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Optics Express

Optics Express

  • Vol. 16, Iss. 16 — Aug. 4, 2008
  • pp: 12060–12068
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Wide band single polarization and polarization maintaining fibers using stress rods and air holes

Xin Chen, Ming-Jun Li, Joohyun Koh, and Daniel A. Nolan  »View Author Affiliations


Optics Express, Vol. 16, Issue 16, pp. 12060-12068 (2008)
http://dx.doi.org/10.1364/OE.16.012060


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Abstract

We propose a new fiber design using both stress rods and air holes for making wide band single polarization fibers as well as polarization maintaining fibers. The key factor that makes the fiber design possible is that the stress-induced birefringence from the stress rods and the form birefringence from air holes are added constructively, which increases the total birefringence and allows more flexible choice of fiber parameters. We established a finite element model that is capable to study both the stress-optic effect and the wave-guide effect. Through the detailed modeling, we systematically explore the role of each major parameter. Different aspects of the fiber properties related to the fundamental mode cutoff, fiber birefringence and effective area are revealed. As a result, fibers with very large single polarization bandwidth as well as larger effective area are identified.

© 2008 Optical Society of America

1. Introduction

Single polarization fibers (SPF) and polarization maintaining fibers (PMF) have found many applications ranging from telecommunications, sensor (gyroscope), and lab measurements. In recent years, we have proposed, implemented, and commercialized a single polarization fiber with dual air holes [1-2

1. D. A. Nolan, G. E. Berkey, M.-J. Li, X. Chen, W. A. Wood, and L. A. Zenteno, “Single-polarization fiber with a high extinction ratio,” Opt. Lett. 29, 1855–1857 (2004). [CrossRef] [PubMed]

]. In order to achieve single polarization operation, the fiber must possess both high birefringence and fundamental mode cutoff. In the dual air hole fibers [1

1. D. A. Nolan, G. E. Berkey, M.-J. Li, X. Chen, W. A. Wood, and L. A. Zenteno, “Single-polarization fiber with a high extinction ratio,” Opt. Lett. 29, 1855–1857 (2004). [CrossRef] [PubMed]

], both features are achieved with the air holes in conjunction with high refractive index in the core. Such fibers can be used with conventional fibers by properly splicing the fibers for a wide range of applications that require polarization management.

However, recent developments such as those in the area of high power fiber laser also created the demand for fibers with larger mode area so that the fiber laser can operate at higher power without suffering from various nonlinear optical effects. It is also desirable that a single polarization fiber can work in a wider wavelength range so that one fiber can accommodate more applications. Different designs of single polarization fibers have emerged in the literature that are based on photonic crystal fibers with [3

3. T. Schreiber, F. Röser, O. Schmidt, J. Limpert, R. Iliew, F. Lederer, A. Petersson, C. Jacobsen, K. Hansen, J. Broeng, and A. Tünnermann, “Stress-induced single-polarization single-transverse mode photonic crystal fiber with low nonlinearity,” Opt. Express 13, 7621–7630 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-19-7621. [CrossRef] [PubMed]

] and without using stress components [4

4. J. R. Folkenberg, M. D. Nielsen, and C. Jakobsen, “Broadband single-polarization photonic crystal fiber,” Opt. Lett. 30, 1446–1448 (2005). [CrossRef] [PubMed]

]. To accommodate a wider range of needs both in terms of larger mode field and high single polarization bandwidth, in this paper we propose a novel fiber design that utilizes both stress rods and air holes. The addition of stress rods, in addition to air hole structure, allows more flexible adjustment of different parameters for desired fiber properties. For example, this new fiber structure can have a core with lower refractive index, resulting in large mode area. The fiber can be designed as either polarization maintaining fiber or single polarization fiber depending on which wavelength window is used. In Section 2, we describe the fiber structure and define the key fiber parameters. In Section 3, we describe the modeling method that addresses the fiber design problem involving multiple physical effects. In Section 4, we present the detailed analysis of various aspects of the fiber design, which carries the main results of this paper. The analysis includes the birefringence properties of the fiber from two different sources, the dependence of the fiber properties on all major fiber parameters and design examples illustrating desired performance. Finally, in Section 5 we present a brief conclusion.

2. Fiber structure

Δi=ni2nclad22ni2
(1)

There are two delta values to be specified, which are delta of the core Δcore, and delta of the stress rod, ΔRod so that “i” in Eq.(1) can either represent the fiber core or the stress rod.

It should be noted that air holes and stress rods have also been used in a different fiber design in a recent paper [5

5. X. Peng and L. Dong, “Fundamental-mode operation in polarization-maintaining ytterbium-doped fiber with an effective area of 1400 μm2,” Opt. Lett. 32, 358–360 (2007). [CrossRef] [PubMed]

]. In [5

5. X. Peng and L. Dong, “Fundamental-mode operation in polarization-maintaining ytterbium-doped fiber with an effective area of 1400 μm2,” Opt. Lett. 32, 358–360 (2007). [CrossRef] [PubMed]

], four air holes have been placed around a pure silica core with two additional stress members placed on each side of the fiber core for the purpose of achieving single mode and polarization maintaining performance through the control of leakage loss of fundamental mode and higher order modes. Even with tight bending, a merely 2-3 dB differential loss between two fundamental polarization modes was achieved when the overall fiber suffers from 20dB/m loss. In contrast, the current paper discusses how the use of air holes in conjunction with two stress rods can result in novel single polarization properties, which are intrinsic to the fiber even without bending.

Fig. 1. Schematic of fiber design with air holes and stress rods.

3. Finite element modeling

In this paper, all the numerical modeling was conducted by using a Finite Element Method (FEM) involving different physical mechanisms, which describes the buildup of anisotropic stress during the fiber making process, the stress-optic effect and electromagnetics dealing with the waveguide effect. In the first step, we calculate the stress distribution due to differential thermal expansion and translate that into anisotropic index distribution via stress-optic effect [6

6. K. Okamoto, T. Hosaka, and T. Edahiro, “Stress Analysis of Optical Fibers by a Finite Element Method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981). [CrossRef]

, 7

7. Jun-Ichi Sakai and Tatsuya Kimura, “Birefringence Caused by Thermal Stress in Elliptically Deformed Core Optical Fibers,” IEEE J. Quantum Electronics , QE-18, 1899–1909 (1982). [CrossRef]

]. The plain strain approximation, which takes into account only the stress and strain on the x-y, is applied to obtain the stress distribution. Note that the length in z direction along the fiber is very large and the stress varies little over z-position. The stress-optic effect causes an anisotropic change of the refractive index at each position at the cross section of the fiber,

Δnx(x,y)=C1σx(x,y)+C2σy(x,y)
(2)
Δny(x,y)=C2σx(x,y)+C1σy(x,y)
(3)

where C1 and C2 are the stress-optical coefficients, σx and σy are the thermal stresses at a given position of the fiber cross section, and Δnx and Δny are the refractive index changes at a given position of the fiber cross section due to the stresses. In the fiber design, the core is doped with GeO2 and the stress rods are doped with B2O3. The material parameters including the coefficients of thermal expansion (CTE) for GeO2 doped and B2O3 doped silica follow those from Refs.[6

6. K. Okamoto, T. Hosaka, and T. Edahiro, “Stress Analysis of Optical Fibers by a Finite Element Method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981). [CrossRef]

, 7

7. Jun-Ichi Sakai and Tatsuya Kimura, “Birefringence Caused by Thermal Stress in Elliptically Deformed Core Optical Fibers,” IEEE J. Quantum Electronics , QE-18, 1899–1909 (1982). [CrossRef]

].

nx(x,y)=n0x(x,y)+Δnx(x,y)
(4)
ny(x,y)=n0y(x,y)+Δny(x,y).
(5)

The effective indices are then calculated for both polarizations of the fundamental mode similarly to that in [8

8. M.-J. Li, Xin Chen, D.A. Nolan, G.E. Berkey, Ji Wang, W.A Wood, and L. A. Zenteno, “High bandwidth single polarization fiber with elliptical central air hole,” J. Lightwave Technol. , 23, 3454–3460 (2005). [CrossRef]

] for different fiber designs. For a polarization maintaining fiber that operates below the cutoff wavelengths of the fundamental polarization modes, the fiber birefringence is determined by the difference between the effective indices nx,eff and ny,eff of the x- and y-polarization modes,

B=nx,effny,eff
(6)

We note that this is a more rigorous way to calculate the birefringence than the simplified method, which calculates the birefringence from refractive index difference in x- and y-direction at the center of the fiber using Eqs.(4, 5) [4

4. J. R. Folkenberg, M. D. Nielsen, and C. Jakobsen, “Broadband single-polarization photonic crystal fiber,” Opt. Lett. 30, 1446–1448 (2005). [CrossRef] [PubMed]

, 9

9. Z. Zhu and T. G. Brown, “Stress-induced Birefringence in Microstructured Optical Fibers,” Opt. Lett. 28, 2306–2308 (2003). [CrossRef] [PubMed]

]. Also Eq.(6) includes both the stress-induced and form birefringence. On the other hand, for a single polarization fiber, the cutoff wavelength of a particular polarization mode can be calculated by searching for the wavelength at which the effective index is equal to the refractive index of the cladding. The single polarization bandwidth is calculated from the difference between the cutoff wavelengths of the two fundamental polarization modes.

The procedure described above can be used to conduct modeling using different parameters. It is difficult to scan all the parameters altogether as too many parameters are involved. To make the study more efficient, we obtain the dependence of the fiber properties on a particular parameter by fixing other parameters and scanning this parameter only.

4. Detailed modeling results

In this section, we present the detailed modeling results using the modeling method described in Section 3, which include the understanding of birefringence mechanism, the roles of various fiber parameters, and design examples.

4.1 The birefringence mechanism

First, we want to analyze and understand the birefringence contributed from the stress rods and the air holes. Note that the birefringence in the proposed fiber structure comes from two different mechanisms. The birefringence contributed from the stress rods is called stress-induced birefringence while the birefringence from the air holes is called form birefringence. The key question here is whether or not the birefringence from the two sources is added constructively.

To answer the question, we look at an example fiber that has the parameters Δcore= 0.35%, Rcore=4.2μm, Δrod = -0.75%, Rrod=15μm, Rhole=10.2μm. With the presence of both the stress rods and dual air holes, the calculated total birefringence is 5.34×10-4. We then model a fiber with the same structure except that we take out the air holes. The modeling shows the birefringence of 4.31×10-4. We subsequently model the fiber by taking out only the stress rods and find that the birefringence is 1.12×10-4. It can be found that the sum of the individual birefringence is approximately equal to the total birefringence with both the air holes and stress rods in place. This indicates that the birefringence from both structures contributes to the total birefringence constructively.

4.2 Role of core parameters

Now, we look at the dependence of the fiber properties on the core parameters. We first fixed all other fiber parameters except the fiber core delta. We have chosen Δrod = -0.75%, RCore=4.2μm, RRod=15μm, DRod=25μm, Rhole=6μm. In Fig. 2, we show the dependence of the cutoff wavelengths of both fundamental polarization modes on the core delta. Due to larger birefringence, the two polarization modes reach the cutoff at different wavelengths. It can be found that the cutoff wavelengths of the two polarization modes can be tuned by changing the core delta. The higher the core delta, the higher the cutoff wavelength for each polarization mode will be.

To understand the role of the core radius, we changed the core radius and locked all other parameters to examine the effect of core radius on the cutoff wavelengths. The parameters used in the calculation are: Δcore=0.35%, ΔRod=-0.75%, RRod = 15μm, DRod=25μm, and Rhole=6μm. The results plotted in Fig. 3 show that the core radius is another parameter that can be used to tune the cutoff wavelengths of both polarization modes. We also calculate the birefringence. For the two examples in Fig. 2 and Fig. 3, the total birefringence normalized to 1550 nm is around 4.0×10-4 to 5.0×10-5, a birefringence that is comparable to the commercial Panda type polarization maintaining fiber [10

10. J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications,” J. Lightwave Technol. LT-4, 1071–1089 (1986). [CrossRef]

].

Core parameters are also important to determine the fiber mode area in addition to their roles in affecting the fundamental mode cutoff. For a standard single mode fiber, the core delta is typically around 0.34% while the core radius is around 4.2 μm. For certain applications when a larger mode area is desired, core delta should be lowered to allow for larger core radius while keeping the fiber single-moded. Therefore, the desired fiber mode area is another factor affecting how the fiber core parameters are chosen. The choice at a particular design is a balance of different considerations.

Fig. 2. Dependence of the cutoff wavelengths of two polarization modes on the core delta.
Fig. 3. Cutoff wavelengths of both fundamental polarization modes as a function of the core radius.

4.3 Roles of the stress rod parameters

Other parameters for the stress rods include the size of stress rods and their distance to the fiber center. As the stress rods are primarily used to provide birefringence, the roles of these parameters are well understood [10

10. J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications,” J. Lightwave Technol. LT-4, 1071–1089 (1986). [CrossRef]

]. In general, larger stress rod size and shorter distance between the stress rod center and the fiber center lead to higher birefringence.

Fig. 4. (a). Birefringence at 1550nm as a function of stress rod Delta. (b) Cutoff wavelengths of both fundamental polarization modes as a function of Boron Delta.

4.4 Roles of the air hole parameters

The size of the air holes and their positions can affect also the performance of the fiber. In Fig. 5, we show the dependence of the cutoff wavelengths of both fundamental polarization modes on the air hole radius. We have chosen the fiber parameters to be Δcore=0.3%, Δrod=-0.75%, Rcore=4.2μm, RRod=15μm, and DRod=25μm. The air holes are positioned in direct contact to the core while other parameters are kept unchanged. As the air hole size increases, the cutoff wavelengths decrease. The single polarization bandwidth remains basically unchanged. The air hole size can be used as a parameter to control the location of the cutoff wavelengths in conjunction with other parameter choice.

Fig. 5. Dependence of the cutoff wavelengths of both polarization modes on the air hole size. The air holes are positioned right next to the core.

Fig. 6. Dependence of the cutoff wavelengths of both polarization modes on the separation between the core and the air holes.

4.5 Additional factors affecting the fiber properties

Fig. 7. Dependence of the cutoff wavelengths of both polarization modes on the core minor dimension.

4.6 Design examples

A single polarization fiber is typically designed to work at a certain wavelength window, for example, around 1550nm. As shown before, adjustment to core radius, core delta, stress rod delta can change the optical performance. It is interesting to know when the single polarization operating window is locked in a wavelength of interest, how the single polarization operating bandwidth changes with the core delta. Once the core delta is chosen the core radius can only be chosen within a narrow range for the fiber to be single moded. The choice of core delta also largely determines the fiber mode area. Fig. 8(a) illustrates the results of single polarization bandwidth versus core delta while keeping the single polarization operating window around 1550nm by adjusting the core dimension. In Fig.8(b) we show the relation between the effective area for the fundamental polarization mode operated at 1550 nm. We have chosen the fixed fiber parameters to be Δrod=-0.75%, Rhole=6μm, RRod=15μm, and DRod=25μm. It is shown that the lower the core delta is, the higher the single polarization bandwidth will be. For the fiber with core delta of 0.2%, the single polarization bandwidth is 178 nm. Similar trend follows for the effective area with higher effective area reached at lower core delta. This means that both large mode area and high bandwidth can be achieved with this new fiber design.

The fibers illustrated in Fig. 8 can also function as PM fibers. Our calculations show that they have the birefringence in the order of 3-5×10-4, similar to that of conventional PM fibers In addition, although in the above example, the single polarization operation occurs around 1550 nm, a wavelength of typical interest, by proper adjusting the fiber parameters, the operating window can be shifted to other wavelength of interest such as 1060 nm and 1310nm.

Fig. 8. (a) Dependence of the single polarization bandwidth as a function of the core delta with core radius adjusted to keep single polarization window at 1550nm. (b) Effective area of the corresponding fiber in (a).

5. Conclusion

In this paper, we propose a new fiber design that is based on the use of air holes and stress rods to perform as single polarization fibers as well as polarization maintaining fibers. The stress rods and air holes both contribute to the overall birefringence of the fiber although through different mechanisms. We have established a finite element model that is capable of studying the design problem by accommodating both the thermal stress effect and waveguide effect. Effects of the fiber parameters to various aspects of the fiber properties are revealed. The modeling results indicate that the fiber structure allows flexible adjustments of fiber parameters for desired properties. A fiber with single polarization bandwidth as high as 178 nm around 1550nm is illustrated with a relative large effective area of 93 μm2.

References and links

1.

D. A. Nolan, G. E. Berkey, M.-J. Li, X. Chen, W. A. Wood, and L. A. Zenteno, “Single-polarization fiber with a high extinction ratio,” Opt. Lett. 29, 1855–1857 (2004). [CrossRef] [PubMed]

2.

D. A. Nolan, M.-J. Li, X. Chen, and J. Koh, “Single polarization fibers and applications,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (Optical Society of America, Washington DC, 2006) OWA1.

3.

T. Schreiber, F. Röser, O. Schmidt, J. Limpert, R. Iliew, F. Lederer, A. Petersson, C. Jacobsen, K. Hansen, J. Broeng, and A. Tünnermann, “Stress-induced single-polarization single-transverse mode photonic crystal fiber with low nonlinearity,” Opt. Express 13, 7621–7630 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-19-7621. [CrossRef] [PubMed]

4.

J. R. Folkenberg, M. D. Nielsen, and C. Jakobsen, “Broadband single-polarization photonic crystal fiber,” Opt. Lett. 30, 1446–1448 (2005). [CrossRef] [PubMed]

5.

X. Peng and L. Dong, “Fundamental-mode operation in polarization-maintaining ytterbium-doped fiber with an effective area of 1400 μm2,” Opt. Lett. 32, 358–360 (2007). [CrossRef] [PubMed]

6.

K. Okamoto, T. Hosaka, and T. Edahiro, “Stress Analysis of Optical Fibers by a Finite Element Method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981). [CrossRef]

7.

Jun-Ichi Sakai and Tatsuya Kimura, “Birefringence Caused by Thermal Stress in Elliptically Deformed Core Optical Fibers,” IEEE J. Quantum Electronics , QE-18, 1899–1909 (1982). [CrossRef]

8.

M.-J. Li, Xin Chen, D.A. Nolan, G.E. Berkey, Ji Wang, W.A Wood, and L. A. Zenteno, “High bandwidth single polarization fiber with elliptical central air hole,” J. Lightwave Technol. , 23, 3454–3460 (2005). [CrossRef]

9.

Z. Zhu and T. G. Brown, “Stress-induced Birefringence in Microstructured Optical Fibers,” Opt. Lett. 28, 2306–2308 (2003). [CrossRef] [PubMed]

10.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-Maintaining Fibers and Their Applications,” J. Lightwave Technol. LT-4, 1071–1089 (1986). [CrossRef]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2420) Fiber optics and optical communications : Fibers, polarization-maintaining

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: April 28, 2008
Revised Manuscript: June 12, 2008
Manuscript Accepted: July 22, 2008
Published: July 28, 2008

Citation
Xin Chen, Ming-Jun Li, Joohyun Koh, and Daniel A. Nolan, "Wide band single polarization and polarization maintaining fibers using stress rods and air holes," Opt. Express 16, 12060-12068 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-12060


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References

  1. D. A. Nolan, G. E. Berkey, M.-J. Li, X. Chen, W. A. Wood, and L. A. Zenteno, "Single-polarization fiber with a high extinction ratio," Opt. Lett. 29, 1855-1857 (2004). [CrossRef] [PubMed]
  2. D. A. Nolan, M.-J. Li, X. Chen, and J. Koh, "Single polarization fibers and applications," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (Optical Society of America, Washington DC, 2006) OWA1.
  3. T. Schreiber, F. Röser, O. Schmidt, J. Limpert, R. Iliew, F. Lederer, A. Petersson, C. Jacobsen, K. Hansen, J. Broeng, and A. Tünnermann, "Stress-induced single-polarization single-transverse mode photonic crystal fiber with low nonlinearity," Opt. Express 13, 7621-7630 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-19-7621. [CrossRef] [PubMed]
  4. J. R. Folkenberg, M. D. Nielsen, and C. Jakobsen, "Broadband single-polarization photonic crystal fiber," Opt. Lett. 30, 1446-1448 (2005). [CrossRef] [PubMed]
  5. X. Peng and L. Dong, "Fundamental-mode operation in polarization-maintaining ytterbium-doped fiber with an effective area of 1400 μm2," Opt. Lett. 32, 358-360 (2007). [CrossRef] [PubMed]
  6. K. Okamoto, T. Hosaka, and T. Edahiro, "Stress Analysis of Optical Fibers by a Finite Element Method," IEEE J. Quantum Electron. QE-17, 2123-2129 (1981). [CrossRef]
  7. Jun-Ichi Sakai and Tatsuya Kimura, "Birefringence Caused by Thermal Stress in Elliptically Deformed Core Optical Fibers," IEEE J. Quantum Electronics,  QE-18, 1899-1909 (1982). [CrossRef]
  8. M.-J. Li, Xin Chen, D.A. Nolan, G.E. Berkey, Ji Wang; W.A Wood, and L. A. Zenteno, "High bandwidth single polarization fiber with elliptical central air hole," J. Lightwave Technol.,  23, 3454-3460 (2005). [CrossRef]
  9. Z. Zhu and T. G. Brown, "Stress-induced Birefringence in Microstructured Optical Fibers," Opt. Lett. 28, 2306-2308 (2003). [CrossRef] [PubMed]
  10. J. Noda, K. Okamoto, and Y. Sasaki, "Polarization-Maintaining Fibers and Their Applications," J. Lightwave Technol. LT-4, 1071-1089 (1986). [CrossRef]

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