## 1032 Quasidistributed Fiberoptic Sensors

When truly distributed sensing is difficult to realize, quasi-distributed fiber-optic sensor technique is used. In this technique, the measurand is not monitored continuously along the fiber path, but at a finite number of locations. This is accomplished either by sensitizing the fiber locally to a particular field of interest or by using extrinsic-type (bulk) sensing elements. By using quasi-distributed fiber-optic sensors, more measurands can be sensed. Fig. 10.2(1. An illustration of...

## 141 Degrees Of Freedom

Let ( ) be a band-limited signal the spectrum of which extends from zero frequency to a definite limit of vm. Assume that (f) extends over a time interval of T, where vmT 1. Strictly speaking, a band-limited signal cannot be time limited or vice versa. Now a question arises How many sampling points (i.e., degrees of freedom) are required to describe the function (f), over T, uniquely To answer this fundamental question we present an example. First, we let (f) repeat itself at every time...

## 13 Communication Channel

An optical communication channel can be represented by an input-output block diagram, for which an input event a can be transferred into an output event b, as described by a transitional probability p(b a). Thus, the input -output transitional probability P(B A) describes the random noise disturbances in the channel. Information channels are usually described according to the type of input-output ensemble and are considered discrete or continuous. If both the input and output of the channel are...

## J

Where h(t) is the impulse response of the filter and (i) is the input signal function. By expanding the preceding equation, it can be shown that the 1*00 p 7(t) h(x)dx h(< T)d(TRu(T - a) - 2 h(x)dxRid(x) + Rdd(0), where Pjj(T) the autocorrelation function of the input signal, Rid x) is the cross-correlation of the input with the desired-output function, and Rdd(0) is the mean-square value of the desired-output function, as given by

## 623 Waveguide Loss Measurement

Waveguide losses are important parameters in determining total insertion loss for transmitters and receivers. Low-loss waveguides significantly ease optoelectronic packaging. However, there is no simple technique available to measure waveguide propagation loss with reasonable accuracy for integrated optical waveguides that are fabricated on substrates. So far the most widely used method is the sliding-prism measurement. In this technique, the optical coupling prism is slid along the streak in...

## T

6.5 In the question above assume nx n3 1.5, and n2 1.58. Estimate the optimum mirror angle for coupling. 6.6 The figure below shows a structure of a multilayer optical interconnect. The output power of the VCSEL is p0, the power of the light coupled into the waveguide nt through the 45 mirror m1 is ply and p2 is the light power coupled into waveguide n2 through mirror m2. The refractive index and thickness of each layer are shown in the figure. Design a structure so that pJpQ 20 and p2 p0 50 ....

## 851 Principle Of Holography

Holography was originally invented by Gabor 37 in 1948 to improve electron microscope images. Holography is a technique to record and to reconstruct wavefronts. Consider that we are in a room looking at an object, such as a flower, through a window. The light from the flower must transmit through the window to form an image on our retinas. If we could record the light at the window plane, then by reproducing the recorded light we would be able to see the flower, although there is no window....

## 1232 Optical Fiber Nonlinearity Limit

Nonlinear optical effects are the responses of the dielectric material at the atomic level to the electric fields of an intense light beam. Nonlinear optical effects in fiber generally fall into two categories inelastic effects such as stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) and elastic effects such as self-phase modulation (SPM), cross-phase modulation (XPM), and four wave mixing (FWM). 12.3.2.1. Stimulated light Scattering In the case of stimulated light...

## 31 Motivation Of Fiberoptic Communication

With the exponential growth in transmission bandwidth usage, in particular (due to the rapid growth of Internet data traffic), there is a huge demand on transmission bandwidth. Fiber-optic communication is the best candidate to fulfill this broad bandwidth due to its following unique features 1. Huge bandwidth due to extremely high carrier frequency The light signal has a very high carrier frequency. For example, at the infrared communication window, assuming that X 1500nm, the corresponding...

## 1233 System Design Examples

The design of a practical optical transport system is complicated. Many factors must be considered, such as the detailed channel (wavelength) plan for DWDM systems, appropriate transmitter and receiver pairs, optical fiber types, optical amplifiers, dispersion compensation modules, multiplexers demultiplexers, and many others. This section briefly discusses system design guidelines. We start from the design of a linear system, considering only the so-called power budget. Then we include the...

## 001011110 100101111

Step 2 (Z ) 001010000 (Z ) 100100001 Multiplication of two N-digit MSD numbers A b0 generates a 2N -digit product P p2n iPin procedure consists of two steps generate the partial products P(l) and add them 123,126 , The product is formed as P AB P,, Abfl'. (9.55) Each partial product P(i) is formulated by multiplying the multiplicand A by the ith digit of the multiplier B and shifting by i digit positions, which corresponds to the weight 2 The partial product is a shifted version of A, or 0, or...

## Exercises

12.1 One digital voice channel takes up 64 kb s. How many voice channels can an OC-192 (9.953.28 Gb s) system deliver 12.2 Decibel (dB) is commonly used in communications. It can represent absolute signal power, defined as P (dBm) 10 log (P(mW)), and relative level, defined as AP (dB) 10 Log (PI (mW) P2 (mW)). 0 dBm represents 1 mW and 3 dB represents two times. An optical amplifier has 5 dBm total input from an 80-channel DWDM signal. Suppose all channels have the same power. What is the input...

## 562 Inverse Transform

The projection of the Wigner distribution function Wf(x, co) in the space frequency joint space along the frequency co-axis gives the square modulus of the signal (t), because according to Eq. (5.22) the projection of Wf(x, o) along the cj-axis is f (x + * x - - exp( -jcox') dx dco 2n f( v) 2. The projection of Wf(x, co) in the space-frequency joint space along the space axis x gives the square modulus of the Fourier transform F(u> ) of the signal, because according to Eq. (5.23) the...

## Info

Where for A 633 nm, T13 9.6 x 1012, T22 6.8 x 1012, T33 30.9 x 10 12, and TS1 32.6 x 10-12m V. What is the half-wave electric field for a LiNb03 modulator where light polarizes along the y axis, and the modulating electric field is applied along the z axis Assume A 633 nm and the length of the modulator L 4 mm. 4.10 Consider the case described in Problem 9. How large an electric field Ey is required to change the index of refraction by 0.0001 4.11 The sensitivity of a device is defined as the...

## Nto n0co n2

Practically, SPM should be considered seriously in high-speed systems and may lead to system launch power under a few dBm, depending on fiber types. The intensity dependence of the refractive index can also cause XPM when two or more channels are transmitted. The nonlinear phase shift for a specific channel arises from the modulation of other channels presented. Similarly, there is spectral broadening The factor of 2 indicates that the effect of XPM is twice that of SPM for the same input...

## 1224 Transponder

The need for the transponder arises when the DWDM system interfaces with other fiber-optic systems. ITU defined a set of optical frequencies with 100 GHz spacing in the 1530 to 1620 nm optical amplifier bandwidth to be used for DWDM, commonly known as the ITU grid. There are two types of transponders, the transmitter transponder and the receiver transponder. The transmitter transponder takes in non-DWDM-complaint signals, such as a short-reach SONET signal at 1310 nm, and converts them into...

## 1998

Photons are incident on the receiver during a single 1 bit (assume equal one and zeros). 3.3 A bare silica fiber has nx 1.46, n2 1.0, and radius a 25 um. Under the maximum angle of incidence, (a) Calculate the number of reflections that would take place in traversing a kilometer length of the fiber. (b) Assuming a loss of only 0.01 of power at each reflection at the core-cladding interface, calculate the corresponding loss in dB km. 3.4 Consider a single mode optical fiber with nx 15 and n2...

## 51 Huygensfresnel Diffraction

As early as 1678, Huygens suggested for interpreting optical diffraction that each element on a wavefront could be the center of a secondary disturbance, which gives rise to a spherical wavelet 10 , and that the wave front at any later time is the envelope of all such wavelets. Later, in 1818, Fresnel extended Huygens's hypothesis by suggesting that the wavelets can interfere with one another, resulting in the Huygens-Fresnel principle, which is formulated as where E(r) is the complex amplitude...

## References

Korpel, 1981, Acousto-optics A Review of Fundamentals, Proc. IEEE, 69, 48 S3. 11.2 P. K. Das and C. M. Decusatis, Acousto-Optic Signal Processing Fundamentals and Applications, Artech House, Boston, 1991. 11.3 A. Vanderlugt, Optical Signal Processing, John Wiley and Sons, Inc., New York, 1992. 11.4 P. Debye and F. W. Sears, 1932, On the Scattering of Light by Supersonic Waves. Proc, Nat. Acad. Sci., 18, 409-414. 11.5 C. V. Raman and N .S. N. Nath, 1935 1936, The Diffraction of Light by...