Status Solidi 2, 984–987 (1962). [CrossRef]

] Interstitial oxygen has been shown to increase the lattice constant in melt-grown silicon.[10

10. W. L. Bond and W. Kaiser, “Interstitial versus substitutional oxygen in silicon,” J. Phys. Chem Solids 16, 44–45 (1960). [CrossRef]

] Further, while the cladding glass does not strongly diffract x-rays it still has some interaction with the beam which could also contribute to this slight deviation.

Figure 3 compares the Raman spectra of the Si core of the optical fiber and the single crystal Si rod that was cored drilled out of a microelectronics-grade silicon boule. Using a Lorentzian peak fit, it can be seen that the Si in the core of the optical fiber is blue-shifted slightly and is broadened in comparison to Si measured directly from a single crystal boule. More specifically, the peak position and full width at half maximum linewidth of the Raman mode for the silicon core were 520.7 cm-1 and 2.3 cm-1, respectively. For the single crystal boule from which the core rod was cut, these values were 521.5 cm-1 and 2.1 cm-1 respectively. Within the resolution used in this Raman study; Figure 3 shows that the Si core vibrationally is very similar to the starting Si boule. This corroborates the XRD results indicating that the Si core has developed a very high degree of crystallinity as the fiber cools and the core freezes after being drawn. The differences, albeit small, may result from structural imperfections and residual stresses arising from the thermal expansion mismatch between the silicon core and the silica clad or, possibly, nanoscale SiO2 precipitates. Based on the Si-O phase diagram, such precipitates would be thermodynamically stable[11

11. S. M. Schnurre, J. Gröbner, and R. Schmid-Fetzer, “Thermodynamics and phase stability in the Si-O system,” J. Non-Cryst. Solids 336, 1–25 (2004). [CrossRef]

] if oxygen were to in-diffuse from the cladding even though the XRD and micro-Raman results showed the core to be highly crystalline and phase pure silicon. However, at the draw temperatures, the silicon core is a liquid well above its melting point and in contact with a softened glass, which certainly would take in oxygen.

Fig. 3. Raman spectrum of the silicon in the core of the optical fiber (solid blue dots) and, for comparison, that of microelectronics grade single crystal (open black dots).

Figure 4 provides the results of cross-sectional elemental analysis using energy dispersive spectroscopy. As is shown, the cladding contains only Si and O, which are found in their proper atomic proportions for the SiO2 glass. The core is dominantly Si with a constant concentration of approximately 17 atom percent oxygen across the core. This is likely due to either the fact that fluidity of the molten core and the flow dynamics associated with the melt traversing the preform neck-down into fiber, or the expected short time required for oxygen diffusion on the scale of the fiber core.[12

12. I. Kensuke, E. Minoru, W. Masahito, and H. Taketoshi, “Electrochemical measurement of diffusion coefficient of oxygen in silicon melt,” Thermophys. Prop. 21, 199–201 (2000).

,13

13. K. Kakimoto, S. Kikuchi, and H. Ozoe, “Molecular dynamics simulation of oxygen in silicon melt,” J. Cryst. Growth 198, 114–119 (1999). [CrossRef]

] Because the solubility limit of oxygen is low, the oxygen present in the core must be precipitated into oxide; it is anticipated that the rapid drop in temperature during processing will cause the precipitates to be small and dispersed. This is born out by our measurements of optical transparency.

As noted above, this oxygen content does not alter the x-ray diffraction spectrum of Figure 2 nor does it appear in the measured Raman spectrum. This latter point could be due to the fact that the Raman mode for the silicon-oxide vibration is too weak to be observed in the measurements made. A rough estimate of this proposition can be made based on the published Raman gain for Si at 1550 nm of 20 cm/GW.[14

14. R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973). [CrossRef]

] By comparison, the gain for fused silica at 1550 nm is 6.2×10-3 cm/GW and the Raman cross section for the 467 cm-1 line of crystal quartz is 28 times the peak cross section of fused silica. The relative Raman cross sections of Si and crystal quartz would be a ratio of 115 because the Raman cross section is proportional to gain. The differences in refractive index between silica and silicon should not enter into the estimate since the silica particulates sit inside the Si core. If the particulates, by order of magnitude, comprise 10% of the volume the peak SiO2 Raman line should be only 0.001 of the peak Si Raman line. This would be about 5% of the thickness of the dots that represent that data in the Fig. 3 Raman spectrum and suggest why such precipitates, if present, have not been experimentally observed to date.

Fig. 4. Elemental profile of silicon (black squares) and oxygen (blue circles) across the core/clad interface of the silicon core optical fiber. Distance arbitrarily defined relative to where compositions go from silicon-rich (approximately core) to silicon-poor (approximately clad).

3.2 Optical transparency

The measured transmission at both 1306 nm and 1532 nm of the 4.5 cm sample was approximately 0.3%. The reflection loss from both ends at 1306 nm is 0.465 so the loss is 2.7 dB/cm or 0.62 cm-1 assuming only coupling loss due to surface reflections. Side scattered light, measured using the infrared viewer, was strong at the input end and decreases smoothly along the sample. There were no bright spots indicative of large scattering centers or strong scattering at the input surface.

Transmission measurements at 2.936 µm were made on a polished 5 cm long sample. The transmission was measured to be 46.2–46.7%. The measured loss was found to be 4.3 dB/m after taking into account the 48.8% Fresnel reflection losses of Si (n=3.436 at 3 µm).

Two general models for the scattering loss can be identified as possibly applicable to this silicon core, silica clad fiber. The first is scattering from the SiO2 precipitates formed as the molten silicon cools. The second is scattering from cracks caused by the difference in thermal expansion coefficients of the silicon core and the fused silica cladding.

A model relating the scattering loss to the density of scattering centers NP was presented in an early paper by W. Kaiser for spherical particles with diameters smaller than the wavelength.[15

15. W. Kaiser, “Electrical and optical properties of heat-treated silicon,” Phys. Rev. 105, 1751–1756 (1957). [CrossRef]

]

NP=24π3α(N0M2ρA)2(n2n02n2+2n02)2n04λ4
(1)

The loss coefficient α is in units of cm-1, N0 is number of oxygen atoms per cm3, λ is the vacuum wavelength, n 0 is the silicon index (3.5), n is the index of the SiO2 particles (1.45), M is the molecular weight of silica (M=60×g/mole), ρ is the density (2.2 g/cm3) and A is Avogadro’s number. Using equation (1) we estimate NP=1.2×1018 cm-3 based on a 10% order-of-magnitude oxygen concentration (5×1021/cm3) and the measured loss of 0.62 cm-1. The volume of a precipitate scattering center is 9.4×10-20 cm3 using [15

15. W. Kaiser, “Electrical and optical properties of heat-treated silicon,” Phys. Rev. 105, 1751–1756 (1957). [CrossRef]

]:

V=N0NP(M2ρA)
(2)

This implies that the diameter of a precipitate is about 5.7 nm or ~19 SiO2 units using an approximate value of 0.3 nm for the diameter of a SiO4 tetrahedron.

It should be reiterated that neither the x-ray diffraction nor the Raman spectroscopy verified the existence of SiO2 precipitates. This calculation is provided in order to show that, if the measured loss was due to precipitates whose numbers are consistent with the measured oxygen content, then they would be too small (<6 nm) to be observed using the techniques employed for this proof-of-concept study. Higher resolution microscopic analysis is underway to better understand the structural nature of the oxygen in what is, crystallographically, a highly crystalline silicon core.

Electron microscope analysis on a side-polished sample did reveal micro-cracks present in the core that likely result from the mismatch in thermal expansion between the Si core and the silica cladding. In the coaxial geometry, with the Si core having a larger thermal contraction, the components of the stress tensor in the plane of the fiber will be isotropic and tensile, which is consistent with the orientation of the observed micro-cracks. Based on room temperature material constants, the in-plane stress are estimated to reach 0.4% of the shear modulus of Si, which probably is sufficient to initiate cracking. Most of the light is not scattered out because of frustrated total internal reflection. If we assume that the cracks make up the difference in thermal expansion between silicon and silica, the predicted loss is a couple of orders of magnitude too large. We suspect that most of the observed cracks occur during polishing.

It is appropriate to note here that the losses would be lower in the near-IR given the strong wavelength dependence on scattering. For example, a λ-4 dependence would give a 2 dB/m loss at 5 µm if no further improvements were made to the transparency. The loss at 3 µm of a 5 cm sample after correction for reflection would be 9 dB/m, in reasonable agreement with the relatively low ~4 dB/m loss measured at 2.936 µm.

Even though the IR loss for the silicon cladding is reasonably low given that this is a non-optimized first set of experiments, the mode tails will experience higher loss in the silica cladding which would be a serious problem in a single mode fiber. However, for applications of large-core multi-mode fibers such as power delivery or Raman beam cleanup, the loss from the silica cladding in the mid-IR would be less problematic since a low fraction of the optical power would be in the cladding.[16

16. A. K. Majumdar, E. D. Hinkley, and R. T. Menzies, “IR transmission at the 3.39 micron helium-neon laser wavelength in liquid-core quartz fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 408–410 (1979). [CrossRef]

,17

17. O. Saracoglu and S. Ozsoy, “Simple equation to estimate the output power of an evanescent field absorption-based fiber sensor,” Opt. Eng. 41, 598–600 (2002). [CrossRef]

]

4. Future considerations

As with any fundamentally new piece of work, there remain many further developments and optimizations. The purpose of this paper was to show that sufficiently long lengths of glass-clad semiconductor core optical fibers to be of interest and value to the optics and optoelectronics communities can be fabricated using scalable manufacturing approaches (e.g., fiber draw).

Continuing efforts should develop a more complete understanding on methods to lessen stresses and the uptake of oxygen by the core. The longer interaction lengths enabled by fiber-based geometry may off-set any diminution in nonlinear coefficients brought about by the presence of the oxygen (i.e, the Raman cross-section for Si is ~104 times higher than for SiO2).

Another area for further attention is reducing the diameter in order to yield fibers of greater flexibility. This will have to be balanced by the effects of diffusion on the optical properties. Better matching of the draw temperature of the cladding to the silicon (or other semiconducting core material) melting point as well as minimizing the tensions due to thermal expansion mismatch should help in this regard.

Lastly, as is done in silicon microelectronics, it should be possible to zone anneal and purify the Si core within the higher temperature glass cladding to significantly improve fiber quality and optical performance.

5. Conclusions

To the best of our knowledge, the first silicon core optical fiber has been fabricated using high speed, high volume fiber draw techniques. X-ray diffraction and Raman analysis indicated that the core was highly crystalline silicon. Diffusion of oxygen from the cladding glass into the core was determined to be approximately 17 atom percent but this did not appear to affect the crystal structure or crystallinity. The fibers exhibited an attenuation of 4.3 dB/m at a wavelength of 2.936 µm, which possibly was due to scattering from SiO2 precipitates in the silicon core. As was noted, several options exist to realize fibers of higher quality and lower attenuation. Optical fibers possessing a silicon core have tremendous potential for Raman and other nonlinear optical fiber devices, mid- and long-wave infrared sensing and power delivery, and terahertz guided wave structures.

Acknowledgments

The authors acknowledge the thoughtful insights and suggestions of Dave Witter (Anaxtal), Larry McCandlish (Ceramare) and Professor Joe Kolis (Clemson University). The State of South Carolina, Northrop Grumman Space Technology, and the US DoD Joint Technology Office is gratefully acknowledged for financial support.

References and links

1.

B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, “Raman-based silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 412–421 (2006). [CrossRef]

2.

V. Raghunathan, D. Borlaug, R. Rice, and B. Jalali, “Demonstration of a mid-infrared silicon Raman amplifier,” Opt. Express 15, 14355–14362 (2007). [CrossRef] [PubMed]

3.

B. Jackson, P. Sazio, and J. Badding, “Single-Crystal semiconductor wires integrated into microstructured optical fibers,” Adv. Mater. 20, 1135–1140 (2008). [CrossRef]

4.

T. Russell, S. Willis, M. Crookston, and W. Roh, “Stimulated Raman scattering in multi- mode fibers and its application to beam cleanup and combining,” J. Nonlinear Opt. Phys. Mater. 11, 301–316 (2002). [CrossRef]

5.

S. Baek and W. Roh, “Single mode Raman laser based on multimode fiber,” Opt. Lett. 29, 153–155 (2004). [CrossRef] [PubMed]

6.

J. Ballato and E. Snitzer, “Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications,” Appl. Opt. 34, 6848–6854 (1995). [CrossRef] [PubMed]

7.

G. M. Sheldrick, “SHELXTL version 6.1, Program for Crystal Structure Refinement,” University of Gottingen: Germany, 2000.

8.

Data from www.ee.byu.edu/photonics/opticalconstants.phtml

9.

B. N. Dutta, “Lattice constants and thermal expansion of silicon up to 900 C,” Phys. Status Solidi 2, 984–987 (1962). [CrossRef]

10.

W. L. Bond and W. Kaiser, “Interstitial versus substitutional oxygen in silicon,” J. Phys. Chem Solids 16, 44–45 (1960). [CrossRef]

11.

S. M. Schnurre, J. Gröbner, and R. Schmid-Fetzer, “Thermodynamics and phase stability in the Si-O system,” J. Non-Cryst. Solids 336, 1–25 (2004). [CrossRef]

12.

I. Kensuke, E. Minoru, W. Masahito, and H. Taketoshi, “Electrochemical measurement of diffusion coefficient of oxygen in silicon melt,” Thermophys. Prop. 21, 199–201 (2000).

13.

K. Kakimoto, S. Kikuchi, and H. Ozoe, “Molecular dynamics simulation of oxygen in silicon melt,” J. Cryst. Growth 198, 114–119 (1999). [CrossRef]

14.

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276–278 (1973). [CrossRef]

15.

W. Kaiser, “Electrical and optical properties of heat-treated silicon,” Phys. Rev. 105, 1751–1756 (1957). [CrossRef]

16.

A. K. Majumdar, E. D. Hinkley, and R. T. Menzies, “IR transmission at the 3.39 micron helium-neon laser wavelength in liquid-core quartz fibers,” IEEE J. Sel. Top. Quantum Electron. 15, 408–410 (1979). [CrossRef]

17.

O. Saracoglu and S. Ozsoy, “Simple equation to estimate the output power of an evanescent field absorption-based fiber sensor,” Opt. Eng. 41, 598–600 (2002). [CrossRef]

OCIS Codes
(060.2290) Fiber optics and optical communications : Fiber materials
(060.2390) Fiber optics and optical communications : Fiber optics, infrared
(160.2290) Materials : Fiber materials
(160.4330) Materials : Nonlinear optical materials
(160.4760) Materials : Optical properties
(160.6000) Materials : Semiconductor materials

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 15, 2008
Revised Manuscript: October 17, 2008
Manuscript Accepted: October 17, 2008
Published: October 28, 2008

Citation
J. Ballato, T. Hawkins, P. Foy, R. Stolen, B. Kokuoz, M. Ellison, C. McMillen, J. Reppert, A. M. Rao, M. Daw, S. R. Sharma, R. Shori, O. Stafsudd, R. R. Rice, and D. R. Powers, "Silicon optical Fiber," Opt. Express 16, 18675-18683 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-18675


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References

  1. B. Jalali, V. Raghunathan, D. Dimitropoulos, and O. Boyraz, "Raman-based silicon photonics," IEEE J. Sel. Top. Quantum Electron. 12, 412 - 421 (2006). [CrossRef]
  2. V. Raghunathan, D. Borlaug, R. Rice, and B. Jalali, "Demonstration of a mid-infrared silicon Raman amplifier," Opt. Express 15, 14355 - 14362 (2007). [CrossRef] [PubMed]
  3. B. Jackson, P. Sazio, and J. Badding, "Single-Crystal semiconductor wires integrated into microstructured optical fibers," Adv. Mater. 20, 1135 - 1140 (2008). [CrossRef]
  4. T. Russell, S. Willis, M. Crookston, and W. Roh, "Stimulated Raman scattering in multi- mode fibers and its application to beam cleanup and combining," J. Nonlinear Opt. Phys. Mater. 11, 301 - 316 (2002). [CrossRef]
  5. S. Baek and W. Roh, "Single mode Raman laser based on multimode fiber," Opt. Lett. 29, 153 - 155 (2004). [CrossRef] [PubMed]
  6. J. Ballato and E. Snitzer, "Fabrication of fibers with high rare-earth concentrations for Faraday isolator applications," Appl. Opt. 34, 6848 - 6854 (1995). [CrossRef] [PubMed]
  7. G. M. Sheldrick, "SHELXTL version 6.1, Program for Crystal Structure Refinement," University of Gottingen: Germany, 2000.
  8. Data from www.ee.byu.edu/photonics/opticalconstants.phtml
  9. B. N. Dutta, "Lattice constants and thermal expansion of silicon up to 900 C," Phys. Status Solidi 2, 984 - 987 (1962). [CrossRef]
  10. W. L. Bond and W. Kaiser, "Interstitial versus substitutional oxygen in silicon," J. Phys. Chem Solids 16, 44 - 45 (1960). [CrossRef]
  11. S. M. Schnurre, J. Gröbner, and R. Schmid-Fetzer, "Thermodynamics and phase stability in the Si-O system," J. Non-Cryst. Solids 336, 1 - 25 (2004). [CrossRef]
  12. I. Kensuke, E. Minoru, W. Masahito, and H. Taketoshi, "Electrochemical measurement of diffusion coefficient of oxygen in silicon melt," Thermophys.Prop. 21, 199 - 201 (2000).
  13. K. Kakimoto, S. Kikuchi, and H. Ozoe, "Molecular dynamics simulation of oxygen in silicon melt," J. Cryst. Growth 198, 114 - 119 (1999). [CrossRef]
  14. R. H. Stolen and E. P. Ippen, "Raman gain in glass optical waveguides," Appl. Phys. Lett. 22, 276 - 278 (1973). [CrossRef]
  15. W. Kaiser, "Electrical and optical properties of heat-treated silicon," Phys. Rev. 105, 1751 - 1756 (1957). [CrossRef]
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