Design and analysis of dual-shape-corelarge-mode-area optical fiber
Ajeet Kumar1,* and Vipul Rastogi2
1Department of Applied Physics, Delhi Technological University, Delhi, India2Department of Physics, Indian Institute of Technology Roorkee, Roorkee, India
Continual efforts have been made to increase thepower level of lasers by various approaches sincethe invention of the laser in 1960 by T. H. Maiman.At present, kilowatt ranges of lasers (gas and solidstate) are commercially available. However, compact-ness and thermal management are the main issueswith the gas and solid state lasers. The effectivesolution of this problem is to develop fiber lasers ofcomparative power levels. A fiber doped with rare-earth elements can serve as a gain medium for thelaser and amplifier applications and canmake a com-pact device. Single-mode (SM) fiber is preferred overmultimode fiber for designing high power fiber laserdue to its good beam quality. However, in small corewaveguides, the tight light confinement can reduceoptical damage threshold and at the same time
can give rise to significant unwanted nonlinear opti-cal effects. Nonlinear effects, such as four wave mix-ing, stimulated Raman scattering and stimulatedBrillouin scattering in a fiber, are the major factors,which limit its applicability in dense wavelength di-vision multiplexing (DWDM) optical communicationand in high power lasers and amplifiers. A large-mode-area (LMA) SM fiber is useful in designing thehigh power fiber laser. Recently, tremendous effortshave been made to realize LMA fibers by variousapproaches [1–22]. Significant work has been done toincrease the core area by tailoring the refractive-index profile in rare-earth doped fiber to achieve thehigh power output in fiber lasers and amplifiers withthe cost of the modal field patterns which deviatedfrom the Gaussian [1,2]. Another way to increasethe modal field area is to control the relative indexdifference between the core and cladding. An SMoperation with a 208 μm2 mode area, which isapproximately four times larger than the typical er-bium doped SM fiber, has been reported [3]. However,
the fibers having small NA are more sensitive tobend loss and can only be useful for Q-switched fiberlasers, which typically requires a fiber of length lessthan 1m. Double clad fiber design has also been uti-lized in the past to realize the LMA fiber by a fewgroups. Double clad fiber geometry has been used toenlarge the core diameter up to twice that of thestandard SM step index fiber [4]. Another doubleclad design was used to fabricate an extremely highpower fiber laser in Ytterbium doped fibers with1:36kW continuous-wave output power [5]. A photo-nic crystal fiber (PCF) or a holey fiber, which is char-acterized by distribution of air holes in claddingregion running through the entire length of the fiber,is another class of fiber for SM operation with a largecore [6]. Large index contrast introduced by air–silicainterfaces in a PCF makes it difficult to keep thebirefringence, and hence the polarization mode dis-persion, low. Leakage channel fiber whose core ismade up of few air holes has also demonstrated thelarge effective mode area propagation [7,8]. In an-other study, higher-order mode discrimination hasbeen achieved by coiling of a multimode fiber to havean effective SM fiber [9,10]. Coiling of the fiber at sui-table bending radius leads to significantly high lossto all the supported higher-order modes, except thefundamental mode since the fundamental mode offiber is least sensitive to bending. However, the bendloss depends upon the refractive-index profile andthe thickness of the core and cladding layers. There-fore, in such an approach the fiber manufacturedat different times would exhibit variation in profileshape and the desired bending radius for higher-order mode filtering could differ from fiber to fiber.To scale up the mode area up to very high level forrobust SM operation, some groups have utilizedthe idea of mode conversion with the help of longperiod gratings and Bragg gratings [11–15]. Overthe past few years, we have proposed some LMA de-signs using leaky fibers, where a large differentialleakage loss between the fundamental and higher-order modes and nominal loss to fundamental mode,is responsible for SM operation [16–21]. These de-signs include periodically arranged high and lowrefractive-index segments in the angular directionof the cladding [16–18], a graded-index cladding withradially rising refractive index [19], the claddingmade of periodically arranged low-index trenches ofvarying strength in an otherwise high-index medium[20], and dual core fiber design [21]. These unconven-tional cladding shapes of the fibers are responsiblefor higher-order mode filtering. However, being acompletely leaky structure, all the supported modesincluding fundamental mode would suffer from finiteleakage loss in above all leaky designs.
In this paper we present the design and analysis ofa simplified LMA fiber having dual-shape core (DSC)and a depressed-index-cladding. Our numerical re-sults show that fundamental mode of the fiber isperfectly guided while the high-order modes are lea-ky in nature. A suitable core and cladding design
parameters can enable this fiber to show SM opera-tion by leaking out all higher-order modes within asmall length of propagation. A proposed fiber showsLMA operation with mode area as large as 580 μm2
and a low bending loss. DSC fiber with such a large-mode area and low bending loss can effectively sup-press the unwanted nonlinear effects and can be agood candidate for optical communication systememploying DWDM and in high power fiber laser.
2. Fiber Design and Method of Analysis
Proposed fiber consists of dual-shape-core anddepressed-index leaky cladding. Refractive-indexprofile of the designed fiber is shown in the Fig. 1 andcan be written as
nðrÞ ¼
8>><>>:
n1; 0 < r < ans; a < r < bn2; b < r < cns; r > c
; ð1Þ
where n1 > ns > n2. ns represents the refractive in-dex of silica, Δþ and Δ− are the relative index differ-ence between the silica and doped layers of refractiveindices n1 and n2, respectively. A high-index centralcore can be formed by doping germanium into silica.Δþ can be carefully chosen to support only a funda-mental mode of the fiber for a given core radius a.A fiber with small Δþ can, however, be highly sensi-tive to bend induced loss. To overcome this problem, atrench of width d2 and relative index difference Δ− isintroduced after distance d1 from the central core.A low-index trench that can be formed by fluorinedoping into silica [23] is surrounded by outermostsilica layer, which makes the fiber leaky only forhigher-order modes. To make the discussion morecomfortable widths of the various layers have beendefined as d1 ¼ b − a, d2 ¼ c − b.
Leakage losses of higher-order modes and theguiding property of the fundamental mode have beenanalyzed by calculating the propagation constant,leakage loss and the modal field profile of the modesby using the transfer-matrix method (TMM), which
n(r)
∆+
∆−
a b c
Cen
tral
Co
re
Sid
eC
ore
n1
ns
n2
d2
d1
r
Fig. 1. Refractive-index profile of the proposed DSC fiber.
is a powerful tool to analyze the propagation charac-teristics of fiber having arbitrary shape [24,25].Being a scalar method, it is fast and easy to imple-ment. This method is particularly useful for analyz-ing a multilayer structure such as the one proposedin this paper. By applying suitable boundary condi-tions at the interface of two consecutive layers, thefield coefficients in the layers can be related by a 2 ×2 matrix, usually referred to as a transfer matrix.The field coefficients of the first and the last layer ofthe profile can be connected by simplymultiplying allthe intermediate matrices of each interface. A suita-ble boundary condition in the first and last layerwould lead to a complex eigenvalue equation. Anysuitable root searching algorithm can be used tosolve the complex roots of the equation. The real partof the propagation constant gives information aboutthe effective index of a mode while the leakage losscan be estimated from the imaginary part.
3. Numerical Results and Discussion
A. Single-Mode Operation
We have carried out numerical simulations and havecalculated the leakage and the bending losses of theproposed fiber for the following parameters unlessstated otherwise:
ns ¼ 1:444388; a ¼ 15 μm; Δþ ¼ 0:05%;
Δ− ¼ 1% and λ ¼ 1:55 μm: ð2Þ
The fiber is analyzed by a TMM [24,25] to calculatethe leakage losses of the modes, which plays animportant role for effective SM operation. In the pro-posed fiber, a fundamental mode is a perfectly guidedmode. So it is sufficient to calculate the leakage lossof the first higher-order mode (LP11) for defining SMoperation of the fiber. This design gives us relaxationin terms of the differential leakage loss of the modesand efficient amplification of the fundamental modein comparison to our previously reported leaky de-signs [19–21]. Effective SM operation of the structurecan be controlled by parameters d1 and d2. Inthe present work, we have investigated the effect ofboth the design parameters (d1 and d2) on the perfor-mance of the fiber. Performance of the proposed fiberis defined by its ability to exhibit effective SM opera-tion with extremely large modal field area of the fun-damental mode. In Fig. 2 we have shown the effect ofthe side-core width d1 on the area of fundamentalmode and the effective length of fiber (LSM) requiredfor leaking out the higher-order modes by introdu-cing a 20dB loss. 20dB rejection ratio is convention-ally used for most of the higher-order mode filteringdesigns as it brings down the power by a factor of100, which is sufficient to strip off an undesired mode[16,17,19–21]. Leakage loss of the LP11 mode de-creases with increase in d1 due to better confinementof the mode inside the core. This allows a maximumpermissible value of d1 beyond which the fiber be-comes multimoded for a given LSM. As an example,
for LSM ≥ 3m the DSC fiber with d1 < 3 μm can effec-tively filter out all unwanted higher-order modes.One can also see from the figure that when d1 is de-creased from 5 μm to 1 μm, LSM goes down by a factorof 11 and the mode area changes by 22%. The param-eter d1 thus shows a good tolerance on the mode areaand can be a useful parameter for designing the LMAfiber. Maximum permissible value of d1 for SM op-eration also depends upon the trench width d2. Itis, therefore, useful to study the effect of d2 on themode area and LSM. In Fig. 3 we have shown the ef-fect of d2 on mode field area and the effective lengthof fiber required to leak out the higher-order modes.From Fig. 3 we can conclude that the present fiberwith trench width smaller than 3 μm can effectivelysuppress the higher-order modes, and thus canshow effective SM operation with mode area∼ð572–580Þ μm2. From Figs. 2 and 3, we can concludethat d1 and d2 can be handy for designing the large-core fiber.
B. Modal Field
We have also studied the modal field confinement inthe DSC fiber. The modal fields of the first three
1 2 3 4 5400
500
600
700
d1 (µm)
0
5
10
15
Mod
e A
rea
(µm
2 )
LSM
(m)
Fig. 2. Effect of d1 on mode field area of the fundamental modeand the SM length LSM.
0
20
40
60
1 2 3 4 5
570
580
590
d2 (µm)
Mode A
rea (µm
2)
LSM
(m)
Fig. 3. Effect of d2 on the mode field area of fundamental modeand the SM length LSM.
modes of the fiber are shown in Fig. 4(a). Fundamen-tal mode of the fiber is well confined in the core whilethe oscillations in the field plots of higher-ordermodes are the signatures of their leaky behavior.Mode field area and the confinement of the funda-mental mode inside the core can also be seen fromits intensity contour plot shown in Fig. 4(b), wherethe dashed line represents the area beyond which theintensity of the mode falls below 1=e2 of its maximumvalue. Field of the fundamental mode is similar tothat of a conventional fiber and should be easy to ex-cite with the Gaussian beams.
C. Spectral Performance
We have also studied the wavelength dependence ofthe mode field area and the effective SM length LSM.The results are shown in Fig. 5. One can see from theplots that a 3m length of the fiber can show SM op-eration for the wavelengths greater than 1500nmwith only 3% variation in the modal field area of thefundamental mode.
D. Bending Performance
For practical applications, the bending loss of thefiber is an important issue to address. To analyze
the bending performance of the proposed fiber, wehave used the method described in [26], which is asuitable method for calculating the bend loss of themultilayer, fiber such as the one proposed here.Bending loss αb (dB=km) of the fiber is given by [26]
αb ¼ 1:09
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiπ
aRW3
rSðV ;WÞ exp
�−4RW3Δ3V2a
�ð3Þ
SðV ;WÞ ¼ a2
K20ðWÞ
�Z∞
0
E2ðρÞE2ðaÞ ρdρ
�−1; W ¼ b1=2V ;
ð4Þ
where EðρÞ represents the radial field distribution inthe straight fiber, a denotes the fiber core radius andR is the bending radius. Other parameters have theirusual meaning. Equation (3) represents an approxi-mate pure bend loss formula applicable to arbitraryrefractive-index profile fibers and neglects small cor-rections due to field deformation at the curved fiber.Such an approximation is justified in view of highsensitivity of bend loss with radius of curvature [26].
10 20 30 40 50 600-0.6
-0.4
-0.2
0.2
0.4
0.6
0.8
1.0
0
Nor
mal
ized
Fie
ld
r (µm)
x (µm)
y(µ
m)
(a)
(b)Fig. 4. (a) Modal field plot of the first three modes of the DSCfiber (b) Contour plot of the fundamental mode.
1400 1500 1600 1700520
530
540
550
0
5
10
15
λ(nm)
Mod
e A
rea
(µm
2 )
LSM
(m)
Fig. 5. Spectral variation of effective mode area and the SMlength LSM.
2 4 6 8 10 12 14 16 18 2010-4
10-3
10-2
10-1
100
101
102
d 1 = 0 µm
d 1 = 2 µm
d 1 = 4 µm
d 1 = 6 µm
d 1 = 8 µm
d 1 = 10 µm
Bending Radius R (cm)
Ben
ding
Los
s (d
B/m
)
Fig. 6. Bend loss of the LP01 mode of the dual-shape-core fiber fordifferent values of side-core width d1.
Our numerical analysis shows that the proposedfiber is less sensitive to bending in comparison toconventional large-core SM fiber (correspondingto d2 ¼ 0) and large-core W-fiber (corresponding tod1 ¼ 0) due to deliberately introduced low-indextrench of width d2 at r ¼ b. Bending performanceof the structure strongly depends on these designparameters. To assess the potential of the presentstructure as an LMA fiber with low bend loss, wehave investigated the bending performance of thestructure with respect to d1 and d2. The resultsare shown in Figs. 6 and 7. Figure 6 shows the bendloss of the DSC fiber for different values of d1. It isclear from the figure that W-fiber (d1 ¼ 0) suffersfrom highest bend loss for all bending radii in therange 2–20 cm. Bend loss of fiber decreases withd1 and converges at large values of d1. Bend lossof the fiber decreases by a factor of 10 by adding aside core of width d1 ¼ 4 μm inW-fiber. Thus, the pro-posed design shows better bending performance thanthe large-core W-fiber. We have also studied the ef-fect of the trench width (d2) on the bend loss of fiberas shown in Fig. 7. As expected, the bend loss of thefiber decreases significantly with the width of trench.Fiber with d2 ¼ 0 (conventional low NA LMA fiber)suffers from the highest bend loss among all the de-signs. Addition of a low-index trench of width 3 μm ina conventional SM fiber at 4 μm distance from thecentral-core reduces the bend loss from 11 dB=m to0:1dB=m at 12 cm bending radius. Thus, the pro-posed DSC fiber has low bend loss in comparisonto corresponding W-fiber (d1 ¼ 0) and conventionallarge-core fiber (d2 ¼ 0) and would be useful in appli-cations like high power fiber lasers and amplifiers.Bending of the fiber also introduces high loss tothe higher-order mode and helps in higher-ordermode suppression.
4. Conclusion
We have presented a DSC fiber design for LMA SMoperation with low bend loss. Modal characteristicsof the fiber have been investigated by TMM. Pro-posed design supports perfectly guided fundamental
mode which makes this design efficient for amplifica-tion of the fundamental mode in comparison to ourpreviously reported leaky design. The fiber is amen-able to fabrication by the modified chemical vapordeposition technique. A fiber with such a largemode area (∼580 μm2) would be useful in high powerapplications.
This work has been partially supported by the UKIndia Education and Research Initiative majoraward on “Application specific microstructured opti-cal fibres.”
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