Analysis and modeling of ridge waveguide quarterly wavelength shifted distributed feedback laser with three rate equations

doi:10.1007/s12200-015-0476-0

Front. Optoelectron.

2015, Vol. 8

Issue (3) : 329-340 https://doi.org/10.1007/s12200-015-0476-0

RESEARCH ARTICLE

Analysis and modeling of ridge waveguide quarterly wavelength shifted distributed feedback laser with three rate equations

Abbas GHADIMI(

),Alireza AHADPOUR SHAL(

)

Department of Electrical Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran

Download: PDF(333 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

In this paper, ridge waveguide quarterly wavelength shifted distributed feedback (RW-QWS-DFB) laser was modeled and analyzed. In this behavioral model, some characteristics of the device, such as threshold current, line width, power of output wave, spectrum of output wave, and laser stability in high powers, were investigated in accordance with different physical and geographical parameters such as sizes and structures of the layers. Considering a new proposed algorithm, the analysis of the mentioned structures was performed using transfer matrix method (TMM), the solution of coupled waves and carrier rate equations. The results showed the advantages of some parameters in this structure.

Keywords distributed feedback laser transfer matrix method (TMM) transversal and lateral mode

Corresponding Author(s): Abbas GHADIMI

Just Accepted Date: 02 February 2015 Issue Date: 18 September 2015

Cite this article:

Abbas GHADIMI,Alireza AHADPOUR SHAL. Analysis and modeling of ridge waveguide quarterly wavelength shifted distributed feedback laser with three rate equations[J]. Front. Optoelectron., 2015, 8(3): 329-340.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-015-0476-0
https://academic.hep.com.cn/foe/EN/Y2015/V8/I3/329

Fig.1 Simple illustration of DFB 5-layered semiconductor laser

Fig.2 Lateral confinement factor changes versus ridge width

Fig.3 Coupling coefficient changes versus ridge width in different thickness of active layers and waveguides

Fig.4 Threshold current density changes versus ridge width in different thickness of active layers and waveguides

Fig.5 Threshold current changes versus ridge width in different thickness of active layers and waveguides

Fig.6 Line width changes of RW-QWS-DFB laser versus different ridge widths

Fig.7 Spectrum of ASE of RW-QWS-DFB laser in threshold condition for three different line widths w = 1, 3, 5 μm

Fig.8 Output power versus normalized current density for RW-QWS-DFB laser for two different value of w

Fig.9 Line width changes versus J/J_th for the proposed RW-QWS-DFB structure in w = 1 and 3 μm

Fig.10 Photons density distribution along the cavity of RW-QWS-DFB structure for w = 1 and 3 μm in above threshold condition

Fig.11 Charge carrier density distribution of RW-QWS-DFB structure for w=1 and 3 μm in above threshold condition

Fig.12 (a) Average changes of the normalized threshold gain αL; (b) deviation from the Bragg normalized condition δL (J/J_th for two different ridge widths of w = 1 and 3 μm)

Fig.13 Output wave spectrum for RW-QWS-DFB for J/J_th = 1.02, 1.5 and 3. (a) w = 1 μm; (b) w = 3 μm

Fig.14 Output wave spectrum of RW-QWS-DFB laser in two different ridge widths for J/J_th = 3

Fig.15 SMSR changes versus input current for two widths of w = 1 and 3 μm in RW-QWS-DFB laser

Fig.16 Uniformity parameter dependence to RW-QWS-DFB ridge width. Curved lines represent RW-QWS-DFB structure and straight lines represent QWS-DFB structure

Fig.17 Optical field intensity curve along cavity in RW-QWS-DFB structure in three different ridge widths

1	Dumke W P. Interband transitions and maser action. Physical Review, 1962, 127(5): 1559–1563 https://doi.org/10.1103/PhysRev.127.1559
2	Hall R N, Fenner G E, Kingsley J D, Soltys T J, Carlson R O. Coherent light emission from GaAs junctions. Physical Review Letters, 1962, 9(9): 366–368 https://doi.org/10.1103/PhysRevLett.9.366
3	Nathan M I, Dumk W P, Burns G, Dill F H, Lasher G. Stimulated emission of radiation from GaAs p-n junctions. Applied Physics Letters, 1962, 1(3): 62–64 https://doi.org/10.1063/1.1777371
4	Quist T M, Rediker R H, Keyes R J, Krag W E, Lax B, Mcwhorter A L, Zeigler H J. Semiconductor maser of GaAs. Applied Physics Letters, 1962, 1(4): 91–92 https://doi.org/10.1063/1.1753710
5	Holonyak N, Bevacqua S F. Coherent (visible) light emission from Ga(As1-xPx) junctions. Applied Physics Letters, 1962, 1(4): 82–84 https://doi.org/10.1063/1.1753706
6	Born M, Wolf E. Principle of Optics. 6th ed. Oxford: Pergamon Press, 1985, Section 7.6.2
7	Hayashi I, Panish M, Foy F. A low-threshold room-temperature injection laser. IEEE Journal of Quantum Electronics, 1969, 5(4): 211–212 https://doi.org/10.1109/JQE.1969.1075759
8	Kressel H, Nelson H. Close confinement gallium arsenide p-n junction laser with reduced optical loss at room temperature. RCA Review, 1969, 30: 106–113
9	Hayashi I, Panish M B. GaAs-GaxAl1-x As heterostructure injection lasers which exhibit low thresholds at room temperature. Journal of Applied Physics, 1970, 41(1): 150–163 https://doi.org/10.1063/1.1658314
10	Alferov Z I, Andreev V M, Korolkov V I, Portnoi E L, Tretyako D N. Injection properties of n-AlxGa1-x As p-GaAs heterojunctions. Soviet Physics Semiconductors, 1969, 2(7): 843–845
11	Hayashi I, Panish M B, Foy P W, Sumski S. Junction lasers which operate continuously at room temperature. Applied Physics Letters, 1970, 17(3): 109–111 https://doi.org/10.1063/1.1653326
12	Alferov Z I, Andreev V M, Garbuzov D Z, Zhilyaev Y V, Morozov E P, Portnoi E L, Triofim V G. Investigation of the influence of the AlAs-GaAs heterostructure parameters on the laser threshold current and the realization of continuous emission at room temperature. Soviet Physics Semiconductors, 1971, 4(9): 1573–1575
13	Ripper J E, Dyment J C, D’Asaro L A, Paoli T L. Stripe-geometry double heterostructure junction lasers: mode structure and CW operation above room temperature. Applied Physics Letters, 1971, 18(4): 155–157 https://doi.org/10.1063/1.1653606
14	Burnham R D, Scifres D R. Etched buried heterostructure GaAs/GaAlAs injection lasers. Applied Physics Letters, 1975, 27(9): 510–512 https://doi.org/10.1063/1.88538
15	Kaminow I P, Stulz L W, Ko J S, Miller B I, Feldman R D, Dewinter J C, Pollack M A. Low threshold ridge waveguide laser at 1.55 μm. Electronics Letters, 1983, 19(21): 877–879 https://doi.org/10.1049/el:19830598
16	Lee T P, Burrus C A, Miller B I, Logan R A. AlxGa1-x As double-heterostructure rib-waveguide injection laser. IEEE Journal of Quantum Electronics, 1975, 11(7): 432–435 https://doi.org/10.1109/JQE.1975.1068671
17	Hill D R. 140 Mbit/s optical fiber field demonstration systems. In: Sandbank C P, ed. Optical Fiber Communication Systems. Chichester: John Wiley & Sons, 1980
18	Zah C E, Pathk B, Favire F J, Pathak B, Bhat R, Caneau C, Lin P S D, Gozdz A S, Andreadakis N C, Koza M A, Lee T P. Monolithic integration of multiwavelength compressive-strained multiquantum-well distributed-feedback laser array with star coupler and optical amplifiers. Electronics Letters, 1992, 28(25): 2361–2362
19	Young M G, Koren U, Miller B I, Chien M, Koch T L, Tennant D M, Feder K, Dreyer K, Raybon G. Six wavelength laser array with integrated amplifier and modulator. Electronics Letters, 1995, 31(21): 1835–1836 https://doi.org/10.1049/el:19951262
20	Katoh Y, Kunii T, Matsui Y, Kamijoh T. Four-wavelength DBR laser array with waveguide couplers fabricated using selective MOVPE growth. Optical and Quantum Electronics, 1996, 28(5): 533–540 https://doi.org/10.1007/BF00943622
21	Ghafouri-Shiraz H, Lo B S K. Distributed feedback laser diodes. Chichester: John-Wiley & Sons, 1996, chapter 1
22	Lang R, Kobayashi K. External optical feedback effects on semiconductor injection laser properties. IEEE Journal of Quantum Electronics, 1980, 16(3): 347–355 https://doi.org/10.1109/JQE.1980.1070479
23	Matthews M R, Cameron K H, Wyatt R, Devlin W J. Packaged frequency-stable tunable 20 kHz linewidth 1.5 μm InGaAsP external cavity laser. Electronics Letters, 1985, 21(3): 113–115 https://doi.org/10.1049/el:19850079
24	Tsang W T. The cleaved coupled cavity (C3) laser. In: Semiconductors and semimetals. New York: Academic Press, 1985, 22(B), chapter 5
25	Coldren L A, Koch T L. Analysis and design of coupled-cavity lasers-Parts 1: threshold gain analysis and design guidelines. IEEE Journal of Quantum Electronics, 1984, 20(6): 659–670 https://doi.org/10.1109/JQE.1984.1072438
26	Tsang W T, Olsson N A, Linke R A, Logan R A. 1.5 μm wavelength GaInAsP C3 lasers: single frequency operation and wideband frequency tuning. Electronics Letters, 1983, 19(11): 415–417 https://doi.org/10.1049/el:19830285
27	Nakamura M, Yariv A, Yen H W, Somekh S, Garvin H L. Optically pumped GaAs surface laser with corrugation feedback. Applied Physics Letters, 1973, 22(10): 515–516 https://doi.org/10.1063/1.1654490
28	Kogelnik H, Shank C V. Coupled-wave theory of distributed feedback lasers. Journal of Applied Physics, 1972, 43(5): 2327–2335 https://doi.org/10.1063/1.1661499
29	Nakamura M, Yariv A, Yen H W, Garmire E, Somekh S, Garvin H L. Laser oscillation in epitaxial GaAs waveguides with corrugation feedback. Applied Physics Letters, 1973, 23(5): 224–225 https://doi.org/10.1063/1.1654867
30	Scifres D, Burnham R, Streifer W. A distributed feedback single heterojunction diode laser. IEEE Journal of Quantum Electronics, 1974, 10(9): 790–791 https://doi.org/10.1109/JQE.1974.1068463
31	Casey H C, Somekh S, Ilegems M. Room-temperature operation of low-threshold separate-confinement heterostructure injection laser with distributed feedback. Applied Physics Letters, 1975, 27(3): 142–144 https://doi.org/10.1063/1.88385
32	Utaka K, Akiba S, Sakai K, Matsushima Y. Room-temperature CW operation of distributed-feedback buried heterostructure InGaAsP-InP laser emitting at 1.57 μm. Electronics Letters, 1981, 17(25–26): 961–963 https://doi.org/10.1049/el:19810672
33	Uematsu Y, Okuda H, Kinoshita J. Room temperature CW operation of 1.3 μm distributed feedback GaInAsP/InP lasers. Electronics Letters, 1982, 18(20): 857–858 https://doi.org/10.1049/el:19820581
34	Streifer W, Burnham R, Scifres D R. Effect of external reflectors on longitudinal modes of distributed feedback lasers. IEEE Journal of Quantum Electronics, 1975, 11(4): 154–161 https://doi.org/10.1109/JQE.1975.1068581
35	Zhou P, Lee G S. Chirped grating λ/4-shifted distributed feedback laser with uniform longitudinal field distribution. Electronics Letters, 1990, 26(20): 1660–1661 https://doi.org/10.1049/el:19901063
36	Utaka K, Akiba S, Sakai K, Matsushima Y. λ/4-shifted InGaAsP DFB laser by simultaneous holographic exposure of positive and negative photoresists. Electronics Letters, 1984, 20(24): 1008–1010
37	Agrawal G P, Geusic J E, Anthony P J. Distributed feedback lasers with multiple phase-shift regions. Applied Physics Letters, 1988, 53(3): 178–179 https://doi.org/10.1063/1.100166
38	Thijs P J A, Tiemeijer L F, Binsma J J M, Van D T. Progress in long-wavelength strained-layer InGaAs(P) quantum-well semiconductor lasers and amplifiers. IEEE Journal of Quantum Electronics, 1994, 30(2): 477–499 https://doi.org/10.1109/3.283797
39	Morthier G, Vankwikelberge P, David K, Baets R. Improved performance of AR-coated DFB lasers for the introduction of gain coupling. IEEE Photonics Technology Letters, 1990, 2(3): 170–172 https://doi.org/10.1109/68.50879
40	Alam M F, Karim M A, Islam S. Effects of structural parameters on the external optical feedback sensitivity in DFB semiconductor lasers. IEEE Journal of Quantum Electronics, 1997, 33(3): 424–433 https://doi.org/10.1109/3.556012
41	Yu S F. Dynamic behavior of double-tapered-waveguide distributed feedback lasers. IEEE Journal of Quantum Electronics, 1997, 33(8): 1260–1267 https://doi.org/10.1109/3.605545
42	Fessant T. Multisection distributed feedback lasers with a phase-adjustment region and a nonuniform coupling coefficient for high immunity against spatial hole burning. Optics Communications, 1998, 148(1–3): 171–179 https://doi.org/10.1016/S0030-4018(97)00650-0
43	Kinoshita J. Analysis of radiation mode effects on oscillating properties of DFB lasers. IEEE Journal of Quantum Electronics, 1999, 35(11): 1569–1583 https://doi.org/10.1109/3.798078
44	Winick K A. Longitudinal mode competition in chirped grating distributed feedback lasers. IEEE Journal of Quantum Electronics, 1999, 35(10): 1402–1411 https://doi.org/10.1109a/3.792552
45	Peral E, Yariv A. Measurement and characterization of laser chirp of multiquantum-well distributed-feedback lasers. IEEE Photonics Technology Letters, 1999, 11(3): 307–309 https://doi.org/10.1109/68.748217
46	Hsu A, Chuang S, Fang W, Adams L, Nykolak G, Tanbun-Ek T. A wavelength-tunable curved waveguide DFB laser with an integrated modulator. IEEE Journal of Quantum Electronics, 1999, 35(6): 961–969 https://doi.org/10.1109/3.766840
47	Shams-Zadeh-Amiri A M, Li X, Huan W. Above-threshold analysis of second-order circular-grating DFB lasers. IEEE Journal of Quantum Electronics, 2000, 36(3): 259–267 https://doi.org/10.1109/3.825871
48	Fernandes C F. Hole-burning corrections in the stationary analysis of DFB laser diodes. Materials Science and Engineering B, 2000, 74(1–3): 75–79 https://doi.org/10.1016/S0921-5107(99)00538-3
49	Wang J Y, Cada M. Analysis and optimum design of distributed feedback lasers using coupled-power theory. IEEE Journal of Quantum Electronics, 2000, 36(1): 52–58 https://doi.org/10.1109/3.817638
50	Morrison G B, Cassidy D T, Bruce D M. Facet phases and sub-threshold spectra of DFB lasers: spectral extraction, features, explanations and verification. IEEE Journal of Quantum Electronics, 2001, 37(6): 762–769 https://doi.org/10.1109/3.922773
51	Agrawal G P, Dutta N K. Semiconductor Lasers. 2nd ed. New York: Van Nostrand Reinhold, 1993
52	Adams M J, Wyatt R. An Introduction to Optical Waveguide. London: John Wiley & Sons, 1981
53	Nakano Y, Luo Y, Tada K. Facet reflection independent, single longitudinal mode oscillation in a GaAlAs/GaAs distributed feedback laser equipped with a gain-coupling mechanism. Applied Physics Letters, 1989, 55(16): 1606–1608 https://doi.org/10.1063/1.102254
54	Morthier G, Baets R. Modelling of distributed feedback lasers. In: Compound Semiconductor Device Modelling. London: Springer-Verlag, 1993, chapter 7, 119–148
55	Vankwikelberge P, Morthier G, Baets R. CLADISS-a longitudinal multimode model for the analysis of the static, dynamic, and stochastic behavior of diode lasers with distributed feedback. IEEE Journal of Quantum Electronics, 1990, 26(10): 1728–1741 https://doi.org/10.1109/3.60897
56	Morthier G. An accurate rate-equation description for DFB lasers and some interesting solutions. IEEE Journal of Quantum Electronics, 1997, 33(2): 231–237 https://doi.org/10.1109/3.552263
57	Henry C H. Theory of the linewidth of semiconductor lasers. IEEE Journal of Quantum Electronics, 1982, 18(2): 259–264 https://doi.org/10.1109/JQE.1982.1071522
58	Pan X, Olesen H, Tromborg B. Spectral linewidth of DFB lasers including the effects of spatial holeburning and nonuniform current injection. IEEE Photonics Technology Letters, 1990, 2(5): 312–315 https://doi.org/10.1109/68.54690
59	Henry C H. Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers. Journal of Lightwave Technology, 1986, 4(3): 288–297 https://doi.org/10.1109/JLT.1986.1074715
60	Sugimura A, Patzak E, Meissner P. Homogenous linewidth and linewidth enhancement factor for a GaAs semiconductor laser. Journal of Physics D: Applied Physics, 1986, 19(1): 7–16 https://doi.org/10.1088/0022-3727/19/1/006
61	Kikuchi K, Okoshi T. Measurement of FM noise, AM noise, and field spectra of 1.3 μm InGaAsP DFB lasers and determination of the linewidth enhancement factor. IEEE Journal of Quantum Electronics, 1985, 21(11): 1814–1818 https://doi.org/10.1109/JQE.1985.1072575
62	Vahala K, Chiu L C, Margalit S, Yariv A. On the linewidth enhancement factor α in semiconductor injection lasers. Applied Physics Letters, 1983, 42(8): 631–633 https://doi.org/10.1063/1.94054
63	Fujise M. Spectral linewidth estimation of a 1.5 μm range InGaAsP/InP distributed feedback laser. IEEE Journal of Quantum Electronics, 1986, 22(3): 458–462 https://doi.org/10.1109/JQE.1986.1072974
64	Kojima K, Kyuma K, Nakayama T. Analysis of spectral linewidth of distributed feedback laser diodes. Journal of Lightwave Technology, 1985, 3(5): 1048–1055 https://doi.org/10.1109/JLT.1985.1074295
65	Tromborg B, Olesen H, Pan X, Saito S. Transmission line description of optical feedback and injection locking for Fabry-Perot and DFB lasers. IEEE Journal of Quantum Electronics, 1987, 23(11): 1875–1889 https://doi.org/10.1109/JQE.1987.1073251
66	Makino T. Transfer-matrix formulation of spontaneous emission noise of DFB semiconductor lasers. Journal of Lightwave Technology, 1991, 9(1): 84–91 https://doi.org/10.1109/50.64926
67	Makino T, Glinski J. Transfer matrix analysis of the amplified spontaneous emission of DFB semiconductor laser amplifiers. IEEE Journal of Quantum Electronics, 1988, 24(8): 1507–1518 https://doi.org/10.1109/3.7077
68	Agrawal G P, Bobeck A. Modeling of distributed feedback semiconductor lasers with axially-varying parameters. IEEE Journal of Quantum Electronics, 1988, 24(12): 2407–2414 https://doi.org/10.1109/3.14370
69	Shahshahani F, Ahmadi V. Analysis of relative intensity noise in tapered grating QWS-DFB laser diodes by using three rate equations model. Solid-State Electronics, 2008, 52(6): 857–862
70	Osinsky M, Polish M, Adams M J. Gain spectra of quarternary semiconductor. In: Proceedings of the IEEE I (Solid-State and Electron Devices). 1982, 129(6): 229–236
71	Rabinovich W S, Feldman B J. Spatial hole burning effects in distributed feedback lasers. IEEE Journal of Quantum Electronics, 1989, 25(1): 20–30 https://doi.org/10.1109/3.16236

[1]	Saeed OLYAEE, Mohammad SOROOSH, Mahdieh IZADPANAH. Transfer matrix modeling of avalanche photodiode[J]. Front Optoelec, 2012, 5(3): 317-321.
[2]	Guodong WANG, Yunjian WANG, Na LI. Axial strain sensitivity analysis of long period fiber grating by new transfer matrix method[J]. Front Optoelec Chin, 2011, 4(4): 430-433.

Viewed

Full text

Abstract

Cited

Shared

Discussed