11 Other 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 maximum 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. 286 OTHER WAVELENGTH TUNABLE OPTICAL FILTERS current I p . Each PC section is sandwiched between two corrugated DFB active sections. A =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 I a . 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 EðzÞ¼E R ðzÞþE S ðzÞ¼RðzÞ exp Àjb o zðÞþSðzÞ exp jb o zðÞ ð11:1Þ where E R ðzÞ and E S ðzÞ are the normalised electric fields that propagate along opposite directions, RðzÞ and SðzÞ are complex amplitudes of the forward and backward electric fields, respectively, b o ¼ 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 dz þ  À jðÞRðzÞ¼j SðzÞð11:2aÞ dSðzÞ dz þ  À jðÞSðzÞ¼j RðzÞð11:2bÞ In eqn (11.2) a is the mode gain per unit length, d ¼ b À b o is the detuning of the propagation constant b from the Bragg propagation constant b o , 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, I a and I p are the bias currents for the active and phase-controlled sections, respectively, L i i ¼ 1; 6ðÞis the ith section length and Z j j ¼ 1; 7ðÞis 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 z i and z iþ1 can be expressed as E R z iþ1 ðÞ E S z iþ1 ðÞ ! ¼ f 11 f 12 f 21 f 22 ! Á E R z i ðÞ E S z i ðÞ ! ¼ F ðiÞ Á E R z i ðÞ E S z i ðÞ ! ð11:3Þ where the matrix elements of matrix F ðiÞ are given as follows f 11 ¼ 1 1 À  2 i E i À  2 i E i  exp Àjb o z iþ1 À z i ðÞ½ ð11:4aÞ f 12 ¼ À i 1 À  2 i E i À 1 E i  exp Àjb o z iþ1 þ z i ðÞ½ ð11:4bÞ f 21 ¼  i 1 À  2 i E i À 1 E i  exp jb o z iþ1 þ z i ðÞ½ ð11:4cÞ f 22 ¼ 1 1 À  2 i 1 E i À  2 i E i  exp jb o z iþ1 À z i ðÞ½ ð11:4dÞ ANALYSIS 287 with E i ¼ exp g i z iþ1 À z i ðÞ½ ð11:4eÞ  i ¼ j  i À j i þ g i ð11:4fÞ In the above equations g i is the complex propagation constant that satisfies the following dispersion equation g 2 i ¼  i À j i ðÞ 2 þ 2 ð11:5Þ On the other hand, since there is no active section and no grating in the planar phase-shift- controlled (PSC) section (i.e.  i ¼ 0 and  i ¼ 0), the transfer matrix for the electric field of this section is simplified to E R z iþ1 ðÞ E S z iþ1 ðÞ ! ¼ exp ðÞ 0 0 exp À ðÞ ! E R z i ðÞ E S z i ðÞ ! ¼ P ðiÞ E R z i ðÞ E S z i ðÞ ! ð11:6Þ where ¼ g p L p À j o L p ÀÁ , g p is the value of g i in the PSC section and L p is the length of the PSC section. P ðiÞ is the corresponding transfer matrix of the PSC section. The amount of phase shift, O, introduced by each PSC section is given by [11] O ¼ Im 2g p L p ÀÁ ¼ 4 n a À n p ÀÁ L p  B ð11:7Þ where I m means the imaginary part, n a and n p are the effective indices of the active and PC sections, respectively. The value of n p decreases 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 E R z iþ1 ðÞ E S z iþ1 ðÞ ! ¼ exp jðÞ 0 0 exp ÀjðÞ ! E R z i ðÞ E S z i ðÞ ! ¼ S E R z i ðÞ E S z i ðÞ ! 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 E R LðÞ E S LðÞ ! ¼ T 11 T 12 T 21 T 22 ! E R 0ðÞ E S 0ðÞ ! ¼ F ð6Þ PF ð4Þ SF ð3Þ PF ð1Þ E R 0ðÞ E S 0ðÞ ! ð11:9Þ For the structures shown in Figs 11.9 and 11.15, respectively, eqn (11.9) becomes E R LðÞ E S LðÞ ! ¼ T 11 T 12 T 21 T 22 ! E R 0ðÞ E S 0ðÞ ! ¼ F ð5Þ SF ð4Þ PF ð2Þ SF ð1Þ E R 0ðÞ E S 0ðÞ ! ð11:10Þ 288 OTHER WAVELENGTH TUNABLE OPTICAL FILTERS and E R LðÞ E S LðÞ ! ¼ T 11 T 12 T 21 T 22 ! E R 0ðÞ E S 0ðÞ ! ¼ F ð7Þ F ð6Þ F ð5Þ F ð4Þ F ð3Þ F ð2Þ F ð1Þ E R 0ðÞ E S 0ðÞ ! ð11:11Þ In the above equation z 1 ¼ 0 and in Figs 11.1, 11.6 and 11.15 z 7 ¼ L, whereas z 6 ¼ 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 E S ðLÞ E R ð0Þ         2 ¼ 1 T 22         2 ð11:12Þ The threshold gain  th and the detuning parameter  can be obtained by solving the following equation numerically T 22  th ;Þ¼0ðð11:13Þ The power transmissivity of the filter can be calculated by using the following expression T ¼ 1 T 22  ¼ 0:98 th ;ðÞ         2 ð11:14Þ In eqn (11.14), we have used  ¼ 0:98 th [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. 11.3.1 A Quarter Wavelength Phase-shifted Double Phase-shift-controlled DFB LD-based Wavelength Tunable Filter In the following analysis we have used the total filter cavity length L ¼ 500 mm and the lengths of PC sections L 2 ¼ L 5 ¼ 50 mm. The lengths of active sections which are optimised to give maximum tuning range [15] are L 1 ¼ 68:5 mm, L 3 ¼ 37 mm, L 4 ¼ 135 mm and L 6 ¼ 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 RESULTS AND DISCUSSIONS OF VARIOUS OPTICAL TUNABLE FILTERS 289 wavelength 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  À  B where  is the operating wavelength of the filter,  B ¼ 2 n eff Lð¼ 1:55 mm) is the Bragg wavelength and n eff is the effective refractive index. The grating period and coupling coefficient of 0:21 mm and 6 mm À1 were 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 I p of the PC section. For example when I p increases, the effective refractive index n p decreases due to the free carrier plasma effect and hence O increases according to eqn (11.7). When O ¼ 0or2p (referred to as the stop band width of the filter, see case (a) in Fig. 11.2), the relative wavelengths are at Æ12.5 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 O ¼ 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  À  B ðÞfor the following different values of O. The parameters used are L 1 ¼ 68:4 mm, L 2 ¼ L 5 ¼ 50 mm, L 3 ¼ 36:98 mm, L 4 ¼ 135:02 mm, L 6 ¼ 159:6 mm,  ¼ =2,  ¼ 6mm À1 , L ¼ 0:21 mm and N ¼ 3:7. (a) O ¼ 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) O ¼ 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) O ¼ 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. 290 OTHER WAVELENGTH TUNABLE OPTICAL FILTERS Fig. 11.2. The result is shown in Fig. 11.3. In this case when O ¼ 0or2p the relative wavelengths are Æ14.15 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 mm À1 while keeping L ¼ 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 mm À1 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 6mm À1 ,  2 ¼ 4mm À1 and L ¼ 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  1 ¼ 4mm À1 ,  2 ¼ 6mm À1 and L ¼ 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  À  B ðÞfor the following different values of O. The parameters used are L 1 ¼ 68:4 mm, L 2 ¼ L 5 ¼ 50 mm, L 3 ¼ 36:98 mm, L 4 ¼ 135:02 mm, L 6 ¼ 159:6 mm,  ¼ =2,  ¼ 6mm À1 , L ¼ 0:238 mm and N ¼ 3:2647. (a) O ¼ 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) O ¼ 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) O ¼ 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. RESULTS AND DISCUSSIONS OF VARIOUS OPTICAL TUNABLE FILTERS 291 Figure 11.4 Power transmissivity versus relative wavelength  À  B ðÞfor the following different values of O. The parameters used are L 1 ¼ 68:4 mm, L 2 ¼ L 5 ¼ 50 mm, L 3 ¼ 36:98 mm, L 4 ¼ 135:02 mm, L 6 ¼ 159:6 mm,  ¼ =2,  ¼ 8mm À1 , L ¼ 0:238 mm and N ¼ 3:2647. (a) O ¼ 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) O ¼ 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) O ¼ 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 11.5 Power transmissivity versus relative wavelength  À  B ðÞfor the following different values of O. The parameters used are L 1 ¼ 68:4 mm, L 2 ¼ L 5 ¼ 50 mm, L 3 ¼ 36:98 mm, L 4 ¼ 135:02 mm, L 6 ¼ 159:6 mm,  ¼ =2,  ¼ 10 mm À1 , L ¼ 0:238 mm and N ¼ 3:2647. (a) O ¼ 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) O ¼ 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) O ¼ 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. minimum 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 L 1 and L 6 ) 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  À  B ðÞfor the following different values of O. The parameters used are L 1 ¼ 68:4 mm, L 2 ¼ L 5 ¼ 50 mm, L 3 ¼ 36:98 mm, L 4 ¼ 135:02 mm, L 6 ¼ 159:6 mm,  ¼ =2,  1 ¼ 6mm À1 ,  2 ¼ 4mm À1 , L ¼ 0:21 mm and N ¼ 3:7. (a) O ¼ 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) O ¼ 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) O ¼ 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. RESULTS AND DISCUSSIONS OF VARIOUS OPTICAL TUNABLE FILTERS 293 11.3.2 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 L ¼ 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  À  B ðÞfor the following different values of O. The parameters used are L 1 ¼ 68:4 mm, L 2 ¼ L 5 ¼ 50 mm, L 3 ¼ 36:98 mm, L 4 ¼ 135:02 mm, L 6 ¼ 159:6 mm,  ¼ =2,  1 ¼ 4mm À1 ,  2 ¼ 6mm À1 , L ¼ 0:21 mm and N ¼ 3:7. (a) O ¼ 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) O ¼ 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) O ¼ 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. 294 OTHER WAVELENGTH TUNABLE OPTICAL FILTERS [...]... Mode in =4-shifted InGaAsP/InP DFB Lasers, IEEE J Quantum Electron., 25(6), 1314–1319, 1989 4 Ghafouri-Shiraz, H and Chu, C Y J Distributed Feedback Lasers: An Overview, Fiber Integ Opt., 10, 23–47, 1991 5 Haus, H A and Lai, Y., Theory of Cascaded Quarter Wave Shifted Distributed Feedback Resonators, IEEE J Quantum Electron., 28, 205–213, 1992 6 Numai, T., Semiconductor Wavelength Tunable Filters Int... Technol Lett., 8(2), 72–75, 1995 13 Makino, T., Transfer-matrix Analysis of the Intensity and Phase Noise of Multisection DFB Semiconductor Lasers IEEE J Quantum Electron., 27(11), 2404–2414, 1991 14 Kogelnik, H and Shank, C V., Coupled-Wave Theory of Distributed Feedback Lasers J Appl Phys., 43(5), 2327–2335, 1972 15 Lew, S H., Design of Wavelength Tunable Optical Filters, Final Year Project Report,... far negative end, drifting towards a more positive value with an increase in O2 The power transmissivities of a few values of O1 and O2 are plotted in Fig 11.18 as a function of the relative wavelength from the Bragg wavelength The figure demonstrates a spectra of high and consistent peak gain, with small bandwidth and high side mode suppression 11.4 SUMMARY The effects of grating period and coupling... J Optoelectron., 6(3), 239–252, 1991 7 Numai, T., Murata, S and Mito, I., Tunable Wavelength Filters Using =4-shifted Waveguide Grating Resonators Appl Phys Lett., 53, 83–85, 1988 8 Kikushima, K and Nawata, K., Tunable Amplification Properties of Distributed Feedback Laser Diodes IEEE J Quantum Electron., QE-25(2), 163–169, 1989 9 Magari, K., Kawaguchi, H., Oe, K and Fukuda, M., Optical Narrow Band... assumption that the relationships of the grating phases at the two sides of the wavelength region are the same for the two O2 phase-control regions 11.5 REFERENCES 1 Brackett, C A., Dense Wavelength division multiplexing networks: principles and applications, IEEE J Select Areas Comm., 8, 948–964, 1990 2 Ghafouri-Shiraz, H and Chu, C Y J Distributed Feedback Lasers: An Overview, Fiber Integ Opt., 10,... 1:6; (c) O1 ¼ 0:5; O2 ¼ 1:8; (d) O1 ¼ ; O2 ¼ 1:9; (e) O1 ¼ 1:5; O2 ¼ 0:2; (f) O1 ¼ 0; O2 ¼ 0:4; (g) O1 ¼ 0:5; O2 ¼ 0:6 maintained over a wide range of normalised detuning coefficient by adjusting the values of O1 and O2 appropriately This will ensure high side mode suppression By varying fit alone with zero phase shift for O2 the normalised detuning coefficient of the main mode varies within... characteristics, eqn (11.13) has been solved numerically In general, for a given value of Figure 11.9 Analytical model for a single-phase-shift-controlled double-phase-shift wavelength tunable filter based on the DFB laser diode structure RESULTS AND DISCUSSIONS OF VARIOUS OPTICAL TUNABLE FILTERS 295 , the numerical solution to eqn (11.13) gives various oscillation modes for this device The one having the lowest... 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 [5] Figure 11.10 shows the transmission spectra of the filter for various values of O ranging from 0 to 2 The parameters... Li ði ¼ 1; 5Þ ¼ 100 mm The sub-lengths are chosen such that the structure remains symmetrical The horizontal axis in Fig 11.10 is the relative wavelength which is defined as  À B where  is the operating wavelength of the filter, B ¼ 2 neff L is the Bragg wavelength and neff is the effective refractive index The analysis indicates that the filter spectrum has shifted towards the negative side of the... assumed RESULTS AND DISCUSSIONS OF VARIOUS OPTICAL TUNABLE FILTERS Figure 11.15 299 Analytical model for the transfer matrix method In eqn (11.6), the imaginary part of determines the phase shift introduced by each phase-shift-control section In the phase-shift-control section, the loss is assumed to be so small that it behaves purely as a phase shifter in which the associated phase change is given . 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. 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