Following the recent rapid advances in lightwave technology, wavelength tunable optical filters are now incorporated in wavelength-division-multiplexed transmission systems to increase t
Trang 1Other Wavelength Tunable Optical Filters Based on the DFB Laser
Structure
11.1 INTRODUCTION
Optical tunable filters are key components of the future dense wavelength division multiplexed (WDM) optical fibre networks In such a network a number of information channels are simultaneously transmitted through a single fibre by putting each channel on a different optical carrier wavelength The wavelength filter allows a single or multiple channel(s) to be isolated at the receiving or routing node The tunability of the filter allows for dynamic network reconfiguration and increases versatility of the system Ideally, the wavelength filter should be tunable over the entire system bandwidth and should have no secondary pass bands, or side lobes in its filter function
WDM systems require optical tunable filters not only as channel selectors, but also as post-optical-amplifier filters that reduce amplified spontaneous emission (ASE) noise [1] Following the recent rapid advances in lightwave technology, wavelength tunable optical filters are now incorporated in wavelength-division-multiplexed transmission systems to increase the line capacity for lightwave telecommunication services Optical filtering for selection of channels separated by 2 nm is currently achievable, and narrower channel separations may be possible as filter technologies improve This would give more than a hundred broadband channels in the low-loss fibre transmission region of 1.3 mm and/or 1.55 mm wavelength bands with each wavelength channel having a transmission bandwidth
of several gigahertz Wavelength tunable optical filters have already been built into the receiver for each subscriber in distribution networks [2] Basically a semiconductor wavelength tunable optical filter is a laser diode which is biased slightly below threshold When an optical signal of a wavelength close to the oscillation wavelength of the device is incident upon the input, the signal is amplified and emitted at the output By changing the injection current, the wavelength can be tuned due to free carrier plasma and quantum confined Stark effects
Distributed feedback laser diode amplifiers (DFB LDAs) can be used as tunable wavelength narrowband optical filters This is because a DFB LDA has two main advantages: single frequency with narrowband amplification and tunability of the lose gain profile
Distributed Feedback Laser Diodes and Optical Tunable Filters H Ghafouri–Shiraz
# 2003 John Wiley & Sons, Ltd ISBN: 0-470-85618-1
Trang 2maximum frequency by changing the amplifier’s bias current DFB LDs have the advantage
of a single resonance at the centre of the stop band Conventional uniform DFB LDs have resonances on both sides of the stop band This is, in general, a disadvantage since they may oscillate at either of the two frequencies Furthermore, the grating is less effective outside its stop band This drawback of index gratings has been overcome by inserting a =4 phase shift
at the centre of the structure [3–4] In this way a resonance is produced at the centre of the stop band A passive index grating can perform useful filtering functions [5] A DFB type filter has the advantages of high gain and narrow bandwidth and disadvantages in that the bandwidth and the transmissivity change with wavelength tuning
Single-electrode wavelength tunable optical filters [6–8] have the problem of a changing transmissivity during tuning This is because the injection current of a single-electrode device affects both the transmissivity and transmission wavelength This problem has been solved by employing a multi-electrode DFB filter which has more than one injection current
to control the gain and the central wavelength [9] The tuning range of this filter is 33 GHz with a constant gain and bandwidth In 1992, Numai [10] reported the phase-controlled (PC) DFB wavelength tunable optical filter In this device the gain and transmission wavelength were controlled independently by applying different injection currents For this filter a tuning range of 43 GHz (3.4 A˚ ) with constant gain of 27 dB and constant bandwidth of 0.4 A˚ has been reported The drawback of this filter is its very limited wavelength tuning range In general, to obtain a wider tuning range, suppression of the sub-modes is essential To achieve this goal, Numai [11] proposed the phase-shift-controlled (PSC) DFB filter where the side modes were suppressed by the large gain margin when it was tuned around the Bragg wavelength This filter has a wider tuning range of 120 GHz (9.5 A˚ ) with constant gain of 24.5 dB and constant bandwidth of 12–13 GHz In 1994, Tan et al [12] proposed the multiple-phase-shift-controlled distributed feedback wavelength tunable filter which has a wavelength tuning range of about 30 A˚ with side mode suppression ratio of more than 25 dB
In this chapter we analyse the performance characteristics of DFB LD-based wavelength tunable optical filters
11.2 ANALYSIS
The analytical model for the filter structure is shown in Fig 11.1 This filter consists of two passive PC waveguides which control the transmission wavelength by changing the bias
Figure 11.1 Analytical model for the =4-phase-shifted double phase-shift-controlled wavelength tunable filter
Trang 3A =4 phase shift is also located at the centre of the middle DFB active section The active sections control the optical gain of the filter through the bias current Ia In the analysis we have used the transfer matrix method to study the characteristics of this filter [4,13] In doing
so, the filter cavity is divided into seven sections and the wave propagation in each section is represented by a transfer matrix Let us assume that the device has zero facet reflectivity and the z-axis is along the filter cavity The electric field EðzÞ within the filter cavity can be expressed as
EðzÞ ¼ ERðzÞ þ ESðzÞ ¼ RðzÞ exp jbð ozÞ þ SðzÞ exp jbð ozÞ ð11:1Þ where ERðzÞ and ESðzÞ are the normalised electric fields that propagate along opposite directions, RðzÞ and SðzÞ are complex amplitudes of the forward and backward electric fields, respectively, bo¼ p=L is the Bragg frequency of the grating and L is the grating period Substituting eqn (11.1) into Maxwell’s equations and neglecting the second derivatives of both RðzÞ and SðzÞ with respect to z, as they are slowly varying functions of z,
we obtain the following pair of coupled mode equations [4,14]
dRðzÞ
dSðzÞ
In eqn (11.2) a is the mode gain per unit length, d¼ b bo is the detuning of the propagation constant b from the Bragg propagation constant bo, and is the grating coupling coefficient The filter structures used in this analysis are shown in Figs 11.1, 11.6, 11.9 and 11.15 where, for example in Fig 11.1, Iaand Ipare the bias currents for the active and phase-controlled sections, respectively, Liði¼ 1; 6Þ is the ith section length and
Zjðj¼ 1; 7Þ is the jth position In order to calculate the transmission characteristics of this filter structure it is more convenient to use the transfer matrix method [4,13] where the cavity
is divided into seven sections In each section we assume parameters ; and are uniform From the coupled wave equations, the transfer matrix which describes the propagating electric field in the corrugated section between zi and ziþ1 can be expressed as
ERðziþ1Þ
ESðziþ1Þ
¼ f11 f12
f21 f22
ERð Þzi
ESð Þzi
¼ FðiÞ ERð Þzi
ESð Þzi
ð11:3Þ
where the matrix elements of matrix FðiÞ are given as follows
f11 ¼ 1
1 2 i
Ei
2 i
Ei
exp½jboðziþ1 ziÞ ð11:4aÞ
f12 ¼ i
1 2 i
Ei 1
Ei
exp½jboðziþ1þ ziÞ ð11:4bÞ
f21 ¼ i
1 2 i
Ei 1
Ei
exp jb½ oðziþ1þ ziÞ ð11:4cÞ
f22 ¼ 1
1 2
1
Ei
2
iEi
exp jb½ oðziþ1 ziÞ ð11:4dÞ
Trang 4i jiþ gi
ð11:4fÞ
In the above equations gi is the complex propagation constant that satisfies the following dispersion equation
On the other hand, since there is no active section and no grating in the planar phase-shift-controlled (PSC) section (i.e i¼ 0 and i¼ 0), the transfer matrix for the electric field of this section is simplified to
ERðziþ1Þ
ESðziþ1Þ
ERð Þzi
ESð Þzi
¼ PðiÞ ERð Þzi
ESð Þzi
ð11:6Þ
where ¼ gpLp joLp
, gpis the value of giin the PSC section and Lp is the length of the PSC section PðiÞis the corresponding transfer matrix of the PSC section The amount of phase shift, O, introduced by each PSC section is given by [11]
O¼ Im 2gpLp
¼4 na np
Lp
where Immeans the imaginary part, naand np are the effective indices of the active and PC sections, respectively The value of npdecreases as the current injection into the PC section increases, hence according to eqn (11.7) the value of O increases The transfer matrix for phase shift in the active section is given by
ERðziþ1Þ
ESðziþ1Þ
0 expðjÞ
ERð Þzi
ESð Þzi
¼ S ERð Þzi
ESð Þzi
ð11:8Þ
where is the phase shift in the active section By multiplying matrices representing the planar phase-control sections, phase-shift section and the corrugated DFB sections together, the overall transfer matrix for the structure shown in Figs 11.1 and 11.6 becomes
ERð ÞL
ESð ÞL
¼ T11 T12
T21 T22
ERð Þ0
ESð Þ0
¼ Fð6ÞPFð4ÞSFð3ÞPFð1Þ ERð Þ0
ESð Þ0
ð11:9Þ
For the structures shown in Figs 11.9 and 11.15, respectively, eqn (11.9) becomes
ERð ÞL
E ð ÞL
¼ T11 T12
ERð Þ0
E ð Þ0
¼ Fð5ÞSFð4ÞPFð2ÞSFð1Þ ERð Þ0
E ð Þ0
ð11:10Þ
Trang 5ERð ÞL
ESð ÞL
¼ T11 T12
T21 T22
ERð Þ0
ESð Þ0
¼ Fð7ÞFð6ÞFð5ÞFð4ÞFð3ÞFð2ÞFð1Þ ERð Þ0
ESð Þ0
ð11:11Þ
In the above equation z1¼ 0 and in Figs 11.1, 11.6 and 11.15 z7 ¼ L, whereas z6¼ L in Fig 11.9 In an optical filter (such as the ones shown in Figs 11.1, 11.6, 11.9 and 11.15), the power transmissivity, T, is defined as
T ¼ ESðLÞ
ERð0Þ
T22
The threshold gain th and the detuning parameter can be obtained by solving the following equation numerically
The power transmissivity of the filter can be calculated by using the following expression
T22ð¼ 0:98th; Þ
2
ð11:14Þ
In eqn (11.14), we have used ¼ 0:98th[7] to achieve a higher output power and hence a smaller 10 dB bandwidth
11.3 RESULTS AND DISCUSSIONS OF VARIOUS OPTICAL
TUNABLE FILTERS
In this section we consider three different filter structures and analyse their performances
DFB LD-based Wavelength Tunable Filter
In the following analysis we have used the total filter cavity length L¼ 500 mm and the lengths of PC sections L2¼ L5¼ 50 mm The lengths of active sections which are optimised
to give maximum tuning range [15] are L1¼ 68:5 mm, L3¼ 37 mm, L4¼ 135 mm and
L6¼ 159:5 mm Equation (11.13) has been solved numerically to analyse the filter structure shown in Fig 11.1 For a given value of , the numerical solution to eqn (11.13) gives various oscillation modes for the device The one having the lowest threshold gain is the main mode Sub-modes are the modes with larger threshold gains The filter operates by biasing the gain of the device slightly below the threshold gain of the main mode The normalised detuning coefficient of the main mode determines the amount of deviation of the oscillation wavelength from the Bragg wavelength The oscillation wavelength is the central
Trang 6wavelength of the filter For a given O the side mode suppression ratio (SMSR) is defined as the ratio of the highest peak to the second highest peak of the filter power transmissivity It determines the amount of interference from the channel at the side mode wavelength As the central wavelength drifts away from the Bragg wavelength, the SMSR reduces If the SMSR
is larger than 10 dB then the adjacent channel interference is minimal [7]
Figure 11.2 shows the calculated transmission spectra of the filter for various values of the phase shift O ranging from 0 to 2 p The horizontal axis is the relative wavelength defined as
B where is the operating wavelength of the filter, B¼ 2 neffLð¼ 1:55 mm) is the Bragg wavelength and neffis the effective refractive index The grating period and coupling coefficient of 0:21 mm and 6 mm1were used in this calculation The figure clearly indicates that as O increases the wavelength of the main mode shifts towards the shorter wavelength side The phase shift O can be controlled by changing the injection current Ip of the PC section For example when Ipincreases, the effective refractive index npdecreases due to the free carrier plasma effect and hence O increases according to eqn (11.7) When O¼ 0 or 2p (referred to as the stop band width of the filter, see case (a) in Fig 11.2), the relative wavelengths are at12.5 A˚ This gives the filter wavelength tuning range of 25 A˚ The filter peak gain varies between 34.9 and 36.1 dB with maximum deviation of 1.2 dB The relative wavelength is zero when O¼ p (see case (l) in Fig 11.2) and the filter SMSR ranges from 15.7 to 29.5 dB
To investigate the effect of the grating period L on the filter performance we have increased its value to 0:238 mm while the rest of the parameters remain identical to those in
Figure 11.2 Power transmissivity versus relative wavelength ð BÞ for the following different values of O The parameters used are L1¼ 68:4 mm, L2¼ L5¼ 50 mm, L3¼ 36:98 mm,
L4¼ 135:02 mm, L6¼ 159:6 mm, ¼ =2, ¼ 6 mm1, L¼ 0:21 mm and N ¼ 3:7 (a) O ¼ 0; 2; (b) O¼ 0:1; (c) O ¼ 0:2; (d) O ¼ 0:3; (e) O ¼ 0:4; (f) O ¼ 0:5; (g) O ¼ 0:6; (h) O ¼ 0:7; ( j) O¼ 0:8; (k) O ¼ 0:9; (l) O ¼ ; (m) O ¼ 1:1; (n) O ¼ 1:2; (p) O ¼ 1:3; (q) O ¼ 1:4; (r) O¼ 1:5; (s) O ¼ 1:6; (t) O ¼ 1:7; (u) O ¼ 1:8; (v) O ¼ 1:9
Trang 7Fig 11.2 The result is shown in Fig 11.3 In this case when O¼ 0 or 2p the relative wavelengths are14.15 A˚ which gives the total filter tuning range of 28.3 A˚ This shows an increase of 3.3 A˚ compared with the filter shown in Fig 11.2 The filter peak gain varies between 35 and 36.1 dB and the filter SMSR ranges from 15 to 30 dB
The effect of increasing to 8 mm1while keeping L¼ 0:238 mm is shown in Fig 11.4
In this case the wavelength tuning range has increased to 31.1 A˚ The filter peak gain varies between 33 and 35.2 dB and the SMSR ranges from 18.2 to 34.3 dB These data indicate that the deviation in the filter peak gain has increased to 2.2 dB compared with the previous two cases The filter spectra for the case where ¼ 10 mm1 is shown in Fig 11.5 where a wavelength tuning range of 34.3 A˚ has been achieved The filter peak gain varies between 31.1 and 34.6 dB, which gives maximum deviation of 3.5 dB The filter SMSR ranges from 19.6 to 34.7 dB
We have also studied the performance characteristics of the filter structure shown in Fig 11.6 where the active sections have different grating coefficients For example, the result shown in Fig 11.7 is for the case where 1 ¼ 6 mm1, 2¼ 4 mm1and L¼ 0:21 mm The achieved peak filter gain varies between 35.6 and 36.4 dB, which gives 0.8 dB deviation The wavelength tuning range of the filter is 25.2 A˚ and its SMSR ranges from 11.5 to 27 dB Figure 11.8 shows the case where 1¼ 4 mm1, 2¼ 6 mm1and L¼ 0:21 mm This filter gives the wavelength tuning range of 24.4 A˚ which is 0.8 A˚ lower than that of Fig 11.7 Also, the SMSR ranges from 8.2 dB to 28.1 dB where the lower part is less than the
Figure 11.3 Power transmissivity versus relative wavelength ð BÞ for the following different values of O The parameters used are L1¼ 68:4 mm, L2¼ L5¼ 50 mm, L3¼ 36:98 mm, L4¼ 135:02 mm, L6¼ 159:6 mm, ¼ =2, ¼ 6 mm1, L¼ 0:238 mm and N ¼ 3:2647 (a) O ¼ 0; 2; (b)
O¼ 0:1; (c) O ¼ 0:2; (d) O ¼ 0:3; (e) O ¼ 0:4; (f) O ¼ 0:5; (g) O ¼ 0:6; (h) O ¼ 0:7; ( j) O¼ 0:8; (k) O ¼ 0:9; (l) O ¼ ; (m) O ¼ 1:1; (n) O ¼ 1:2; (p) O ¼ 1:3; (q) O ¼ 1:4; (r)
O¼ 1:5; (s) O ¼ 1:6; (t) O ¼ 1:7; (u) O ¼ 1:8; (v) O ¼ 1:9
Trang 8Figure 11.4 Power transmissivity versus relative wavelength ð BÞ for the following different values of O The parameters used are L1¼ 68:4 mm, L2¼ L5¼ 50 mm, L3¼ 36:98 mm, L4¼ 135:02 mm, L6¼ 159:6 mm, ¼ =2, ¼ 8 mm1, L¼ 0:238 mm and N ¼ 3:2647 (a) O ¼ 0; 2; (b)
O¼ 0:1; (c) O ¼ 0:2; (d) O ¼ 0:3; (e) O ¼ 0:4; (f) O ¼ 0:5; (g) O ¼ 0:6; (h) O ¼ 0:7; ( j) O¼ 0:8; (k) O ¼ 0:9; (l) O ¼ ; (m) O ¼ 1:1; (n) O ¼ 1:2; (p) O ¼ 1:3; (q) O ¼ 1:4; (r)
O¼ 1:5; (s) O ¼ 1:6; (t) O ¼ 1:7; (u) O ¼ 1:8; (v) O ¼ 1:9
Figure 11.5 Power transmissivity versus relative wavelength ð BÞ for the following different values of O The parameters used are L1¼ 68:4 mm, L2¼ L5¼ 50 mm, L3¼ 36:98 mm, L4¼ 135:02 mm, L6¼ 159:6 mm, ¼ =2, ¼ 10 mm1, L¼ 0:238 mm and N ¼ 3:2647 (a) O ¼ 0; 2; (b) O¼ 0:1; (c) O ¼ 0:2; (d) O ¼ 0:3; (e) O ¼ 0:4; (f) O ¼ 0:5; (g) O ¼ 0:6; (h) O ¼ 0:7; ( j) O¼ 0:8; (k) O ¼ 0:9; (l) O ¼ ; (m) O ¼ 1:1; (n) O ¼ 1:2; (p) O ¼ 1:3; (q) O ¼ 1:4; (r)
O¼ 1:5; (s) O ¼ 1:6; (t) O ¼ 1:7; (u) O ¼ 1:8; (v) O ¼ 1:9
Trang 9minimum required value of 10 dB The gain of this filter varies between 37 and 37.8 dB Comparison of Figs 11.7 and 11.8 indicates that when 1> 2, both the tuning range and the SMSR of the filter are larger because of better suppression of side modes In fact with a larger 1, the feedback from both ends (i.e sections L1 and L6) is larger This results in a stronger effect of the phase-control region and hence a better suppression of the side modes
Figure 11.6 Analytical model for the =4-phase-shifted double phase-shift-controlled wavelength tunable filter
Figure 11.7 Power transmissivity versus relative wavelength ð BÞ for the following different values of O The parameters used are L1¼ 68:4 mm, L2¼ L5¼ 50 mm, L3¼ 36:98 mm,
L4¼ 135:02 mm, L6¼ 159:6 mm, ¼ =2, 1¼ 6 mm1, 2¼ 4 mm1, L¼ 0:21 mm and N ¼ 3:7 (a) O¼ 0; 2; (b) O ¼ 0:1; (c) O ¼ 0:2; (d) O ¼ 0:3; (e) O ¼ 0:4; (f) O ¼ 0:5; (g) O ¼ 0:6; (h) O¼ 0:7; ( j) O ¼ 0:8; (k) O ¼ 0:9; (l) O ¼ ; (m) O ¼ 1:1; (n) O ¼ 1:2; (p) O ¼ 1:3; (q) O¼ 1:4; (r) O ¼ 1:5; (s) O ¼ 1:6; (t) O ¼ 1:7; (u) O ¼ 1:8; (v) O ¼ 1:9
Trang 1011.3.2 A Single-phase-shift-controlled Double-phase-shift DFB Wavelength
Tunable Optical Filter
The filter structure used in the analysis is shown in Fig 11.9 It has a passive phase-shift-controlled waveguide (O) which is sandwiched between two phase-shifted active sections 1 and 4 The total length of the filter cavity L¼ 500 mm To analyse this filter’s characteristics, eqn (11.13) has been solved numerically In general, for a given value of
Figure 11.8 Power transmissivity versus relative wavelength ð BÞ for the following different values of O The parameters used are L1¼ 68:4 mm, L2¼ L5¼ 50 mm, L3¼ 36:98 mm,
L4¼ 135:02 mm, L6¼ 159:6 mm, ¼ =2, 1¼ 4 mm1, 2¼ 6 mm1, L¼ 0:21 mm and N ¼ 3:7 (a) O¼ 0; 2; (b) O ¼ 0:1; (c) O ¼ 0:2; (d) O ¼ 0:3; (e) O ¼ 0:4; (f) O ¼ 0:5; (g) O ¼ 0:6; (h) O¼ 0:7; ( j) O ¼ 0:8; (k) O ¼ 0:9; (l) O ¼ ; (m) O ¼ 1:1; (n) O ¼ 1:2; (p) O ¼ 1:3; (q)
O¼ 1:4; (r) O ¼ 1:5; (s) O ¼ 1:6; (t) O ¼ 1:7; (u) O ¼ 1:8; (v) O ¼ 1:9
Figure 11.9 Analytical model for a single-phase-shift-controlled double-phase-shift wavelength tunable filter based on the DFB laser diode structure
... is the operating wavelength of the filter, B¼ neffLð¼ 1:55 mm) is the Bragg wavelength and neffis the effective refractive index The grating period... side mode wavelength As the central wavelength drifts away from the Bragg wavelength, the SMSR reduces If the SMSRis larger than 10 dB then the adjacent channel interference is minimal... example when Ipincreases, the effective refractive index npdecreases due to the free carrier plasma effect and hence O increases according to eqn (11.7) When O¼ or 2p