Recent Res. Devel. Optics, 8 (2013): 11-30 ISBN: 978-81-308-0478-1 2. Experimental ... · · 2015-02-12Recent Res. Devel. Optics, 8 (2013): 11-30 ISBN: 978-81-308-0478-1 2. Experimental

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Original Article

Recent Res. Devel. Optics, 8 (2013): 11-30 ISBN: 978-81-308-0478-1

2. Experimental polarimetric properties of

long-period fiber gratings

Karla M. Salas-Alcántara, Rafael Espinosa-Luna and Ismael Torres-Gómez Centro de Investigaciones en Óptica, A. C., Loma del Bosque 115, Colonia Lomas del

Campestre, 37150 León, Guanajuato, México

Abstract. A Mueller-Stokes analysis of the polarization characteristics of both mechanical and UV-induced long-period fiber gratings is presented. An explicit methodology for the experimental determination of the complete Mueller matrix is reported. Some scalar polarimetric metrics are applied for the determination of the diattenuation (absorption), PDL, gain, attenuation, depolarization degree of anisotropy, among others. The results show a clear dependence on the incident polarization states, which could be employed to design and control the output signal from these fibers or from potential polarization-based devices.

Introduction

Long-period fiber gratings (LPFGs) are in-fiber optic components, which

have found attractive applications in optical communication networks and

optical measurement systems [1]. In optical telecommunication, this

component has been used in the equalization spectral gain of erbium doped

fiber amplifiers (EDFAs) and fiber lasers also band-rejection filters [2-3].

LPFGs have found application as polarization-dependent multi-wavelength

filter, polarization dependent loss compensation. In optical measurement systems,

Correspondence/Reprint request: Dr. Rafael Espinosa-Luna, GIPYS Lab, Centro de Investigaciones en Óptica

León, Guanajuato, México. E-mail: [email protected]

Karla M. Salas-Alcántara et al. 12

LPFGs have shown applications as optical transducers to sense physical and

chemical parameters, such as temperature, torsion, bending, stress, refractive

index, O2 concentration and pH, between others [4-5].

Long-period gratings are periodic structures that couple co-propagating

modes in optical fibers. Since the coupling ratio changes with wavelength,

the LPFG acts as a wavelength-dependent loss element. Phase matching

condition occurs at a range of different wavelengths associated to the

excitation of specific higher order cladding modes. The specific cladding

mode through which the core mode is coupled is determined by the following

resonance condition:

)( m

cladcoreresm nn (1)

where ncore and nclad are the effective refraction indices of the fundamental

guided mode and the m-th order cladding mode, Λ is the period of the

grating, and λm res is the resonance wavelength. The resonant wavelengths

depend on the fiber characteristics through the effective indices of the core

and cladding. Hence, the change of the grating period Λ and the effective

refraction index of the cladding mode will affect the resonant wavelength of

the corresponding cladding mode. This property of the LPFGs makes

attractive for applications in optical, biological and chemical sensing and

many more [6-8]. According to the LPFG fabrication technique, the

respective fabrication parameters, and also on the fiber type, several

mechanisms may contribute simultaneously to the grating formation [9].

Consequently, the polarization optical response depends on the characteristics

of the grating. Several studies about the polarization dependent loss (PDL)

have been published; however, these studies are focused on the response to

only two states of polarization mutually orthogonal [10].

This chapter is dedicated to the determination of the Mueller matrix

associated to both a mechanical- and an ultraviolet (UV)- induced long-

period fiber gratings. The Mueller matrix, MM, is determined through the

Stokes vectors, which are measured by using an incomplete, commercially

available, Stokes polarimeter. The 4-method has been used for the

determination of the MM associated to a commercially available ultraviolet

long-period fiber grating (UV-LPFG) in a H2 pre-loading fiber (all fiber

measurement) and a mechanically induced long-period fiber grating

(M-LPFG) in a photonic crystal fiber, in an open space measurement. Results

show an increasing in the birefringence when the LPFG is present in the

fiber. The PDL values of the UV-LPFG are intrinsically low in comparison to

the grating produced by mechanically induced technique. It should be noted

that the method employed here to determine the scalar depolarization metrics

Experimental polarimetric properties of long-period fiber gratings 13

provides more accurate information than the usually reported, where only two

orthogonal linear polarizations are used.

1. Long-period fiber gratings fabrication technique

The fabrication of LPFGs implies the introduction of a periodic index

modulation of the core in the optical fiber. This can be obtained by

permanent modification of the refractive index of the fiber core or by

temporal physical deformation of the fiber, respectively. Techniques like UV

irradiation, laser CO2 exposure, electric arc discharge, mechanical

microbends, etched corrugations, ion beam implantation, and femtosecond

laser exposure, among others [11-13]. In the following section, a brief

overview of the manufacture of LPFGs by UV induced and mechanical

methods will be described. In sections 8 and 9 we will determine the Mueller

matrix and calculated some scalar polarimetric metrics for LPFGs

manufactured by these two techniques.

2. LPFGs manufactured by UV radiation

The ultraviolet (UV) irradiation was the first method used to manufacture

gratings in 1989 by Meltz et al., who used holographic interference between

two coherent beams directed to the fiber core [14]. The UV exposure method

requires that the fiber first be made receptive to UV irradiation, i.e. the fiber

must be made photosensitive prior to writing the grating. It can be obtained

by doping the fiber core (usually of silica) with impurity atoms (such as

germanium, boron or a combination of these elements through the fabrication

process) or by hydrogen loading exposing the fiber to high-pressure H2 gas at

elevated temperatures for a long period of time so that hydrogen diffusion

into the core material takes place. The later method is preferable because

hydrogen loading can be achieved in standard fibers, providing a cheaper and

simpler way to obtain UV photosensitivity fibers [15].

The UV inscription method for LPFGs can be made in two other ways.

One of them consists on the irradiation of the fiber through an amplitude

mask with the desired period [16]. The inscription occurs when the UV

irradiation is exposed in front of the mask where alternate bands of maximum

intensity are transmitted. The exposure is repeated until the index modulation

has reached a sufficient level to provide the desired attenuation depth in the

LPFG transmission spectrum. This technique implies a permanent

modification of the refractive index of the fiber core. A second way to

generate gratings with UV irradiation is based on a periodic point by point

modulation of the core refractive index until the desired grating length is


obtained. In general, both techniques above described are considered

expensive.

3. Mechanically induced long-period fiber gratings

The optical refractive index of glass can be modulated when the glass is exposed to stress. Because the index modulation period in a LPFG can be as large as hundreds of micrometers, it is possible to induce it mechanically via the photoelastic effect. Different techniques of mechanically induced LPFGs (M-LPFGs) have been reported in standard fibers and microstructured fibers, where corrugated plates, strings, and springs have been used to apply periodic mechanical stress on the optical fiber in order to induce the effective index modulation to obtain the coupling of light from the fundamental mode to cladding modes [17-19]. One of the most relevant characteristics that share these techniques is their tunability by simple adjustment of the mechanical stress period. Under this concept, mechanically induced LPFGs offer a tuning range at least one order of magnitude wider than other methods reported in tunable permanent recorded LPFGs with similar isolation loss and line-width.

4. Mueller matrix method

Polarization effects play a key role in the operation of many important optical devices. The complete characterization of scattered light is described by Stokes vectors and Mueller matrices. The most general form of the scattering matrix coupled with polarizer and quarter wave plates demonstrates the physical relationships among the matrix elements and polarization measurements. The Mueller matrix method is most commonly suited for describing irradiance-measuring instruments, including most polarimeter, radiometers and spectrometers. In the Mueller matrix method (MMM), the Stokes vector S is used to describe the polarization state of a light beam, and the Mueller matrix M to describe the polarization-altering characteristics from a sample. This sample may be a surface, a polarization element, an optical system, biological tissues, and any other light-matter interaction, which produces a reflected, refracted, diffracted, absorption, or scattering of the light beam. Popular theories of polarized light interaction with optical elements or scattering media may be divided into two groups: Jones matrix, which assumes a coherent addition of waves; and the Stokes-Mueller matrix, which assumes an incoherent addition of waves. In both approaches, one usually starts a theoretical analysis with severely restrictive assumptions. In the Jones matrix, one starts out with Maxwell´s equations, whereas in the Mueller matrix, it starts by postulating a linear relation between the input Stokes vector and the


output Stokes vector emerging from the optical medium. The development of the Mueller analysis is heuristic and has an advantage in that it deals with intensities rather than field vectors. The Mueller matrix represents the polarization rotation characteristics of

an optical device such as an optical fiber, which is determined by the

relationship between a set of input polarization vectors and their

corresponding output polarization vectors. The linear response of a physical

system can be expressed in terms of the intensities, through the relation [20]

iiii

iiii

iiii

iiii

i

i

i

i

o

o

o

o

io

smsmsmsm

smsmsmsm

smsmsmsm

smsmsmsm

s

s

s

s

mmmm

mmmm

mmmm

mmmm

s

s

s

s

MSS

333232131030

323222121020

313212111010

303202101000

3

2

1

0

33323130

23222120

13121110

03020100

3

2

1

0

(2)

where M is called the Mueller matrix of the system, represented as a 4 4

matrix with real elements, and S is the Stokes vector. S represents the

polarization state of light, defined in terms of the orthogonal components of

the electric field vector (Ep, Es) and its phase difference.

)**(

**

**

**

3

2

1

0

a

p

a

s

a

s

a

p

a

p

a

s

a

s

a

p

a

s

a

s

a

p

a

p

a

s

a

s

a

p

a

p

a

a

a

a

a

EEEEi

EEEE

EEEE

EEEE

s

s

s

s

S

(3)

where a = incidence (i) or output (o). Angular brackets represent temporal

averages and * indicates complex conjugation of a

spE , , 12i is the complex

number. The upper (lower) sign in the right-hand side of as3 corresponds to a

description of polarization states as looking to the source (propagation

direction).

The normalized Stokes parameters can be displayed in a real three

dimensional space as a function of the azimuth 0 and the ellipticity

angles 44

of the polarization ellipse, respectively.

)2sin(

)2sin()2cos(

)2cos()2cos(

1

0sS

(4)


Where 0s represents the average intensity associated to the Stokes parameters;

usually, it is fixed to the unitary value.

5. Ideal polarimeter arrangement (IPA)

A typical polarimeter arrangement consists of a Source + PSG + Sample

+ PSA + Detector. See figure 1. The incident Stokes vectors are generated by

a Polarizer State Generator, PSG, and a source; while the scattered Stokes

vector from the sample under study is analyzed or “filtered” by a Polarizer

State Analyzer, PSA. The exiting intensity from the PSA is measured by a

sensor or detector device. Usually a PSA is named as a Polarization State

Detector, PSD, when the analyzer is a system composed of a PSA plus a

sensor (detector) of intensity. It is common to find a mirror-symmetry order

between the optical components that constitute a PSG (linear polarizer +

quarter-wave retardation plate) and a PSA (quarter-wave retardation plate +

linear polarizer), for a complete polarimeter arrangement. For a passive Ideal

Polarimeter Arrangement, IPA, the output Stokes vector reaching the detector

is given as

3

0

3

0

det

k

i

kjk

j

ij

oi smaASAMSS

(5)

Where A is the Mueller matrix that describes the action of the PSA on the

Stokes vector scattered (So) from the sample (M). An IPA arrangement is

formed by classical, passive, optical polarization elements, like linear

polarizers (LP) based in calcite crystal (of the Glan-Thompson, Glan-Laser,

Glan-Taylor, Rochon, or of the Wollaston-type), wave-plate retarders made

of mica, quartz, polarizing thin-films, among many other possibilities, and

where the theoretical linear response is supposed to be ideal. Indeed, there is

not any formal restriction if the passive retarders of an IPA are changed by

Liquid Crystal Variable Retarders, LCVR, set to a fixed voltage.

Figure 1. A typical complete polarimeter arrangement (IPA).


6. Mueller matrix determination

For an arbitrary optical system and by considering an IPA setup, it has

been shown that the 16 Mueller elements can be obtained from a set of 4

incident Stokes vectors (PSG) and 4 states filtered or analyzed (PSA) [21].

The Stokes vectors correspond to linear polarization states parallel (p),

perpendicular (s), and to +45 degrees (+) respect to the incidence plane,

respectively, and to a right-hand (r) polarization state. The polarized states

mentioned above, form a tetrahedron inscribed into/within the Poincaré

sphere, whose vertexes are contained on the surface. The 16 arbitrary Mueller

elements can be determined from the following 16 intensity-measurements

taken from the so detected Stokes element [22]:

)(2

1);(

2

1

)(2

1);(

2

1

)(2

1);(

2

1

)(2

1);(

2

1

)(2

1);(

2

1

)(2

1);(

2

1

)(2

1);(

2

1

)(2

1);(

2

1

3330030023200300

1310030013100300

3230020022200200

1210020012100200

3101300021012000

1001110011011000

3130010021200100

1110010011100100

mmmmImmmmI

mmmmImmmmI

mmmmImmmmI

mmmmImmmmI

mmmmImmmmI

mmmmImmmmI

mmmmImmmmI

mmmmImmmmI

rrr

rsrp

r

sp

srs

sssp

prp

pspp

(6)

where Imn = (s0)mn denotes the intensity measured when an m-polarized state

illuminates the sample and an n-polarized state is analyzed. The Mueller

matrix is obtained by solving the equation (6) for each of the 16 mij elements.

On the other hand, we have used a commercially available deterministic

polarizer generator and an incomplete polarimeter analyzer (PAX) for the

determination of the Mueller matrix, where the normalized output is registered

as:

3

2

1

´

´

´

1

s

s

sS PAX

(7)


From Eq. (2), the scattered Stokes vector incident onto the PSD analyzer is

closely related to the incident Stokes vector on the sample. For the set of 4

incident polarization states considered here, the scattered Stokes vectors from

the sample (represented as sio

) are expressed by [22, 25]

3330

2320

1310

0300

3230

2220

1210

0200

3130

2120

1110

0100

3130

2120

1110

0100

,,,

mm

mm

mm

mm

S

mm

mm

mm

mm

S

mm

mm

mm

mm

S

mm

mm

mm

mm

S roosopo

(8)

The “power” detected is given by the total intensity associated to each

scattered Stokes vector, according to

03000020000100001000 ,,, mmsmmsmmsmms rddsdpd

(9)

On the other hand, the detected normalized Stokes vectors (Sid

) are displayed

as

3130

2120

1110

0100

0

3

2

1

3130

2120

1110

0100

0

3

2

1 1

1

,1

1

mm

mm

mm

mm

s

s

s

sS

mm

mm

mm

mm

s

s

s

sS

sd

sd

sd

sd

sd

pd

pd

pd

pd

pd

(10a)

And

3330

2320

1310

0300

0

3

2

1

3230

2220

1210

0200

0

3

2

1 1

1

,1

1

mm

mm

mm

mm

s

s

s

sS

mm

mm

mm

mm

s

s

s

sS

rd

rd

rd

rd

rd

d

d

d

d

d

(10b)

The 16 elements of the Mueller matrix are obtained from eqs. (9 and 10)

300333300332030331030330

2002232002220202210202120

100113100112010111010110

000030000200010000

,),(2

1),(

2

1

,),(2

1),(

2

1

,),(2

1),(

2

1

,),(2

1),(

2

1

mssmmssmssssmssssm

mssmmssmssssmssssm

mssmmssmssssmssssm

msmmsmssmssm

rdrdddsdsdpdpdsdsdpdpd



rddsdpdsdpd

(11)


7. Polarimetric scalar metrics

By using the following depolarization scalar metrics (see Table 1) it is

possible to analyze the polarimetric properties associated to the long-period

fiber grating and its capability to depolarize light, in order to predict and

understand the LPFGs behavior [22-24].

Table 1. Polarimetric scalar metrics applied for the analysis of the obtained Mueller

matrix.

Depolarization index,

DI(M). 13/)(0 00

2/13

0,

2

00

2 mmmMDIkj

jk

Degree of polarization,

DoP(M,S). 1

)()()()(

),(0303202101000

2

1

3

1

2

33221100

0

2

3

2

2

2

1

iiii

j

i

j

i

j

i

j

i

j

o

ooo

smsmsmsm

smsmsmsm

s

sssSMDoP

Anisotropic degree of

depolarization, Add. 1

)()(

)()(0

min

min

oo

Max

oo

Max

DoPDoP

DoPDoPAdd

Diattenuation parameter,

D(M).

1/)(0 00

2

03

2

02

2

01 mmmmMD

Polarizance parameter,

P(M).

1/)(0 00

2

30

2

20

2

10 mmmmMP

The Q(M) metric.

3)]([1

)]([/

)]([1

)]([)]([3)(0

2

22

00

3

1,

2

2

22

3

0

2

0

3

0,1

2

MD

MPmm

MD

MDMDI

m

m

MQkj

jk

k

k

kj

jk

The Gil-Bernabeu

theorem.

2

004)( mMMTr t

The polarization

dependent loss, PDL.

2/12

03

2

02

2

0100

2/12

03

2

02

2

0100

)(

)(log10min)max/log(10

mmmm

mmmmTTPDL

Gain, g. 10

0

303202101000

0

0

i

iiii

i

o

s

smsmsmsm

s

sg

8. MM of the LPFG induced by UV radiation

In Section 2, we have described briefly the technique used to fabricate

the UV-long-period fiber grating. Now, we present the Mueller matrix and

the polarimetric characterization associated to a commercially available UV


induced long-period fiber in a H2 pre-loading fiber, when the PSG and the

PSA are contained into an enclosed space (all optical fiber). In order to

determine the MM of the UV-LPFG, the setup shown in figure 2 was used.

The source is a Tunable Laser at 1450-1590 nm, from Anritsu, Tunics Plus

SC. This laser is connected to a Deterministic Polarization Controller

(Thorlabs, model DPC5500) input. The output signal from the DPC is used as

a PSG for the fiber under study, which is connected directly to the polarizer

state analyzer PSA (Thorlabs, model PAX5710/IR3) and the measurements

are taken for the 4 incident polarization states p, s, +45, and r, respectively. A

laptop computer controls the PSG and the PSA and a software program

provides the results obtained.

Figure 3 shows the transmission spectra of the UV-LPFG studied here.

The UV-LPFG transmission spectra have been measured using an un-polarized

Figure 2. Experimental setup applied for the determination of the Mueller matrix

associated to a UV-LPFG in a H2 pre-loading fiber.

Figure 3. Transmission wavelength response of UV long-period fiber grating with

resonance centered at 1543 nm.


source (white-light source AQ4305) and an optical spectrum analyzer

(AQ6315A) with a wavelength resolution of 2 nm.

For the analysis of the polarimetric properties, we have determined the

Mueller matrix of the fiber with and without the UV-LPFG, at the main

resonance (1543 nm). The normalized Mueller matrix obtained for the fiber

without grating, at 1543 nm, is given by

1343.04444.08884.00007.0

8235.04294.01339.00483.0

4540.07746.04351.00166.0

0000.00000.00000.00000.1

FiberM

(12)

We can obtain some insight about the polarimetric characteristics of a given

system, by analyzing the form of its associated Mueller matrix. The form of

this matrix, Eq. (12), suggests a depolarization effect (the presence of non-

zero values on the upper and the lower side of the main diagonal) and phase

retardation also. It should be noted that this information could not be obtained

if only the p- and the s-polarization states were employed as the incident

Stokes states.

To show the general potential from the MM obtained, Eq. (12), we have

calculated the polarimetric response for some characteristic parameters (table 2

and figure 4). The gain has the unitary value for all the incident polarization

states, according to Fig. 4(a). The degree of polarization DoP, Fig 4(b), has

some kind of anisotropy behavior dependent of the incident polarization

states. The deterioration mechanism in the polarization degree is based on the

assumption that an arbitrary incident polarized light is split into two separate

eigen-polarization modes, which propagate at different group velocity values.

Calculating the anisotropic degree of depolarization, a value of 0.022 is

obtained. The Poincaré output response, Figure 4(c), has not a spherical

symmetry, which can be interpreted as the presence of depolarization effects

due to the reduction of the degree of polarization of light at the propagation

through the optical fiber. As a consequence of the birefringence, due to possible

deviations of the core from the circular cross section, as well as transverse

stress, the poles of the sphere rotate.

In order to investigate the influence of UV-LPFG on the fiber, at 1543 nm,

the corresponding (normalized) Mueller matrix obtained is given by

0971.02047.09611.00092.0

3487.08472.02451.00421.0

8735.03532.01139.00331.0

0067.00069.00023.00000.1

1543LPFGM

(13)


Figure 4. Analysis of the Mueller matrix associated to H2 pre-loading fiber. Fig. (4a)

gain, (4b) degree of polarization, (4c) the Poincaré output sphere, and (4d) attenuation

(dB).

The form of this matrix, suggests the presence of diattenuation effects,

polarizance and a marked depolarization effect that can be attributed to the

presence of UV-LPFG in the fiber (the exposure of the fiber to the UV beam

creates an index change in the core). The grating coupling strength occurs at

1543 nm for un-polarized broadband white light source. In this way, the

transmission is reduced; that is, the diattenuation increases also. The results

obtained are shown in figure 5 and table 2.

According to figure 5(a), the gain depends strongly of the polarization

state incident in the optical fiber (basal plane); the variation is due to the

intrinsic birefringence of the fiber. On the other hand, the output degree of

polarization, figure 5(b), shows a tendency to polarize light linearly and to

depolarize slightly for some incident polarization states. The Poincaré sphere

representation of the output polarization states, figure 5(c), confirms the

presence of depolarization effects and an increase of birefringence induced in


Figure 5. Analysis of the Mueller matrix associated to the UV-LPFG fiber. Fig. (5a)

gain, (5b) output degree of polarization, (5c) the Poincaré output sphere, (5d)

attenuation (dB).

Table 2. Polarimetric data obtained from the Mueller matrix associated to the fiber

without and with UV-LPFG.

D(M) P(M) DI(M) Q(M) Tr PDL Add

Fiber 0.0000 0.0511 0.9804 2.8834 0.9709 0.0000 0.0222

UV-LPFG 0.0671 0.0543 0.9631 2.7658 0.9547 1.3449 0.0574

the fiber core due to the UV radiation exposure. The attenuation, figure 5(d),

shows a strong dependence of the polarization state incident in the optical

fiber, which is caused because the transmission is reduced due to the presence

of the UV-LPFG.

Additional information about the behavior of the pre-loading H2 fiber,

and the fiber, with and without a UV-LPFG can be obtained from the

polarimetric data (table 2).

From previous results (table 2) we can build the following conclusions:

The diattenuation parameter, D(M), indicates the UV-LPFG generates a


diattenuation effect, not present without the induced grating. In this sense the

diattenuation, D(M), increases greatly with the presence of the UV-LPFG.

This behavior can be understood as follows: The period of the LPFG shows a

resonance wavelength at 1543 nm. In this way, the transmission is reduced

because the resonance occurs; that is, the diattenuation is increased. The

LPFG affects the response to the transmitting polarization also. The physical

mechanism responsible of this behavior must be associated to a dichroic,

highly birefringent change in the core due to the UV-LPFG. The

depolarization index, DI(M), the Q(M) depolarization scalar metric, and the

theorem of Gil-Bernabeu, all of them provide consistent results that indicate

effect of depolarization. We can also observe that the PDL parameter value

just indicates that the fiber is affected by the presence of the UV-LPFG as a

consequence of the birefringence present in the grating structure. The PDL

values are intrinsically low in comparison to gratings produced by other

techniques used to fabricate them like through mechanical stress [22, 26],

electric arc discharges, gratings produced by CO2 laser radiation, among

others. Even more when the response to each of the 4-polarization incident

states generates a high degree of polarization output states (see table 1), the

arithmetic average behavior shows a tendency to a loss of the DoP for any

PSG when the UV-LPFG is on the fiber.

9. MM of the mechanically induced long-period fiber grating

In this section the Mueller matrix associated to a mechanically induced

long-period fiber grating is analyzed. The MM measurements have been

performed in the fiber before and after grating inscription, respectively. For

the measurements, we have used the experimental setup depicted schematically

in figure 6. It consists of a source (continuous-wave Ytterbium Doped Fiber

Laser at 1064 nm, from IPG Photonics, PYL-10LP). This laser illuminates

the polarizer state generator, PSG, which consists of a linear polarizer of the

Glan-Laser type (Thorlabs, model GL10), a half-wave plate (Thorlabs,

WPMH05M-1064) and a quarter-wave plate (Thorlabs, WPMQ05M-1064).

The fiber used in the experiment is a commercial photonic crystal fiber

(PCF) denominated F-SM10, figure 7. The Mechanically induced LPFG

(M-LPFG) was generated by pressing a section of the Photonic Crystal Fiber

between two corrugated grooved plates (CGPs). In figure (7a) it can be

observed the spectrum of a LPFG with a period of 480 µm; the period of the

M-LPFG has been designed to show resonance at the wavelength employed

(1064 nm). The PCF is connected directly to the polarizer state analyzer, PSA

(Thorlabs Polarimeter, PAX5710/IR2) and the measurements are taken for


Figure 6. Experimental setup employed for the determination of the Mueller matrix

associated to a photonic crystal fiber and to a photonic crystal fiber with a

mechanically induced long-period fiber grating, respectively [22].

Figure 7. a) The transversal structure of the F-SM10. b) Transmission wavelength

response of the M-LPFG in the PCF.

the 4-incident polarization states p, s, +45 and r respectively. In order to show

the quality of the polarization states generated and detected by our

polarimetric system. We have self-calibrated our equipment with respect to

the air [22].

Using the PCF as the calibration reference, the normalized Mueller

matrix obtained for the PCF, is given by

9651.03109.00250.00220.0

1641.09183.00669.00128.0

1641.02206.09970.00014.0

0000.00000.00000.00000.1

PCFM

(14)

where we can observe that the value of elements of the main diagonal

Mueller matrix are close to unitary values. An important result we have found


here, is just that the PCF has a tendency to maintain the incident polarization

states. The first row indicates there is not diattenuation (light travels through

the fiber without perturbation). However, the presence of non-zero values on

the upper and the lower side of the main diagonal, indicates the presence of

phase retardation effects. The following information can be deduced of the

graphical elements of the Mueller matrix (see figure 8).

According to figure (8a), the gain has the unitary value for all the

incident polarization states. The output degree of polarization varies around

the unitary value and the PCF has a strongly dependence on the input

polarization states, figure (8b). The anisotropic degree of depolarization

provides a value of 0.1718. We believe this value reflects an intrinsic

anisotropic depolarization behavior associated to the PCF, which can not be

identified if only the orthogonal polarizations p and s are used. Finally, the

Poincaré output sphere suffers a slightly deformation with respect to the

spherically symmetric Poincaré sphere associated to the input polarization

states. This is a consequence of the non-zero value associated to Eq. (14).

Figure 8. Analysis of the Mueller matrix associated to the PCF. Figures (8a) show the

gain, (8b) the output degree of polarization, (8c) the Poincaré output sphere and (8d)

the attenuation.


Finally, the attenuation in the fiber is practically zero due to the length of the

PCF is short (140 cm), see figure (8d).

In order to know the polarimetric response of a LPFG formed by

mechanical-induced pressure technique, the normalized Mueller matrix was

obtained also [22]

3266.03759.08056.00077.0

0762.05138.04730.00070.0

4761.05622.03471.00812.0

3463.02004.00187.00000.1

LPFGPCFM

(15)

The M-LPFG on the PCF fiber produces evident effects such as diattenuation (first row) and a marked depolarization effect (first row and the main diagonal values). In this case there is an increase of phase retardation and depolarization effects also, according to the values shown in the upper and the lower diagonal parts of the matrix given by Eq. (15). The transmission is reduced because the phase matching condition is fulfilled; that is, the diattenuation is increased. The polarizance, P(M), increases 320% with the presence of the M-LPFG (see table 3). The Add value increases with the presence of the M-LPFG on the PCF, which means the system becomes more anisotropic for some incident polarization states. By drawing the Mueller elements in a real three dimensional space as a function of the azimuth and the ellipticity angles of the polarization ellipse, the following information was obtained. The gain, figure (9a) depends strongly of the polarization state incident in the photonic crystal fiber. On the other hand, the output degree of polarization, figure (9b), shows a tendency to polarize light linearly and to depolarize with the presence of the M-LPFG. Finally, the Poincaré sphere, figure (9c) confirms the previous arguments: a reduction of the unitary radius is associated to anisotropic depolarization effects, and a deviation of the spherical shape is associated to an anisotropic degree of depolarization, Eq. (15), and the rotation of the axis, is associated to the presence of birefringence. These effects increase with the presence of the M-LPFG in the PCF. Experimentally it is very hard to obtain a perfect generation and analysis of the polarization states, mainly for circular polarization. This is the reason why the output degree of polarization is slightly up to its physical limit. However, the results we have reported here are as close as possible within the precision values considered by the manufacturer of our equipment. Additional information about the behavior of the UV-LPFG can be

obtained from the polarimetric data, through their respective Mueller matrices,

see table 3.


Figure 9. Analysis of the Mueller matrix associated to the PCF with M-LPFG. Figures

(9a) show the gain, (9b) the output degree of polarization, (9c) the Poincaré output

sphere and (9d) the attenuation.

Table 3. Polarimetric data obtained from the Mueller matrix associated to the PCF and to the PCF+M-LPFG.

D(M) P(M) DI(M) Q(M) Tr PDL(dB) Add

PCF 0.0000 0.0255 0.9914 2.9489 0.9872 0.0000 0.1718

PCF+LPFG 0.4006 0.0818 0.8604 1.7755 0.8052 8.4864 0.1751

The diattenuation parameter, D(M), indicates the M-LPFG generates a

diattenuation effect, not present without the induced grating (which is used

here as the reference). The depolarization index, DI(M), the Q(M)

depolarization scalar metric, and the theorem of Gil-Bernabeu, all of them

provide consistent results that indicate the presence of the LPFG increases in

a 15% the effect of depolarization. This numerical result is coherent with the

qualitative behavior presented with the deformation spherical shape of the


Poincaré output sphere, Fig. (9c). We can also observe that the PDL

parameter value just indicates that the PCF is affected by the presence of the

M-LPFG. Even more when the response to each of the 4-polarization incident

states generates a high degree of polarization output states (see table 3), the

arithmetic average behavior shows a tendency to a loss of the DoP for any

PSG when the M-LPFG is in the PCF.

10. Conclusions

We have presented the explicit relationships for the intensity

measurements required for the experimental determination of the Mueller

matrix associated to an arbitrary optical system. The 4-method has been used

in the determination of the Mueller matrix associated to both UV-and

mechanical- induced and long-period fiber gratings. Because the performance

of the optical fiber is directly related to its polarization properties, we have

calculated the depolarization index, DI(M), the Q(M) depolarization scalar

metric, the theorem of Gil-Bernabeu, the degree of polarization, DoP, and

the anisotropic depolarization degree, Add. These metrics provide consistent

results that indicate an increasing in the birefringence when the LPFG is

presented in the fiber. The PDL values of the UV-LPFG are intrinsically low

in comparison to gratings produced by mechanically induced technique. It

should be noted that the method employed here to determine the scalar

depolarization metrics provides more accurate information than the usually

reported where only two orthogonal linear polarizations are used, which

could be used to design and control the output signal from these fibers or

from potential polarization-based-devices such as optical detectors, optical

components, optical testing sets, and optical fiber sensing.

Acknowledgements

K. M. Salas-Alcántara and R. Espinosa-Luna acknowledge to CONACYT

for the economical support provided for the realization of this work, under

projects 100361 and Bisnano.

References

1. Vengsarkar, A. M., Pedrazzani, J. R., Judkins, J. B., Lemaire, P. J. 1996, Opt.

Lett., 21, 336.

2. Pandit, M. K., Chiang, K. S., Chen Z. H., Li., S. P. 2000, Microwave Opt.

Technol. Lett., 25, 181.


3. Eggleton, B. J., Slusher, R. E., Judkins, J. B., Stark, J. B., Vengsarkar, A. M.

1997, Opt. Lett., 22, 883.

4. Yan, M., Luo S., Zhan L., Zhang, Z., Xia, Y. 2007, Opt. Express, 15, 3685.

5. Ceballos-Herrera, D. E., Torres-Gómez, I., Martínez-Rios, A., Sanchez-

Mondragon J. J. 2010, IEEE Sens. J., 10, 1200.

6. Tang, J. L, Wang J. N. 2008, Sensors, 8, 171.

7. Rindorf L., Jensen J. B. 2006, Opt. Express, 14, 8224.

8. Tatam J. S. 2003, Meas. Sci. Technol., 14, R49.

9. Martinez-Rios A., Monzon-Hernández D., Torres-Gomez, I., Salceda-Delgado G.

2012, Fiber Optic Sensors, InTech. 11, 275.

10. Rego G., Melo M, Santos J. L., Salgado H.M. 2006, Opt. Commun., 262, 152.

11. Davis, D. D., Gaylod, T. K., Glytsis, E. N., Kosinski, S. G., Mettler S. C.,

Vengsarkar, A. M. 1998, Electron. Lett., 26, 61.

12. Hwang, I. K., Yun, S. H., Kim, B. Y. 1999, Opt. Lett., 24, 1263.

13. Rego G., Dianov E., Sulimov, V. 2001, Lightwave Technol., 19, 1547.

14. Meltz G., Morey, W., Glenn W. 1989, Opt. Lett., 14, 823.

15. Hill, K., Fuji, Y., Johnson, D., Kawasaki, B. 1987, Appl. Phys. Lett., 62, 647.

16. Kashyap R. 1999, Optics and Photonics, 3, 85.

17. Savin, S., Digonnet, M. J. F., Kino, G. S., Shaw, H. 2000, Opt. Lett., 25, 710.

18. Rego, G., Fernandez, J. R. A., Santos, J. L., Salgado, H. M., Marques, P. V. S.

2003, Opt. Commun., 220, 111.

19. Yokouchi, T., Suzaki, Y., Nakagawa, K., Yamauchi, M., Kimura, M., Mizutani,

Y., Kimura, S., Ejima, S. 2005, Appl. Opt., 44, 5024.

20. Goldstein D. 2003, Polarized Light, second ed., Marcel Dekker.

21. Espinosa-Luna R., Mendoza-Suárez, A., Atondo-Rubio, G., Hinojosa, S., Rivera-

Vázquez, J. O, Guillén-Bonilla, J. T. 2006, Opt. Commun., 259, 60.

22. Salas-Alcántara, K., Espinosa-Luna, R., Torres-Gómez, I. 2012, Opt. Eng.,

51, 085005.

23. Peinado, A., Lizana, A., Vidal, J., Iemmi, C., Campos, J. 2010, Opt. Express,

18, 9815.

24. Gil, J. J., Bernabeu, E. 1985, Opt. Acta 32, 259.

25. Atondo-Rubio, G., Espinosa-Luna, R., Mendoza-Suárez, A. 2005, Opt. Commun.,

244,7.

26. Efimov, T. A., Bock, W. J., Chen J., Mikulic P. 2009, Lightwave Tech., 27, 3759.

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Recent Res. Devel. Optics, 8 (2013): 11-30 ISBN: 978-81-308-0478-1 2. Experimental ... · · 2015-02-12Recent Res. Devel. Optics, 8 (2013): 11-30 ISBN: 978-81-308-0478-1 2. Experimental