Intensity Modulation

Wei-Chih Wang Department of Mechanical Engineering University of Washington

W. Wang Why Intensity Modulation

• Simple optical setup • Broadband or mono-chormatic light source • Less sensitive but cheaper to make

W. Wang Intensity (Amplitude) Sensors

In this case, the signal to be measured (the measurand), intensity (amplitude) modulates the light carried by an optical fiber or waveguide. For this class of sensors a normalized modulation index (m) can be defined as

where, ∆ I = change in optical power as a result of modulation by the measurand; I0 = optical power reaching the detector when there is no modulation; and P = perturbation (measurand).

W. Wang Intensity Sensors

The sensor response expressed as a differential voltage per unit change in measurand is given by

S = q Io R m

Where q = detector responsivity (A/W); R = load resistance. m= normalized modulation index

W. Wang Limits on Performance

1. Signal voltage ~ noise voltage

The minimum measurable quantity in the shot noise limit is given by,

2 id = 2eBId “white noise” 2 With light: id = 2eBIp

where e = electronic charge and B=detection bandwidth.

W. Wang Noise in photodetectors

Nλ Ip hυ detector electronics

Radiation noise Internal detector System noise Output

(quantum noise) noise Signal Ip

W. Wang Four noise sources often encountered in connection with optical detectors.

•Johnson noise

•Shot noise

•1/f noise

•Photon noise

W. Wang Sources of internal detector noise

Johnson (thermal) noise

1. All resistive materials 2. Depends only on temp. and bandwidth of measuring system

W. Wang The Johnson noise contribution is provided by the shunt resistance of the device, series resistance and the load resistance. The Johnson noise (thermal noise) is given by:

W. Wang Johnson noise is generated by thermal fluctuations in conducting materials. It is sometimes called thermal noise. It results from the random motion of electrons in a conductor. The electrons are in constant motion, colliding with each other and with the atoms of the material. Each motion of an electron between collisions represents a tiny current. The sum of all these currents taken over a long period of time is zero, but their random fluctuations over short intervals constitute Johnson noise. To reduce the magnitude of Johnson noise, one may cool the system, especially the load resistor. One should reduce the value of the load resistance, although this is done at the price of reducing the available signal. One should keep the bandwidth of the amplification small; one Hz is a commonly employed value. W. Wang Shot noise

• Seen in photodiodes under reverse bias (dark current noise) with no photon input,

eqV/kt I = Isat ( –1) = -Id (dark current) 2 id = 2eBId “white noise” 2 With light: id = 2eBIp (a function of light instead)

where e = electronic charge and B=detection bandwidth. W. Wang The term shot noise is derived from fluctuations in the stream of electrons in a vacuum tube. These variations create noise because of the random fluctuations in the arrival of electrons at the anode. The shot noise name arises from the similarity to the noise of a hail of shots striking a target. In semiconductors, the major source of shot noise is random variations in the rate at which charge carriers are generated and recombine. This noise, called generation-recombination or gr noise, is the semiconductor manifestation of shot noise. Shot noise may be minimized by keeping any DC component to the current small, especially the dark current, and by keeping the bandwidth of the amplification system small.

W. Wang 1/f noise

Larger noise powers at lower frequencies. No theory: not well understood. Seems to be related to contacts, surfaces, other potential barriers

2 2 If ~ I B/f

B = bandwidth f = frequency

Usually much smaller than shot noise except at very low frequency

W. Wang The term 1/f noise (pronounced one over f) is used to describe a number of types of noise that are present when the modulation frequency f is low. This type of noise is also called excess noise because it exceeds shot noise at frequencies below a few hundred Hertz. The mechanisms that produce 1/f noise are poorly understood. The noise power is inversely proportional to f, the modulation frequency. This dependence of the noise power on modulation frequency leads to the name for this type of noise. To reduce 1/f noise, an optical detector should be operated at a reasonably high frequency, often as high as 1000 Hz. This is a high enough value to reduce the contribution of 1/f noise to a small amount.

W. Wang Noise spectrum

1/f

Measured Squared noise shot Current Per BW Johnson

frequency

W. Wang As an example: If a photodiode has a dark leakage current of 2 nA and a shunt resistance of 5E8 Ohms, and a responsivity of 0.5 A/W, and letting the bandwidth of the system be 1 Hz,

As an example: If a photodiode has a dark leakage current of 2 nA and a shunt resistance of 5E8 Ohms, and a responsivity of 0.5 A/W, and letting the bandwidth of the system be 1 Hz, Shot noise is the dominant component of the noise current of a reverse-biased photodiode. This is particularly true at higher voltages (at break down i.e.). If devices are operated in a photovoltaic mode with zero bias, the Johnson noise dominates, as dark current approaches zero. When operating in the zero bias mode the noise current is reduced such that the NEP, and hence the minimum detectable signal, is reduced in spite of some loss of absolute sensitivity. W. Wang Macrobend (intrinsic)

A large-scale bend that is visible; for example, a fiber wrapped around a person's finger. To prevent macrobends, all optical fiber (and optical fiber cable) has a minimum bend radius specification that should not be exceeded. W. Wang Macrobend (intrinsic)

Macro-bend losses are losses observed when a fiber is bent to a radius of several centimeters. Large bending loss occurs at a critical bending radius of 3n2λ R = 1 c 2 2 3/ 2 4π()n1 − n2

where n1and n2 are the indexes of refraction of core and cladding and λ is the operating wavelength. The optimum conditions for a large bending radius occur when refractive index difference between core and cladding is small or operating at a long wavelength.

W. Wang Macrobend

. Under the condition which a /R∆ is to remain small, the light intensity attenuation is equal to

a + 2 r  γ B =10(log R)  2a R∆  where r is the core radius, and a specifies the shape of index of refraction (for a parabolic profile, a = 2 and for a step profile a = ∞,) R is radius of curvature of the bend, ∆ is the relative refractive index difference between core and cladding. Based on the above equation, it is apparent that the bend loss can be enhanced with a smaller refractive index difference between core and cladding or by using a larger core radius of the guide.

W. Wang WWaveguideaveguide SensorSensor ArrayArray

•Higher spatial resolution (250µm x 250µm)

W. Wang BasicBasic PressurePressure SensorSensor DesignDesign

dimmer pressure

dimmer W. Wang

bend loss BasicBasic ShearShear SensorSensor DesignDesign

shear displacement applied compression force

sensor layers

applied shear force

original position sheared position

sensor mesh high compliance

W. Wang Microbend loss sensor (intrinsic)

In an optical waveguide, a sharp curvatures involving local axial displacements of a few micrometers and spatial wavelengths of a few millimeters. microbending can cause significant radiative loss and mode coupling.

W. Wang Microbend Sensor (intrinsic)

Multimode fiber

* fiber experiences multiple bends * lower order guided modes are converted to higher order modes and are eventually lost W. Wangby radiation Microbend Theory

For pressure sensor, the transmission coefficient for light propagating through the bend fiber changed by the amount of applied pressure is equal to [1]

∆T Es As −1 ∆T −1 ∆T = Ap (k f + ) ∆P ≅ Ap k f ∆P (1) ∆x ls ∆x

Where Ap is area under the load, kf is the bent fiber force constant and As, Es, ls are cross sectional area, Young’s modulus and length of the mechanical deformer. The approximation is assume the deformer’s AsEs/ls is much smaller than the fiber’s kf.

W. Wang For the optical portion of the modulation index ∆T/∆x, the loss occurs when wave number of the spatial distortion is equal to the difference in wave number between the modes. The period microbending induced along the fiber axis couples power between modes with longitudinal propagation constant is [1] β 2π m − β n = (2) Λ

β m = n 1 k cos( θ m ) , with θ m representing where each mode has propagation constant the angle which the mode’s equivalent rat makes with the fiber axis, n 1 core refractive index, and k is free space propagation, constantΛ is the mechanical distortion wavelength. Based on WKB approximation, the distance in β space between adjacent δβ guide modes inβ a fiber is given by [2] α − 2 β 1 / 2  α  2 ∆  m  α + 2 = m + 1 − m =     (3)  α + 2  r  M 

α = 2 for parabolic whereindex m fiber,is the order of modal αgroup= ∞ and for M is step total numberindex fiber),of modes, α is a constantr is the core d ∆ is the fractional( radius differencean in refractive index between core and cladding [2]:

2 2 n 1 − n 2 n 1 − n 2 ∆ = 2 ≅ for ∆ 〈〈 1 2 n 1 n 1

where n 1 and n 2 are refractive indices for core and cladding.

W. Wang In the case of parabolic index fiber, the equation (3) becomes,

2 ∆ δβ = (4) r

δβ is independent of order of mode since all modes are equally spacing in k space (to withinIt showsWKB approximation).that This means that an efficient coupling between modes can be achieved with just one single spatial period. Since numerical aperture is

defined as 2 2 0 .5 0 .5 NA = n o sin θ o = ( n 1 − n 2 ) ≅ n 1 ( 2 ∆ ) (5)

∆ is [2] the spatialπ period based on the above NA and 2 2 π rn Λ = r = 1 (6) ∆ NA

In the case of step index, modes are not equally spaced and 2 ∆  m  δβ =   (7) r  M 

The separation of modes in k space for step index is therefore depends on the order of theΛ and while mode, m. Basedlower on equation order mode (2) and require (7), welarger see period.larger the The m, spatial the smaller period for highest order core modes coupledπ to radiated modes (assume m = M) is given by r 2 π rn Λ = ≅ 1 (8) ∆ NA W. Wang The mechanical parameter also affects the outcome of the sensitivity of the sensor. The applied force and the resulted displacement ∆x are related by simple ∆F = fk ∆x. Considering the bent fiber or waveguide as a bar loaded at the center and clamped at its ends [4]

π 4 3 Esd η k = (9) f Λ3

Where d is diameter of the fiber η isand the number of bent intervals.

W. Wang SMS Fiber Optics Sensor

Electrical Engineering and Computer Science Laboratory for Electro-Optics and Sensor Systems Smetanova 17, SI-2000 Maribor, SLOVENIA

The structure is composed of single mode leads and graded multimode sensor fiber. W. Wang SMS Fiber Optics Sensor

Advantages

•higher sensitivity than classical microbend structures •use of shorter deformers •single mode leads, which eliminate intermodal interference problems •sensitivity of 120%/N by use of low-sensitivity standard multimode fiber •high insensitivity to macrobends

W. Wang SMS Fiber Optics Sensor

Faculty of Electrical Engineering and Computer Science Laboratory for Electro-Optics and Sensor Systems W. Wang Smetanova 17, SI-2000 Maribor, SLOVENIA SMS Fiber Optics Sensor

Faculty of Electrical Engineering and Computer Science W. Wang Laboratory for Electro-Optics and Sensor Systems Smetanova 17, SI-2000 Maribor, SLOVENIA SMS Fiber Optics Sensor

Faculty of Electrical Engineering and Computer Science Laboratory for Electro-Optics and Sensor Systems Smetanova 17, SI-2000 Maribor, SLOVENIA W. Wang SMS Fiber Optics Sensor

Faculty of Electrical Engineering and Computer Science Laboratory for Electro-Optics and Sensor Systems W. Wang Smetanova 17, SI-2000 Maribor, SLOVENIA OTDR

Optical Time Domain Reflectometer (OTDR)

Intrinsic distributed sensors based on Rayleigh backscatter utilize either the measurand-dependent loss coefficient α(z) or backscattering coefficient r(z) mechanism in a single length of optical fiber which forms an extended sensor.

The backscattering method was invented by M. Barnoskim and M. Jensen in 1976

W. Wang OTDR

Position of the optical impulse in the fiber core at time t

W. Wang Basic Mechanisms of OTDR

W. Wang OTDR

•Coherent OTDR (CO-OTDR) - The week returned backscattered signal is mixed with a strong coherent local oscillator optical signal to provide coherent amplification •Correlation OTDR (COR-OTDR) •COR-OTDR based on pseudorandom signal •COR-OTDR based on Golay code signal •Low correlation OTDR (LC-OTDR) •Photon-Counting OTDR (PC-OTDR) •Optical Frequency-Domain Reflectometry (OFDR) •OFDR with the frequency scanning (OFDR-FS) •OFDR with the synthesized coherence function (OFDR-SCF) •Polarization OTDR (PO-OTDR)

W. Wang Proximity Sensor (extrinsic)

Liquid Level Sensors Distance Detection

tube-mountable immersion type Reflective Transmissive liquid level liquid level type type detection detection

By KEYENCE CORPORATION OF AMERICA W. Wang Liquid level sensor (extrinsic)

A liquid-level sensor based on changes in the critical angle due to liquid level moving up to contact the sides of the prism (using total internal reflection in air).

W. Wang Displacement Sensor (extrinsic)

A change in the transverse alignment between two fibers changes the coupling and hence the power falling on the detector.

W. Wang Accelerometer or Pressure Sensor (extrinsic)

W. Wang By W. Wang, UW Intensity modulation sensor (extrinsic)

Quadrant fiber detector

incoming coherent light source C

A D

B Y waveguide in motion

X

By W. Wang, UW Figure 10. Quad cell photodiode position detector

W. Wang Detector Scheme

X = ((IA+IB)- (IC+ID))/((IA+IB)+ (IC+ID))

Y= ((IA+IC)- (IB+ID))/((IA+IB)+ (IC+ID))

IA, IB, IC, ID are Intensity from fiber A, B, C and D.

W. Wang