Structure of this thesis

The main purpose of this thesis is to experiment the bidirectional transmission systems and to discuss the feasibility of bidirectional transmission in real application. This thesis comprises six chapters. Chapter 1 is an introduction of bidirectional DWDM systems. In chapter 2, the theory and characteristics of a four-port interleaver will be described, as well as the experimental measurement and its application in bidirectional amplification. Experiments of 160-km and 210-km bidirectional transmissions using novel four-port interleavers will be presented in chapter 3. Furthermore, in chapter 4, a bidirectional loop transmission with novel four-port interleaver utilization in a recirculating loop scheme will be proposed and experimentally demonstrated. In chapter 5, a concept is proposed that a bidirectional loop configuration may be inadequate to represent a bidirectional transmission thoroughly.

Therefore, the simulations, which based on the bidirectional transmission and bidirectional loop system, for comparing the performances of the two systems will be included. Finally, in chapter 6, a brief conclusion and discussion for experimental and simulation results will be given.

Chapter 2

Characteristics of Interleaver

2.1 Introduction

An interleaver is a periodic optical filter that combines or separates a comb of dense wavelength-division multiplexed (DWDM) signals. The periodic nature of the interleaver filter reduces the number of Fourier components required for a flat passband and high-isolation rejection band. As a functional block, interleavers come in many varieties. The original design separates (or combines) even channels from odd channels across a DWDM comb. The filter function of an interleaver and its period are separable. Interleavers have been demonstrated that resolve a comb of DWDM frequencies on 100, 50, 25, and 12.5 GHz centers. The period is governed by the free-spectral range of the core elements, where narrower channel spacing is achieved by a longer optical path. [6]

There are three categories of interleaver filter technologies: lattice filter (LF), Gires-Tournois (GT) based Michelson interferometer, and arrayed-waveguide router (AWG).

This chapter will focus on the detail of the theory and design process of the LF interleavers which we used in our experiments. Moreover, the measurement of the interleaver will be shown to compare with the simulation results. [7]

2.2 Digital Concepts for Optical Filters

Digital filter, or discrete time filter [8], has been widely used in digital electronic circuit.

The advantages of relating digital and optical filters are that numerous algorithms developed for digital filters can be used to design optical filters. Borrowed from the electronic world, optical engineer follows the same concept and uses optical delay line to create the desired filter function. Depending on whether the transfer function has poles, an optical filter can be classified as a finite impulse response filter and an infinite impulse response filter. Before

describing the design process of the interleaver filter, the basic knowledge about the representations of digital signals, the Z-transform, the zeros, and the poles were needed to be introduced in followed sub-sections.

2.2.1 Discrete Signals and Z-transform

A similar set of properties applied for discrete signals. A discrete signal can be obtained by sampling a continuous time signal x

(t )

at t

=

nT where the sampling interval is, T and n is the sample number. For a digital filter, T is the unit delay associated with the discrete impulse response. The impulse response of an optical filter, where each stage has a delay that is an integer multiple of the unit delay, is described by a discrete sequence [2.4].

The Fourier transform of a sequence has a sum instead of an integral as follows:

∑

^∞

where f denote the absolute frequency. A normalized frequency is defined as FSR

f fT

= /

ν ≡

, where the free spectral range (FSR) is the period of the absolute frequency response. The normalized angular frequency is given by

ω = 2 πν

. A discrete signal is often represented by x

(n )

, leaving T implied. The discrete-time Fourier transform (DTFT) is defined as

∑

^∞

The Z-transform is an analytic extension of the DTFT for discrete signals, similar to the relationship between the Laplace transform and the Fourier transform for continuous signals.

The Z-transform is defined for a discrete signal [9] by substituting z for

e

^jωin Eq. (2) as

where

h ( n )

is the impulse response of a filter or the values of a discrete signal, and z is a complex number that may have any magnitude. For the power series to be meaningful, a region of convergence must be specified, for exampler_min ≤ z ≤r_max wherer_min and r_max are

radii. Of particular interest is

z = 1

, called the unit circle, because the filter’s frequency response is found by evaluating H

(z )

along

z = e

^jω, The inverse Z-transform is found by applying the Cauchy integral theorem to Eq. (3) to obtain:

∫

⁻

The convolution resulting from filtering in the time domain

∑

^∞

reduces to multiplication in the Z-domain.

)

Equation (6) shows that a filter’s transfer function, H

(z )

, can be obtain by dividing the output by the input in the Z-domain.

)

results in multiplication by z⁻¹ in the Z-domain, and a delay of N units results in multiplication byz^−N.

The Z-transforms are introduced for two examples here. First, let the output of a filter be

the sum of the last N

+ 1

inputs:

y ( n ) = x ( n ) + x ( n − 1 ) + + x ( n − N ).

Such a filter contains N delays, which are feed-forward paths. The impulse response is

)

H . The transfer function is equivalent to the infinite

sum 2.2.2 Poles and Zeros

A discrete linear system with a discrete input signal in Eq. (10) as follows:

)

function that is a ratio of polynomials.

)

)

zm results in zero transmission at that frequency. The roots of the denominator polynomial are designed by p_n . The

Γ

has a maximum value determined by

Digital filters are classified by the polynomials defined in Eq. (11). A moving average (MA) filter has only zeros and also belongs to a finite impulse response. It consists only of feed-forward paths. A single stage MA digital filter is shown in Figure 2.1(a). An autoregressive (AR) filter has only poles and contains one or more feedback paths as shown in Fig. 2.1(b). A pole produces an impulse response with an infinite number of terms in contrast to the finite number of terms for MA filters.

(a) (b) Fig. 2.1 Illustrations of single-stage (a) MA digital filter and (b) AR digital filter.

2.2.3 Magnitude Response and Group Delay

A filter’s magnitude response is equal to the modulus of its transfer function,

H (z )

_,

evaluated at z

=

e^jw. Based on the pole/zero representation of H(z),only the distance of each pole and zero from the unit circle affects the magnitude response, i.e.

e

^jω

− z

_m or

n

j

p

e

^ω

−

. One trip around the unit circle is equal to one FSR. A convenient graphical method for estimating a filter’s response is shown in Fig. 2.2. Zeros with a magnitude >1 are called maximum-phase, and those with magnitude <1 are called minimum-phase. A pole-zero diagram with a pair of zeros that are located reciprocally about the unit circle is shown in Fig. 2.3.

Fig. 2.2 Pole-zero diagram showing the unit circle, one pole, and one zero.

Fig. 2.3 Pole-zero diagram showing a maximum- and a minimum-phase

zero.

The group delay of the filter is defined as the negative derivative of the phase of the transfer function with respect to the angular frequency as follows:

{ }

where

τ

_n is normalized to the unit delay, T. The absolute group delay is given by

n

g

T τ

τ = ×

. To obtain the group delay for a single zero, considering the transfer function

1

⎥ ⎦

the group delay is

[ ] _{1 ( , )}

The sum of the group delays is a constant value indicating that the filter has linear phase with the same magnitude response as shown in Fig. 2.4.

Fig. 2.4 Phase response of maximum and minimum phase MA filers.

8

2.3 Interleaver

2.3.1 Interleaver technology approaches

There are three broad classes of interleaver filter technologies: lattice filter (LF), Gires-Tournois based Michelson interferometer, and arrayed-waveguide router (AWG).

Within the lattice filter class there is the birefringent filter, employing birefringent crystals and classically known as a Lyot or Solc filter; the glass-based filter which substitutes an artificial polarization-dependent delay for the birefringent elements of the preceding type; and the Mach-Zehnder filter, which is the analog to the Lyot filter and is generally made with planar waveguides. Within the Gires-Tournois (GT) class there is the interference filter and the birefringent analog (B-GT). Arrayed-waveguide routers have designs for single-channel and banded filters.

2.3.2 Lattice Interleaver

Lattice filters are made from a cascade of differential-delay elements where the differential-delay of each element is an integral multiple of a unit delay and power is exchanged across paths between the elements. There are three issues to address in the study of lattice filters: the realization of the unit cell that generates the differential delay; the number of unit cells and associated intermediate power exchange; and the cascade of multiple filters.

Figure 2.5 shows the configuration of the interleaver consisting of the birefringent crystals. The basic principle is based on interference between polarized light, which depends on phase retardation between the components of light polarized parallel to the slow and the fast axes of the crystal. Consequently, birefringent crystal is used to perform as optical delay, and half-wave plates are used to change the polarization direction between the delay components. An optical FIR digital filter can, thus, be made by cascading delay lines and controlling the angle of rotation between half-wave plates. The half-wave plates can also be considered to be rotated to generate require Fourier frequency components.

θ

1

Fig. 2.5 Brief configuration of an L-2L interleaver

Actually, the design goal is to generate a periodic rectangular function as displayed in Fig. 2.6.

The function could be defined as

)

Expand to Fourier series 1

Fig. 2.6 The periodic rectangular function y( f )

f

3

Therefore, the final rectangular function could be written as Eq. (23)

+

Here we know that the square-wave amplitude function has only odd Fourier frequency components with appropriate Fourier coefficients.

According to the Jones matrix theory [12], a half-wave plate has a phase retardation of

π

=

Γ

, and the thickness of =λ/2(n_e−n_o). The Jones matrix for the half-wave plate is obtained by using Eq. 24.

⎥ ⎦

We can write the Jones matrix for the delay line as

⎥ ⎥

specify the input light is linearly polarized on the x axis. By adjusting the angles of the half-wave plates appropriately, we can get the odd channels and even channels lying the x and y axes, respectively, at the output port.

in

Change the angle of the two half-wave plates to fit the Fourier series For Example: 1L-2L

By combining all Jones matrices of the birefringent crystals, we can write the transmission as

2 1

(22.5 ) (2 ) ( ) ( ) ( )

out hp delay hp delay hp in

E =W ^° iW L Wi

θ

iW L Wi

θ

iE (26) where W_delay( L2 ) and W_L(L) are the Jones matrices of the two crystals

Nevertheless, how to get the angles to fit the Fourier coefficients in Eq. (22) is the critical point. Utilizing the optimization tools in Matlab programs is the solution. The goal is to minimize the error function by sweeping the half-wave plate angles as

( ) ( )

transmission function. The transmission function is periodic, so the errors are only summed over one FSR at the central frequency, w_c [13]. The last three approximation criteria include errors at all points of frequency in the interval; therefore, they include more error data

than the first for each y

(w )

considered. We choose the last approximation criterion because it is the energy in the error signal. [14]

2.3.3 Mathematical Derivation

Here we use the easiest case: one stage interleaver includes a delay line and two half-wave plates in which the second plate is determined to 22.5 degree. Assume that there

is an incident beam V_x(=

⎥

1

) injected to the first half-wave plate, then the Jones matrix

M1at the output can be written as

e⁻j can be neglected if interference effects are not important, or not observable. Then use

M2 to multiply the second half-wave plate (

⎥

⎦

⎥ ⎦

Compare with Eq. (23), the first term needs to equal 1/2 and the coefficient of the second term needs to equal the Fourier coefficient by optimizing the angle of

θ

₁. By this way, we can easy to understand the theory of interleaver.

2.3.4 Interleaver Simulation Results & Practical Device Measurement

The lengths of delay-line crystals in the program are determined using Eq. (32).

FSR

frequencies;

m

is the order of the birefringent wave plate.

L-2L Interleaver

The found angles for two half-wave plates are 7.7356 and 29.5286 degrees. Figure 2.7 shows the transmission responses of the even and odd channels; the isolation is about 18 dB.

Fig. 2.7 Transmission responses of the even and odd channels.

Fig. 2.8 The bandwidth estimations of -0.1dB and -0.5dB for L-2L interleaver.

The ripple is about 0.0026 dB; the bandwidths of -0.1dB and -0.5dB are 24 GHz and 36 GHz, respectively, as shown in Fig. 2.8.

~ 18 dB

~24 GHz

~36 GHz

Fig. 2.9 Dispersion compensating interleavers for add/drop node

In Fig. 2.9, the path with the negative group delay is called Type-I here, and another path with the positive group delay is called Type-II. The Type-I and Type-II have the same transmission response.

The corresponding parameters for simulation are given below:

Central wavelength = 193.00 THz;

Difference of index between n0 and ne=0.2138;

C = 2.997925x10⁸ m/s;

Channel spacing = 100 GHz;

The interleaver we used is a symmetrical four-port interleaver with two input and two output ports. The detail configuration is shown in Fig. 2.10. It incorporates the birefringent crystal cells; half wave plates (HWP), YVO4 walk off crystals (YWC) and polarization beam splitters (PBS).

L ^2L PBS

HWPs.

Birefringent crystal cell port1

port2

port3

port4 (a)

YWC PBS YWC

L ^2L

PBS

HWPs.

Birefringent crystal cell port1

port2

port3

port4 (a)

YWC PBS YWC

Fig. 2.10 Detail configuration of an L-2L interleaver

Fig. 2.11. Measured amplitude response of the interleaver for even and odd channels

Figure 2.11 illustrates the measured amplitude response of the interleaver for even and odd channels. The channel spacing of this interleaver is 50-GHz with insertion loss of 2.2-dB and 0.5-dB pass bandwidth of around 36-GHz, respectively. The two mirrored corresponding group delay curves are measure by the channel analyzer (Q7760), shown in figure 2.12(a) and figure 2.12(b).

Fig. 2.12(a). Amplitude response and the corresponding group delay of the interleaver for odd channels (type II)

Fig. 2.12(b). Amplitude response and the corresponding group delay of the interleaver for even channels (type I)

1 2

3 (o d d ) T y p e I 4 (o d d ) T y p e II

1 2

3 (e v e n ) T y p e II 4 (e v e n ) T y p e I In te r le a v e r

• C h a n n e l s p a c in g : 5 0 G H z

• In s e r tio n lo s s : 2 .2 d B

• 0 .5 d B b a n d w id th : ~ 3 6 G H z

2.4 Application of using an Interleaver in bi-directional amplification

We design the interleaver to have complementary wavelength dependent routing characteristics. For example, if λ1 (odd/west channel) enters port 1, it will be routed to port 3.

On the other hand, when λ2 (even/east channel) goes into port 2; it will also be directed to port 3. A more detail wavelength routing diagram is displayed in Fig. 2.14.

Fig. 2.13. Passband of the interleaver for even and odd channel

Such interleaving property is exploited to route simultaneously both the even channels, which arrive at the interleaver at port 2; and the odd channels, which enter the interleaver at port 1, to port 3. Therefore, the even and odd channels, which propagate in opposite directions, can be transformed into a co-propagating transmission in a single amplification section to achieve unidirectional amplification using a single EDFA, as shown in Fig. 2.15. The proposed innovative interleaving configuration not only supports the use of a single EDFA to achieve bidirectional transmission, but also eliminates the presence of a dead zone in the blue-red splitting technology due to this interleaver is implemented to cover the whole C band (1530 nm to 1560 nm), thus further increases the bandwidth utilization.

The transmission of interleaver we used is shown in Fig. 2.14.

Fig. 2.14. Transmission of Interleaver

West (Odd) East (Even) DCF

EDFA EDFA

Interleaver

West East

Fig. 2.15. Wavelength re-routing scheme for bidirectional transmission

Along side with bidirectional amplification function, dispersion compensation issue is also considered in this wavelength re-routing scheme. As described in Fig. 2.13, the group delay of routing port 2 to port4 and port 1 to port 3 are a pair of mirrored group delay and vice versa in the case of port 2 to port 3 and port 1 to port 4. The group delay of Type I and Type II

are displayed in Fig. 2.16(a), as well as the group delay after connecting Type I and Type II.

Consequently, the wavelength re-routing scheme not only benefits bidirectional amplification but also provides a dispersion compensated environment.

Fig. 2.16 (a) In-band group delay for two types of interleaver, (b) group delay of cascading Type I and Type II.

Chapter 3

Experiment of bi-directional straight line transmission

3.1 Bidirectional Optical Amplifier Configurations

Optical amplifiers are usually equipped with optical isolator, which make them unsuited for bidirectional transmission, in principle. However, it is possible to construct optical amplifiers for bidirectional transmissions. In the following section, we will consider the configuration of bidirectional optical amplifiers.

The simplest configuration for an optical amplifier is obtained by just omitting the optical isolators; since the operation of optical amplifiers is reciprocal. However, when a single EDFA (optical amplifier) is used bidirectionally without optical isolators or filters, interaction between the bidirectional channels may occur. There are at least three mechanisms for this interaction.

„ Reflections and Rayleigh backscattering cause crosstalk between bidirectional channels. A bidirectional amplifier will enhance this crosstalk, since it amplified the reflected signal.

„ Gain saturation will also cause mutual interaction, since if the signal in one direction saturates the gain, the signal in the other direction will also experience gain saturation.

„ Similarly the signal in one direction may influence the noise behavior of the optical amplifier for the signal in the other direction.

The omission of the optical isolators makes the bidirectional amplifier less expensive than a conventional unidirectional amplifier. However, several other configurations have been proposed in literature, see Fig. 3.1

„ Ref. [15] demonstrates the use of a unidirectional erbium-doped fiber amplifier

(EDFA) in a circuit, which combines and separates the bidirectional signals with wavelength splitters. The application of WDM makes this bidirectional amplifier configuration insensitive to optical reflections.

„ Ref. [16] uses a combination of two wavelength splitters and two optical isolators to have both optical isolation at all wavelengths, and bidirectional transmission.

„ Ref. [17], [18] and [19] propose the use of two separate EDFAs to decouple the saturation in the two directions. Here, each EDFA can have optical filters and isolator(s) or circulators.

Fig. 3.1 (a) Bidirectional amplification with unidirectional optical amplifier (b) Bidirectional amplifier with optical isolation (c) double optical amplifier with shared

pump laser.

3.2 Non-linear effects

The response of any dielectric to light becomes nonlinear for intense electromagnetic fields, and optical fiber are no exception. On a fundamental level, the origin of nonlinear response is related to anhormonic motion of bond electrons under the influence of an applied field. As a result, the induced polarization P from the electric dipoles is not linear in the electric field E, but satisfies the more general relation

...}

:

{ ^{(1) (2) (3)}

0 ⋅ + + +

= E EE EEE

P ε χ χ χ , where ε₀ is the vacuum permittivity and χ^{( j)} (j=1,2,3,…) is j th order susceptibility. To account for the light polarization effects, χ^{( j)} is a tensor of rank j+1. The linear susceptibility χ⁽¹⁾ represents the dominant contribution to P.

Its effects are included through the refractive index n and the attenuation coefficientα .

The nonlinear effects governed by the third-order susceptibility χ⁽³⁾ are elastic in the sense that no energy is exchanged between the electromagnetic field and the dielectric medium. Thus, a second class of nonlinear effects results from stimulated inelastic scattering in which the optical field transfers part of its energy to the nonlinear medium. Two important nonlinear effects in optical fiber fall in this category; both of them are related to vibrational excitation mode of silica. These two phenomena are known as stimulated Raman scattering (SRS) and stimulated Brillouin scattering. The fundamental difference is that SBS in optical fiber occurs only in the backward direction whereas SRS dominates in the forward direction.

Another nonlinear effect called Rayleigh backscattering (RB) will also deteriorate the bidirectional transmission system. Because any backward scattering will interfere the backward signal directly, the following discussions will focus on SBS and RB effects.

3.2.1 Stimulated Brillouin scattering

Stimulated Brillouin scattering can be understood as scattering of a photon to a lower energy photon such that the energy difference appears in the form of a phonon. The special

在文檔中 利用無色散間隔器探討雙向光纖傳輸系統 (頁 15-0)