Loss properties due to Rayleigh scattering in different types of fiber

doi:10.1364/OE.11.000039

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Loss properties due to Rayleigh scattering in different types of fiber

Wang Zhi, Ren Guobin, Lou Shuqin, and Jian Shuisheng »View Author Affiliations

Optics Express, Vol. 11, Issue 1, pp. 39-47 (2003)
http://dx.doi.org/10.1364/OE.11.000039

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Abstract

The effects of fiber structure on Rayleigh scattering were investigated in detail. Some step-index fibers such as GeO_2- and F-doped silica-based fibers and total-internal-reflection photonic crystal fiber are examined. The Rayleigh scattering loss (RSL) depends on the fiber materials and index profiles, and different types of fiber have different dependencies on those parameters because of the different optical power confinement factors in every layer. On the basis of these results, the RSL can be optimized by adjusting the fiber structure or by selecting different materials.

[Optical Society of America ]

1. Introduction

Silica-based optical fibers are used throughout the world for large-capacity and long-distance transmission systems with erbium-doped fiber amplifiers (EDFAs). Fiber loss reduction will accelerate the construction of various transmission systems with longer repeater spacing.

With the development of fiber fabrication techniques, it becomes possible to reduce optical losses, such as OH^- absorption loss, induced by impurities in optical fiber; an optical loss as low as 0.154dB/km @1560 nm has been obtained [1

H. Kanamori, H. Yokota, G. Tanaka, M. Watanabe, Y. Ishiguro, I. Yoshida, T. Kakii, S. Ito, Y. Asano, and S. Tanaka, “Transmission characteristics and reliability of pure-SiO₂-core single-mode fibers,” J. Lightwave Technol. 4, 1144–1150 (1986). [CrossRef]

]. To reduce the additional imperfection loss, the viscosity-matching technique has been proposed, which utilized the dopants GeO₂ and fluoride (F) to match the core and cladding viscosity [2

M. Tateda, M. Ohashi, K. Jajima, and K. Shiraki, “Design of viscosity matched optical fibers,” Photon. Technol. Lett. 4, 1023–1025 (1992). [CrossRef]

–3

M. Ohashi, M. Tadeda, K. Shiraki, and K. Tajima, “Imperfection loss reduction in viscosity-matched optical fibers,” Photon. Technol. Lett. 5, 1532–1535 (1993). [CrossRef]

]. Rayleigh scattering loss (RSL), which has also been investigated in detail, accounts for the majority of fiber loss in the 1550-nm wavelength region [4

K. Tsujikawa, K. Tajima, and M. Ohashi, “Rayleigh scattering reduction method for silica-based optical fiber,” J. Lightwave Technol. 18, 1528–1532 (2000). [CrossRef]

–9

M.E. Lines, “Scattering losses in optic fiber materials (I. A new parametrization),” J. Appl. Phys. 55, 4052–4057 (1984). [CrossRef]

]. It was found that the Rayleigh scattering of glass/silica depends on the fictive temperature [9

M.E. Lines, “Scattering losses in optic fiber materials (I. A new parametrization),” J. Appl. Phys. 55, 4052–4057 (1984). [CrossRef]

]; moreover, it has been reported that Rayleigh scattering in optical fibers can be reduced by lowering the fictive temperature [6

K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, “Effect of thermal treatment on Rayleigh scattering in silica-based glasses,” Electron. Lett. 31, 1940–1941 (1995). [CrossRef]

K. Tajima, “Low-loss optical fibers realized by reduction of Rayleigh scattering loss,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 305–306.

M.E. Lines, “Scattering losses in optic fiber materials (I. A new parametrization),” J. Appl. Phys. 55, 4052–4057 (1984). [CrossRef]

], which can be achieved by annealing treatment or by lowering the fiber-drawing temperature [4

K. Tsujikawa, K. Tajima, and M. Ohashi, “Rayleigh scattering reduction method for silica-based optical fiber,” J. Lightwave Technol. 18, 1528–1532 (2000). [CrossRef]

K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, “Effect of thermal treatment on Rayleigh scattering in silica-based glasses,” Electron. Lett. 31, 1940–1941 (1995). [CrossRef]

,10

P. Guenot, P. Nouchi, and B. Poumellec, “Influence of drawing temperature on light scattering properties of single-mode fibers,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1999), pp. 84–86.

In this paper, the effects of the fiber structure on Rayleigh scattering were investigated in detail, including some step-index fibers, such as GeO_2- and F-doped silica-based fibers and total-internal-reflection (TIR) photonic crystal fiber (PCF). The RSL depends on fiber materials and index profiles, and different fiber types have different dependencies on those parameters. From these results, we can optimize RSL by adjusting the optical power confinement in the fibers.

2. Fiber Loss

The spectral loss of an optical fiber can be expressed as

α = α_{R} + α_{IM} + α_{OH} + α_{IR} + α_{UV} + α_{im},

(1)

where α _R is the RSL, α _IM the imperfection loss, α _OH the OH^- absorption loss, α _IR the infrared absorption loss, α _UV the ultraviolet absorption loss, and α _im the absorption loss of other impurities. The infrared absorption loss is given by α _IR =C exp(-D/λ) [8

M. Ohashi, K. Shiraki, and K. Tajima, “Optical loss property of silica-based single-mode fibers,” J. Lightwave Technol. 10, 539–543 (1992). [CrossRef]

], where coefficients C and D are dependent on materials. The OH^- absorption spectrum in optical fibers between 1200 and 1550 nm has been modeled. It can be fitted with high accuracy to the sum of four Lorentz components and one Gaussian component [11

M. Bredol, D. Leers, L. Bosselaar, and M. Hutjens, “Improved model for OH absorption in optical fibers,” J. Lightwave Technol. l8, 1536–1540 (1990). [CrossRef]

]. It has been reported that α _OH can be greatly reduced by many fabrication processes, such as all wave fiber fabricated by MCVD. Absorption by the UV tail of germanium (α _UV ) can be ignored because it is very small in the low-loss window. α _IM and α _im can be also ignored because they can be reduced to almost zero by improving the fiber fabrication techniques.

The RSL is proportional to λ^-4 and to the light intensity propagating in the fiber and is given by the light intensity P(r) and Rayleigh scattering coefficient A(r) (RSC) in the radial distance r as [8

M. Ohashi, K. Shiraki, and K. Tajima, “Optical loss property of silica-based single-mode fibers,” J. Lightwave Technol. 10, 539–543 (1992). [CrossRef]

]

α_{R} = \frac{\frac{1}{λ^{4}} \int_{0}^{+ \infty} A (r) P (r) r d r}{\int_{0}^{+ \infty} P (r) r d r} .

(2)

3. Rayleigh Scattering Coefficient of Fibers

From Eq. (2), we can introduce a parameter Ā as the average RSC of the fiber; this can be expressed as Eq. (3):

\bar{A} \equiv \frac{\int_{0}^{+ \infty} A (r) P (r) r d r}{\int_{0}^{+ \infty} P (r) r d r} .

(3)

The RSCs of fiber preforms can be measured and then fitted as a function of the dopant concentration, i.e., the relative refractive-index difference between the pure silica glass and the fiber preform induced by GeO₂ and fluoride. The RSC of GeO₂ and fluoride codoped silica glass is reported to be [5

K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, “Scattering property of F and GeO2 codoped silica glasses,” Electron. Lett. 30, 351–352 (1994). [CrossRef]

]

A (r) = A_{0} (1 + 0.62 [{GeO}_{2}] + 0.60 {[F]}^{2} + 0.44 [{GeO}_{2}] {[F]}^{2}),

(4)

where A ₀, discussed in many articles [4

K. Tsujikawa, K. Tajima, and M. Ohashi, “Rayleigh scattering reduction method for silica-based optical fiber,” J. Lightwave Technol. 18, 1528–1532 (2000). [CrossRef]

K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, “Effect of thermal treatment on Rayleigh scattering in silica-based glasses,” Electron. Lett. 31, 1940–1941 (1995). [CrossRef]

–9

M.E. Lines, “Scattering losses in optic fiber materials (I. A new parametrization),” J. Appl. Phys. 55, 4052–4057 (1984). [CrossRef]

], is the RSC of pure silica glass; in this paper, A ₀=0.8 dB/km.µm⁴, and [GeO₂] and [F] are the dopant concentrations of GeO₂ and fluoride, respectively.

According to Sellmeier’s law [12

A.W. Snyder, Optical Waveguide Theory (Chapman and Hall, New York, 1983).

] and Flemming’s interpolation equation [13

G. Cancellieri, Single Mode Optical Fibers (Pergamon, New York, 1991).

], at the radial distance r, the relationship between the relative refractive-index difference Δ(r) and the dopant concentration D(r) can be expressed as Eq. (5):

Δ (r) = C_{0} D (r) + C_{1},

(5)

where D(r) is [GeO₂] or [F] and constants C ₀ and C ₁ are dependent on the dopant materials. Substituting Eq. (5) into Eq. (4), and neglecting the higher-order term, the RCS will be [8

M. Ohashi, K. Shiraki, and K. Tajima, “Optical loss property of silica-based single-mode fibers,” J. Lightwave Technol. 10, 539–543 (1992). [CrossRef]

]

A (r) = {\begin{matrix} A_{0} (1 + 41 ∣ Δ (r) ∣) & for F-doped glass \\ A_{0} (1 + 44 ∣ Δ (r) ∣) & for {GeO}_{2} -doped glass \end{matrix} .

(6)

It is found that the RSC increases as the dopant increases and that the dependence is the same for F- and GeO₂-doped glass. This is because concentration increases with increasing dopant added to the silica. For GeO₂-doped fibers, the refractive index increases as the dopant of GeO₂ increases. On the other hand, the refractive index of F-doped glass decreases as the F concentration increases.

Comparing Eqs. (4) and (6), there exists divergence for F-doped fiber. A(r) increases linearly with [GeO₂] and parabolically with [F] in Eq. (4), but linearly with both Δ in Eq (6). We do not further pursue this question or use of Eq. (6) in this paper.

Referring to the optical fiber, which has the step-index profile, the RSCs are different in every layer because of different dopants. The average RSC of the fiber can be derived from Eq. (3) and expanded as the sum of Eq. (7):

\bar{A} = \frac{\int_{0}^{r_{1}} A_{1} (r) P (r) r d r + \int_{r_{1}}^{r_{2}} A_{2} (r) P (r) r d r + \dots + \int_{r_{m - 1}}^{+ \infty} A_{m} (r) P (r) r d r}{\int_{0}^{+ \infty} P (r) r d r}

= A_{1} \frac{\int_{0}^{r_{1}} P (r) r d r}{\int_{0}^{+ \infty} P (r) r d r} + A_{2} \frac{\int_{r_{1}}^{r_{2}} P (r) r d r}{\int_{0}^{+ \infty} P (r) r d r} + \dots + A_{m} \frac{\int_{r_{m - 1}}^{+ \infty} P (r) r d r}{\int_{0}^{+ \infty} P (r) r d r} \equiv \sum_{i = 1}^{m} A_{i} Γ_{i},

(7)

where i denotes the ith layer from the fiber core (i = 1) to the out-cladding (i=m); A_i is the RSC in the ith layer, which can be obtained from Eq. (7) and is assumed to be constant for every layer; and Γ _i is the optical power confinement factor in the ith layer.

4. Estimation of Rayleigh Scattering Loss

On the basis of the RSC of preform prepared for fibers, the loss property due to dopant, drawing temperature, and drawing tension has been investigated in detail [4

K. Tsujikawa, K. Tajima, and M. Ohashi, “Rayleigh scattering reduction method for silica-based optical fiber,” J. Lightwave Technol. 18, 1528–1532 (2000). [CrossRef]

K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, “Effect of thermal treatment on Rayleigh scattering in silica-based glasses,” Electron. Lett. 31, 1940–1941 (1995). [CrossRef]

,10

,11

M. Bredol, D. Leers, L. Bosselaar, and M. Hutjens, “Improved model for OH absorption in optical fibers,” J. Lightwave Technol. l8, 1536–1540 (1990). [CrossRef]

]. In this section, we discuss the RSL caused by the optical property of different fibers with different dopants and different index profiles.

4.1 GeO₂-Doped Silica-Based SMF (G.652)

Fig. 1. Refractive-index profile of G652 fiber.

ITU-T G.652 fiber is a GeO₂-doped core, pure silica cladding fiber; its Rayleigh scattering loss index profile is shown as Fig. 1. Its RSC can be expressed as Eq. (8), referring to Eq. (6) and Eq. (7):

\bar{A} = A_{0} (1 + 44 Δ) Γ_{1} + A_{0} (1 - Γ_{1}) = A_{0} (1 + 44 Δ Γ_{1}) .

(8)

For single-cladding step-index fiber, Γ₁, the power confinement factor in the core of the fundamental mode LP₀₁ depends on the fiber structure parameters (a and Δ) and on the propagation constant β. According to the solution of the scalar-wave equations of step-index weakly guided fiber, as discussed in many books on optical waveguides, Γ₁ can be expressed as Eq. (9):

Γ_{1} \equiv \frac{\int_{0}^{2 π} \int_{0}^{a} (E \times H) \cdot \hat{z} r d r d φ}{\int_{0}^{2 π} \int_{0}^{+ \infty} (E \times H) \cdot \hat{z} r d r d φ} = \frac{β^{2} - k_{0}^{2} n_{0}^{2}}{k_{0}^{2} n_{1}^{2} - k_{0}^{2} n_{0}^{2}} [1 + \frac{J_{0}^{2} (U)}{J_{1}^{2} (U)}],

(9)

where E and H are the electric field and the magnetic field, respectively; ẑ denotes unit vector along the longitudinal direction of the fiber; k ₀=2π/λ is the wave number in vacuum; U ²=a ²[

{k_{0}}^{2}

{n_{0}}^{2}

/(1–2Δ)-β²]; the relative refractive-index difference is defined as Δ=(

{n_{1}}^{2}

{n_{0}}^{2}

)/2

{n_{1}}^{2}

; and J _i(U) (i=0,1) is the ith-order Bessel function. Then the RSC can be expressed as Eq. (10) after substituting Eq. (9) into Eq. (8):

\bar{A} = A_{0} + 44 A_{0} \frac{W^{2} (1 - 2 Δ)}{2 k_{0}^{2} n_{0}^{2} a^{2}} [1 + \frac{J_{0}^{2} (U)}{J_{1}^{2} (U)}],

(10)

where W ²=a ²(β²-

{k_{0}}^{2}

{n_{0}}^{2}

Fig. 2. Relationship between a and RSL for SMF.

Fig. 3. Relationship between Δ and RSL for SMF.

From Eq. (10), the dependence of the relative-refractive index difference Δ and the fiber core radius a can be obtained through numerical computation. Figure 2 shows the relationship between a and RSL at 1550 nm for various Δ. Figure 3 shows the relationship between Δ and RSL at 1550 nm for various a. It is found from Figs. 2 and 3 that the loss limitation due to Rayleigh scattering is ~0.153 dB/km for conventional fibers with Δ of 0.3%, a of 4.5 µm. It is also shown that the RSL increases as Δ increases or a increases, i.e., the fiber parameters greatly influence the optical loss, but the dependence of Δ is larger than that of the core radius for GeO₂-doped fibers. This is because the RSC of the core increases as Δ increases, and because Γ₁ increases as Δ or a increases. These are discussed in detail in Ref. [8

M. Ohashi, K. Shiraki, and K. Tajima, “Optical loss property of silica-based single-mode fibers,” J. Lightwave Technol. 10, 539–543 (1992). [CrossRef]

4.2 Pure Silica Core Fiber

Fig. 4. Refractive-index profile of PSCF

Figure 4 shows the refractive-index profile of the pure silica core fiber (PSCF) with depressed cladding; the core is pure silica, and the inner cladding and the outer cladding are F-doped. It is well known that the depressed cladding is introduced to a large effective area (A_eff ) to improve the bending characteristics by confining the optical power into the core [14

T. Kato, M. Hirano, M. Onishi, and M. Nishimura, “Ultra low nonlinearity low loss pure silica core fiber for long-haul WDM transmission,” in Optical Fiber Communication Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 95–97.

According to Eq. (7), the average RSC for the PSCF can be expressed as

\bar{A} = A_{0} Γ_{1} + A_{0} (1 + 41 ∣ Δ^{+} - Δ^{-} ∣) Γ_{2} + A_{0} (1 + 41 ∣ Δ^{+} ∣) Γ_{3}

\approx A_{0} [1 + 41 ∣ Δ^{+} - Δ^{-} ∣ (1 - Γ_{1})] .

(11)

The third term on the right-hand side of Eq. (11) is ignored because the power confinement factor in the out-cladding is very small. Thus the PSCF fiber can be treated as a step-index fiber with parameter a and Δ ≡ |Δ⁺-Δ^-|, and Γ₁ can be obtained from Eq. (9) as well. As a result, Eq. (11) will have the form

\bar{A} = A_{0} + \frac{41 A_{0}}{2 k_{0}^{2} n_{0}^{2} a^{2}} [U^{2} - \frac{W^{2} J_{0}^{2} (U)}{J_{1}^{2} (U)}],

(12)

where U ²=a ²[

{k_{0}}^{2}

{n_{0}}^{2}

-β²], W ²=a ²[β²-

{k_{0}}^{2}

{n_{0}}^{2}

(1–2Δ)], Δ=(

{n_{0}}^{2}

n_{2}^{2}

)/2

{n_{0}}^{2}

Fig. 5. Relationship between a and RSL for PSCF.

Fig. 6. Relationship between Δ and RSL for PSCF.

Fig. 7. Derivation of RSC to Δ for PSCF.

Figure 5 shows the relation between a and RSL at 1550 nm for various Δ, and Fig. 6 shows the relation between Δ and RSL at 1550 nm for various a. It is found that the RSL decreases because Γ₁ increases with increase of a. As shown in Figs. 5 and 6, when the fiber core is narrower, for example, a < 3 µm, RSL increases as Δ increases, but when a > 3 µm, RSL decreases as Δ increases. For clarity and simplicity, the derivation of the RSC of PSCF to the relative-index difference, i.e., ∂Ā/∂Δ, at 1550 nm, will be derived in the following progression.

In Eq. (12), all parameters, except U, W, and β, are independent of Δ; thus we can write ∂Ā/∂U as follows:

\frac{\partial \bar{A}}{\partial Δ} = \frac{\partial \bar{A}}{\partial U} \frac{\partial U}{\partial Δ} + \frac{\partial \bar{A}}{\partial W} \frac{\partial W}{\partial Δ},

(13)

where ∂Ā/∂U and ∂Ā/∂W can be obtained from Eq. (12) and expanded as

\frac{\partial \bar{A}}{\partial U} = \frac{41 A_{0}}{k_{0}^{2} n_{0}^{2} a^{2}} {U + \frac{W^{2} J_{0} (U)}{J_{1}^{3} (U)} [J_{1}^{2} (U) - \frac{J_{0} (U) J_{2} (U)}{2} + \frac{J_{0}^{2} (U)}{2}]},

\frac{\partial \bar{A}}{\partial W} = - \frac{41 A_{0}}{k_{0}^{2} n_{0}^{2} a^{2}} \frac{J_{0}^{2} (U)}{J_{1}^{2} (U)} W .

(14)

U and W are the structural parameters of optical fibers, and they depend on Δ. The derivation of U or W to Δ can be calculated from their definitions and expressed as

\frac{\partial U}{\partial Δ} = \frac{1}{2 U} \frac{\partial U^{2}}{\partial Δ} = - \frac{a^{2} β}{U} \frac{\partial β}{\partial Δ},

\frac{\partial W}{\partial Δ} = \frac{1}{2 W} \frac{\partial W^{2}}{\partial Δ} = \frac{a^{2} β}{W} \frac{\partial β}{\partial Δ} + \frac{k_{0}^{2} n_{0}^{2} a^{2}}{W},

(15)

where ∂β/∂Δ is the derivation of β to Δ; this can be obtained by solving the scalar wave equation of step-index fiber.

From Eq. (13) to Eq. (15), ∂Ā/∂Δ is calculated and plotted in Fig. 7 for various fiber core radii. The figure shows that for greater a (4 µm, 7 µm in Fig.7), ∂Ā/∂Δ is negative, i.e., Ā decreases as Δ increases, and for thinner fiber core [2 µm, 3µm in Fig.4(c)], ∂Ā/∂Δ is positive when Δ is not too high, i.e., Ā increases as Δ increases. From these findings we can determine that there is an optimized Δ for certain a. For example, when a=2 µm, the first zero point of ∂Ā/∂Δ is ~Δ=0.36%, i.e., PSCF fiber with parameters (a=2 µm, Δ ≈ 0.36%) has the lowest RSL. Another example is a=3 µm, Δ ≈ 0.24%.

In general, both parameters a and Δ influence the optical loss, but the core radius dependence is larger than that of the refractive-index difference for F-doped fibers.

4.3 Total-Internal-Reflection Guided Photonic Crystal Fiber

A promising new field in optical fiber technology has appeared within the past few years through the realization of so-called PCF. The recently fabricated PCF has been design following the model of a triangular photonic crystal cladding structure and centrally a single, missing air hole forming the core, as shown in Fig. 8. Remarkable properties for this type of PCF have been reported, for example, single-mode operation over an unusually wide wavelength range (at least 337–1550 nm) [15

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am A 15, 748–752 (1998). [CrossRef]

], and many other properties significantly different from standard optical fibers are expected [16

S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 117–119.

,17

A. Bjarklev, Jes Broeng, Kim Dridi, and Stig E. Barkou, “Dispersion properties of photonic crystal fibres,” in European Conference on Optical Communication (Madrid, Spain, 1998), pp. 135–136.

]. However, it is important to note that no photonic bandgap (PBG) effects occur in these PCFs. This is because the fundamental mode confined to the high-index core region experiences the surrounding photonic crystal cladding as a medium with an effectively lower index, thereby allowing total internal reflection (TIR) to take place. An effective-index model [15

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am A 15, 748–752 (1998). [CrossRef]

,18

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

] for the TIR PCF was presented a few years ago, and we will use this model to investigate the RCL property of the TIR PCFs.

Fig. 8. TIR PCF cross section.

Fig. 9. Effective refractive-index profile of TIR PCF.

According to the effective-index model, the effective refractive index n_eff in the photonic crystal cladding can be obtained by solving the scalar-wave equations within a unit cell centered on one of the holes. We can establish an effective step-index profile for the PCFs as shown in Fig. 9. The effective core radius is a=0.625D [19

T. A. Birks, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1999), pp. 114–116.

], and the effective relative refractive-index difference is

Δ_{eff} \equiv \frac{n_{0}^{2} - n_{eff}^{2}}{2 n_{0}^{2}} .

(16)

Then, through the same processing as with GeO₂-doped or F-doped fibers, the average RSC of TIR PCFs can be obtained and expressed as

\bar{A} = A_{0} Γ_{1} + A_{2} (1 - Γ_{1}) = A_{2} - Γ_{1} (A_{2} - A_{1}),

(17)

where A ₂ is the effective RSC in the photonic crystal cladding. A ₂ is usually much larger than A ₀ [20

L. Farr, J.C. Knight, B.J. Mangan, and P.J. Roberts, “Low loss photonic crystal fibre,” in European Conference on Optical Communication (Copenhagen, Denmarak, 2002), PD1.3.

,21

K. Tajima, K. Nakajima, K. Kurokawa, N. Yoshizawa, and M. Ohashi, “Low loss photonic crystal fibers,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 523–524.

]. It is a reasonable hypothesis that A ₂ depends on the background material and the air filling ratio d/D. For the case of simplicity, it is assumed to be a constant of 4.0 dB/km.um⁴ in this paper.

Figure 10 shows the relationship between the nearest-neighbor hole spacing D and RSL at 1550 nm for various d/D, and Fig. 11 shows the relationship between d/D and RSL at 1550 nm for various D. From Fig. 10 and Fig. 11, the RSL decreases as D increases or d/D increases. This is because Γ₁ increases as D increases or d/D increases.

Fig. 10. Relationship between D and RSL for PCF.

Fig. 11. Relationship between d/D and RSL for PCF.

5. Discussion

5.1 Rayleigh Scattering Loss of Doped Silica-Based Fibers

The RSL of GeO₂-doped silica-based fiber is greater than that of F-doped silica-based fiber, because there is major power confined to the pure silica core of the PSCF where the RSC is the lowest. We have estimated a RSL of 0.153 dB/km for GeO₂-doped fiber and 0.142 dB/km for PSCF when the fiber structure parameters are the same as a=4.5 µm, Δ=0.3% (shown in Figs. 2, 3, 5–7). Many different records have been recorded for the lowest RSL for F-doped fibers, such as 0.128 dB/km [22

K. Nagayama, T. Saitoh, M. Kahui, K. Kawasaki, M. Matsui, H. Takamizawa, and H. Miyaki, “Ultra low loss (0.151dB/km) fiber and its impact on submarine transmission systems,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), Postdeadline papers, FA10.

], 0.142 dB/km [4

K. Tsujikawa, K. Tajima, and M. Ohashi, “Rayleigh scattering reduction method for silica-based optical fiber,” J. Lightwave Technol. 18, 1528–1532 (2000). [CrossRef]

], and 0.11 dB/km [23

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Novel hole-assisted lightguided fiber exhibiting large anomalous dispersion and low loss below 1 dB/km,” in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), PD5.

]. The reason for such variation is that the researchers used different A ₀, the RSC of pure silica as it varies with the fabrication process.

5.2 Rayleigh Scattering Loss of Total-Internal-Reflection Photonic Crystal Fiber

In Ref. [20

L. Farr, J.C. Knight, B.J. Mangan, and P.J. Roberts, “Low loss photonic crystal fibre,” in European Conference on Optical Communication (Copenhagen, Denmarak, 2002), PD1.3.

], two PCFs with RSLs of 0.36 dB/km and 0.18 dB/km were fabricated. They have different D (3.2 and 4.2 µm, respectively) with the same d/D=0.44.In this paper, it can be understood qualitatively that the RSL decreases as D increases. There are some errors between our estimation and the experiments, because the average RSC in the photonic crystal cladding A ₂ cannot be set accurately.

5.3 Power Confinement Factor of G.652 Fiber and Total-Internal-Reflection Photonic Crystal Fiber

As discussed in above, the power confinement factor will be predominant when we consider the RSL of a fiber, and each layer of the fiber will contribute its own characteristic to the RSL. Figure 12 illustrates the power confinement factor in the core region of G.652 fiber (SMF) and TIR PCF, with structural parameters (a=4.5 µm, Δ=0.3%) and (D=2.3 µm, d/D=0.6), respectively. It can be found that Γ₁ of the TIR PCF is greater than that of the single step-index G.652 fiber (SMF). As we know, when the fiber core is pure silica, the RSL decreases as Γ₁ increases, so the RSL of TIR PCF will possibly be less than that of the PSCF and much less than that of the G.652 fiber. Hence we can design TIR PCF for low-loss transmission systems based on consideration of the power confinement factor.

Fig. 12. Power confinement factor in the core region.

6. Conclusion

In this paper the effect of the fiber structure on Rayleigh scattering has been investigated in detail. Three different fibers, GeO_2- and F-doped silica-based fibers and total-internal-reflection photonic crystal fiber (PCF), are included here. The RSL depends on fiber materials and on index profiles, and different types of fiber have different dependencies on those parameters because of different optical power confinement factors in every layer. For GeO₂-doped fiber, RSL increases as the fiber core radius increases or as the relative index difference increases. For F-doped PSCF, RSL decreases as the fiber core radius increases, and it varies in a complicated manner with the dopant concentration. For TIR PCF, RSL decreases as the hole spacing increases or as the air filling ratio increases. From these results, we can design and fabricate the optimized fiber with the best loss property.

References and links

1.	H. Kanamori, H. Yokota, G. Tanaka, M. Watanabe, Y. Ishiguro, I. Yoshida, T. Kakii, S. Ito, Y. Asano, and S. Tanaka, “Transmission characteristics and reliability of pure-SiO₂-core single-mode fibers,” J. Lightwave Technol. 4, 1144–1150 (1986). [CrossRef]
2.	M. Tateda, M. Ohashi, K. Jajima, and K. Shiraki, “Design of viscosity matched optical fibers,” Photon. Technol. Lett. 4, 1023–1025 (1992). [CrossRef]
3.	M. Ohashi, M. Tadeda, K. Shiraki, and K. Tajima, “Imperfection loss reduction in viscosity-matched optical fibers,” Photon. Technol. Lett. 5, 1532–1535 (1993). [CrossRef]
4.	K. Tsujikawa, K. Tajima, and M. Ohashi, “Rayleigh scattering reduction method for silica-based optical fiber,” J. Lightwave Technol. 18, 1528–1532 (2000). [CrossRef]
5.	K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, “Scattering property of F and GeO2 codoped silica glasses,” Electron. Lett. 30, 351–352 (1994). [CrossRef]
6.	K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, “Effect of thermal treatment on Rayleigh scattering in silica-based glasses,” Electron. Lett. 31, 1940–1941 (1995). [CrossRef]
7.	K. Tajima, “Low-loss optical fibers realized by reduction of Rayleigh scattering loss,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 305–306.
8.	M. Ohashi, K. Shiraki, and K. Tajima, “Optical loss property of silica-based single-mode fibers,” J. Lightwave Technol. 10, 539–543 (1992). [CrossRef]
9.	M.E. Lines, “Scattering losses in optic fiber materials (I. A new parametrization),” J. Appl. Phys. 55, 4052–4057 (1984). [CrossRef]
10.	P. Guenot, P. Nouchi, and B. Poumellec, “Influence of drawing temperature on light scattering properties of single-mode fibers,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1999), pp. 84–86.
11.	M. Bredol, D. Leers, L. Bosselaar, and M. Hutjens, “Improved model for OH absorption in optical fibers,” J. Lightwave Technol. l8, 1536–1540 (1990). [CrossRef]
12.	A.W. Snyder, Optical Waveguide Theory (Chapman and Hall, New York, 1983).
13.	G. Cancellieri, Single Mode Optical Fibers (Pergamon, New York, 1991).
14.	T. Kato, M. Hirano, M. Onishi, and M. Nishimura, “Ultra low nonlinearity low loss pure silica core fiber for long-haul WDM transmission,” in Optical Fiber Communication Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 95–97.
15.	J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am A 15, 748–752 (1998). [CrossRef]
16.	S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 117–119.
17.	A. Bjarklev, Jes Broeng, Kim Dridi, and Stig E. Barkou, “Dispersion properties of photonic crystal fibres,” in European Conference on Optical Communication (Madrid, Spain, 1998), pp. 135–136.
18.	T. A. Birks, J. C. Knight, and P. St. J. Russel, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]
19.	T. A. Birks, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1999), pp. 114–116.
20.	L. Farr, J.C. Knight, B.J. Mangan, and P.J. Roberts, “Low loss photonic crystal fibre,” in European Conference on Optical Communication (Copenhagen, Denmarak, 2002), PD1.3.
21.	K. Tajima, K. Nakajima, K. Kurokawa, N. Yoshizawa, and M. Ohashi, “Low loss photonic crystal fibers,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 523–524.
22.	K. Nagayama, T. Saitoh, M. Kahui, K. Kawasaki, M. Matsui, H. Takamizawa, and H. Miyaki, “Ultra low loss (0.151dB/km) fiber and its impact on submarine transmission systems,” in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), Postdeadline papers, FA10.
23.	T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Novel hole-assisted lightguided fiber exhibiting large anomalous dispersion and low loss below 1 dB/km,” in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), PD5.
24.	K. Tajima, M. Ohashi, K. Shiraki, M. Tateda, and S. Shibata, “Low Rayleigh scattering P₂O₅-F-SiO₂ glasses,” J. Lightwave Technol. 10, 1532–1535 (1992). [CrossRef]

OCIS Codes
(060.2400) Fiber optics and optical communications : Fiber properties
(290.5870) Scattering : Scattering, Rayleigh

ToC Category:
Research Papers

History
Original Manuscript: November 21, 2002
Revised Manuscript: December 27, 2002
Published: January 13, 2003

Citation
Wang Zhi, Ren Guobin, Lou Shuqin, and Jian Shuisheng, "Loss properties due to Rayleigh scattering in different types of fiber," Opt. Express 11, 39-47 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-1-39

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References

H. Kanamori, H. Yokota, G. Tanaka, M. Watanabe, Y. Ishiguro, I. Yoshida, T. Kakii, S. Ito, Y. Asano, and S. Tanaka, �??Transmission characteristics and reliability of pure-SiO2-core single-mode fibers,�?? J. Lightwave Technol. 4, 1144-1150 (1986). [CrossRef]
M. Tateda, M. Ohashi, K. Jajima, and K. Shiraki, �??Design of viscosity matched optical fibers,�?? Photon. Technol. Lett. 4, 1023-1025 (1992). [CrossRef]
M. Ohashi, M. Tadeda, K. Shiraki, and K. Tajima, �??Imperfection loss reduction in viscosity-matched optical fibers,�?? Photon. Technol. Lett. 5, 1532-1535 (1993). [CrossRef]
K. Tsujikawa, K. Tajima, and M. Ohashi, �??Rayleigh scattering reduction method for silica-based optical fiber,�?? J. Lightwave Technol. 18, 1528-1532 (2000). [CrossRef]
K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, �??Scattering property of F and GeO2 codoped silica glasses,�?? Electron. Lett. 30, 351-352 (1994). [CrossRef]
K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, �??Effect of thermal treatment on Rayleigh scattering in silica-based glasses,�?? Electron. Lett. 31, 1940-1941 (1995). [CrossRef]
K. Tajima, �??Low-loss optical fibers realized by reduction of Rayleigh scattering loss,�?? in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 305-306.
M. Ohashi, K. Shiraki, and K. Tajima, �??Optical loss property of silica-based single-mode fibers,�?? J. Lightwave Technol. 10, 539-543 (1992). [CrossRef]
M.E. Lines, �??Scattering losses in optic fiber materials (I. A new parametrization),�?? J. Appl. Phys. 55, 4052-4057 (1984). [CrossRef]
P. Guenot, P. Nouchi, and B. Poumellec, �??Influence of drawing temperature on light scattering properties of single-mode fibers,�?? in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1999), pp. 84-86.
M. Bredol, D. Leers, L. Bosselaar, and M. Hutjens, �??Improved model for OH absorption in optical fibers,�?? J. Lightwave Technol. 18, 1536-1540 (1990). [CrossRef]
A.W. Snyder, Optical Waveguide Theory (Chapman and Hall, New York, 1983).
G. Cancellieri, Single Mode Optical Fibers (Pergamon, New York, 1991).
T. Kato, M. Hirano, M. Onishi, and M. Nishimura, �??Ultra low nonlinearity low loss pure silica core fiber for long-haul WDM transmission,�?? in Optical Fiber Communication Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 95-97.
J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, �??Properties of photonic crystal fiber and the effective index model,�?? J. Opt. Soc. Am A 15, 748-752 (1998). [CrossRef]
S. E. Barkou, J. Broeng, and A. Bjarklev, �??Dispersion properties of photonic bandgap guiding fibers,�?? in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 117-119.
A. Bjarklev, Jes Broeng, Kim Dridi, and Stig E. Barkou, �??Dispersion properties of photonic crystal fibres,�?? in European Conference on Optical Communication (Madrid, Spain, 1998), pp. 135-136.
T. A. Birks, J. C. Knight, and P. St. J. Russel, �??Endlessly single-mode photonic crystal fiber,�?? Opt. Lett. 22, 961-963 (1997). [CrossRef] [PubMed]
T. A. Birks, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, �??The analogy between photonic crystal fibres and step index fibres,�?? in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1999), pp. 114-116.
L. Farr, J.C. Knight, B.J. Mangan, and P.J. Roberts, �??Low loss photonic crystal fibre,�?? in European Conference on Optical Communication (Copenhagen, Denmarak, 2002), PD1.3.
K. Tajima, K. Nakajima, K. Kurokawa, N. Yoshizawa, and M. Ohashi, �??Low loss photonic crystal fibers,�?? in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 523-524.
K. Nagayama, T. Saitoh, M. Kahui, K. Kawasaki, M. Matsui, H. Takamizawa, and H. Miyaki, �??Ultra low loss (0.151dB/km) fiber and its impact on submarine transmission systems,�?? in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), Postdeadline papers, FA10.
T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, �??Novel hole-assisted lightguided fiber exhibiting large anomalous dispersion and low loss below 1 dB/km,�?? in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), PD5.
K. Tajima, M. Ohashi, K. Shiraki, M. Tateda, and S. Shibata, �??Low Rayleigh scattering P2O5-F-SiO2 glasses,�?? J. Lightwave Technol. 10, 1532-1535 (1992). [CrossRef]

Electron. Lett.

K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, �??Scattering property of F and GeO2 codoped silica glasses,�?? Electron. Lett. 30, 351-352 (1994). [CrossRef]
K. Tsujikawa, M. Ohashi, K. Shiraki, and M. Tateda, �??Effect of thermal treatment on Rayleigh scattering in silica-based glasses,�?? Electron. Lett. 31, 1940-1941 (1995). [CrossRef]

J. Appl. Phys.

M.E. Lines, �??Scattering losses in optic fiber materials (I. A new parametrization),�?? J. Appl. Phys. 55, 4052-4057 (1984). [CrossRef]

J. Lightwave Technol.

K. Tsujikawa, K. Tajima, and M. Ohashi, �??Rayleigh scattering reduction method for silica-based optical fiber,�?? J. Lightwave Technol. 18, 1528-1532 (2000). [CrossRef]
M. Ohashi, K. Shiraki, and K. Tajima, �??Optical loss property of silica-based single-mode fibers,�?? J. Lightwave Technol. 10, 539-543 (1992). [CrossRef]
H. Kanamori, H. Yokota, G. Tanaka, M. Watanabe, Y. Ishiguro, I. Yoshida, T. Kakii, S. Ito, Y. Asano, and S. Tanaka, �??Transmission characteristics and reliability of pure-SiO2-core single-mode fibers,�?? J. Lightwave Technol. 4, 1144-1150 (1986). [CrossRef]
M. Bredol, D. Leers, L. Bosselaar, and M. Hutjens, �??Improved model for OH absorption in optical fibers,�?? J. Lightwave Technol. 18, 1536-1540 (1990). [CrossRef]
K. Tajima, M. Ohashi, K. Shiraki, M. Tateda, and S. Shibata, �??Low Rayleigh scattering P2O5-F-SiO2 glasses,�?? J. Lightwave Technol. 10, 1532-1535 (1992). [CrossRef]

J. Opt. Soc. Am A

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, �??Properties of photonic crystal fiber and the effective index model,�?? J. Opt. Soc. Am A 15, 748-752 (1998). [CrossRef]

Opt. Lett.

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

Optical Fiber Communication Conference

T. A. Birks, D. Mogilevtsev, J. C. Knight, P. St. J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. C. Allan, and J. C. Fajardo, �??The analogy between photonic crystal fibres and step index fibres,�?? in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1999), pp. 114-116.
K. Tajima, K. Nakajima, K. Kurokawa, N. Yoshizawa, and M. Ohashi, �??Low loss photonic crystal fibers,�?? in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), pp. 523-524.
K. Nagayama, T. Saitoh, M. Kahui, K. Kawasaki, M. Matsui, H. Takamizawa, and H. Miyaki, �??Ultra low loss (0.151dB/km) fiber and its impact on submarine transmission systems,�?? in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), Postdeadline papers, FA10.
T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, �??Novel hole-assisted lightguided fiber exhibiting large anomalous dispersion and low loss below 1 dB/km,�?? in Optical Fiber Communication Conference, Vol. 54 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), PD5.
S. E. Barkou, J. Broeng, and A. Bjarklev, �??Dispersion properties of photonic bandgap guiding fibers,�?? in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 117-119.
K. Tajima, �??Low-loss optical fibers realized by reduction of Rayleigh scattering loss,�?? in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 305-306.
P. Guenot, P. Nouchi, and B. Poumellec, �??Influence of drawing temperature on light scattering properties of single-mode fibers,�?? in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 1999), pp. 84-86.
T. Kato, M. Hirano, M. Onishi, and M. Nishimura, �??Ultra low nonlinearity low loss pure silica core fiber for long-haul WDM transmission,�?? in Optical Fiber Communication Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 95-97.

Photon. Technol. Lett.

M. Tateda, M. Ohashi, K. Jajima, and K. Shiraki, �??Design of viscosity matched optical fibers,�?? Photon. Technol. Lett. 4, 1023-1025 (1992). [CrossRef]
M. Ohashi, M. Tadeda, K. Shiraki, and K. Tajima, �??Imperfection loss reduction in viscosity-matched optical fibers,�?? Photon. Technol. Lett. 5, 1532-1535 (1993). [CrossRef]

Other

A. Bjarklev, Jes Broeng, Kim Dridi, and Stig E. Barkou, �??Dispersion properties of photonic crystal fibres,�?? in European Conference on Optical Communication (Madrid, Spain, 1998), pp. 135-136.
A.W. Snyder, Optical Waveguide Theory (Chapman and Hall, New York, 1983).
G. Cancellieri, Single Mode Optical Fibers (Pergamon, New York, 1991).
L. Farr, J.C. Knight, B.J. Mangan, and P.J. Roberts, �??Low loss photonic crystal fibre,�?? in European Conference on Optical Communication (Copenhagen, Denmarak, 2002), PD1.3.

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