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Post-processing ZnSe optical fibers with a micro-chemical vapor transport technique

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Abstract

Polycrystalline zinc selenide optical fibers and fiber lasers are expected to provide powerful capabilities for infrared waveguiding and laser technology. High pressure chemical vapor deposition, which is the only technique currently capable of producing zinc selenide optical fibers, leaves a geometric imperfection in the form of a central pore which is detrimental to mode quality. Chemical vapor transport with large temperature and pressure gradients not only fills this central pore but also encourages polycrystalline grain growth. Increased grain size and a reduction in defects such as twinning are demonstrated with transmission electron microscopy, Raman spectroscopy, and X-ray diffraction, supporting that high-quality material is produced from this method. Finally, the mode structure of the waveguide is improved allowing most of the guided optical intensity to be centrally positioned in the fiber core. Loss as low as 0.22 dB/cm at 1908nm is demonstrated as a result of the material improvement.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

There is substantial demand for high power fiber-optics which function in the mid-infrared (mid-IR), as fiber-based systems are more rugged and safer than free-space optics [1]. Current mid-IR fibers include ZBLAN fibers, chalcogenide fibers and silver halide fibers, but these do not serve as widely available, rugged systems because of various materials limitations. ZBLAN fibers are difficult to manufacture, fragile, and susceptible to degradation in wet environments [24]. Chalcogenide fibers suffer from phase and chemical impurity as well as inhomogeneity [5,6] and silver halide fibers suffer from photo darkening [7,8]. These issues significantly limit their lifetime and power handling and therefore make existing mid-infrared fibers expensive and unsuitable for many applications. A low loss zinc selenide (ZnSe) optical fiber would not suffer from these same drawbacks and would have wide-ranging applications in areas such as defense [9,10], mid-infrared remote sensing [11,12], and nonlinear optics [13,14]. Thus far, the only method capable of producing low-loss ZnSe-core optical fibers is high-pressure chemical vapor deposition (HPCVD) [15]. This specialized technique infiltrates microscale capillary voids to produce ZnSe optical fibers with losses on the order of 1 dB/cm as well as transition metal doped ZnSe fiber lasers [16,17] HPCVD utilizes high pressure to force precursors into micro-templates such as hollow capillaries, where they are thermally decomposed to deposit a material of interest such as silicon or ZnSe. When using hydride precursors, including silane, hydrogen diffuses through the material at elevated temperatures and lead to completely filled capillaries (optical fibers) that are nearly geometrically perfect [18]. In depositions where hydride precursors are not suitable, byproducts of larger kinetic diameters are produced and leave behind a central pore in the material. This is the case for ZnSe HPCVD, in which dimethylzinc and dimethylselenide are decomposed based on the following reaction:

$$\begin{array}{c}Zn{({C{H_3}} )_{2(g )}} + {H_{2(g )}} \to Z{n_{(g )}} + 2C{H_{4(g )}} \\ Se{({C{H_3}} )_{2(g )}} + 2{H_{2(g )}} \to Se{H_{2(g )}} + 2C{H_{4(g )}} \\ Se{H_{2(g )}} + Z{n_{(g )}} \to ZnS{e_{(s )}} + {H_{2(g )}}\end{array}$$

In this reaction, small, nm scale grains nucleate on the ZnSe surface before maturing into larger µm-scale polycrystalline grains. As these grains impinge towards the center of the fiber, methane builds up and prevents complete filling of the capillary due to its large kinetic diameter, eventually preventing mass transport before the fiber core is completely filled. This results in a central hollow pore that acts as a geometric imperfection within the fiber. Although HPCVD ZnSe fibers do possess low loss and are shown to lase if doped with transition metal ions such as Cr2+ and Fe2+ [19,20], this central pore is expected to decrease fiber laser performance by preventing strong optical feedback. The higher-order modes that do propagate have deleterious effects on fiber laser beam quality. Additionally, the polycrystalline nature of these fibers leads to high degrees of optical scattering and increased fiber loss. Here, high temperature post-processing in the form of micro-chemical vapor transport (micro-CVT) [21,22] is used to remove the central pore as well as to increase the overall crystallinity of ZnSe optical fiber cores. This improvement in materials quality is likewise predicted to improve lasing characteristics such as threshold and slope efficiency if the material is doped, as seen in bulk doped-ZnSe lasers [23,24].

In order to remove the central pore, it is informative to investigate post-processing techniques that have been successful in bulk ZnSe crystals. Bulk ZnSe is widely used for mid-infrared optics due to its wide transparency, out to 20 µm, its ability to act as a gain material for broadly tunable mid-IR lasers, and its high second order nonlinearity [2527]. ZnSe has a fundamental loss three orders of magnitude lower than that of silica, owed largely to its wide mid-IR transmission windows and reduced Rayleigh scattering [28]. To improve these properties in bulk ZnSe optics, considerable research has been pursued in post-processing ZnSe to reduce defects and increase its crystalline grain size. This improved materials quality has effectively reducing scattering losses from grain boundaries and improving optical clarity in ZnSe [2933]. In certain cases, due to the high vapor pressure of ZnSe [34], chemical vapor transport has been shown to completely recrystallize bulk ZnSe at high temperatures, minimizing surface area and smoothening edges [35]. Furthermore, chemical transport agents such as I2 or H2 may be used to shift the equilibrium values for reactive species, promoting transport and growth at much lower temperatures via the following mechanism [36,37]:

$$ZnS{e_{(s )}} + {H_{2(g )}}\rightleftharpoons Z{n_{(g )}} + {H_2}S{e_{(g )}}$$
Any remaining hydrogen would able to pass through the glass cladding or ZnSe core because of its small kinetic diameter, leaving fully filled zinc selenide.

To encourage chemical transport of zinc selenide, temperature and pressure gradients are typically employed in a vacuum. Although chemical vapor transport has been widely applied to bulk ZnSe optical components in large chambers, there are no reports of chemical vapor transport being performed inside of micro-capillaries because the micron-scale dimensions prevent transport due to the low mean free paths of gas-phase molecules. However, by encasing ZnSe fibers in a silica cladding during the HPCVD procedure, high pressures of hydrogen may be loaded to effectively form a micro-ampoule. Applying a strong pressure and temperature gradient to this ampoule then provides sufficient driving force to move ZnSe vapor from one end of the fiber to another and fully fill the capillary over a section of several cm.

Here, micro-CVT utilizes high pressure and employs H2 as a transport agent, allowing for the full filling of high aspect ratio polycrystalline ZnSe optical fibers in a matter of hours. High-pressure forces transport of gaseous species through the crystalline matrix at high temperatures, allowing transport to occur even after the pore has closed. Recrystallization occurs simultaneously with micro-CVT and is shown to dramatically improve the grain microstructure of the fibers. This technique significantly reduces the loss of such fibers due to waveguiding by improving the mode structure so that light may be guided through the center of the fiber core, as well as by the removal of twinning and other scattering defects. This improvement in the mode structure and optical loss bodes well for zinc selenide optical fibers and fiber lasers, opening the possibility for extraordinarily low-loss mid-infrared fibers or high power doped ZnSe fiber lasers.

2. Experimental methods

2.1 Zinc selenide high-pressure deposition and transport

Polycrystalline zinc selenide was deposited into silica capillaries using high-pressure chemical vapor deposition. Dimethylzinc and dimethyl selenide were flowed at 20 MPa or greater through silica capillaries with inner diameters ranging from 15 µm to 50 µm, where they were decomposed at 450 °C. The reaction was carried out for a minimum of 24 hours, or until flow was arrested, and ZnSe crystal growth had ceased. The fibers were left with a central pore, which was imaged, from the side using an Olympus microscope in transmission mode. When viewed from the side it is important to note that the pore is magnified by cylindrical lensing and appears larger than it is relative to the fiber inner diameter. Then, the fibers were cleaved and the facets were polished, after which the facets were imaged in reflection mode.

To transport ZnSe optical fibers, they were spliced into micro-ampoules using an Ericsson fusion splicer. In this process, plasma is used to precisely melt and fuse separate glass fibers into a single unit. The 50 µm inner diameter (ID) ZnSe fibers were spliced to an empty 150 µm ID capillary and a 10 µm flow limiter to prevent the fiber from being rapidly depressurized [Fig. 1]. This micro-ampoule was vacuumed with a dry scroll pump and purged several times with hydrogen before being filled with 40 MPa or greater of hydrogen gas, which acts as a transport agent. This fiber was left under pressure for several hours to allow hydrogen to flow through the small ZnSe pore into the sealed ampoule. A vacuum of 2·10−5 Torr was then applied to the opposite end using an oil diffusion pump after which a home-built cylindrical furnace was used to heat the fibers to a temperature between 650 °C and 850 °C at a ramp rate of 2 °C/s or greater so that transport could proceed. The ZnSe fibers were optically imaged before and after post-processing to verify that the central pore had closed.

 figure: Fig. 1.

Fig. 1. A diagram of the fiber transport setup is shown. A large inner diameter capillary with a sealed end and a small inner diameter fiber are spliced to a ZnSe core fiber and filled with hydrogen gas over several hours. The fiber is then attached to an oil diffusion pump to reach medium vacuum pressures and heated using an external furnace.

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2.2 Characterization: electron microscopy, Raman, and X-ray diffraction

Transmission electron microscope (TEM) samples were prepared using a Helios NanoLab 660 focused ion beam instrument to remove 10 µm x 10 µm TEM lamella, which contained sections of the fiber core as well as the ZnSe and silica interface. Samples were then thinned before being imaged in a FEI Titan3 G2 TEM microscope. The samples were imaged at 200 kV accelerating voltage in both TEM and scanning TEM mode to examine crystallinity and defects. Fast Fourier transforms (FFT) of high-resolution TEM images were made in ImageJ.

The micro-CVT post-processed ZnSe fibers were characterized using 633 nm Raman Spectroscopy with a Renishaw microfocus spectrometer. A 20x microscope objective was used to focus a 1 mW laser onto the ZnSe core and the final spectra were collected through a 20 µm slit and OptiGrate notch filter. The characteristic LO and TO Raman peaks were then analyzed for their position and full-width half-maxima (FWHM) as an indication of crystallinity. The Lorentzian components of the lines were extracted using Igor Pro’s multi-peak fitting package.

X-ray diffraction was performed using a Malvern Panalytical Empyrean II X-ray diffractometer and silver radiation with Kα1 = 0.559421 Å and Kα2 = 0.563812 Å in Bragg-Brentano geometry over an angle of 4°−36°. The close Kα1 and Kα2 mean that two peaks are present at each reflection and doublets are observed. The peak fitting was performed in IgorPro Version 6.3.

Waveguiding was accomplished with an IPG 1908nm thulium fiber laser. Up to 1 W of laser power was coupled into the fiber with a 50 mm antireflective coated CaF2 lens and collimated using a second antireflective coated CaF2 lens. The final image was acquired with a PV320 V infrared camera. Loss was measured using a Coherent PM10 power meter to determine the input and output power of a 2 mm section of fiber. Coupling loss was estimated by assuming 17.5% Fresnel reflection from the ZnSe core at either facet. Cutback methods may provide more accurate results but were not performed given the short lengths of fiber.

3. Results and discussion

3.1 Geometric improvement in zinc selenide fibers

Utilizing the micro-CVT fiber setup closed the central pore of the ZnSe fibers [Fig. 2]. Notably, this process was most effective when temperature ramp rates were exceedingly fast (>2 °C/s). After annealing, the ZnSe optical fiber pore was fully collapsed over 3 cm in length when examined with optical microscopy. Although transport occurred over several centimeters in length, transverse cracks caused by thermal expansion mismatch between silica and ZnSe were present throughout the fibers (see Appendix; Figs. 710). This can be addressed by a recently designed glass that is thermal expansion matched to ZnSe [38]. Regardless, geometrically perfect sections as long as 3 mm with no transverse cracking were recovered and polished. Furthermore, the optical microscope images reveal a smooth core-cladding interface.

 figure: Fig. 2.

Fig. 2. Optical micrographs showing both the side and cross-sectional view of HPCVD ZnSe fibers (a) as-deposited with a small pore due to the HPCVD process and (b) after chemical vapor transport where the pore was removed. All images were taken with equal magnification.

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Figure 3 shows the TEM images of the fiber TEM lamella before and after CVT. When first deposited, ZnSe fibers are highly polycrystalline and crystallites are elongated along the growth direction towards the center of the fiber core. Crystallite dimensions are on the order of several hundred microns wide and several microns long. Both low- and high-resolution TEM images show stacking faults and twinning, which can be observed clearly in the image inset FFT [Fig. 3(c)]. In contrast, post-processed fibers can be tens of microns, oriented in any direction, and show few defects. Because the polycrystalline grains are on the order of the size of the TEM lamella we could not obtain a statistical average grain size with clear certainly. However, this strong improvement in crystal grain size and quality is expected to strongly reduce optical scattering and improve waveguide quality.

 figure: Fig. 3.

Fig. 3. (a-b) Low magnification TEM images of a ZnSe fiber (a) as-deposited and (b) after CVT. Crystallites in HPCVD samples are elongated and grow radially towards the center of the core with significant twinning. After CVT, grains are several microns large, indicated with dotted lines, and no twinning is seen. (c-d) High-resolution transmission electron images for (c) an as-deposited ZnSe fiber and (d) a post-processed ZnSe fiber. The FFT of each image is shown in the inset of (c-d).

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3.2 Increased crystallinity and reduced defects in micro-CVT ZnSe fibers

Micro-CVT-processed fibers were analyzed using 633 nm Raman. The full-width half-maximum of their LO- and TO- Raman modes was examined, as shown in [Fig. 4], and used to qualitatively assess their crystallinity. These fibers were compared to those of an unprocessed HPCVD ZnSe optical fiber and to those of a ZnSe window purchased from Thorlabs, which was grown using traditional CVD techniques. When compared to ZnSe crystals grown using conventional CVD techniques, micro-CVT post-processed HPCVD ZnSe fibers have a smaller FWHM for their TO modes and larger FWHM for their LO modes. This is hypothesized to be a result of the as-deposited fibers having preferential radial orientation in the (111) direction as well higher defect density. In a zinc blende (ZB) crystal such as zinc selenide, selection rules suggest that both the TO and LO mode will be present parallel to a (111) facing crystal, but the LO mode is only observed by scattering from the (100) face and the TO only by the (110) face [39]. In addition, the zinc selenide wurtzite phase, which commonly appears as a defect in twinned ZnSe [4042], possesses a TO mode that is less sensitive to polarization. It has been previously reported in [43] that fully ZB crystals possess a TO mode with wider FWHM than those of mixed ZB and wurtzite phase, although the reason for this is not understood. When compared to a commercially bought ZnSe window, micro-CVT post-processed ZnSe fibers show a reduction in their TO modes and an LO mode that is similar in FWHM to the standard ZnSe window. This suggests that preferential orientation was lost and crystallinity increased during the transport process. The Raman shifts matched well to the standard both before and after chemical transport, meaning that there is no evidence of residual stress on the ZnSe after the post-processing procedure.

 figure: Fig. 4.

Fig. 4. The Raman spectra of as-deposited ZnSe fibers is compared with that of a commercial ZnSe window. The peak positions of all three samples matched well to each other, suggesting that there is no residual strain in the fiber samples. The micro-CVT processed sample experienced a reduction in LO mode, which signifies grain growth, and an increase in its TO mode that signifies the loss of preferential crystallite orientation.

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X-ray diffraction was taken between 4° and 36° using silver K alpha radiation with wavelength 0.55941 Å, which provided enough energy to penetrate through the 155 µm silica cladding on either side of the core (Fig. 5). Two peaks are observed for each reflection because of the close Kα1 and Kα2 wavelengths. The high background is immediately noticed and is a result of the amorphous glass cladding, while sharper peaks result from the polycrystalline ZnSe. The first three ZnSe diffraction peaks were analyzed for their position and their FWHM, as well as their expected reflection intensities (Fig. 7). The loss of texturing in micro-CVT-processed fibers is apparent by comparing the relative reflection intensities from each set of planes. As-deposited ZnSe fibers have reduced intensities for all peaks except for the (111) reflection, suggesting that this orientation is strongly preferred during HPCVD grain growth. In contrast, the post-processed fiber reflection intensities exactly match that of their expected values. FWHM are greatly reduced in the post-processed ZnSe fiber, qualitatively indicating that grain sizes have increased. This is consistent with both Raman and TEM data.

 figure: Fig. 5.

Fig. 5. The X-ray diffraction of two ZnSe fibers is shown. The top graph (in red) was taken from an as-deposited HPCVD fiber with no post-processing while the bottom graph (in blue) was transported using CVT in vacuum. The as-deposited fiber has wider FWHM line widths and is textured radially in the (111) direction, which is erased by the post-processing.

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3.3 Waveguide mode structure improvement in zinc selenide fibers

Finally, waveguiding was performed on the micro-CVT post-processed fibers to analyze their waveguide mode structure and loss [Fig. 6]. Waveguiding on a 2 mm section of fiber shows a profile with high optical intensity confined largely to the center of the fiber core rather than at its edges, suggesting that the central pore was fully closed. Finite element analysis has shown that even the presence of a sub-wavelength sized pore will lead to a donut-shaped mode [Fig. 8], which has been confirmed experimentally. Modeling also suggests that asymmetry in the pore shape will likewise induce strong asymmetry in the optical mode, which is likely the reason that the mode in [Fig. 6] is directed to one side of the core. The optical loss of HPCVD fibers processed with micro-CVT were measured to be in the 0.5 dB/cm range, with the lowest at 0.22 dB/cm at 1.908 µm, as compared to as-deposited samples which typically measure near 1 dB/cm. Even in samples where the pore did not fully collapse, loss improvements were seen due to crystalline grain growth and defect reduction. To improve the lengths of low loss fibers with high mode quality, process optimization may be carried out. In addition, claddings that are thermal expansion-matched to zinc selenide would assist the process greatly and prevent cracking [38]. Finally, this CVT method is expected to be successful for post-processing doped-ZnSe gain material.

 figure: Fig. 6.

Fig. 6. The waveguide mode structure is seen for a HPCVD ZnSe fiber (a) that was not post-processed in comparison to (b) a ZnSe fiber that was post-processed using CVT. The as-deposited fiber shows a characteristic donut-shaped mode, while the fully filled fiber is circular with improved mode structure.

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4. Conclusions

Zinc selenide optical fibers would allow for numerous applications in the mid-infrared, which are currently inaccessible to standard glass optical fibers. Here, zinc selenide fibers were deposited with high-pressure chemical vapor deposition, which produces low-loss waveguides but leaves a central pore that reduces mode quality, resulting in a donut-shaped waveguide mode. These fibers were post-processed with chemical vapor transport, which fully closes the pore and leads to a high mode quality. Recrystallization during chemical vapor transport likewise leads to increased crystallite grain sizes and a reduction of crystalline defects such as twinning as shown by transmission electron microscopy, Raman spectroscopy, and X-ray diffraction. These materials improvements predictably decrease the fiber loss to below 1 dB/cm at 1908nm. Micro-CVT is promising for the future of mid-infrared fiber lasers and can lead to long lengths of low-loss mid-infrared optical fibers if materials and process limitations are overcome.

Appendix

7.1 Micro-CVT post-processed ZnSe fibers

 figure: Fig. 7.

Fig. 7. An optical micrograph with 5X magnification shows the length over which zinc selenide fibers may be post-processed with micro-CVT. The central pore is closed over several millimeters, and even up to several centimeters in some cases. However, the presence of transverse cracks currently limits usable fiber sections to 2-3 mm in length. Sections without transverse cracks may be removed or polished away.

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7.2 Transverse cracks created by thermal expansion mismatch

 figure: Fig. 8.

Fig. 8. An optical micrograph showing that both complete pore filling and transverse cracking will occur at slow furnace ramp rates. These cracks are spaced approximately 50 µm apart and prevent the fiber from acting as an optical waveguide.

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7.3 Predicted X-ray reflection intensities

 figure: Fig. 9.

Fig. 9. The X-ray diffractions of the first three sets of reflections are shown as well as their expected positions and intensities (solid lines). Background subtraction was performed with a polynomial fit and peaks were compared to database diffraction patterns for zinc selenide. The as-deposited high-pressure CVD samples have reduced intensities for their (220) and (311) reflections, indicating preferential orientation in the (111) direction. After micro-CVT, these fibers are close to their expected intensities, indicating that preferential orientation is lost. Neither sample shown has significant shifts in their peak positions, indicating that lattice constants are similar to each other and to commercially available ZnSe.

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7.4 Modeling the effects of a pore on loss and mode structure

 figure: Fig. 10.

Fig. 10. The lowest loss waveguide mode of a zinc selenide optical fiber at 1.908 µm is shown. (a) Finite element analysis reveals that even a sub-wavelength sized pore will create a donut-shaped mode (Loss = 4.7489 dB/km). (b) Only when the pore is completely filled will a Gaussian waveguide mode form. This pore filling will marginally decrease waveguide loss (Loss = 4.7485 dB/km) but does have a dramatic effect on mode structure, even with slight pore asymmetry. Note that these theoretical loss values correspond to perfect materials with no defect scattering and thus represent a far-off goal. Decreases in loss from materials improvement, including grain growth and defect reduction, have much greater effects and are easily achieved.

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Funding

Air Force Research Laboratory (FA8650-13-2-1615); Penn State MRSEC, Center for Nanoscale Science (NSF DMR-1420620).

Disclosures

The authors declare no conflicts of interest.

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Figures (10)

Fig. 1.
Fig. 1. A diagram of the fiber transport setup is shown. A large inner diameter capillary with a sealed end and a small inner diameter fiber are spliced to a ZnSe core fiber and filled with hydrogen gas over several hours. The fiber is then attached to an oil diffusion pump to reach medium vacuum pressures and heated using an external furnace.
Fig. 2.
Fig. 2. Optical micrographs showing both the side and cross-sectional view of HPCVD ZnSe fibers (a) as-deposited with a small pore due to the HPCVD process and (b) after chemical vapor transport where the pore was removed. All images were taken with equal magnification.
Fig. 3.
Fig. 3. (a-b) Low magnification TEM images of a ZnSe fiber (a) as-deposited and (b) after CVT. Crystallites in HPCVD samples are elongated and grow radially towards the center of the core with significant twinning. After CVT, grains are several microns large, indicated with dotted lines, and no twinning is seen. (c-d) High-resolution transmission electron images for (c) an as-deposited ZnSe fiber and (d) a post-processed ZnSe fiber. The FFT of each image is shown in the inset of (c-d).
Fig. 4.
Fig. 4. The Raman spectra of as-deposited ZnSe fibers is compared with that of a commercial ZnSe window. The peak positions of all three samples matched well to each other, suggesting that there is no residual strain in the fiber samples. The micro-CVT processed sample experienced a reduction in LO mode, which signifies grain growth, and an increase in its TO mode that signifies the loss of preferential crystallite orientation.
Fig. 5.
Fig. 5. The X-ray diffraction of two ZnSe fibers is shown. The top graph (in red) was taken from an as-deposited HPCVD fiber with no post-processing while the bottom graph (in blue) was transported using CVT in vacuum. The as-deposited fiber has wider FWHM line widths and is textured radially in the (111) direction, which is erased by the post-processing.
Fig. 6.
Fig. 6. The waveguide mode structure is seen for a HPCVD ZnSe fiber (a) that was not post-processed in comparison to (b) a ZnSe fiber that was post-processed using CVT. The as-deposited fiber shows a characteristic donut-shaped mode, while the fully filled fiber is circular with improved mode structure.
Fig. 7.
Fig. 7. An optical micrograph with 5X magnification shows the length over which zinc selenide fibers may be post-processed with micro-CVT. The central pore is closed over several millimeters, and even up to several centimeters in some cases. However, the presence of transverse cracks currently limits usable fiber sections to 2-3 mm in length. Sections without transverse cracks may be removed or polished away.
Fig. 8.
Fig. 8. An optical micrograph showing that both complete pore filling and transverse cracking will occur at slow furnace ramp rates. These cracks are spaced approximately 50 µm apart and prevent the fiber from acting as an optical waveguide.
Fig. 9.
Fig. 9. The X-ray diffractions of the first three sets of reflections are shown as well as their expected positions and intensities (solid lines). Background subtraction was performed with a polynomial fit and peaks were compared to database diffraction patterns for zinc selenide. The as-deposited high-pressure CVD samples have reduced intensities for their (220) and (311) reflections, indicating preferential orientation in the (111) direction. After micro-CVT, these fibers are close to their expected intensities, indicating that preferential orientation is lost. Neither sample shown has significant shifts in their peak positions, indicating that lattice constants are similar to each other and to commercially available ZnSe.
Fig. 10.
Fig. 10. The lowest loss waveguide mode of a zinc selenide optical fiber at 1.908 µm is shown. (a) Finite element analysis reveals that even a sub-wavelength sized pore will create a donut-shaped mode (Loss = 4.7489 dB/km). (b) Only when the pore is completely filled will a Gaussian waveguide mode form. This pore filling will marginally decrease waveguide loss (Loss = 4.7485 dB/km) but does have a dramatic effect on mode structure, even with slight pore asymmetry. Note that these theoretical loss values correspond to perfect materials with no defect scattering and thus represent a far-off goal. Decreases in loss from materials improvement, including grain growth and defect reduction, have much greater effects and are easily achieved.

Equations (2)

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Z n ( C H 3 ) 2 ( g ) + H 2 ( g ) Z n ( g ) + 2 C H 4 ( g ) S e ( C H 3 ) 2 ( g ) + 2 H 2 ( g ) S e H 2 ( g ) + 2 C H 4 ( g ) S e H 2 ( g ) + Z n ( g ) Z n S e ( s ) + H 2 ( g )
Z n S e ( s ) + H 2 ( g ) Z n ( g ) + H 2 S e ( g )
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