Lasers usually emit beams with a Gaussian profile. A Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are described by Gaussian functions.

For a Gaussian beam, the  amplitude of the complex electric field is given by

where,

r       – radial distance from the centre axis of the beam

z       – axial distance from the beam’s narrowest point

i        – imaginary unit (for which i2 = − 1)

k       – wave number (in radians per meter).

w(z)    – radius at which the field amplitude drops to 1/e and field intensity to 1/e2 of their axial values, respectively.

w(0)   – waist size.

E0     =  |E( 0,0) |

R(z)     – radius of curvature of the beam’s wavefronts

ζ(z)   – Gouy phase shift. It is an extra contribution to the phase that is seen in  beams which obey Gaussian profiles.

The corresponding time-averaged intensity (or irradiance) distribution is

where I0 = I(0,0) is the intensity at the center of the beam at its waist. The constant  is defined as the characteristic impedance of the medium through which the beam is propagating.

For vacuum,

An IP address is assigned to every computer on an Ethernet network. Like the street address for your home, an IP address identifies network computers. It helps traffic flow between computers because each one has its own IP address.

An IP address is formatted as a series of four values separated by periods:

192.168.0.1

Each value ranges from 0 through 255.

• The IP address assigned to your PC on a network is a local address. Similar IP addresses are used on the Internet to identify domains and other resources. Those are Internet IP addresses, separate from your local address.

• The router is assigned an IP address by your Internet service provider (ISP). That IP address is an Internet IP address. It’s shared by all PCs on your network.

• Local IP addresses start with 192.168 and 10.0.

• The IP addresses discussed here are IPv4 addresses. Because the number of unique IP addresses is limited, a second standard, IPv6, has been established. The IPv6 standard allows for many more addresses, which will help accommodate future growth of the Internet.

• If the router doesn’t assign an IP address, one must be configured manually.

• No two computers on the network can have the same IP address.

• IP is often prefixed by the acronym TCP, as in TCP/IP. The TCP part stands for Transfer Control Protocol: It’s simply a set of rules for transmitting information on a network. Technically, TCP/IP refers to the methods and engineering as opposed to a specific address or value.

1. A high output power can be achieved with a high power efficiency.
2. The cooling system can be relatively simple.
3. The beam quality can be high; it is often close to diffraction-limited.
4. The gain can easily be as high as tens of decibels. For comparison, most bulk amplifiers, particularly those with high average output power, have a much lower gain.
5. master oscillator fiber amplifier (fiber MOPA)
   

1. Various kinds of fiber nonlinearities can make it difficult to reach very high peak powers and pulse energies in pulsed systems. For example, a few millijoules of pulse energy in a nanosecond pulse system are already considered high for a fiber device, whereas bulk lasers can provide much higher energies. In single-frequency systems, stimulated Brillouin scattering (SBS) can severely limit the output power.
   
2. Due to the high gain, fiber amplifiers are relatively sensitive to back-reflections e.g. from a workpiece. At high power levels, it is not easy to use a Faraday isolator for solving this problem.
   
3. The polarization state is often undefined and unstable, unless polarization-maintaining fibers are used.
   
4. It can be attractive to use a gain-switched laser diode as seed laser for a fiber MOPA. Such devices compete with Q-switched lasers, e.g. for application in laser marking. Their advantages partly lie in their flexibility concerning output formats: it is easy to modify not only the pulse repetition rate but also the pulse duration and shape, and of the course the pulse energy.
   
5. A special aspect of MOFAs is that the saturation power even of a large mode area double-clad fiber is low compared with the typical output power. Therefore, the power extraction can be as efficient as in a fiber laser, even for relatively low seed powers.
   

1. With a MOPA instead of a laser, it can be easier to reach the required performance e.g. in terms of linewidth, wavelength tuning range, beam quality or pulse duration if the required power is very high. This is because various performance aspects are decoupled from the generation of high powers. This gives extra flexibility, e.g. when a gain-switched laser diode is used as a seed laser. Note also that it can be advantageous to avoid the presence of additional optical components such as wavelength tuning elements in a high-power laser resonator; with a MOPA architecture, one can place these in the oscillator, where they do not have to withstand high optical intensities, do not spoil the power efficiency, etc.
   
2. The same aspects apply to other kinds of modulation, e.g. intensity or phase modulation: it may be advantageous to modulate the low-power seed laser, or to use an optical modulator between seed laser and power amplifier, rather than to modulate a high-power device directly. Slower power modulation may be done by adjusting the amplifier’s pump power, without significantly affecting e.g. the obtained pulse duration or wavelength.
   
3. The combination of an existing laser with an existing amplifier (or an amplifier chain) may be simpler than developing a new laser with higher output power.
   
4. The optical intensities are lower in an amplifier, compared with the intracavity intensities in a laser.
   

1. The complexity of the setup is higher.
   
2. The wall-plug efficiency is often lower. However, it may also be higher, e.g. if that approach allows to remove lossy optical elements from the high-power stage.
   
3. The resulting laser noise tends to be higher, since an amplified source can not reach the shot noise level (→ amplifier noise). Effects of drifts of the seed power may be suppressed, however, if the amplifier is operated in a strongly saturated regime.
   
4. A MOPA can be sensitive to back-reflections, which are amplified again before entering the master laser. This feedback sensitivity can often be cured only by placing a Faraday isolator behind the amplifier. Particularly for high-power pulsed devices, this can introduce serious limitations.
   

1. Electrical modulation of a laser power supply to produce discreet pulses of energy at a given pulse length and pulse period (pulse repetition rate).
   
2. Mechanical interruption of the laser beam by a rotating chopper, which alternately blocks or passes the laser beam.
   
3. Acousto-optical modulation of the beam within the laser resonator, caused by a device generically called a Q-switch. See Q-Switch.
   

Spot size is nothing but the radius of the beam itself and is technically not the same as the beam diameter. The irradiance of the beam decreases gradually at the edges. The distance across the center of the beam for which the irradiance (intensity) equals 1/e 2 of the maximum irradiance (1/e 2 = 0.135) is defined as the beam diameter.

The spot size (w) of the beam is defined as the radial distance (radius) from the center point of maximum irradiance to the 1/e2 point.

Gaussian laser beams are said to be diffraction limited when their radial beam divergence  is close to the minimum possible value, which is given by

where  λ is the wavelength of the given laser and w0 is the radius of the beam at the narrowest point, which is termed as the beam waist.