CHI R PED G RAT1 N G l.14-S H I FTE D DISTRIBUTED FEEDBACK LASER WITH UNIFORM LONGITUDINAL FIELD DISTRIBUTION

Indexing term: Semiconductor laser

A ,?/+shifted distributed feedback laser with linearly chirped grating was theoretically analysed using the coupled mode equations. The proposed structure shows a good single mode behaviour with very uniform field distribution.

The nonuniform field distribution in distributed feedback (DFB) lasers degrades the laser behaviour, causing multimode operation, linewidth broadening, intermodulation distortion and chirp, through the spatial hole burning. Several appro ache^'^^ to suppress the nonuniform field distribution have been reported. A 1/4-shifted DFB laser with chirped grating (1/4-shifted CG-DFB) can greatly suppress the longi- tudinal nonuniform field distribution maintaining a better single mode behaviour than 1/4-shifted DFB with uniform pitch grating.

- L / 2 0 L 12

19L5/11 Fig. 1 Grating shape of 2/4-shifted CG-DFB laser

The structure of the 1/4-shifted CG-DFB is shown in Fig. 1. The phase shift is at the cavity centre (0), and the pitch of the grating can be expressed as

A ( z ) = I\o + (Ai z (1)

where A, is the grating pitch at point 0, and q' is the chirping factor. The mode behaviour of the DFB laser with a chirped grating can be described by solving the coupled mode equa- tions

where 9 = 2 x 4 , A' is the forward wave, A - is the backward wave, and g is the mode field gain. 6 is the difference of the

21

x 0 8 ?

' 0 4 ?

r + V aJ -

0 0 -300 -200 -100 0 100 200 300

6 , c m ' p15121

Fig. 2 Rejlectivity spectrum chirped grating waveguide of 2/4-shifed CG-DFB laser

Line 1 is for waveguide 1 Line 2 is for waveguide 2 Line 3 is the squareioot of the product of 1 and 2 nL? = 10: uL = 2.5: aL = 0.66

propagation constant of the wave and the Bragg constant of the grating at point 0.

Fig. 2 shows the reflectivity spectrum (RS) of the chirped grating waveguide in Fig. 1. Line 1 corresponds to the RS if we see from point 0 to the left end of the cavity (waveguide I), line 2 corresponds to the RS if we see from point 0 to the right end of the cavity (waveguide 2), and line 3 corresponds to the square root of the RS product of line 1 and 2. At low level gain and not too large qL?, the maximum reflectivity of line 3 is fixed at the Bragg constant which corresponds to the point 0 (6 = 0). The product spectrum (3) is narrower com- pared with 1 and 2. The reason is that the difference of the Bragg constants of waveguides 1 and 2 (corresponding to the pitch at the waveguide centres of 1 and 2) gets larger when qL2 increases.

The nonuniform field distribution of DFB lasers is quite serious for 1/4-shifted DFB laser. The reason is that for 1/4- shifted DFB laser, the wavelength of the lasing mode is the Bragg wavelength of the grating (the lasing mode is at the stop band centre). If the lasing mode is moved away from the stop band centre, the field distribution will be more uniform

\ 0 10 20 30

'zL2

Fig. 3 Normalised threshold gain difference between lasing mode and next competitive mode of ,?/4-sh$ted CG-DFB with the normalised chirping factor

Lines 1 and 2 correspond to K L of 2.5 and 4, respectively.

rn 7 6

1 x g A Z o l . , , I +

-0 5 0 0 5 z i L a

U1 c

30 3 1

-0 5 0 0 0 5 z / L b m

Fig. 4 Longitudinalfield distribution of 1/4-shifed CG-DFB a uL = 2.5 qL? are 0, 10, and 15 for lines 1 ,2 and 3, respectively b u L = 4 nl? are Q 16 and 21.7 for linep 1 3 and 1 rpcwrtivdv

than the mode at the stop band centre (like the common DFB laser). So we need to move the lasing mode away from the stop band centre to obtain a uniform field distribution. The problem is that if the lasing mode is moved away from the stop band centre, the threshold gain difference between the lasing mode and the first side mode will be decreased (which is zero for the common DFB laser). To solve this problem, the maximum reflectivity at low gain away from the stop band centre is required. As discussed above, the 1/4-shifted CG-DFB can solve this problem.

Fig. 3 illustrates the relation of the normalised threshold gain difference A g t h L between the lasing mode and the first side mode with the normalised chirped factor qc. A g t h L increases with qL’ initially since the RS (Fig. 2) gets narrower when qI? increases. If qL’ is too large, the RS gets wider when

increases since the side peaks in RS get higher. So A g t h L begins to decrease as qL’ increases further. The mode is fixed at the Bragg wavelength corresponding to point 0 because of the compensation effect of the reflection phase (positive q and negative q) from waveguides 1 and 2.

Fig. 4 is the longitudinal field distribution of the lasing mode of a I/4-shifted CG-DFB with different qL’ values. When qI? increases, the lasing mode gets further away from the Bragg centres of waveguides 1 and 2 as mentioned above, so the field distribution becomes more uniform. With strong coupling (large KL, where K is the coupling coefficient and L is the laser cavity length), this behaviour (Fig. 4b) is the same while Agth L is even larger.

In conclusion, a 1/4-shifted CG-DFB laser is proposed to suppress the nonuniform field distribution of DFB lasers. The superior behaviour and simple technique for fabrication make this kind of structure more attractive.

P. ZHOU G. S. LEE Department of Electrical and Computer Engineering Louisiana State Uniuersity Baton Rouge, LA 70803-5901, USA

7th August 1990

References SCHRANS, T., and YARIV, A.: ‘Semiconductor laser with uniform longitudinal intensity distribution’, Appl. Phys. Lett., 1990, 56, pp. 15261 528 KIMURA, T., and SUGIMURA, A.: ‘Coupled phase-shift distributed feedback semiconductor laser for narrow linewidth operation’, IEEE J . Quantum Electron., 1989, QE25, pp. 678-683 MORTHIER, G., DAVID, K., VANKWIKELBERGE, P., and BAETS, R.: IEEE Photon. Tech. Lett., 1990,2, pp. 388-390 NAKANO, Y., and TADA, K.: ‘Analysis, design, and fabrication of GaAlAs/GaAs DFB lasers with modulated stripe width structure for complete single longitudinal mode oscillation’, IEEE J . Quantum Electron., 1988, QE-24, pp. 2017-2033 ZHOU, P., and LEE, G. s.: ‘Mode selection and spatial hole burning suppression of a chirped grating distributed feedback laser’, Appl. Phys. Lett., 1990,56, pp. 1400-1402

EFFECT OF ENHANCING THE RAMAN GAIN FACTOR ON THE LINEARITY OF RAMAN FIBRE AMPLIFIERS

Indexing terms: Optical$bres, Amplifiers

The effect of enhancing the Raman gain factor on the linear- ity characteristics of Raman fibre amplifiers is analysed. In addition to providing higher Raman gain per unit pump power, a higher value for the Raman gain factor also results in a lower value for the maximum gain, and therefore the maximum output power, available from the amplifier if it is to operate in the linear regime. This has important implica- tions for optimising the design of Raman fibre amplifiers.

Introduction: There is great interest in direct optical amplifica- tion for applications in future fibre transmission systems.’ Semiconductor laser optical amplifiers appear very attractive in this context because of their potentially wide bandwidth and relatively simple and well understood structure. The main drawbacks to such amplifiers are their limited output power, of the order of OdBm, and relatively low fibre to fibre gain. This has led to an increasing amount of attention being paid to the Raman fibre amplifier (RFA) as an alternative optical amplification device since the RFA is considered to be able to deliver much higher output powers, perhaps up to +20dBm or more. The RFA also has a drawback, namely that it requires large optical pump powers for its operation. To reduce the required level of optical pump power, efforts have been made to design special fibres with increased optical gain per unit of pump power. This is usually achieved by doping the fibre core with GeO, to increase the Raman gain coeffi- cient, g , and using a small fibre core diameter to reduce the effective fibre cross-sectional area, A, with the aim of enhanc- ing the fibre gain factor K O , defined as K O = g /Aa , where a is the fibre attenuation coefficient. In addition to lowering the optical pump power requirement, increasing the fibre gain factor also has implications for the linearity properties of Raman fibre amplifiers, and although this is clearly an equally important consequence of enhancing the value of KO, it has not yet been discussed in the literature.’

The relationship between the Raman gain factor, K O , and the linearity properties of a Raman fibre amplifier is exam- ined. It is found that the two are closely related so that if the value of K O is enhanced for example by fibre design then, in addition to lowering the required optical pump power level, the hieher value of Kn also imnoses a lower value for the

maximum possible output signal power from the RFA if it is to function within its linear regime as an amplifier. A higher fibre gain factor leads to a limitation on the maximum pos- sible linear gain for a significant range of input signal levels. This has important implications for optimising the design of Raman fibre amplifiers to be used as linear gain blocks in future fibre transmission systems.

Theory: Consider a forward Raman fibre amplifier with both the pump optical power, P , , and the signal optical power, P,, , being input at z = 0, and propagating along the fibre in the + z direction. Evolution of the signal and pump optical powers along the fibre may then be expressed

(1) P,, exp [r(l - e-“‘) - az ]

1 + F(z ) PXZ) =

P,, e 1 + F(z )

P,(z) = ~

where

v p pso v s p ,

F(z) = - exp [r(l

with

r = K , P ,

and

(3)

(4)

In the above expressions v p and v, are the pump and signal light frequencies, respectively, and a is assumed to be the same at the two frequencies.

For a RFA of length z, the amplifier gain, G, may therefore be expressed as

P,(z) PSO 1 + F(z )

exp [r(l - e-“’) - az ] G(z) = - = ( 5 )

which shows that in general the gain, G, is not independent of the input signal power P , , since F is a function of P,, . Eqn. 5 also indicates that a RFA will operate as an essentially linear amdifier nrovided that F d 1 The linearitv of a RFA can