The formula of FBG Fiber Bragg Grating characteristics and ...optoelec- formula of FBG_Fiber Bragg...

download The formula of FBG Fiber Bragg Grating characteristics and ...optoelec- formula of FBG_Fiber Bragg Grating_

of 6

  • date post

    11-Mar-2020
  • Category

    Documents

  • view

    12
  • download

    0

Embed Size (px)

Transcript of The formula of FBG Fiber Bragg Grating characteristics and ...optoelec- formula of FBG_Fiber Bragg...

  • The formula of FBG(Fiber Bragg Grating) characteristics and principle of the differential FBG optical circuit

    Opto-Electronic Engineering Laboratory Corporation 1. FBG characteristics The equations of the FBG wavelength deviations by the strain forces and by the temperature deviations, is shown below. (eq.1) λB ; filter wavelength of FBG, λB= 1550[nm], n ; refractive index, n=1.45, αs ; temperature coefficient, αs=0.55 [u-strain/ deg C], εs ; external stress strain [u-strain], GF ; conversion coefficient of strain, GF=0.78, δT ; temperature deviation [deg C]

    Formula of FBG transfer function ; the normalized power transmittance (eq.2) Formula of FBG transfer function ; the normalized reflection , (eq.3) Here, κ; the coupling coefficient for the 1-st order for unblazed Bragg grating

    δ; the detuning parameter L; the grating length

    Ω; effective wave number λB; Bragg wavelengths Λ ; period of index modulation m ; mode index neff ; the effective index of guided mode(Clad) η ; the overlap integral between the forward and reverse propagating guided modes calculated over

    sFs B

    B GT T n

    n εδα

    λ δλ

    ⋅+⋅⎟ ⎠ ⎞

    ⎜ ⎝ ⎛ +

    ∂ ∂

    ⋅= 1

    ( ) ( )

    ( )

    ( )

    ( )

    ( )

    ( )

    2

    22 2

    1

    1cos

    ⎟⎟ ⎠

    ⎞ ⎜⎜ ⎝

    ⎛ +

    ⎟⎟ ⎠

    ⎞ ⎜⎜ ⎝

    ⎛ +

    ⎥ ⎥

    ⎢ ⎢

    ⎟⎟ ⎠

    ⎞ ⎜⎜ ⎝

    ⎛ +

    =

    m

    m

    m

    m

    m

    m m L

    T

    κ δ

    κ δ

    κ δκ

    22 2

    2 2

    1cos

    1sin

    ⎟ ⎠ ⎞

    ⎜ ⎝ ⎛−

    ⎥ ⎥

    ⎢ ⎢

    ⎡ ⎟ ⎠ ⎞

    ⎜ ⎝ ⎛−

    ⎥ ⎥

    ⎢ ⎢

    ⎡ ⎟ ⎠ ⎞

    ⎜ ⎝ ⎛−−

    =

    κ δ

    κ δκ

    κ δκ

    L

    L

    R 1 2

    >⎟ ⎠ ⎞

    ⎜ ⎝ ⎛ κ δ

    Bλ πηκ =

    Λ −Ω= πδ

    λ π effn2=Ω

    Λ= effB n2λ

    Fn ⋅Δ=η

  • the fiber core of Bragg grating Δn ; the amplitude of induced refractive index perturbation 0.1×10^-4 to 0.5×10^-4 Δn=n1-n2 F ; the fractional modal power in the core V ; Normalized Frequency a ; Core Radius λ; Optical Wavelength Δ ; relative refractive index difference n1 ; Core Refractive Index n2 ; Clad Refractive Index d ; Core Diameter Vc ; Cut-off V-value λc ; Cut-off Wavelength ・Parameter Example ・Simulation Result

    Fig-1 Simulation Result of FBG transfer function

    ⎥⎦ ⎤

    ⎢⎣ ⎡ −= 2

    11 V

    F

    Δ= 22 1anV λ π

    1

    21 2 1

    2 2

    2 1

    2 n nn

    n nn −

    ≈ −

    Δ= 22 1anV c

    c λ π

    a d n1 n2 n1-n2 Δ um um %

    5 10 1.45 1.4448 0.0052 0.36 V Δn neff λB L m

    nm mm 2.49 0.00005 1.4448 1550 10 1.0000

    Λ F η κ Ω δ nm

    536.4 0.84 4.192E-05 84.964 5.86E+06 1889.9

    10 

    20 

    30 

    40 

    50 

    60 

    70 

    80 

    90 

    100 

    110 

    1549.5 1549.6 1549.7 1549.8 1549.9 1550 1550.1 1550.2 1550.3 1550.4 1550.5

    Re fle

    ct io n  &  T ra ns m it ta nc e[ % ]

    WaveLength[nm]

    Simulation of FBG Characteristics R=50%, BW=0.2nm

    Reflection

    Transmittance

  • 2. Characteristics of the differential FBG optical circuit The equations of the differential FBG optical circuit by the strain forces and by the temperature deviations, is shown below. (eq.4)

    Fig-2 the differential FBG optical circuit

    ・Simulation Result of the differential FBG optical circuit via (eq.2)&(eq.3) FBG1&2 Condition ; R=80%, BW=0.3nm

    Fig-3 Transfer characteristics of the differential FBG optical circuit with pre-tension to FBG1 via simulation

    ( ) ( ) 0

    0

    21

    0

    22

    20

    11

    10

    21 11 sF

    B

    BB s

    B

    B

    B

    B

    B

    BB GTT T n

    nT n

    n εδ

    λ λλαδ

    λ λ

    λ λ

    λ δλδλ

    ⋅+⋅ −

    ⋅+⋅⎟⎟ ⎠

    ⎞ ⎜⎜ ⎝

    ⎛ ⋅

    ∂ ∂ ⋅−⋅

    ∂ ∂ ⋅=

    ( ) 2

    21 0

    BB B

    δλδλλ +=

    FBG1(Sensing)

    FBG2(Reference)

    3dB CUP AR Cutting

    Connector

    Connector

    Optical Source

    Optical  Monitor

    Strain Sensor

    Transforming W.L. to Optical Power Level

    The Optical Circuits of Differential FBG Sensor

    10 

    20 

    30 

    40 

    50 

    60 

    70 

    80 

    90 

    100 

    110 

    1549.5 1549.6 1549.7 1549.8 1549.9 1550 1550.1 1550.2 1550.3 1550.4 1550.5

    Re fle

    ct io n  &  T ra ns m it ta nc e[ % ]

    WaveLength[nm]

    Simulation of FBG Characteristics R=80%, BW=0.3nm

    Reflection

    Transmittance

    FBG1

    FBG2

  • Fig-4 Strain sensing Signal at optical receiver in the case of Fig-3 The Strain sensing Signal is reflected by FBG1 and going through FBG2.

    Fig-5 Simulation of shifted motion for FBG1 wavelength by external compressive stress

    10 

    20 

    30 

    40 

    50 

    60 

    70 

    80 

    90 

    100 

    110 

    1549.5 1549.6 1549.7 1549.8 1549.9 1550 1550.1 1550.2 1550.3 1550.4 1550.5

    Re fle

    ct io n  &  T ra ns m it ta nc e[ % ]

    WaveLength[nm]

    Simulation of FBG Characteristics

    Transmittance

    Rshift0

    Rshift1

    Rshift2

    Rshift3

    Rshift4

    Rshift5

    Rshift6

    Rshift7

    Rshift8

    Rshift9

    Rshift10

    Rshift11

    FBG1

    FBG2

    10 

    20 

    30 

    40 

    50 

    60 

    70 

    80 

    90 

    100 

    110 

    0.0E+00

    1.0E‐08

    2.0E‐08

    3.0E‐08

    4.0E‐08

    5.0E‐08

    6.0E‐08

    7.0E‐08

    8.0E‐08

    9.0E‐08

    1.0E‐07

    1.1E‐07

    1549.5 1549.6 1549.7 1549.8 1549.9 1550 1550.1 1550.2 1550.3 1550.4 1550.5

    Tr an sm

    it ta nc e[ % ]

    D iff er en

    ti al  F BG

     S en

    so r  O ut pu

    t P ow

    er [W

    ]

    WaveLength[nm]

    Simulation of FBG Characteristics

    Shift0

    Transmittance

    FBG2

    Strain sensing Signal

  • Fig-6 Strain sensing Signal at optical receiver in the case of Fig-5 The strain sensing signal generates the wavelength deviation of FBG1, and is converted into the optical power level via FBG2. As a result, the strain sensing signal is converted into the optical power level without optical wavelength meter. FBG1 and FBG2 are mutual complementary pair, so the differential FBG optical circuit cancels the wavelength deviation of FBG as to a temperature factor. It is necessary for the operation of the differential FBG optical circuit to use the broadband optical source such as LED, SLED, ASE.

    Fig-7 Simulation result of strain sensing signal via the differential FBG optical circuit

    10 

    20 

    30 

    40 

    50 

    60 

    70 

    80 

    90 

    100 

    110 

    0.0E+00

    1.0E‐08

    2.0E‐08

    3.0E‐08

    4.0E‐08

    5.0E‐08

    6.0E‐08

    7.0E‐08

    8.0E‐08

    9.0E‐08

    1.0E‐07

    1.1E‐07

    1549.5 1549.6 1549.7 1549.8 1549.9 1550 1550.1 1550.2 1550.3 1550.4 1550.5

    Tr an sm

    it ta nc e[ % ]

    D iff er en

    ti al  F BG

     S en

    so r  O ut pu

    t P ow

    er [W

    ]

    WaveLength[nm]

    Simulation of FBG Characteristics

    Shift0

    Shift1

    Shift2

    Shift3

    Shift4

    Shift5

    Shift6

    Shift7

    Shift8

    Shift9

    Shift10

    Shift11

    Transmittance

    0.5 

    0.6 

    0.7 

    0.8 

    0.9 

    1.0 

    1.1 

    1.2 

    1.3 

    1.4 

    1.5 

    1.6 

    0 20 40 60 80 100 120 140 160 180 200

    O pt ic al  L ev el  o f  D iff er en

    ti an ti al  F BG

     S en

    so r  O ut pu

    t[ uW

    ]

    FBG Strain [u‐strain]

    Strain Characteristics of Differential FBG Sensor R=80%, BW=0.3nm 

  • Fig-8 Actual experimental result of the differential FBG optical circuit 3. Strain Reduction