Basic Concepts of Chain Amplifiers

The simplest way to analyze a cascade of optical amplifiers is to assume that all amplifiers have the same gain and that the loss between amplifiers exactly matches the amplifier gain. The signal output power at the end of the chain is assumed to be equal to the signal input power at the beginning of the chain, a relatively accurate assumption when the ASE generated is small compared to the signal power.

In fact, the ASE is growing at the expense of the signal in saturated amplifier chains, but this does not obviate the main conclusions of the following discussion. Each amplifier generates an equal amount of ASE as the other amplifier, and this ASE propagates transparently to the output of the chain, much as the signal does. Thus, the ASE at the output of the chain is linear addition of the ASE generated by each amplifier. The SNR at the output of the amplifier chain in then obtained by replacing the inversion parameter n_sp by Nn_sp where N is the number of the amplifiers in the chain and

2 where σ_e and σ_a are the emission and absorption cross section of erbium-doped fiber respectively, and and are the population in low and high level of erbium-doped fiber respectively.

N1 N₂

Figure 2.1 Two cases of amplifier chains.

We consider the case of the configuration of Fig. 2.1 A, which corresponds to an amplifier chain where the input power to the amplifiers is independent of the amplifier gain G or the span loss L. We compute the SNR under the assumption that it is determined by signal-spontaneous beat noise. The SNR at the output of the amplifier chain can be written, as noted above, using the fact that the ASE at the output of the amplifier chain is N times the ASE generated by one amplifier. The signal input to the receiver is , when GL=1

Pin The SNR after the last amplifier can then be written as

1/

Equation (2.33) yields the result that the SNR is maximized when N=1. In other words, there should be only one amplifier and the amplifier spacing should be the longest possible. From the point of view that each amplifier adds noise, it makes sense that we find that the minimum number of amplifies gives the best system performance.

We now turn our attention to the system in Fig. 2.1 B, this configuration corresponds to a situation where the amplifier output power is held constant, since whatever the span loss L, the amplifier will be selected to have a gain G such that the output of each lossy span an amplifier unit is equal to the signal input power , to ensure a fully transparent chain. The SNR at the output of the amplifier chain is given by

Pin The difference with respect to equation (2.33) is that here is measured at the beginning of the chain, whereas in equation (2.33) was measured at the input to the amplifier.

Similarly to the derivation of , we can write

Pin

where the of the signal-spontaneous beat noise is just calculated before first amplifier.

Equation (2.35) can be written as In this case the SNR is improved by increasing the number of amplifiers and reducing the gain G correspondingly. In the limit where the number of amplifier goes to infinity the SNR is maximized and is equal to

(max) 1 This result can be understood from the fact that as we decrease the amplifier gain, the

amplifier input power increases since the preceding span is now shorter and its loss less. Any loss prior to the input of an amplifier degrades the noise figure and the output SNR.

How do we resolve the apparent contradiction between the conceptual conclusions of cases A and B? The maximum SNR for case A is the high SNR for either configuration. But it is not a practical construction to use just one amplifier for the chain loss. In addition, the onset of nonlinear effects above a certain power level limits the output power to be launched in the chain. Real life systems are similar to the configuration B where amplifier output power is held constant. In this case short amplifier spacings are desirable. Given the economic cost of amplifiers, practical systems use amplifier spacings as long as possible while still maintaining a minimum system SNR for low error rate detection.

The discussion above we consider the expression for the SNR with a continuous signal . For configuration B, a random pattern of 1s and 0s, and an infinite extinction ratio, one can derive, given that the signal-spontaneous noise is only present during the 1s, that the electrical SNR is given by

The optical SNR is often used to quickly characterize the system properties of a cascaded amplifier chain, since the SNR can be directly measured on an optical spectrum analyzer.

The noise figure for a system consisting of a chain of optical amplifiers can be computed from the noise figure for an individual amplifier. Consider a system of N amplifiers where denotes the SNR after amplifier I, and each amplifier provides a gain G to exactly compensate the span loss. The overall noise figure (F) of the system is given by

SNRi

where SNR₀ is the SNR at the input of the system immediately after the transmitter and

prior to the first span of fiber. The SNR ratios are the noise figures of each amplifier multiplied by 1/L since the amplifier noise figure is defined by the SNR’s immediately prior and after the amplifier. Each is separated form the following amplifier by a span with loss L, hence we obtain for the system noise figure, in logarithmic units

SNRi

1 2 ...

sys N

F =GF +GF + +GF =NGF (2.40) assuming all the amplifiers have an equal noise figure and G=L, and noise figure with shot noise without considering the ASE and signal-spontaneous beat noise. The SNR degradation in a cascaded amplifier transparent chain is seen to be linear with the number of amplifiers.

An interesting result can be derived when G and L are different, as is the case for a multistage amplifier constructed by piecing together several amplifiers. Equation (2.40) is then written more generally as

Chapter 3

WDM Source of 10 Gb/s Channels and Key Component of Loop Experiment

3.1 Description of DFB Laser

In WDM systems, we want to carry many multiplexed optical signals on the same fiber. To do this it is important for each signal to have as narrow as spectral width as possible and to be as stable as possible. DFB lasers are one answer to this requirement. The idea is that you put a Bragg grating in the laser cavity of an index-guided Fabry-Perot laser. This is just a periodic variation in the refractive index of the gain region along its length. The presence of the grating causes small reflections to occur at each reflective index change (corrugation).

When the period of the corrugations is a multiple of the wavelength of the incident light, constructive interference between reflections occurs and a proportion of the light is reflected.

Other wavelengths destructively interfere and therefore cannot be reflected. The effect is strongest when the period of the Bragg grating is equal to the wavelength of light used (first order grating). Mode selectivity of the DFB mechanism results from the Bragg condition: the coupling occurs only for wavelengths λ_B satisfying

( _B/ 2 m λ n)

Λ = (3.1) where Λ is the grating period, n is the average mode index, and the integer m represents the order of Bragg diffraction. The coupling between the forward and backward waves is strongest for the first-order Bragg diffraction (m=1). So the device will work when the grating period is any small integer multiple of the wavelength. Thus only one mode, the one that conforms to the wavelength of the grating, can be lasing. Early devices using the principle had the grating within the active region and were found to have too much attenuation. As a result the grating was moved to a waveguide layer immediately adjacent to (below) the cavity as

into the adjacent layer and interacts with the grating to produce the desired effect.

In principle a DFB laser does not need end mirrors. The grating can be made strong enough to produce sufficient reflection for lasing to take place. However, in a perfect DFB laser there are actually two lines produced, one at each side of the Bragg wavelength. We only want one line. A way of achieving this and improving the efficiency of the device is to place a high reflectance end mirror at one end of the cavity and either an anti-reflection coating or just a cleaved facet at the output end. In this case the grating does not need to be very strong, just sufficient to ensure that a single mode dominates. The added reflections from the end mirrors act to make the device asymmetric and suppress one of the two spectral lines. Unfortunately, they also act to increase the line width.

Some DFB lasers are constructed with a quarter-wave grating shift in the middle section of the grating to introduce a π/ 2 phase shift as show in Fig. 3.1 (b). This phase shift grating introduces a sharp transmission fringe into the grating reflection band as shown in Fig.

3.2. What happens is that the reflected waves from each end of the grating will be out of phase with each other and hence will destructively interfere. The fringe acts to narrow the linewidth of the laser significantly. The output spectrum of light is shown in Fig. 3.3. It shows apparently that the number of output signals can be reduced from two to one by π/ 2 phase shift grating. [9]

(a) (b)

Figure 3.1 Structure of DFB laser (a) without π/ 2 (b) with π/ 2 phase shift grating.

Figure 3.2 Reflection Characteristics (a) without phase shift grating (b) with phase shift grating.

(a)

(b)

Figure 3.3 Reflectivity Spectrum (a) without π/ 2 (b) with π/ 2 phase shit grating.

3.2 Electro-Optical Effect

In certain types of crystals, the application of an electric field results in a change in both the dimensions and orientation of the index ellipsoid. This is referred to as the electro-optic effect. The electro-optic effect affords a convenient and widely used means of controlling the phase or intensity of the optical radiation. According to the quantum theory of solids, the optical dielectric impermeability tensor η_ij depends on the distribution of charges in the crystal. The application of an electric field will result in a redistribution of the bond charges and possibly a slight deformation of the ion lattice. The net result is a change in the optical impermeability tensor. The electro-optic coefficients are defined traditionally as:

( ) (0)

ij ij ij r Eij k s E Eijkl k l f Pijk k g P Pijkl k l

η E −η ≡ ∆η = + = + (3.2)

where is the applied electric field and is the polarization field vector. The constants and

E P

rij f are the linear (or Pockels) electro-optic coefficients, and _ijk and are the quadratic (or Kerr) electro optic coefficients. In the above expansion, terms higher than the quadratic are neglected because these higher-order effects are too small for most applications.

sijkl g_ijkl

The electro-optic coefficients of theLiNbO₃ crystal are in the form:

22 13

We now consider the case when the electric field is along the c axis of the crystal so that the equation of the index ellipsoid can be written as:

2 2 2 where and are the ordinary and extraordinary refractive indecies, respectively. Since no mixed terms appear in equation (3.4), the principal axes of the new index ellipsoid remain

n0 n_e

unchanged. The lengths of the new semi-axes are: Note that under the influence of the electric field in the direction of c axis, the crystal remains

uniaxially anisotropic. If a light beam is propagating along the y axis, the birefringence seen by it is The phase retardation of this plate is:

3 3 where V is the voltage applied and d is the thickness of crystal. The voltage making the retardation Γ = is known as the “half-wave voltage,” and is given in the case by: π

The electrically induced birefringence causes a wave incident at y=0 with its polarization along x to acquire a z polarization, which grows with voltage at the expense of the x component until at V =V_π and then the polarization becomes parallel to z. If at the output plane one inserts a polarizer at right angles to the input polarization then with the field on, the optical beam passes through unattenuated, the output beam is blocked off completely by the crossed output polarizer. This control of the optical flow serves as the basis of the electro-optic amplitude modulation of light. [10]

3.3 Key component of Loop Experiment 3.3.1 Acousto-Optic Effect

Acousto-optic interaction occurs in all optical mediums when an acoustic wave and a laser beam are present in the medium. When an acoustic wave is launched into the optical medium, it generates a refractive index wave that behaves like a sinusoidal grating. An incident laser beam passing through this grating will diffract the laser beam into several orders as shown in Fig. 3.4.

Figure 3.4 Principle of AO effect.

With appropriate design, the first order beam has the highest efficiency. Its angular position is linearly proportional to the acoustic frequency, so that the higher the frequency, the larger the diffracted angle.

θ is the angle between the incident laser beam and the diffracted laser beam, with the acoustic wave direction propagating at the base of the triangle formed by the three vectors. The intensity of light diffracted (deflected) is proportional to the acoustic power , the material figure of merit

Pac

M2, geometric factors (L/H) and inversely proportional to the

square of the wavelength. This is seen in the following equation: In the AO interaction, the laser beam frequency is shifted by an amount equal to the acoustic frequency.

The principal performance parameter is the modulation speed which is primarily determined by the transit time, t. The transit time t and the rise time t_r are given by:

t V

= d (3.13)

r 0.85

t = t (3.14) The AO device is be used to shutter the laser beam “on” and “off” by an external digital TTL signal. It must have low insertion loss, low polarization dependency, high extinction ratio, and small rise and fall time to minimize transients. The repetition rate of the switch is a function of the loop delay time. Typical repetition rates are in the kHz range. [11]

Circulating loop experiments require AO switches to have high extinction ratio (>50dB), low polarization dependent loss (<0.5dB), moderate switching speed (~70ns) and low insertion loss (<3dB). A high extinction ratio is especially important on the transmitter switch, since data is launched into the loop for only a small fraction of the experimental period. Light that leaks through this switch during the loop phase looks like optical noise injected every span. Thus light that leaks through the switch trends to corrupt the data signal and diminished the accurate emulation of a straight system. Low loss is important since any attenuation inside the loop looks like a periodic loss in every circulation, which means added noise and/of diminished SNR. Low polarization dependent loss in the optical switch is necessary to prevent high and low polarization loss modes from accumulating in the loop. To perform effective switching, the AO switches should have a short switching time compared to the loop time in the loop. When the AO switches are operated in deflection mode, the frequency of light passing through it is shifted by an amount equal to the RF drive frequency

(MHz). Thus every time the optical signals pass through the loop it incurs a MHz frequency shift. For practical numbers of circulations, this frequency shift is small and does not adversely affect the expected results. [12]

3.3.2 The Gain Flatten of EDFA

The main practical limitation of an EDFA stems from the spectral non-uniformity of the amplifier gain. Even though the gain spectrum of an EDFA is relatively broad, the gain is far from uniform (of flat) over a wide wavelength. As a result, different channels of a WDM signal are amplified by different amounts. This problem becomes quite severe in long-haul systems employing a cascaded chain of EDFAs. The reason is that small variations in the amplifier gain for individual channels grow exponentially over a chain of in-line amplifiers if the gain spectrum is the same for all amplifiers. Even a 0.2dB gain difference grows to 9.6dB over a chain of 48 EDFAs.

The usable bandwidth of inline EDFA can be increased by using passive gain equalizing filters. The idea of gain equalizing filters is designed to approximate the inverse of gain spectrum. Our EDFAs are specially designed and have flat gain spectrum as shown in Fig. 3.5.

Figure 3.5 Output power versus wavelength of one of the inline EDFAs.

CHAPTER 4 Dispersion Management

4.1 Dispersion Compensation

For long-haul transmission systems, the nonlinear refractive index can couple different signal channels, and can also couple the signal with noise. It will cause the distortion, spectrum broadening and other degradations. If it is operated around the zero dispersion wavelength in fiber, the data signals and the amplifier noise with wavelengths similar to the signal travel at similar velocity. Under these conditions the signal and noise waves have long interaction lengths and can mix together. Especially the NRZ format is affected severely by nonlinearity because it has long interaction lengths. [13] Chromatic dispersion causes different wavelengths to travel at different group velocities in single mode transmission fiber.[8][14] Chromatic dispersion can reduce phase matching, or the propagation distance over which closely spaced wavelengths overlap, and can reduce the amount of nonlinear interaction in the fiber. Thus, in a long undersea system, the nonlinear behavior can be managed by tailoring the accumulated dispersion so that the phase-matching lengths are short, and the end-to-end dispersion is small. The technique has been used in both single channel systems to reduce nonlinear interaction between signal and noise as well as in WDM system.

[15]

Before we compensate the dispersion, the bit stream is Fig. 4.1, 4.2. It has peaks in the rising edge and falling edge of the bit stream. And so the eye diagram is distortion seriously. The walkoff can be minimized if the pulse wavelength and the zero dispersion wavelength of the fiber are very close. This is not often a good solution since operating near zero dispersion leads to significant impairment from the phase-matched mixing between the signal and the amplifier noise. In addition, if any optical filter clips the broadened spectrum

Figure 4.1 The bit stream after 150km.

Figure 4.2 The eye diagram after 150km.

admitted to the receiver then no pulse distortion will occur, although this may lead to impairment of the SNR due to the increased ASE noise admitted. Thus, dispersion compensation which null the overall dispersion of the chain can significantly reduce the combined effect of SPM and group velocity dispersion.

There is a brief method to measure the coarse dispersion parameter (D). By use a tunable laser as source when changing its wavelength the final signal bit stream will delay some nanosecond after one loop as show in Fig. 4.3 and 4.4. The quotient of delay time over wavelength variation over transmission length can give the coarse dispersion parameter.

We use two DCFs (D=-86.6231ps/nm/km and loss=0.37dB/km at 1553.33nm) to compensate the accumulated chromatic dispersion. One is 4.37896km and the other is 10.81287km. The dispersion map similar to that is shown in Fig. 4.5. The locally dispersion is

We use two DCFs (D=-86.6231ps/nm/km and loss=0.37dB/km at 1553.33nm) to compensate the accumulated chromatic dispersion. One is 4.37896km and the other is 10.81287km. The dispersion map similar to that is shown in Fig. 4.5. The locally dispersion is