Dispersive-grating distributed feedback lasers - OSA Publishing

Dispersive-grating distributed feedback lasers Yanping Xi1,*, Xun Li1, Seyed M. Sadeghi2, and Wei-ping Huang1 1

Department of Electrical and Computer Engineering, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada 2 Department of Physics, University of Alabama in Huntsville, Huntsville, Alabama 35899, USA email: [email protected]

Abstract: This paper proposed a novel distributed feedback (DFB) laser by incorporating a dispersive grating, whose coupling strength is dependent on the operating wavelength. Analysis of the laser threshold conditions shows that the proposed structure guarantees single-mode operation due to the inherent threshold gain discrimination on the two otherwise degenerated lasing modes. ©2008 Optical Society of America OCIS codes: (140.3490) Lasers, distributed-feedback; (140.3570) Lasers, single-mode.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

13. 14. 15. 16.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Total dispersion in graded index single-mode fibers,” Electron. Lett. 15, 474-476 (1979). J. P. Laude, Wavelength division multiplexing (Prentice Hall, New York, 1993). H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327-2335 (1972). J. Buus, “Mode selectivity in DFB lasers with cleaved facets,” Electron. Lett. 21, 179-180 (1985). H. A. Haus and C. V. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12, 532-539 (1976). H. Soda, Y. Kotaki, H. Ishikawa, and H. Imai, “Stability in single longitudinal mode operation GaInAsP/InP phase-adjusted DFB laser,” IEEE J. Quantum Electron. 23, 804-814 (1987). E. Kapon, A. Hardy, and A. Katzir, “The effects of complex coupling coefficients on distributed feedback lasers,” IEEE J. Quantum Electron. 18, 66-71 (1982). K. David, G. Morthier, P. Vankwikelberge, and R. Baets, “Yield analysis of non-AR-coated DFB lasers with combined index and gain coupling,” Electron. Lett. 26, 238-239 (1990). J. Zoz and B. Borchert, “Dynamic behavior of complex-coupled DFB lasers with in-phase absorptive grating,” Electron. Lett. 30, 39-40 (1994). L. Olofsson and T. G. Brown, “The influence of resonator structure on the linewidth enhancement factor of semiconductor lasers,” IEEE J. Quantum Electron. 28, 1450-1458 (1992). P. Yeh, “Christiansen-Bragg filters,” Opt. Comm. 35, 9-14 (1980). X. Li, Y. Xi, and W.-P. Huang, “Threshold analysis of a novel dispersive grating distributed feedback laser diode,” presented at the Asia optical fiber communication & optoelelctronic exposition & conference, Shanghai, China, Oct. 2007. S. M. Sadeghi and W. Li, “Electromagnetically induced distributed feedback intersubband lasers,” IEEE J. Quantum Electron. 41, 1227-1234 (2005). S. M. Sadeghi, W. Li, X. Li, and W.-P. Huang, “Tunable infrared semiconductor lasers based on electromagnetically induced optical defects,” IEEE J. Sel. Top. Quantum Electron. 13, 1046-1053 (2007). T. L. Koch and U. Koren, “Semiconductor lasers for coherent optical fiber communications,” IEEE J. Lightwave Technol. 8, 274-292 (1990). W. Streifer, R. D. Burnham, and D. R. Scifres, “Effect of external reflectors on longitudinal modes of distributed feedback lasers,” IEEE J. Quantum Electron. 11, 154-161 (1975).

1. Introduction Semiconductor lasers are one of key components in optical fiber communications. “Spectral purity”, i.e. single longitudinal mode operation, is often required to reduce effects of fiber group-velocity dispersion [1] and hence allow longer reach with low error rate. A narrow spectral width for a laser diode is also required to enhance the transmission capacity of the networks where wavelength-division multiplexing (WDM) systems [2] are applied, among #95679 - $15.00 USD

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Received 2 May 2008; revised 25 Jun 2008; accepted 26 Jun 2008; published 3 Jul 2008

7 July 2008 / Vol. 16, No. 14 / OPTICS EXPRESS 10809

other applications. One of the dominant structures being widely used is the distributed feed back (DFB) lasers. The uniform index-coupled DFB lasers with perfectly AR coated facets have the intrinsic drawback of the two degenerated modes spectrally symmetric with respect to the Bragg frequency [3]. Although, this degeneracy may be lifted by introducing facet asymmetry, the yield is hard to control due to the random facet phases [4]. A quarter wavelength shifted grating can break this degeneracy, leading to the single-mode operation at the Bragg wavelength [5]. However, with the increase of κ L , quantum efficiency decreases and also the photon/carrier distributions become highly non-uniform along the laser cavity, known as spatial hole burning effects, causing a reduced side-mode suppression [6]. Another solution is the introduction of complex coupling, i.e., the gain (or loss)-coupled DFB lasers. Various degrees of gain (or loss) coupling have been investigated [3, 7, 8]. It was shown that there will not be any degeneracy problem for purely gain coupling DFB lasers and the lasing mode is locating exactly at the Bragg wavelength for devices with AR coated facets. The complex-coupled DFB lasers will also introduce a large enough threshold gain difference to two otherwise degenerated modes, leading to the single-mode operation. However, saturation instabilities may occur for loss grating [9] and the gain coupling is highly dependent on the carrier density which varies greatly with current injection level for gain grating [10]. In [11], Yeh proposed a new type of passive filters, called Christiansen-Bragg filter, where the property of two different dispersion curves of two media are utilized. Inspired by this work, we found that, for the conventional uniform grating DFB lasers, the degeneration of two modes symmetric to the Bragg wavelength will be lifted if the coupling strength between two counter propagating waves is wavelength dependent [12]. Detailed descriptions are shown in this paper. In Sec. 2, the basic theory and the feasibility of the proposed design are discussed; in Sec. 3, the proposed design is validated by the analysis of the laser threshold conditions. The conclusion is given in Sec. 4. 2. Theory For conventional uniform grating DFB laser with both facets AR-coated, the threshold gain constant α and the detuning δ of the corresponding propagation constant was obtained through the following transcendental equation under the small gain and small perturbations assumptions [3]

α − jδ = γ cosh γ L sinh γ L

(1)

with the complex propagation constant γ obeying

γ 2 = (α − jδ ) + κ 2 2

(2)

where κ denotes the coupling strength and L is the grating length. δ is a measure of the propagation constant detuning from the Bragg wavelength through

δ = β − β 0 = 2π neff / λ − π / Λ

(3)

where λ denotes the lasing wavelength; neff and Λ the laser waveguide effective index and grating period, respectively. For the index-coupled DFB lasers, κ is a real number, i.e. κ = κ * . Take complex conjugate on both sides of Eqs. (1) and (2), we obtain

α + jδ = γ * ( cosh γ * L sinh γ * L ) with

(γ ) = ((α − jδ ) ) + (κ ) *

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2

2

*

2

*

(4)

= (α + jδ ) + κ 2 . 2

(5)



It is seen that if (α , δ ) is a solution set, (α , −δ ) is also a solution set, which means that for any lasing wavelength we obtained with detuning δ and threshold gain α , there is always an accompanying lasing wavelength at detuning −δ with identical threshold gain. From Eqs. (1) and (2), we have

γ 2 − κ 2 = γ cosh γ L sinh γ L .

(6)

We further notice that δ = 0 cannot be a solution of the above lasing condition since a real γ (due to δ = 0 in Eq. (2)) makes the left hand side of Eq. (6) smaller than γ whereas the right hand side larger than γ . As a result, conventional DFB laser with uniform indexcoupled grating can never achieve single mode operation due to the threshold gain degeneracy at two different lasing wavelengths symmetrically located at the two sides of the Bragg wavelength. Based on such understanding, we further deduce that, for complex-coupled DFB lasers in which κ becomes a complex number, i.e. κ ≠ κ * , the fact (α , δ ) is a solution set does not necessarily lead to the conclusion that (α , −δ ) is also a solution set of Eq. (1) since Eq. (5) is no longer valid. Consequently, the original degeneracy is broken for complex coupling coefficients. For a purely gain (or loss)-coupled DFB lasers, κ is an imaginary number. δ = 0 can thus be a solution since both sides of Eq. (6) are larger than the real γ now. The single-mode operation is achieved at Bragg wavelength. Another widely employed method for forcing the DFB lasers to lase at Bragg wavelength is to add an extra section of quarter wavelength in between two uniform grating sections, i.e. λ 4 -shifted shifted DFB lasers, where the solution set is however not obtained through searching the roots of Eq. (1) directly. The uniform index-coupled DFB lasers using a dispersive grating is introduced in this work as an alternative method to break the inherent degeneracy as follows

κ = κ 0 + ηδ

(7)

where κ 0 is the “background” coupling strength and η the detuning coefficient. Assume the grating is formed through periodic change between the index n1 of high index region and n2 of low index region, and dn1( 2) n1( 2) = n10( 20) + (λ − λ0 ) , (8) dλ with dn1 / d λ ≠ dn2 / d λ and n10 , n20 denoting the effective index of high and low index region at Bragg wavelength respectively. The coupling coefficient [3] of this dispersive grating can be calculated by

π κ = ( )(n1 − n2 ) . λ

(9)

By using Eqs. (3), (7), (8), (9) and λ0 = 2neff Λ , we obtained

π κ 0 ≡ ( )(n10 − n20 ) , λ

(10)

η ≡ −[d (n1 − n2 ) / d λ ]Λ .

(11)

It is seen from (11) that η in quantity is the effective index dispersion difference within one grating period. By the definition of (8), κ remains real, however it changes with the sign of δ . A different threshold gain α is obtained for the two otherwise degenerated modes, leading to the single mode operation. #95679 - $15.00 USD

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The grating dispersion is generated by introducing non-equal effective index dispersions in the two different sections of every grating period. One possible realization method is to apply the electromagnetically induced transparency (EIT) [13, 14], where the index corrugation is not formed by the periodic variation of semiconductor materials with different effective indexes. Rather, they are generated by the coherent processes associated with the interaction of an intense IR laser beam with a corrugated quantum well (QW) structure. The structure view is shown in Fig. 1 (a) and one simulation example is shown in Fig. 1 (b), which indicates a detuning coefficient of ∼ −12% with an incident beam of 0.7mW/cm2. Control light Upper cladding

QW Region

Trench Lower cladding

(a)

(b)

Fig. 1. (a) Schematic view of electromagnetically Induced Transparency; (b) Variations of refractive indices of QW regions and trenches with wavelength

3. Threshold analysis The devices under investigation in this section are the dispersive grating DFB lasers with κ 0 ≠ 0 . The results shown here are obtained numerically through a root searching routine that solves for Eqs. (1), (2) and (7). Fig. 2 (a), (b) show the threshold condition (α , δ ) of two dispersive grating designs with κ L = 2 and κ L = 4 , respectively. Cases with different detuning coefficient are investigated, i.e. η = 5%, 10% (square, star) and η = −5%, − 10% (circle, triangle). Threshold conditions of conventional DFB lasers (η = 0 ) with the same normalized coupling strengths are also plotted (cross) for the purpose of comparison. It is observed from Fig. 2 that there is only one mode at one side of the stopband edge takes the lowest threshold gain with either positive or negative η . If η > 0 , the coupling strength for the (+1) mode at the right hand side of the centre frequency increases, leading to a lower threshold gain; while that for the (-1) modes decreases, causing a higher threshold gain due to a negative δ . Also, we noticed from Fig. 2 that both a larger η and a smaller κ 0 L will help to increase the gain margin between (+1) and (-1) modes. We also found that it is the relative change of the coupling strength that is actually responsible to control the gain margin. To further examine this, we define the relative change of the coupling strength as

ξ=

ηδ . κ0

(12)

Figure 3 shows the change of the magnitude of the normalized gain margin with the magnitude of ξ for the different detuning coefficient. According to T. L. Koch et al. [15] a normalized gain/loss margin in excess of Δα L ∼ 0.015 is necessary to achieve a 25dB side mode suppression ratio (SMSR) for typical laser parameters under CW operation. While for dynamic single mode operation of intensity modulated lasers, the typical normalized gain/loss margin of 0.15 is desired to achieve a SMSR of ~25dB. We here take Δα L = 0.2 as our single mode operation criterion. It is observed from Fig. 3 that ξ > 0.1 is required for η = 5% . This actually corresponds to κ 0 L ≤ 2 from Eq. (12). If a larger η is applied, the constraint on

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κ 0 L will be greatly relaxed. Figure 4 shows the transmission spectrum of a typical dispersive grating DFB laser design with κ 0 L = 2 , η = ±5% . It is clearly shown that the (+1) mode is favored if η = +5% , while the (-1) mode is selected if η = −5% , consequently the single mode operation is achieved for either case with a SMSR as much as 50dB near the threshold. This is obviously attributed to the threshold gain discrimination brought by the grating coupling strength dependence on the detuning, as we previously analyzed. 2.0

3.0

η =0 η =5% η =-5% η =10% η =-10%

κ0L=2 2.5

η= 0 η= 5% η= -5% η= 10% η= -10%

κ0L=4 1.5

αL

αL

2.0

1.0

1.5

1.0

(a)

0.5

(b)

0.5 -10

-5

0

5

δL

10

-10

-5

0

5

10

δL

Fig. 2. Threshold condition of dispersive grating DFB lasers with different η under normalized background coupling strength (a) κ 0 L = 2 and (b) κ 0 L = 4 . 2.0

80

|Δα L|

1.5

Transmissivity (dB)

|η | =5% |η | =10%

1.0

0.5

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

|ξ | Fig. 3. Change of the magnitude of the normalized gain margin with that of the relative change of the coupling strength for the different detuning coefficient.

n1

η = +5%

η = −5%

40 20 0 -20 -10

-5

0

Fig. 4. Transmission spectrum of dispersive grating DFB lasers with η = 5% (solid line) and η = −5% (dashed line).

n2

n1

n2

n2

λ

Fig. 5. Illustration of a dispersive grating with n10 = n20 , dn1 / d λ ≠ dn2 / d λ

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10

Λ

λ0

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5

Normalized Detuning δ L

n1

n

n10 = n20

60

.



η=0 η=−10% η=−30% η=10%

0.8

80

Tra nsm issivity (d B)

0.9

αL

0.7

0.6

60

40

20

0

0.5 -10

-5

0

5

10

δL Fig. 6. Threshold condition of dispersive grating DFB lasers with different η under κ 0 L = 0 .

-20 -10

-5

0

5

10

Normalized Detuning δ L Fig. 7. Transmission spectrum of dispersive grating DFB lasers with η = −10% under κ 0 L = 0 .

So far, we consider the dispersive grating structure with κ 0 ≠ 0 and both facets AR-coated. It is naturally interesting to explore what performances the structure will have if κ 0 = 0 at the Bragg wavelength λ0 . Both facets are as cleaved in this case. As such, the propagating waves see no reflections from the grating at λ0 except for the reflection from the facets. An illustration of this structure is shown in Fig. 5. To include the effects of facet reflections, the modified transcendental equation of Eq. (1) is used [16]. The corresponding threshold conditions for the cases of η > 0 and η < 0 are calculated and shown in Fig. 6. The results for η = 0 are also added for comparison, which actually indicate the conventional FP cavity modes since reflections are only come from two facets for the whole wavelength range. Also, for all cases of the different values of η , the modes at the Bragg wavelength are overlapped due to δ = 0 . It is observed in Fig. 6 that if η > 0 , the central mode (at Bragg wavelength) bears the highest threshold gain, while the threshold gains of other modes are almost indistinguishable, which is absolutely not a candidate for lasers. However, if η > 0 , the central mode has the lowest threshold gain which indicates the possible realization of the single-mode lasers. It is seen that a detuning coefficient of -30% is required to achieve a gain margin of ∼ 0.2 in this case. Figure 7 shows the transmission spectrum for this structure. We observe from Fig. 6 that the performance of this structure is quite sensitive to the phase of the detuning coefficient η . This may be a problem for utilizing this structure for practical applications and therefore warrants further investigations. One possible solution is to add an adjustable phase section to compensate for the phase variation. 4. Conclusion This paper proposed a novel design of a single mode DFB lasers. Simulation results show that the dual-mode operation problem in uniform grating DFB laser can be cured by incorporating a grating dispersion, rather than by implementing the existing methods such as quarterwavelength shifted or complex-coupled gratings. The feasibility of this design is also discussed in this paper.

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