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Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 12 — Jun. 16, 2003
  • pp: 1365–1370

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Development of a system for laser splicing photonic crystal fiber

Joo Hin Chong and M. Rao  »View Author Affiliations


Optics Express, Vol. 11, Issue 12, pp. 1365-1370 (2003)
http://dx.doi.org/10.1364/OE.11.001365


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Abstract

Silica photonic crystal fiber (PCF) is a new type of fiber that has an array of microscopic air holes running along its length. Splicing PCF to standard single-mode fiber (SMF) is a challenging task, but it is also important because of the potential broad applications. Proper splicing of SMF to PCF is imperative in order to avoid collapsing of the PCF on the air holes; however, the two types of fiber require different laser powers for melting. A laser splicing system is developed to demonstrate its effectiveness at splicing between the large-mode-area PCF and SMF with low splice loss.

© 2003 Optical Society of America

1. Introduction

Interest in photonic crystal fiber (PCF) has been growing since it was invented in 1996. PCF technology is capable of providing single-mode operation from UV to IR spectral regions [1

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996). [CrossRef] [PubMed]

], where the standard single-mode fiber (SMF) cannot be used effectively. A typical PCF has a two-dimensional (2-D) cross-sectional structure in which the solid pure silica core region is surrounded by a cladding region that contains air holes. If the fiber end is left unsealed, the fiber capillary effect may absorb unwanted liquids or gases. The best way to avoid this is to splice the PCF to a standard fiber or terminate it with a connector. In addition, splicing PCF to SMF extends its potential to many applications such as spectroscopy, biomedicine, imaging, and telecommunications. The core diameter of PCF can be as small as 1 µm or as large as 20 µm or more; the numerical aperture (N.A.) values can be from arbitrarily low to ~0.9. Indeed, splicing of two fibers with different thermal characteristics is a great challenge; it is also extremely important to avoid serious collapsing of the air holes during splicing. Thus there are extra constraints on system design. The mode-field discrepancy between the PCF and the SMF varies with the type of PCF; perhaps it is difficult to have a simple solution for eliminating the mode-field mismatch problem. In the present paper, we describe the implementation of laser fusion technology for splicing PCF to SMF. Our focus is to achieve low splice loss and minimum collapse of air holes during the splicing process.

2. Analysis of factors affecting splicing loss

The transmission losses for PCF are affected by both parametric mismatch and misalignment losses. The parametric mismatch losses are caused by mismatch of numerical apertures, core/clad diameters, or index profiles of the fibers to be joined. The misalignment losses are caused by the physical misalignment or macro-bending of fibers. For splicing any two fiber end faces, the additional losses [3

A. Ishikura, Y. Kato, T. Ooyanagi, and M. Miyauchi, “Loss factors analysis for single mode fiber splicing without core axis alignment,” J. Lightwave Technol. 7 (1989). [CrossRef]

] may be contributed by fiber end-face stuffing, fusion power, or fusion duration.

PCF is fabricated by use of microstructural technology, and this makes the splicing process more complex. To minimize splice loss, three additional factors have been carefully considered in the system design: one is structural loss caused by the deformation of PCF geometry (especially the hole size and hole spacing); another is the scattering loss caused by the unevenness of the cleaved surfaces of the fibers. The final factor is the contamination loss caused by condensation trapped inside the air holes. In our experiment, we focus on the splicing of the large-mode-area (LMA) PCF to SMF. The LMA PCF has been widely addressed and is considered to be the cheapest among the PCFs; its waveguide is index guiding and can be analyzed by the principle of modified total internal reflection [4

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

]. The mode area is tailored by choice of hole spacing (Λ), because the size of the core is defined by Λ and hole size (d). A LMA fiber is designed by arrangement of smaller air holes to transmit high power without nonlinear effects; whereas the small-mode-area fiber enhances nonlinear effects by large hole spacing. Single-mode operation for the PCF is ensured by keeping the normalized frequency V≤2.405. The effective refractive index (n eff) of PCF is wavelength dependent and is affected by Λ, d, or the composite trapped inside the air holes [4

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

].

Veff= 2πΛ ( n02− neff2) 12,
(1)

Physically, PCF is different from SMF. SMF has a standard core diameter of 5 or 9 µm, whereas the core diameter of PCF can vary from a few micrometers to 20 µm, depending on its application. In most splicing systems, precise fiber alignment [5

T. Onodera, I. Suzuki, T. Yamada, Y. Osato, O. Watanabe, and T. Kato, “The development of an optical fiber splicer using a profile alignment system,” Fujikura Tech. Rev. (1987).

] is commonly obtained by the passive alignment technique or the active alignment technique. The passive alignment technique using digital images to analyze the positions (core/cladding) of the fibers is widely implemented in commercial electrical arc splicing systems. For the PCF, the small core size (say, 1 µm) and the stack of capillaries overlapping the core area make it difficult to identify the core by the digital imaging technique. This fact has been proven to be the main cause of failure in splicing SMF to PCF by use of the electric arc splicing system. In addition, the condensation trapped inside the air holes halts the electric arc splicing process and affects the completion of splicing.

To design a laser splicing system for PCF-to-SMF splicing, we can implement a passive alignment technique based on alignment of the cladding profiles [6

W. Zheng, “Real time control of arc fusion for optical fiber splicing,” J. Lightwave Technol. 11 (1993). [CrossRef]

] if the PCF core diameter is approximately 5–9 µm. If the core diameter of the PCF is much smaller, perhaps an active alignment technique may be a better solution. Below, we discuss the possible factors affecting the splice loss between the LMA PCF to SMF.

2.1 Core-size discrepancy and lateral offset

A SMF with 9-µm core diameter has been spliced with a LMA PCF. The core radius of the PCF [1

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996). [CrossRef] [PubMed]

] is taken as 0.62 times the typical cladding hole spacing; therefore the diameter of the PCF used in this experiment is ≅11.57 µm. According to manufacturer’s specifications, the unevenness of the SMF diameter is kept within ±1 µm, and the standard deviation is ~125 µm ±0.33 µm [6

W. Zheng, “Real time control of arc fusion for optical fiber splicing,” J. Lightwave Technol. 11 (1993). [CrossRef]

]. In SMF-to-SMF splicing, self-alignment is regulated between two cores/claddings because of the similar refractive-index profiles. For SMF to PCF, the lateral offset may be affected during splicing, owing to the refractive-index mismatch and differing surface tensions of the two fibers. The optimum splice loss [7

S. A. Cooper and R. W. Erskine Jr., “Practical guidelines for mass splicing,” National Fiber Optic Engineers Conference, Technical Proceedings, 2001.

] can be obtained from the following relationship as

ηint= −10log [ ( 2 ω1 ω2 ω12+ ω22)2×exp ( − 2d2 ω12+ ω22)],
(2)

where 2ω1=MFD of fiber1, 2ω2=MFD of fiber2, d=fiber axial misalignment.

Assuming negligible lateral offset, the optimum loss due to mode-field discrepancy in PCF to SMF is 0.278 dB.

2.2 Fiber end-face stuffing stroke (fiber overlapped)

Once the fiber ends are cleaved and cleaned, they are pressed against each other. The additional pressure at the fiber joint is proportional to the linear movement Δd of each fiber end [3

A. Ishikura, Y. Kato, T. Ooyanagi, and M. Miyauchi, “Loss factors analysis for single mode fiber splicing without core axis alignment,” J. Lightwave Technol. 7 (1989). [CrossRef]

, 8

A. K. Das and S. Bhattacharyya, “Low-loss fusion splices of optical fibers,” J. Lightwave Technol. LT-3, (1985).

]. The fiber overlap (Δd) must be carefully computed for low splice loss. The purpose of introducing fiber end-face stuffing is to compensate for the irregularities of the fiber surface after cleaving. Second, the stuffing results in achieving equilibrium of (a) the axial force Fp caused by the pressure applied to the fiber ends, (b) the horizontal expansion force FT that results from thermal expansion, and (c) the inner surface tension force Fs of molten glass [8

A. K. Das and S. Bhattacharyya, “Low-loss fusion splices of optical fibers,” J. Lightwave Technol. LT-3, (1985).

]. The choice of Δd is affected by the viscosity of fibers, laser power, and lasing duration. For normal SMF-to-SMF splicing, Δd is typically in the range of 3–10 µm. If Δd is too small, the surface tension force will pull the fiber ends apart, and rounded fiber ends are observed. If fibers overlap (Δd) is slightly excessive, the splice loss increases but fiber tensile strength may increase. Therefore, an appropriate fiber end-face stuffing must be carefully determined to maintain low splice loss as well as high tensile strength.

2.3 Condensation trapped inside the air capillaries

If a silica fiber contains water or water vapor near a crack, the fiber may become fatigued. The crack will grow, and the tensile strength of the fiber will weaken [10

C. R. Kurkjian, J. T. Krause, and M. J. Mathewson, “Strength and fatigue of silica optical fibers,” J. Lightwave Technol. 7 (1989). [CrossRef]

]. The interaction of water with the silica material will break the bond between (Si) and (O2) as shown below.

The strength (and fatigue) is a function of both temperature (T) and humidity (Z); with R=fatigue resistance, the failure strain ε (or stress) can be expressed as [10

C. R. Kurkjian, J. T. Krause, and M. J. Mathewson, “Strength and fatigue of silica optical fibers,” J. Lightwave Technol. 7 (1989). [CrossRef]

] − Si││− O− Si││−+ H2O → − Si││− O−H+ H− O− Si││−

ε= 2.28Z0.093exp ( 2400RT).
(3)

If the humidity is high, the failure strain becomes serious. It has been noted that condensation is easily trapped inside the air capillaries. This may cause a reduction in the strength of the fiber as well as lowering of its melting temperature [11

M. Tachikura and T. Haibara, “Devitrification effect on optical fiber strength reduction by fusion splicing,” J. Lightwave Technol. LT-3 (1985).

]. It may also result in significant change in the spectral characteristics of the PCF, where the refractive index of the cladding is determined by the air-filled capillaries (and not by the water-filled capillaries) as shown in Eq. (1). It has been reported that OH loss in PCF transmission typically occurs at wavelengths of 1274 and 1380 nm [11

M. Tachikura and T. Haibara, “Devitrification effect on optical fiber strength reduction by fusion splicing,” J. Lightwave Technol. LT-3 (1985).

].

2.4 Laser power and lasing duration

With the use of a direct electric arc, the heat energy tends to diffuse from the cladding surface to the core. The fusion temperature depends on the viscosity of the silica fiber [14

S. Pradihan, A. Mazloom, J. Arbulich, and K. Srihari, “Minimization of splice loss between a single mode fiber and an erbium doped fiber,” Electronic Components and Technology Conference, 2002.

], whereas the diffusion speed depends on the temperature [2

D. -L. Kim, M. Tomozawa, S. Dubois, and G. Orcel, “Fictive temperature measurement of single-mode optical-fiber core and cladding,” J. Lightwave Technol. 19, 1155–1158 (2001). [CrossRef]

,3

A. Ishikura, Y. Kato, T. Ooyanagi, and M. Miyauchi, “Loss factors analysis for single mode fiber splicing without core axis alignment,” J. Lightwave Technol. 7 (1989). [CrossRef]

], the composition of silica material, and the composite trapped within the air holes. In our present studies, it has been observed that the heat flow within the PCF is impeded by the air holes if the direct electric fusion technique is applied. Laser fusion creates plasma [15

K. Mima, H. A. Baldis, A. Nishiguchi, H. Takabe, and C. Yamanaka, Laser Plasma Theory and Simulation (Harwood Academic, Chur, Switzerland, 1994).

] over the cross section of silica capillary arrays and permits higher power absorption coefficient than the electric arc fusion. The required melting power for silica material is a function of laser intensity and exposure time. Increasing the lasing power indeed reduces the laser exposure time, but high laser power introduces high lasing pressure to the fiber surface, which may damage the capillaries easily. Also, the fiber strength is dependent on the exposure time. We recommend the use of lower laser power with longer exposure time to reduce the collapse of air holes and to obtain strong splice joints and low splice loss.

3. System design and experimental investigations

Initially the splicing of PCF to SMF was carried out by an electric arc fusion splicing system; however, no single splice joint could be obtained even after numerous attempts. The problems are either that the splicing systems failed to recognize the PCF fiber or that the process could not progress because of bubbles created at the fibers’ interface as shown in Fig. 2. The bubble formation occurs mainly as a result of the cleaning solution (alcohol) or because of the condensation trapped within the air holes. It is observed that if the air holes are wide, the condensation is more serious and bubble formation is much more difficult to avoid. Let us look into the thermodynamic principle with the assumption that direct heating is applied to the fiber surface. Because the PCF consists of a stack of alternating layers of silica and air, heat transmitted from a silica layer has to pass through a layer of air hole; therefore, the heat energy takes a longer time to reach the core. The thermal conductivities for silica (K Si) and atmospheric air K air satisfy the following relationships:

KSi= 0.78−0.054exp ( T+379354)+0.165exp ( T+379405),
(4)
Kair≈ 4.675× 10 −4 T.
(5)

At temperature of 1300°C, K Si=8 Wm-1 K-1 and K air=1.87×10-2 Wm-1 K-1; it is obvious to note that the heat flow in the air is slower than the heat flow in the silica. If the air hole of PCF contains alcohol, its thermal conductivity would be much lower. On the basis of the literature [12

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants , 16th ed. (Longman, New York, 1995).

], the thermal conductivity of nonmetallic liquid tends to decrease at higher temperatures and for methanol alcohol (K m) is approximately 0.18 Wm-1K-1. Therefore, if the alcohol is trapped within the air capillaries, the silica temperature may be very high, but the inner liquid temperature is sufficient only to vaporize the liquid. Subsequently, the fluid expands in volume, and a bubble is created; finally, it is pushed out of the interface between the two fiber ends.

Fig. 1. Condensation is trapped inside the air holes of the PCF (left image) with profile index ofd/Λ=0.682 and period Λ=12.22 µm. The PCF used has a diameter of 100 µm, and the size of the air holes is relatively larger than that of the PCF as shown in Fig. 2. When the electric arc is applied, the condensation expands and escapes out from the joint. The volume expansion of PCF is observed (right image).

The above-mentioned problem is not observed in the laser splicing technique. It is because laser interaction with a silica fiber is different from the electric arc fusion process. Once the laser energy is absorbed, it is not the heat but the excess electron energy that creates additional electron ions on the fiber surface. The continuation of this process results in the generation of hot plasma accelerating inward and rapidly penetrating through the fiber. Therefore, alcohol trapped inside the air holes will vaporize rapidly before the two fiber ends are joined.

Fig. 2. Complete laser splicing system setup with control by personal computer.

In addition to the above-mentioned points, we recommend laser splicing instead of electric arc splicing for the following reasons: adjustable laser beam size, precise control of laser power and beam position, and no residue left after splicing. The electrodes of electric arc fusion are easily contaminated; replacement costs time and money.

We designed a complete laser splicing system consisting of three main units: a laser control unit, an image processing unit, and a fiber alignment unit. All the units are controlled by a personal computer. An automatic core/cladding alignment is done by digital imaging for SMF-SMF splicing. However, for the PCF-to-SMF splicing, the cladding alignment is performed instead. An ≈1–4 W, cw Gaussian profile laser beam with a beam diameter of approximately 500-600 µm is applied perpendicular to the fiber axis.

A brief description on the splicing process is as follows: After the stripping and cleaning process, the fibers are placed on an alignment stage. The peak of the laser beam is positioned a micrometers offset toward the SMF to ensure delivery of higher laser power to the SMF than to the PCF. During the splicing process, preheat power from a 1-W laser for 1 s is applied to a fiber joint for removing unwanted particles and condensation. SMF PCF fibers are aligned precisely by two sets of digital cameras positioned 45° with respect to the fiber axes. After introduction of the 5-µm fiber end-face stuffing, the laser beam with a power of 3.2 W is fired several times (for durations of milliseconds) to fuse the two fiber ends together. The final step is to anneal the fibers with a 1-W laser for ~1 s to remove any cracks and strengthen the splice joint. During the splicing process, the results are monitored by means of injecting light from a low-power laser source at one fiber end and detecting the signal at the other end of the fiber by an optical power meter. A detailed illustration is shown in Fig. 3.

Fig. 3. Complete splicing process starting from fiber end-face stuffing to final fiber fusion.

Figure 4 demonstrates the splice formation between PCF and SMF. The splice loss obtained is in the range of 0.6–0.9 dB, if the mode field discrepancy is ignored.

Fig. 4. Left-hand image, cross section of PCF; its index profile is d/Λ=0.388 and Λ=8.5 µm. Right-hand image, PCF-to-SMF splice joint. Prior to splicing, condensation is first removed by laser, and a careful control of the laser power and exposure time limit the collapse of air holes.

4. Conclusion

The development of a PCF-to-SMF laser splicing [16

P. J. Bennett, T. Monro, and D. J. Richchardson, “Toward practical holey fiber technology: fabrication, splicing, modeling, and characterization,” Opt. Lett. 24, 1203–1205 (1999). [CrossRef]

, 17

J. T. Lizier and G. E. Town, “Splice losses in holey optical fibers,” IEEE Photon. Technol. Lett. 13 (2001). [CrossRef]

] system is indeed very challenging. Many design parameters must be carefully considered to ensure low splice loss as well as to retain the characteristics of the PCF. A capillary effect in the PCF is one of the main concerns in the system design for minimizing the degradation of fiber quality and avoiding changing of the spectral characteristics of the PCF. A laser splicing technique has been introduced, and the laser plasma effect has demonstrated its effectiveness in removing condensation and achieving low splice loss. We recommend fiber-to-fiber alignment using digital imaging techniques, but for PCF with core diameters of less than 5 µm, active alignment may be a better solution to ensure low offset misalignment. In the SMF-to-SMF splicing, the cohesive forces between the core and cladding make it possible to achieve self-alignment during fusion. However, the balancing of surface tension between the molten PCF and SMF is crucial for minimizing misalignment offsets. The melting power for the PCF depends very much on the absolute thickness of the silica and the size of the air holes; if the total cross section of the air holes is larger, lower laser power is required. Therefore, a computation of lasing power and exposure time must be carefully calculated for every new design of PCF.

References and links

1.

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996). [CrossRef] [PubMed]

2.

D. -L. Kim, M. Tomozawa, S. Dubois, and G. Orcel, “Fictive temperature measurement of single-mode optical-fiber core and cladding,” J. Lightwave Technol. 19, 1155–1158 (2001). [CrossRef]

3.

A. Ishikura, Y. Kato, T. Ooyanagi, and M. Miyauchi, “Loss factors analysis for single mode fiber splicing without core axis alignment,” J. Lightwave Technol. 7 (1989). [CrossRef]

4.

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

5.

T. Onodera, I. Suzuki, T. Yamada, Y. Osato, O. Watanabe, and T. Kato, “The development of an optical fiber splicer using a profile alignment system,” Fujikura Tech. Rev. (1987).

6.

W. Zheng, “Real time control of arc fusion for optical fiber splicing,” J. Lightwave Technol. 11 (1993). [CrossRef]

7.

S. A. Cooper and R. W. Erskine Jr., “Practical guidelines for mass splicing,” National Fiber Optic Engineers Conference, Technical Proceedings, 2001.

8.

A. K. Das and S. Bhattacharyya, “Low-loss fusion splices of optical fibers,” J. Lightwave Technol. LT-3, (1985).

9.

A. Ide, M. Tachikura, and Y. Nomura, “Fiber misalignment method by the reflected light from fibers,” J. Lightwave Technol. 8 (1990). [CrossRef]

10.

C. R. Kurkjian, J. T. Krause, and M. J. Mathewson, “Strength and fatigue of silica optical fibers,” J. Lightwave Technol. 7 (1989). [CrossRef]

11.

M. Tachikura and T. Haibara, “Devitrification effect on optical fiber strength reduction by fusion splicing,” J. Lightwave Technol. LT-3 (1985).

12.

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants , 16th ed. (Longman, New York, 1995).

13.

M. Bredol, D. Leers, L. Bosselaar, and M. Hutjens, “Improved model for OH absorption in optical fibers,” J. Lightwave Technol. 8 (1990). [CrossRef]

14.

S. Pradihan, A. Mazloom, J. Arbulich, and K. Srihari, “Minimization of splice loss between a single mode fiber and an erbium doped fiber,” Electronic Components and Technology Conference, 2002.

15.

K. Mima, H. A. Baldis, A. Nishiguchi, H. Takabe, and C. Yamanaka, Laser Plasma Theory and Simulation (Harwood Academic, Chur, Switzerland, 1994).

16.

P. J. Bennett, T. Monro, and D. J. Richchardson, “Toward practical holey fiber technology: fabrication, splicing, modeling, and characterization,” Opt. Lett. 24, 1203–1205 (1999). [CrossRef]

17.

J. T. Lizier and G. E. Town, “Splice losses in holey optical fibers,” IEEE Photon. Technol. Lett. 13 (2001). [CrossRef]

OCIS Codes
(220.4830) Optical design and fabrication : Systems design
(350.4600) Other areas of optics : Optical engineering

ToC Category:
Research Papers

History
Original Manuscript: April 24, 2003
Revised Manuscript: May 29, 2003
Published: June 16, 2003

Citation
Joo Hin Chong and M. Rao, "Development of a system for laser splicing photonic crystal fiber," Opt. Express 11, 1365-1370 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-12-1365


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References

  1. J.C. Knight, T.A. Birks, P.St.J. Russell and D.M. Atkin, "All-silica single-mode fiber with photonic crystal cladding," Opt.Lett. 21 1547-1549 (1996). [CrossRef] [PubMed]
  2. Dong-Lae Kim; M Tomozawa,.; Dubois, S.; Orcel, G.; ???Fictive temperature measurement of single-mode optical-fiber core and cladding??? J. Lightwave Technol. 19, 1155 ???1158 (2001). [CrossRef]
  3. A. Ishikura, Y. Kato, T. Ooyanagi and M. Miyauchi, ???Loss Factors Analysis for single mode Fiber Splicing without core axis Alignment,??? J. Lightwave Technol. 7, (1989). [CrossRef]
  4. T.A. Birks, J.C. Knight and P.St.J. Russell, "Endlessly single-mode photonic crystal fibre," Opt. Lett. 22, 961-963 (1997). [CrossRef] [PubMed]
  5. T. Onodera, I. Suzuki, T. Yamada, Y. Osato, O. Watanabe and T. Kato, ???The development of an optical fiber splicer using a profile alignment system,??? Fujikura Technical Review, 1987.
  6. W. Zheng, ???Real time control of arc fusion for optical fiber splicing,??? J. Lightwave Technol. 11, (1993). [CrossRef]
  7. S.A. Cooper, R.W. Erskine Jr., ???Practical guidelines for mass splicing,??? National Fiber Optic Engineers Conference, Technical Proceedings 2001.
  8. A.K. Das, S. Bhattacharyya, ???Low-loss fusion splices of optical fibers,??? J. Lightwave Technol. LT-3, (1985).
  9. A. Ide, M. Tachikura, and Y. Nomura, ???Fiber misalignment method by the reflected light from fibers, ??? J. Lightwave Technol. 8, (1990). [CrossRef]
  10. C.R. Kurkjian, J.T. Krause, and M.J. Mathewson, ???Strength and fatigue of silica optical fibers,??? J. Lightwave Technol. 7, (1989). [CrossRef]
  11. M. Tachikura and T. Haibara, ???Devitrification effect on optical fiber strength reduction by fusion splicing,??? J. Lightwave Technol. LT-3, (1985).
  12. G.W.C. Kaye & T.H. Laby, Tables of physical and chemical constants, 16th edition, Longman 1995
  13. M. Bredol, D. Leers, L. Bosselaar and M. Hutjens, ???Improved model for OH absorption in optical fibers,??? J. Lightwave Technol. 8, (1990). [CrossRef]
  14. S. Pradihan, A. Mazloom, J??? Arbulich & K.Srihari, ???Minimization of splice loss between a single mode fiber and an erbium doped fiber,??? Electronic Components and Technology Conference, 2002.
  15. K. Mima, H.A. Baldis, A. Nishiguchi, H. Takabe & C. Yamanaka, Laser plasma theory and Simulation, (Harwood Academic Publishers, 1994).
  16. P.J. Bennett, T. Monro, and D.J. Richchardson, ???Toward practical holey fiber technology: Fabrication, splicing, modeling, and characterization,??? Opt. Lett. 24, 1203-1205 (1999). [CrossRef]
  17. J.T. Lizier and G.E. Town, ???Splice Losses in Holey Optical Fibers,??? IEEE Photonics Technol. Lett. 13, (2001). [CrossRef]

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