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  • 1

    Optoelectronics

    Optical fiber

    (Optical fiber sensors)

    Institutionen frFysik ochMtteknik

    Arno Platau11-02-2001Version 1

  • 2

    Table of content

    1. Introduction. 3

    2. Some propertis of optical fibers. 4

    2.1. Graded index lenses. 7

    3. Wave optics and modes in optical fibers. 8

    Project #1: Measuring the numerical aperture. 11

    Project #2: Observing fiber modes. 12

    Project #3: Proximity sensor. 12

    Project #4: Pressure sensor. 14

    Project #5: Interferometric temperature sensor. 16

    References. 19

  • 3

    1. Introduction.

    In recent times optical fiber have been developed for application in communication systems.

    The achievement of low-loss transmission, along with the additional advantages of large infor-

    mation carrying capacity, immunity from electromagnetic interference, and small size and

    weight, has created a new technology. Optical fiber has become the medium of choice for

    communications applications. For example, the TAT-8 (Trans-AtlanticTelephon #8) system

    (1988), is a 6500-km all-fiber link which has trans-Atlantic telephone capacity to the equivalent

    of 20 000 voice channels. Compare this with TAT-1, completed in 1955, which carried 50 voice

    channels over coaxial cable. Optical fiber is also being used extensively in Local Area Networks

    (LANs), which are used for voice or data communications within or between buildings. Many

    new buildings are now being built with fiber installed in their framework for future LAN use.

    Optical fiber is also used in sensor applications, where the high sensitivity, low loss,

    and electromagnetic interference immunity of the fibers can be expoited. Optical fibers are

    versatile and sensors can be designed to detect many physical parameters, such as temperature,

    pressure, strain, and electrical and magnetic fields, using either the power transmission

    properties of multimode fibers or the phase sensitive properties of single-mode fibers.

    In the laboratory You will have the opportunity to study five projects i fiber optics.

    1. Measuring the numerical aperture .

    2. Observing fiber modes.

    3. Proximity sensor.

    4. Pressure sensor.

    5. Interferometric temperature sensor.

    In the first two projects some basic properties of the optical fibers are examinated.

    The other projects show how optical fiber can be used as sensors.

  • 4

    2. Some propertis of optical fibers.

    The optical fiber is a cylindrical waveguide. The basic structure consists of a central

    light-carrying portion, called the core, which is surrounded by a cylindrical region, called the

    cladding. The cladding is then covered with a protective plastic jacket.

    The three major fiber configurations used in communication today are illustrated in fig. 1.

    a) the single-mode step-index fiber, b) the multimode step-index fiber, and

    c) the multimode graded index fiber.

    The refractive index as a function of the radius is shown in fig. 1 above the corresponding fiber.

    (nr1 is the refractive index of the core, nr2 ist the refractive index of the cladding.)

    a) b) c)

    Fig. 1. a) Single-mode step-index fiber, b) multimode step-index fiber, and

    c) multimode graded index fiber.

    The only difference between the single-mode step-index fiber, a), and the mulitmode multimode

    step-index fiber, b), is the size of the core. Typical core diameters for single-mode step-index

    fibers range in the region from 2 m to 9 m. Multimode step-index fibers have diameters in

    the region from 50 m to 150 m or more.

    The outer diameters of the cladding (which are of course larger than the core diameters) are

    roughly 50 m to 250 m for both kinds of optical fibers.

  • 5

    Typically, a multimode graded index fiber has a core diameter of about 20 m to 90 m.

    From theoretical treatment of light propagation along the step-index fiber it can be shown

    that only certain electromagnetic waves can propagate along the fiber as guided modes.

    Different modes correspond to light rays at different angles relative to the fiber axis.

    The lowest mode corresponds to a ray which propagates into the axial direction. The highest

    allowed mode corresponds to a ray which has the largest allowed angle relative to the fiber axis,

    t, but in order to be a guided mode the ray should arrive at the core-cladding interface with an

    incident angle just larger than the critical angle for total internal reflexion, crit, thus

    . (See fig. 2.)

    In a single-mode step-index fiber only the ray propagating into the axial direction is guided.

    The maximum core radius allowed for a single-mode optical fiber is according to theory

    (1)

    is the wavelenght of the light, (NA) is the numerical aperture, .

    Notice: A step-index fiber which is a single-mode fiber using infra-red light ( = 1.3 m) will

    show some higher modes when HeNe-laser light is used ( = 0.633 m).

    On the other hand, if the radius of the core is much larger than the expression in equation (1),

    many modes can propagate along the optical (multimode) fiber.

    The numerical aperture is connected to the acceptance angle, A, in the following manner:

    nro is the index of refraction of the surrounding medium (air, ).

    As seen in fig. 2, the ray which has the

    maximal allowed incident angle, A,

    will contiue to the core-cladding

    interface at an incident angle roughly

    equal to the critical angle for total inter-

    nal reflexion, crit. Applying Snells law

    for the refraction air-core we get:

    Fig. 2. Step-index fiber. The refractive index

    nro is the refractive index of air ( ). profile is shown at the right.

    t 90o crit

    a2.405 2 NA( )------------------------=

    NA( ) nr12

    nr22

    =

    nro Asin NA( )=

    nro 1

    nro Asin nr1 tsin=

    1

  • 6

    Further is and by applying Snells law for the critical angle,

    , we get

    and finally we get for the numerical aperture:

    (2)

    The last expression can be modified by introducing the

    fractional refractive index difference, ,

    (3)

    and if , called as weakly-guiding approximation, the numerical aperture can be

    approximated as:

    (4)

    In step-index fibers the wave-guiding property is due to total internal reflexion at the

    core-cladding interface.

    In graded index fibers the wave-guiding property is due to a bending of the rays

    towards the fiber axis because of the radial variation of the refractive index.

    The most usefull refractive index profile, nr1(r), is given by

    (5)

    , the fractional refractive index is for this case , no is the refractive index at the

    fiber axis, and nr2 is the refractive index of the cladding. (a is the radius of the core.)

    The path of a ray follows a sine function in space.

    tsin critcos=

    nr1 critsin nr2=

    critcos 1 critsin( )2

    1nr2nr1-------

    2

    1nr1------- nr1

    2nr2

    2= = =

    NA( ) nro Asin nr12

    nr22

    =

    nr1 nr2

    nr1---------------------=

    NA( ) nr1 nr2+( ) nr1 nr2( ) nr1 nr2+( ) nr1 = =

    1

    NA( ) nr1 2 =

    nr1 r( )[ ]2

    no( )2

    1 2 ra---

    2 =

    no nr2

    no------------------=

  • 7

    A fan of rays injected at a point in a

    graded index fiber spreads out and then

    recrosses the axis at a common point just

    as rays from a small object are reimaged

    by a lens.

    The distance it takes for a ray to traverse

    one full sine path is called the pitch of

    the fiber. The length of the pitch is

    determined by , Fig. 3. Graded index fiber. The refractive

    the fractional index difference. . index profile is shown at the right.

    Diverging rays are refocussed at a point further down the fiber.

    1.1 Graded index lenses.

    If a graded index fiber is cut to a length of one quarter of the pitch of the fiber it can serve as

    extremely compact lens, somtimes called GRIN lens. Light focussed on an axial point will

    leave the GRIN lens parallell. Increasing the lenght of the GRIN lens to 0.29 of a pitch will give

    the possibility to refocusse divergent light. Both 0.25 and 0.29 pitch GRIN lenses are usefull for

    coupling light sources to optical fibers and fibers to detectors.

    The HeNe-laser in our project is mainly coupled using objective lenses (20X and 40X).

    .Fig. 4 Graded index (GRIN) lens.

    a) 0.25 pitch lens.

    , b) 0.29 pitch lens.

  • 8

    3. Wave optics and modes in optical fibers

    The description for the modes that propagate in a fiber is found by solving the wave equation in

    cylindrical coordinates for the electric field of the light in the fiber. The solutions, which are

    found to be harmonic in space and time, are of the form

    (6)

    where, = 2, and is the frequency of the light, is the propagation constant, is a phase

    constant, and q is an integer. The parameter, , is important for specifying how light propagates

    in a fiber. In the ray optics description, is the projection of the propagation vector on the z

    axis, where the magnitude of th propagation vector is k = 2/, being the wavelength of light

    in vacuum. It is important to make the distinction between the magnitude of the propagation

    vector, k, and the propagation constant, , which is the z-componenet of the propagation vector,

    in order to avoid later confusion.

    Solutions for , f(r), and q are obtained by substituting (6) into the wave equation. The

    solution will depend on the particular fiber geometry and index profile, including both the core

    and the cladding, under consideration. The step-index profile is one of the few refractive index

    profiles for which exact solutions may be obtained. For this case the solutions for f(r) are Bessel

    functions.

    An important quantity in determining which modes of an electromagnetic field will be

    supported by a fiber is a parameter called the characteristic waveguide parameter or the

    normalized wavenumber, or, simply the V-number of the fiber. It is written as

    (7)

    where k is the free space wavenumber, , is the radius of the core, and (NA) is the numerical

    aperture of the fiber.

    E r z, ,( ) f r( ) t z +( ) q( )coscos=

    V k a NA( ) =2

    ------ a

  • 9

    When the propagation constants,

    (-s) of the fiber modes are plotted as a

    function of the V-number, it is easy to

    determine the number of modes that can

    propagate in a particular fiber. In fig. 5,

    such a plot is given for some of the

    lowest order modes. The number of

    propagating modes is determined by the

    number of curves that cross a vertical

    line drawn at the V-number of the fiber.

    Not that for fibers with V

  • 10

    The patterns are symmetric about the center of the beam and show bright regions separated by

    dark regions (the nodes that determine the order numbers m and n). Some of these are schown

    in fig. 6. It ist assumed that the zero field at the outer edge of the field distribution is counted as

    a node, so . For the azimuthal nodes, . The lowest order HE11 mode consists of two

    P01 modes with polarization at right angles to one another. Fig. 7 shows the propagation

    constants of these modes as a function of V-number.

    (Compare this figure with the exact solutions in fig. 6.)

    When the V-number is greater

    than 2.405 (the value at which the

    first zero of the zero-order Bessel

    function occurs), the next linearly-

    polarized mode, LP11, can be sup-

    ported by the fiber, so that both the

    LP01 and LP11 modes will propagate.

    For a fiber with a V-number of 3.832

    (corresponding to th first zero of the

    first-order Bessel function), two

    more linearly-polarized modes can

    propagate: the LP21 and the LP02 Fig. 7. Low order linearly polarized modes of an

    modes. By changing the position optical fiber. Compare with fig. 5.

    and angle of the input beam incident

    on a low-V-number multimode fiber, individual linaearly-polarized modes can be lauched in

    the fiber and observed at the output. The propagation of individual modes in such a fiber will

    be observed in project #2. This will help overcome one of the difficulties of the concept of

    modes in optical fiber, which is understanding what they are and how they differ from one an-

    other.

    n 1 m 0

  • 11

    Project #1: Measuring the numerical aperture.

    Values of the numerical aperture range from about 0.1 for single-mode fibers to 0.2-0.3

    for multimode communications fibers up to about 0.5 for large-core fibers.

    The way in which light is lauched into the fiber in

    the method used here to measure the fiber (NA) is

    shown in fig. 8. The light from the laser represents a

    wave front propagating in the z-direction. The width of

    the laser beam is much larger than the diameter of the

    fiber core. In the neighborhood of the fiber core, the

    wave front of the laser light takes on the same value at

    all points having the same z, so we say that we have a

    plane wave propagating parallel to the z-axis. Fig. 8. Geometry of a plane-wave launch

    When a plane wave is incident on the end face of of a laser beam into an optical fiber.

    a fiber, then we can be sure that all of the light

    launched into the fiber has the sam incident angle, c, in fig. 8.

    If the fiber end face is then rotated obout

    the point O in fig. 8, we can then measure the

    amount of light accepted by the fiber as a function

    of the incident angle.

    The Electronic Industries Association uses

    the angle at which the accepted power has fallen

    to 5% of the peak accepted power as the

    definition of the experimentally determinde (NA). Fig. 9. Laboratory set-up for

    determination of fiber (NA).

    The 5% intensity points are chosen as a

    compromise to reduce requirements of the power level which has to be distinguished from back-

    ground noise.

    Rotate the fiber and measure the accepted power as a function of the angle. Make a plot and

    determine the acceptance angle and (NA).

  • 12

    Compare Your result with a rough measure as shown in

    fig. 10. Launche laser light into one end face of the fiber by a

    objetive lense and measures the diameter of the light cone, w,

    which the other end face will project onto a screen at a dis-

    tance L. The acceptance angle, A, is calculated from:

    (8) Fig. 10. Approximate measure of

    the (NA) of a fiber.

    Project #2: Observing fiber modes.

    Lauche light of the HeNe-laser by an objective lens into a single-mode fiber (of a length

    of 1-2 m). (Single-mode, when using infra-red light.)

    Observe on a screen the light which is emerging from the other end face of the fiber.

    How many modes do You get. What kind of modes ?

    Project #3: Proximity sensor.

    Fotonic sensor.

    The proximity sensor is one of the simplest

    extrinsic fiber-based sensors for measurement

    of position or movement. It was one of the first

    commercially available displacement sensors

    named Fotonic sensor.

    It uses a bundle of fibers, half of which are

    connected to a source of radiation, the other

    half to a detector. ( See fig. 11.) Fig. 11 Illustration of the Fotonic sensor.

    If the bundle is placed in close proximity to a reflecting surface then the light will be reflected

    back from the illuminating fibers into the detecting fibers. The ammount detected will depend

    on the distance from the fiber ends to the surface.

    Atan12--- w

    L----=

  • 13

    The form of the relationship between displacement

    and light output can be estimated from a calculation

    on a model consisting of two fibers as shown in fig. 12.

    Taking a core radius, a = 100 m, a core separation,

    s = 100 m, and a numerical aperture, NA = 0.4, results

    in a coupling efficiency as function of the distance d as

    shown in fig. 13.

    Fig. 12 Two-fiber model

    Fig. 13 Coupling efficiency as function of the distance calculated for a two-fiber model.

    For the sensor shown in fig. 11 the form of the relationship between light output and displace-

    ment is similar to that for the two-fiber model.

    The Fotonic sensor was originally developed for non-contact vibration analysis.

    Measure the power of the output as a function of the displacement.

  • 14

    Project #4: Pressure sensor.

    In fig. 14 a pressure sensor is illustrated.

    Unpolarized light is linearly polarized by the

    polaroid, P, at an angle of 45o with respect to

    the stress axis, S. Stress applied to the plexi-

    glass piece, G, causes stress-induced

    birefringence. Within the plexi-glass the

    incident light splits into two linearly polarized

    rays, one polarized parallell to the stress-axis,

    the other perpendicular to the first.

    Fig. 14. Pressure sensor using the photoelastic effect.

    The difference in phase velocity of the two linearly polarized rays depends on the amount of

    stress applied (and on the material properities). After passing the plexi-glass piece the rays will

    have a phase difference and their superposition will result in elliptically polarized light.

    A second polarizer, A, which acts as an analyzer selects the component of the transmitted beam

    perpendicular to the first polarizer.

    For the configuration shown, the optical power transmitted by the sensor is

    (9)

    where t ist the thickness of the plexi-glass cube, S is the applied stress, and f = 2tSo, where So

    is the stress required to make the transmitted power through the transducer go from a maximum

    to a minimum. It is called the material fringe value. Typical values for f are in the range of

    0.2-0.3 MPa-m. This type of sensor has been used to measure pressures of up to 21 MPa with a

    resolution of better than .

    I I0tS

    f--------

    sin

    2=

    P( )P

    ------------ 104

    =

  • 15

    In fig. 15 the pressure sensor assembly is

    illustrated. The polarizers, P and A, are

    glued to the plexi-glass surfaces.

    Multimode graded index fibers are used as

    light pipe-lines.

    Two 1/4-pitch GRIN-rod lenses

    (GRIN = graded index) are uses in order to

    maximize the fiber-to-fiber coupling

    through the assembly.

    Fig. 15. Pressure sensor assembly

    In fig. 16 the labortory set-up of the pressure sensor is shown.

    Fig. 16. Laboratory set-up of the pressure sensor.

    Measure the power of the detected light as a function of the applied pressure.

  • 16

    Project #5: Interferometric temperature sensor.

    Interferometric sensors are sophisticated sensors

    which detect the influence of physical perturba-

    tions on the phase of the light propagating in a

    single-mode fiber. These sensors offer the

    potential of extremely high sensititvity, but also

    require the best single-mode fiber technology

    available for their construction.

    The most common phase sensors use the

    Mach-Zehnder interferometer. Fig. 17. Mach-Zehnder fiber optic

    A fiber optics version is illustrated in fig. 17. interferometer configuration.

    As first beamsplitter a bidirectional

    coupler is used and the light is lauched into two single-mode fibers of equal lengths. One of the

    fibers serves as the reference arm, which is kept isolated from external perturbations, while the

    other fiber serves as the sensor arm of the interferometer, which is exposed to the perturbation

    to be measured. The external perturbation induces the phase shift in the sensing arm by means

    of a change in the optical path length, which is caused by a change in the index of refraction of

    the glass of the fiber and/or a change in the length of the fiber. The phase shift is detected when

    the two beams are recombined at the receiver end of the sensor. This results in fringes which

    can be detected and counted. Sensors using the Mach-Zehnder

    configuration can be constructed to measure a wide variety of physical parameters, including

    stress, strain, acoustic waves, magnetic field, and temperature. Single- ode optical fibers are em-

    ployed in sensors using other types of interferometers, also.

    When the Mach-Zehnder interferometer has been constructed, the light from the two

    fibers interferes to form a series of bright and dark fringes. A change in the phase of the light in

    the sensor fiber with respect to the phase of the light in the reference fiber appears as a

    displacement of the fringe pattern; a phase change of 2 radians causes a displacement of one

    fringe. The magnitude of the change in the physical parameter to be measured can be

    determined directly by counting the fringe displacement.

  • 17

    The phase of a light wave which travels a distance, L, in an optica fiber is given by

    = L, where is the propagation constant of the light in the fiber. Changing any physical

    parameter of the fibers environment causes a phase change given by

    (10)

    The first term on the right hand side of the equation is due to a change in the lenght of the

    fiber, while the second term is due to a change in the propagation constant. The length, L, now

    represents the length over which the physical change affects the fiber. The quantity which we

    actually wish to determine is the phase change per fiber length per physical stimulus ()/SL,

    where S is the stimulus. The magnitude of the stimulus can then be measured by counting the

    shift of the fringes for a fiber of known interaction length.

    As an example, consider the effect of a temperature change, T, which affects a length, L,

    of the fiber in the sensor arm of the interferometer. There are two effects which occur: the

    change of length due to thermal expansion or contraction, and the change of the propagation

    constant due to the temperature dependence of the index of refraction.

    Thus equation (10) becomes

    (11)

    where and

    For the case of a fused silica fiber and a HeNe laser sourec, the following values for pure

    silica might be used:

    n = 1.456 and

    This gives

    (12)

    this corresponds to 17 fringes per oC per meter of fiber.

    L L+=

    TL---------- 2

    ------ n

    L---L

    T------ n

    T------+=

    LT------

    L T1( ) L T2( )[ ]T1 T2

    ---------------------------------------=nT------

    n T1( ) n T2( )[ ]T1 T2

    --------------------------------------=

    1L--- L

    T------ 5 710 1

    oC

    --------=nT------ 10

    610 1oC

    --------=

    632.8 910 m=

    LT---------- 107

    radiansoC m

    --------------------=

  • 18

    Polarization problems.

    The polarization of the light traveling in the interferometric sensor is important because

    if the polarization of the two output beams are no plane parallel, sharp fringes will not be seen.

    In the worst case, when the two polarizations are orthogonal to each other, no interference will

    occur at all.

    When long lengths of fiber are used in the interferometer, polarization-preserving fiber is

    used. When short lenths of fiber, such as the approximately two meters required for this project,

    are used in the interferometer, standard single-mode fiber may be used. If plane-polarized light

    is launched in the fiber, the light will stay pretty well in its original plane-polarized mode as long

    as the perturbations which would cause mode coupling are kept to a minimum. The output ends

    of the fibers can then be manipulated to cause the polarizations of the output beams to be

    parallalel.

    This last statement may sound highly qualitative, but this approach works well for shorter

    fiber lenghts, and avoids the need for handling an aligning the polarization-preserving fibers.

    Doing the experiment:

    1. In the discussion above, it was found that the fringe displacement of the interferometer

    is highly temperature dependent. You can get a good feeling for this by trying a simple

    qualitative demonstration. After the interferometer has been set up, place your hand around one

    of the fibers withour touching it. The heat from your hand will cause a rapid displacement of the

    fringes, even though you are not in direct contact with the fiber. As you perform this and the

    following exercise, be aware of the environmental conditions of your interferometer, especially

    if there is an air-conditioner outlet near your apparatus.

    2. A simple quantitative experiment to calibrate the temperature sensitivity of the

    interferometer can be done using ice. Before doing the experiment, use the data from equation

    .... to calculate the expected fringe displacement between a typical room temperature and 0oC.

    You should ge a value of about 9 fringes for an interaction lenght of about 2 cm.

    3. Get some ice cubes and allow them to stand until they have become wet to the touch.

    If they feel dry, they may be at a temperature which is significantly less than 0oC. If they feel

    wet then their surfaface should be right at 0oC.

    4. Lay one of the ice cubes on a straight section of one of the fibers on the breadboard.

    Because of the large thermal mass of the breadboard, it may take 30-60 seconds for the fiber to

    come into thermal equilibrium with the ice. This will ensure that you have plenty of time to

  • 19

    count the fringes as they change.

    5. Compare the number of fringes which you counted with the value that you got when

    you did the calculation in step 2. How good is the order of magnitude calculation leading to

    equation (12)?

    References.

    Newport Corporation: Projects in fiber optics.

    Hecht: Optics.

    Wilson/Hawkes: Optoelectronics.

    Singh: Optoelectronics