## Basic Fibre Optics

### Important Formulae

i= -log p(a) = log[1/p(a)]
p(a) is the probability of event a occuring. The information given in a message or event increases as the probability of that event or message occuring becomes less likely. Log 1/0.01 is larger than log 1/0.50.
H(A) = M (log[1/p(a)] = Σ pi log[1/pi]
H is the average amount of information given in each event, called Entropy. It is the sum of the information of each event multiplied by the likelihood of that event. This is like taking a weighted average of all the informations as opposed to simply summing all the informations and dividing by the number of them.
Entropy
the average unpredictability in a random variable, which is equivalent to its information content.
X = [logk - H(A)]/logk
If all K events have identical probablities, then the redundacy , called X, is the number of bits used in the message (for example if k is 8, then logk would be 3 bits) minus the theoretical information in the bits H(A). we then divide by logk to normalize the number. Imagine in our example if H(A) were 3 then we would have zero redundancy.
Statistical Redundancy
is the number of bits used to transmit a message minus the number of bits of actual information in the message. Compression based on this is lossless.
Δf * Δt = 1
λ μm = 300 /fTHz
attenuation in a Fibre
λ m = 300 /fMHz

## Three types of Amplification

Control of feeding source current
Using vacuum tube or transistor
Grouping Electrons
Resonator Device (Klystron) or TWT long term reaction device advantage of being among the lowest-noise microwave sources available, and they coherently amplify a reference signal so its output may be precisely controlled in amplitude, frequency and phase see TWT
optical parametric amplifier, abbreviated OPA, or Pump Generation
a laser light source that emits light of variable wavelengths by an optical parametric amplification process, or a MASER.
multimode
single mode
The main difference between multi-mode and single-mode optical fiber is that the former has much larger core diameter, typically 50.100 micrometers; much larger than the wavelength of the light carried in it. Because of the large core and also the possibility of large numerical aperture, multi-mode fiber has higher "light-gathering" capacity than single-mode fiber. In practical terms, the larger core size simplifies connections and also allows the use of lower-cost electronics such as light-emitting diodes (LEDs) and vertical-cavity surface-emitting lasers (VCSELs) which operate at the 850 nm and 1300 nm wavelength (single-mode fibers used in telecommunications operate at 1310 or 1550 nm and require more expensive laser sources. Single mode fibers exist for nearly all visible wavelengths of light). However, compared to single-mode fibers, the multi-mode fiber bandwidth-distance product limit is lower. Because multi-mode fiber has a larger core-size than single-mode fiber, it supports more than one propagation mode; hence it is limited by modal dispersion, while single mode is not.

The LED light sources sometimes used with multi-mode fiber produce a range of wavelengths and these each propagate at different speeds. This chromatic dispersion is another limit to the useful length for multi-mode fiber optic cable. In contrast, the lasers used to drive single-mode fibers produce coherent light of a single wavelength. Due to the modal dispersion, multi-mode fiber has higher pulse spreading rates than single mode fiber, limiting multi-mode fiber's information transmission capacity.