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Long Period Gratings

109

4.1 Introduction

Optical communication network has become one of the essentials for human life

as people can communicate; acquire knowledge and entertainment through the

internet. Wavelength division multiplexing (WDM) and erbium doped fiber amplifier

(EDFA) are the two important technologies in realization of modern optical

communication networks. A WDM system allows simultaneous transmission of

multiple wavelengths and thus increases the transmission capacity. EDFA provides

direct optical amplification over a wide band at around 1550nm, which is the

wavelength window for long distance telecommunication applications. To realize

these two technologies, fiber gratings which are wavelength selective components,

play an important role. Long period gratings (LPGs) which behave as band rejection

filters are commonly used for gain flattening in EDFA. In addition, many other

applications based on wavelength selective components have emerged, such as

add/drop multiplexing, dispersion compensation, optical switching and optical

sensing. Therefore, in-fiber wavelength selective components are playing important

role in modern optical science and communication technology [1].

Although fiber gratings of period much more greater than the FBGs (several

hundred micrometers) have been demonstrated in the past for coupling from one

guided mode to another, for example, a blazed grating in a two-mode fiber has been

used to induce an LP0l � LP11 mode conversion [2], LP01 � LP02 mode convertors

have been demonstrated [3], the breakthrough came out in the year 1996 when

Asheesh. M. Vengsarkar and team demonstrated these fiber gratings of longer periods

as multifunctional element. In their article LPGs were presented as low insertion loss

in-fiber devices that function as spectrally selective loss elements, gain-flattening

element for EDFA and sensors for measuring strain, temperature and refractive index.


110

Long period optical fiber gratings are compact. These devices have been used as

amplified spontaneous emission filters in erbium doped fiber amplifiers [4]. Many

other performances of LPG are - band rejection filters to remove undesirable Stoke’s

lines in cascaded Raman lasers/amplifiers [5]; as optical attenuators [6]; as gain

equalizers in multichannel WDM systerms [7] and as temperature stablizers for Er-

doped superfluorescent fiber sources[8]. Due to wide attenuation band, they are also

useful for polarization dependent loss component [9] and as narrow band filters by

cascading two identical LPGs [10].

Fiber gratings of period ranging between 100µm and 1mm are called long period

gratings as the length of periodicity suggest. Practically hundreds of micrometers are

used. Periodicities in this order promote the coupling of the guided core mode to

cladding modes as shown in the Fig 4.1, resulting in the transmission spectrum of the

fiber containing a series of attenuation bands centered at discrete wavelengths (Fig.

1.14). Each attenuation band corresponds to the coupling to different cladding modes.

Since cladding modes are typically not guided, the light will dissipate in the

surroundings. Coupling between the two modes is governed by the phase matching

condition that gives the wavelength of resonance dip in the transmission spectrum.

Phase matching between the mode propagating in the core of the fiber and a co-

propagating cladding mode is achieved at the wavelength mλ given by [4, 11]

(4.1)

where, mλ is the peak wavelength of the resonance band. 01n and mn1 are the

effective refractive indices of the core mode and of the mth order cladding mode

respectively. Λ is period of the LPG. In the above equation, ‘01’ refers to LP01 mode

and ‘1m’ refers to HE1m axially symmetric cladding modes. Period of grating

determines the wavelength of interaction and the strength of coupling is determined

Λ−= )( 101 mm nnλ


111

by the modal overlap given by coupling coefficient. Since the coupling is wavelength

selective, the grating acts as a wavelength dependent loss element.

Figure 4.1: Operating principle of LPG.

In general, LPGs possess low insertion loss (<0.2 dB), low back reflection (<-80 dB),

large bandwidth (10-20 nm), high coupling strength (>25 dB is achievable), low

polarization mode dispersion loss (<0.02dB) and polarization dependent losses

(<0.02dB) that depends on the fabrication technique and respective fabrication

parameters [4].

4.2 Ray Theory of LPG

Let us consider the coupling between two bounded waves traveling in the same

direction. Fig. 4.2 shows the coupling between a core mode and a cladding mode.

Incoming beam with an angle θ1 is diffracted into a smaller positive angle θ2. As θ2 is

smaller than the critical angle θc, light radiates out of the core and can be guided into

the cladding if 2π/λ nsurr < β2 < 2π/λ ncl. Grating equation can be written as [12, 13]

Λ−=

λθθ 12 sin)sin( nn (4.2)


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Fig. 4.2: Ray illustration of in long period fiber grating.

Propagation constants for core mode is β1 =(2π/λ) n01 and that for mth

cladding mode

is β2 =(2π/λ) n1m, where “n sinθ” represents effective refractive index of the

respective mode [13,14]. Substituting these values in the above equation and

rearranging the terms, for β2 >0, the wavelength of resonances leads to the Eq.(4.1).

Therefore, for co-propagating coupling at a given wavelength, a much longer grating

period (Λ>100µm) is required than for propagating coupling (as in FBG).

4.3 Coupled Mode Theory of LPG

Let us consider two modes propagating in single mode step index optical fiber of

radius ‘a’ and refractive index profile n(x, y). In a single mode fiber, only the

fundamental core mode (HE11) is guided. Coupling between the core mode and the

co-propagating cladding modes is brought out by long period grating. The refractive

index modulation brings about the coupling between HE11 (or LP01) and other higher

order modes. The couple mode equations [1, 15] are,

ziBei

dz

dA Γ= κ (4.3)

(4.4)

Λ−−=Γ

πββ

221 (4.5)

ziAeidz

dB Γ−= κ


113

∫∫ ∆=

core

dxdyn 2

*

10

8ψψ

ωεκ (4.6)

where, A0 and Am are the amplitudes of the guided core mode and the cladding mode

respectively, β1 is propagation constant of the guided core mode, β2 is propagation

constant of mth cladding mode, κ is coupling coefficient proportional to ∆n and

overlap integral over the core area between the coupling modes, Γ is mode

confinement factor, ε0 is free space dielectric constant and ω is frequency. The

normalized transmission coefficient of the guided core mode of grating length L is

calculated by solving the above equations and is given by [1]

[

(4.7)

As we know for uniform gratings,

Γ=0 (4.8)

Now the above equation becomes

)(cos)(sin1)( 22 LLT κκλ =−= (4.9)

From this equation, coupling between two modes is strongest when

2

)12( πκ

+=

nL n=0, 1, 2… (4.10)

Eq. (4.5) becomes, The phase matching condition

Λ=−

πββ

221 (4.11)

With Coupled mode theory, the interaction strength between two modes in a fiber

can be expressed using a proportionality coefficient called the coupling coefficient.

The coupling coefficient depends on the similarity of the propagation constants and

the overlap integral of the mode fields. Coupling will be strong if the fields overlap

)4

(sin

4

1)(

)()(

222

22

2

2

2

LLA

LAT

Γ+

Γ+

−== κ

κ

κλ


114

more, i.e. the overlap integral is larger. At the same time, if the modes do not

propagate at the same speed along the fiber axis, the interaction will be limited.

Without the grating, the coupling between the modes in the fibers in question would

be negligible as they all have very different propagation constants. The grating allows

the coupling of modes having distinct propagation constants. However, the difference

in the propagation constants needs to be close to a specific value in order to enable

strong coupling. The magnitude of this value depends on the periodicity of the grating

[16].

4.4 Methods of LPG Fabrication

In the beginning LPG were fabricated by irradiating photosensitive core with UV

radiation through amplitude mask [4]. Later many other methods were introduced. No

need of highly coherent source in LPG fabrication makes fabrication of LPG simple

compared to FBG fabrication. Amplitude mask method and point by point method

are two popular methods of LPG fabrication in practice.

4.4.1 Amplitude Mask Method

A typical LPG fabrication by amplitude mask method is shown in Fig.4.3.

Optical fiber fixed at two points is exposed to UV radiation through amplitude mask

[4]. Cylindrical lens is used to focus light beam parallel to the fiber axis. The grating

period is same as that of amplitude mask. Since the period of amplitude mask is much

greater than the wavelength of incident UV radiation, no diffraction is produced and

rays pass on and strike the fiber. The refractive index of fiber core area receiving UV

rays increases due to photosensitivity. The stable UV source is the only requirement

for the LPG fabrication. Coherence of the UV source has no important role here.


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Amplitude masks are fabricated with chrome plated silica or from metal foil.

Amplitude mask in silica plate is produced by coating the UV photoresistive material

and exposing the silica plate to UV laser to produce photoresist. Then uncoated fringe

pattern is etched with HF solution to produce amplitude mask. Radiation is

transmitted through the etched region when amplitude mask is exposed to UV

radiation [17]. Amplitude mask in metal foil is produced by milling foil with vapour

laser [18]. Amplitude mask method is useful in mass production of LPG.

Figure 4.3: Amplitude mask method.

4.4.2 Pont by Point Method

Point by point method of LPG fabrication is a very flexible method. Fiber is

exposed to index modifying radiation one shot after the other, by translating fiber or

laser beam to create next grating period [19]. The growth of LPG can be observed at

each shot in transmitted spectrum. Using this method many configurations were

demonstrated. In one configuration the fiber is fixed at two ends and exposed to

radiation as shown in Fig 4.4 [20].


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Figure 4.4: LPG fabrication with point by point method, with both the fiber ends fixed.

In another configuration one end of the fiber is fixed and other end running on

friction less pulley is attached with small mass (50-500mg) to provide constant strain

in the fiber. The laser is scanned along the fiber axis with required period [20, 21]

Schematic diagram is shown in the Fig. 4.5. In this configuration laser beam is

controlled by the computer.

Figure 4.5: LPG fabrication point by point method, one end of a fiber fixed and other attached with mass.

In point by point method of fabrication, grating marking source need not be of

UV wavelength. Even IR lasers are also used for fabrication – CO2 laser (10.6µm)

[20-22], femto second laser pulses of 800µm [23, 24]. Electric arc produced by the

splicing machine is also used to produce high quality LPGs [25].


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Using point by point method LPGs of high quality were reported and they were

used in both communication and sensing fields. The basic requirement of point by

point method is high precision translation system to give accurate displacement to

either fiber or grating marking source.

4.4.3 Other Methods of LPG Fabrication

Apart from above mentioned methods, various other methods of LPG fabrication

were reported.

i) Diffusion of dopants: Dianov et al. proposed a technique for long-period fiber

grating fabrication using thermally activated diffusion of a core dopant to the

cladding region. LPGs written in nitrogen-doped and phosphorous doped fibers

with the help of a CO laser, exhibited a high resistance to thermal decay [26, 27].

ii) Electric discharge method: Electric discharge from splicing machine is used to

modify the refractive index of the fiber. Different currents were applied to

fabricate LPG [25, 28]. Electric arc fabrication of an LPG relies upon a

combination of up to four effects to generate the periodic modulation of the fiber

properties. The mechanisms exploited include the induction of microbends into

the fiber, the periodic tapering of the fiber, the diffusion of dopants and the

relaxation of internal stresses. Such LPGs have been shown to operate at

temperatures of up to 800OC without permanent modification of their properties

and if annealed appropriately, they may operate at temperatures up to 1190OC

[11]. Using electric discharge, LPGs were fabricated in various fibers.

iii) Deformation by mechanical strain: LPG can be produced by pressing the

optical fiber with metal slab with corrugations carved at desired pitch. When a

tensile load is applied to the fiber, the periodic variation in the diameter of the

fiber results in a periodic strain variation across the corrugated structure, with a


118

simultaneous periodic refractive index induced via the photoelastic effect. Thus

the coupling strength increases with applied load, with a small change in

wavelength of the attenuation bands [11]. This method is least expensive and

applicable to any type of fibers. LPGs were demonstrated as sensors to measure

bend etc [29-31].

4.5 Lasers used for LPG Fabrication

Generally UV radiations are used for LPG fabrication. Following are some of

lasers used:

KrF(248nm) laser [4], F2 Laser (157nm) [32], Argon ion laser (448nm) [33], ArF

laser (193nm) [34], continuous wave Ar ion laser working in single-line (334 nm)

[35], in a multi-line regime: (300-305 nm) [36] and (333-364 nm) [37]; through

exposure to nanosecond pulses from ArF excimer laser (193 nm) [38,39] or from the

frequency quadrupled and tripled of the Nd:YAG laser (266 nm and 355 nm) [40],

high-intensity femtosecond laser radiation at several wavelengths have also been

used: 211 nm [41], 264 nm [42] and 352 nm [43] corresponding respectively, to the

fifth, fourth and third harmonics of a Nd:glass laser; and the second harmonic of Ti+3:

Al2O3 laser (400 nm) [44]. Grating fabrication using a broadband UV source was also

demonstrated [45]. To induce refractive index change in fiber with UV laser, fiber

should be photosensitive. In order to reduce the fabrication time, photosensitivity has

to be enhanced by some other techniques such as adding co-dopant or hydrogen

loading of fiber under high pressure [46]. Phtosensitivity enhancement techniques in

optical fibers have been discussed in Chapter-2 (2.2.2).

Femto second laser of wavelength 800nm was reported for LPG fabrication even

in pure silica core fiber. The irradiation is believed to cause a densification of glass


119

resulting into index change. In this case the gratings spectra strongly depend on the

ability to keep the alignment between the fiber core and the laser beam [47].

Electric arc-induced LPG was proposed in various types of fibers. Arc-induced

gratings which can be produced by microbending [48], by glass structure

rearrangements as a result of using high electric currents (>20 mA) of short duration

(<100 ms) [49]. CO2 laser is widely used in LPG fabrication [22]. LPG fabrication

using CO2 laser and arc –induced techniques have been drawing an increasing

attention by the fiber gratings community. It is believed that LPGs produced through

exposure to CO2 laser radiation and to arc discharges have many common properties

[50].

4.6 Writing Mechanism by CO2-Laser

The CO2-laser writing method has been widely used for LPG fabrication.

Different mechanisms have been suggested for this phenomenon. Possible

mechanisms for refractive index modulation in the CO2-laser induced LPGs could be

attributed to residual stress relaxation, glass densification depending on the types of

the optical fiber used and on the practical fabrication techniques. A few methods have

been demonstrated to measure the refractive index modulation in the CO2-laser

induced LPGs [1, 20].

4.6.1 Residual Stress Relaxation

Residual stress relaxation is found to be the main mechanism for the refractive-

index change in the CO2-laser-induced LPGs written in optical fibers drawn at high

drawing forces. The total residual stress in an optical fiber is combination of thermal

stress and mechanical stress. Residual stress is formed in optical fibers during the

fiber drawing process, resulting from a superposition of thermal stress caused by a


120

difference in thermal expansion coefficients between core and cladding and

mechanical stress caused by a difference in the elastic properties of the two regions.

Such residual stress can change refractive index in the fibers through the stress-optic

effect and thus affect the optical properties of the fibers. When fiber is irradiated with

CO2-laser pulses, the thermal stress in the core is relaxed by intense heating effect,

which results in a decrease of the refractive index at the point of irradiation [1, 20].

4.6.2 Glass Structure Change

When a fiber is irradiated with CO2-laser pulses, the fiber glass is heated at the

point of irradiation because of infrared absorption. If the glass is heated in the glass

transition temperature range, the glass will undergo structural relaxation that is

controlled by the glass viscosity. The glass structure changes according to the rate of

cooling. Depending on the cooling process, the density of glass can be either

increased or decreased. Thus refractive index of the glass depends upon the glass

volume after cooling [1].

4.7 LPG Fabrication using CO2 Laser

Long period gratings were fabricated using point by point technique. LPG was

fabricated in single mode communication grade fiber (SMF-28). Table 4.1 provides

details of the fiber used. About 5cm of acrylate coating of the fiber was stripped off at

the center of long length fiber (nearly 1meter). Ends of the fiber were connected to

white light source and OSA. The schematic diagram of fabrication of LPG is as in Fig

4.6. Light emitted from white light source (400-1800nm) was launched into fiber and

transmitted spectrum was measured in optical spectrum analyzer. The acrylate

removed part of fiber was fixed infront of CO2 laser at distance 1.5meter. Details of

CO2 laser are given in Table 4.2. The fiber was mounted on fiber holder which keeps


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fiber in position by holding it tightly at two points. The fiber holder clamped the fiber

such that there was no bending effect on the fiber. This fiber holder was fixed on

motor controlled translation stage. Lens is used to focus CO2 laser beam on the fiber.

The fiber was irradiated with laser beam for less than one second. Then displacement

of 600µm was given to fiber along its axis. Again fiber was exposed to laser output

for less than one second. The same steps were repeated to complete 60 exposures. The

formation of grating was monitored online by observing transmission spectrum of the

grating using optical spectrum analyzer. The transmission spectrum is given in

Fig.4.7. Using the same technique we fabricated the LPG of grating period 610 µm

and transmission spectrum of the same is given in Fig. 4.8.

Figure 4.6: Schematic diagram of fabrication of LPG.

Table 4.1 Fiber Details

Refractive Index Profile Step Index

Numetical Aperture 0.13

Mode Field Diameter 9.3±0.5µm

Core Material Germano Silicate

Cladding Diameter 125±1µm

Cladding material Pure silica

Buffer Coating diameter 245±1µm

Buffer Coating Acrylate

Operating Wavelength 1550nm

Cut off wavelength 1260±40nm


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This point by point method of LPG fabrication using CO2 laser is a very

simple and less expensive method. It can be implemented with full reliability. The

basic need of this method is precise translation stage and stable laser source.

4.8 LPG Characterization

The LPGs were characterized using transmission spectrum recorded on OSA.

The transmitted spectrum of LPG with grating period 600µm is shown in the Fig. 4.7.

The length of LPG is 3.9mm. It has two low resonant dips at 1.446µm and 1.522µm

with transmission loss -5.98dB and -10.02dB respectively.

Figure 4.7: Transmission spectrum of LPG of period 600µm.

Table 4.2 CO2 Laser details

Wavelength 10.6µm

Output Power 12W

Beam diameter 2.4mm

Divergence angle 5.5mrad

Make Access Laser Company

Model: LASY -12

1.6

-10

0

-20

1.1 1.35

TRANSMISSION

dB

µm


123

The transmission spectrum of another LPG of grating period 610µm is shown in Fig.

4.8. The length of this LPG is 4mm. It has two attenuation bands centered at

1.5192µm and 1.44µm with transmission loss of –8.56dB and -5.43dB respectively.

Figure 4.8: Transmission spectrum of 610µm period LPG.

Table 4.3. Characteristic Parameters of Fabricated LPGs

S. No Fiber used Period

in µm

Transmission

dips in µm

Amplitude

of dip in dB

LPG 1 Communication

grade fiber

600

1.522 -10.02

1.446 -5.98

LPG 2 Communication

grade fiber

610

1.5192 -8.56

1.440 -5.43

1.6

-10

0

-20

1.1 1.35

TRANSMISSION

dB

µm


124

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