Research Article Theoretical Modeling of Intensity Noise in … · 2019. 7. 31. · Research...

Research ArticleTheoretical Modeling of Intensity Noise in InGaNSemiconductor Lasers

Moustafa Ahmed

Department of Physics Faculty of Science King Abdulaziz University PO Box 80203 Jeddah 21589 Saudi Arabia

Correspondence should be addressed to Moustafa Ahmed mostafahafezscienceminiaunivedueg

Received 20 April 2014 Accepted 14 July 2014 Published 22 July 2014

Academic Editor Paolo Colantonio

Copyright copy 2014 Moustafa Ahmed This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper introduces modeling and simulation of the noise properties of the blue-violet InGaN laser diodesThe noise is describedin terms of the spectral properties of the relative intensity noise (RIN) We examine the validity of the present noise modeling bycomparing the simulated results with the experimental measurements available in literature We also compare the obtained noiseresults with those of AlGaAs lasers Also we examine the influence of gain suppression on the quantum RIN In addition weexamine the changes in the RIN level when describing the gain suppression by the case of inhomogeneous spectral broadeningThe results show that RIN of the InGaN laser is nearly 9 dB higher than that of the AlGaAs laser

1 Introduction

InGaN laser diodes have been the subject of considerableattention because of their applications in high density opticaldisc storage and optical data processing In particular blue-violet laser diodes operating at a wavelength around 400 nmare required for Blu-ray disc systems if the disk storage capac-ity is to be increased up to 25 Gbytes [1] Much progress inthe developments of violet-blue lasers has been made sincethe first operation of such a laser was reported by Naka-mura et al [2 3] Meanwhile several groups have reportedcontinuous-wave operation at room temperature using dif-ferent fabrications methods [4ndash8]

A typical limiting factor for the optic-disc application isthe noise in the laser emission which may cause errors in thereadingrecording processes Semiconductor laser radiationintrinsically shows intensity and phase fluctuations whichinduce broadening of the spectral line These fluctuationsare associated with quantum transitions of charge carriersbetween the conduction and valence bands through therecombination processes of charge carriers and the processesof photon emission and absorption [9]This intrinsic noise isunavoidable and is called quantum noise [10] or ldquooptical shotnoiserdquo [11] The laser noise may be amplified by other effectssuch as competition among the oscillating modes [12] exter-nal modulation [13] and external optical feedback [14]These

types of noise have been intensively investigated in boththeory and experiment for near infrared GaAs and InP-basedlaser diodes [14ndash20] Experimental studies on the noise ofblue-violet InGaN lasers showed that the properties of noisein the blue-violet laser are not so different qualitatively fromthose in the infrared lasers [11] However the quantum noisein the blue-violet laser is eight times higher than that in thenear infrared lasers in terms of RIN at the same output power[11] To the best of the authorsrsquo knowledge no theoreticalinvestigations on the noise issue in these short-wavelengthlaser candidates have been reported

The dynamics and noise of semiconductor lasers aredescribed by a set of stochastic rate equations that describethe mechanisms of time evolution of the addingdroppingof photons and charge carriers [21] The intensity noise ischaracterized in terms of the spectral properties of RINAnalysis of noise and dynamics in semiconductor lasers isdependent on the form of the optical gain in the rate equa-tions and more realistic model should include the effect ofthe gain suppression [22] Abdullah [23] indicated that thegain suppression has an important effect on the dynamics ofInGaN-based laser diodes because these lasers may operatewith high power where the gain suppression is pronouncedAhmed and Yamada [24] showed that in the limit of highpower nonlinear gain is inaccurately described by the com-monly used third-order gain expression which corresponds

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 475423 6 pageshttpdxdoiorg1011552014475423

2 The Scientific World Journal

to partial homogeneous broadening of gain [25] Instead thenonlinear gain expression should include higher-order termsfrom the infinite gain expansion in terms of the electric fieldintensity to account for the case of high power emission [23]

In this paper we introduce modeling and simulation onthe spectral properties of RIN in the blue-violet InGaN laserdiode The studies are based on appropriate modeling of therate equations and intensive computer simulations of the laserdynamics and noise We enhance the novelty of the presentwork by comparing the simulated results with the previouspublications such as in [11] In addition we compare the noiseresults of 410 nm InGaN lasers with those of 830 nm AlGaAslasers Also we study the influence of gain suppression onthe noise properties and compare the noise results whenusing the expressions of inhomogeneous gain broadeningWe show that RIN is suppressed remarkably with the increasein the injection current in the regime near the threshold leveland that the RIN level in the InGaN laser is nearly 9 dBhigher than that of the AlGaAs laser The noise results arecompared with the experimental results in [11] The increasein the gain suppression was found to suppress the quantumnoise within 1 dBHz Finally we point out that the caseof inhomogeneously broadened gain overestimates the RINlevel by about 4 dB in the limit of high power emission

2 Theoretical Model

The noise properties of the InGaN laser are described bysolving the following rate equations of the photon number119878(119905) and injected carriers119873(119905) in the active region at a givencurrent 119868

119889119878

119889119905= (119866 minus 119866th) 119878 +

119886120585

119881119873 + 119865119878 (119905)

119889119873

119889119905=119868

119890minus119873

120591119904

minus 119866119871119878 + 119865119873 (119905)

(1)

where119866 is the optical gain and is composed of linear term119866119871

and nonlinear term 119866119873119871 [25]

119866 = 119866119871minus 119866119873119871119878 (2)

The linear term 119866119871is a linear function of119873 and is character-

ized by the gain slope 119886 and the injected carrier number attransparency119873

119892as [25]

119866119871=119886120585

119881(119873 minus 119873

119892) (3)

whereas the nonlinear gain 119866119873119871

is given in terms of theinjected carrier number119873 as [25]

119866119873119871

= 119861119888 (119873 minus 119873

119904) (4)

where 119861119888 and119873119904 are characteristic parameters of the nonlin-ear gain The influence of the nonlinear gain is to suppressthe optical gain under the threshold gain level 119866th due tothe increase in the photon number 119878 when the laser operatesabove threshold [24] In (3) 120585 is the confinement factor of theoptical field in the active layer whose volume is 119881 The other

parameters in (1) include 119890 as the electron charge and 120591119904as the

electron lifetime due to the spontaneous emission The lastterms 119865

119878(119905) and 119865

119878(119905) are Langevin noise sources with zero

mean values and are added to the equations to account forintrinsic fluctuations in 119878(119905) and119873(119905) respectively [9] Thesenoise sources are assumed to have Gaussian probability dis-tributions and to be 120575-correlated processes [9]The frequencycontent of intensity fluctuations is measured in terms of RINwhich is calculated from the fluctuations 120575119878(119905) = 119878(119905) minus 119878 in119878(119905) where 119878 is the time-average value of 119878(119905) Over a finitetime 119879 RIN is given as [14]

RIN =1

11987821

119879

100381610038161003816100381610038161003816100381610038161003816

int

119879

0

120575119878 (119905) 119890minus1198952120587119891120591

119889120591

100381610038161003816100381610038161003816100381610038161003816

2

(5)

where 119891 is the noise frequencyThe noise performance of thelaser is evaluated also in terms of the average value of the RINcomponents at frequencies lower than 100MHz LF-RINThepower 119875(119905) emitted from the front facet is determined fromthe photon number 119878(119905) as [9]

119875 (119905) =ℎ1198882

2119899119863119871119863120582

(1 minus 119877119891) ln (1119877

119891119877119887)

(1 minus radic119877119891119877119887) (1 minus radic119877119891119877119887)

119878 (119905) (6)

where 120582 is the emission wavelength ℎ is Planckrsquos constantand 119877119891 and 119877119887 are the power reflectivities at the front and theback facets respectively

3 Numerical Calculations

Rates (1) are solved by the 4th order Runge-Kutta methodusing a time integration of Δ119879 = 10 ps At each integrationinstant the noise sources 119865

119878(119905) and 119865

119873(119905) are generated fol-

lowing the technique developed in [14] using two uniformlydistributed random numbers generated by the computerRIN of the total output is calculated from the fast Fouriertransform (FFT) of the time fluctuations 120575119878(119905

119894) via (5) as

follows

RIN =1

1198782

Δ1199052

119879

1003816100381610038161003816FFT [120575119878 (119905119894)]1003816100381610038161003816

2 (7)

In the calculations we assume 410 nmmultiple quantumwell(MQW) InGaN single mode laser with the parameters listedin Table 1 The active region is assumed to contain threequantum wells (QWs) with well thickness barrier thicknessand stripe width of 5 nm 10 nm and 5 120583m respectively Theoptical confinement factor in each quantum well layer is00342

4 Results and Discussion

41 RIN in InGaN Laser Diodes Figure 1 plots the spectralcharacteristics of RIN at different injection levels near abovethreshold (119868 = 101 and 11119868th) above threshold (119868 = 15119868th)and far above threshold (119868 = 30119868th) The RIN spectra are flat(white noise) in the low-frequency regime due to the smallamplitude of the intensity fluctuations and the large signal-to-noise ratio In the high-frequency regime the spectra exhibit

The Scientific World Journal 3

Table 1 Definition and numerical values of the InGaN laserparameters

Symbol Definition Value120582 Wavelength 410 nm119899119863

Refractive index of active layer 26119871119863

Active layer length 300 120583m119886 Differential gain coefficient 185 times 10

minus12m2

119861119888

Nonlinear gain coefficient 27 times 10minus5 sminus1

119873119892

Carrier number at transparency 252 times 108

119873119904

Carrier number characterizing 119866NL 201 times 108

120572 Linewidth enhancement factor 2120591119904

Spontaneous emission lifetime 2 ns119877119891

Front facet reflectivity 04119877119887

Back facet reflectivity 07119866th Threshold gain 22 times 10

11 sminus1

10 M 100 M 1 G 10 GNoise frequency (Hz)

RIN

(dB

Hz)

minus180

minus160

minus140

minus120

minus100

minus80

I = 101Ith I = 11IthI = 15Ith I = 30Ith

Figure 1 Spectra of RIN as functions of 119868119868th for InGaN lasers

the well-known carrier-photon resonance peak around therelaxation frequency 119891

119903 The figure shows suppression of

RIN with the increase in the injection current 119868 due tothe improvement in the degree of laser coherency [9] Thisincrease in the injection level is associated also with anincrease in the relaxation oscillation peak 119891119903 = 330MHzwhen 119868 = 101119868th and 119891119903 = 51 GHz when 119868 = 301119868th

It is of practical interest to study variation of the lowfrequency level of RIN and LF-RIN with the increase in theinjection current 119868 Figure 2 plots such a variation showingthat LF-RIN increases with the increase in 119868 around thethreshold current 119868th The further increase in 119868 results in adrop of LF-RIN to lower orders of magnitude up to 119868 sim 16119868th(LF-RINdecreases from the peak ofminus918 dBHzwhen 119868 = 119868thto minus157 dBHz when 119868 = 16119868th) When 119868 increases beyond16119868th the decrease in LF-RIN with the increase in 119868 becomesas small as sim05 dBHz This suppression of RIN is associatedwith a decrease in the amplitude of intensity fluctuations in

TheoryExperiment

LF-R

IN (d

BH

z)

minus160

minus140

minus120

minus100

09 10 11 12 13 14 15 16Injection current IIth

Figure 2 Variation of LF-RIN with the injection current 119868119868th ofInGaN lasers (solid) The experimental results in [11] are shown(circles) for comparison

the laser signal and improvement in the signal to noise ratio[9] We plot also in Figure 2 the experimental results on thequantum noise of InGaN laser reported by Matsuoka et al[11]The figure shows that the simulated noise results fit qual-itatively the experimental data in [11] The differences in thenoise level between the simulated and experimental resultscould be a mode competition effect in the measured laserwhichmay change the noise level of themodeled singlemodelaser [26]

42 Comparison of RIN in InGaN Lasers with InGaN andAlGaAs Lasers In this subsection we compare the lasingcharacteristics of the 410 nm GaInN laser with those of830 nm AlGaAs laser diode For AlGaAs laser we considerthe following parametric values 119886 = 27 times 10

minus12m2 119899119863=

359119873119892= 189times10

8119873119904= 163times10

8119861119888= 395times10

minus5 sminus1 and120591119904= 27 ns Figure 3 compares the 119871-119868 characteristics of the

two laser diodes showing that the laser operation is linearover the relevant range of injection current 119868 The thresholdcurrent 119868th which is the intercept of the 119871-119868 line with thecurrent axis is shown to increase from 142mA in theAlGaAslaser to 282mA in the InGaN laser

Figure 4 plots variation of the LF-RIN level with theemitted power for the two laser diodes The figure shows theeffect of noise suppression with the increase in the lasingpower 119875 with the suppression being stronger in the regimeof the near above threshold The figure shows that LF-RIN inthe InGaN laser is nearly 9 dB higher than that of the AlGaAslaser This higher level of the LF-RIN in the InGaN laser isdue to the inverse proportionality of RIN on the third powerof the emission wavelength 120582 [10]

RIN prop1

12058231198753 (8)


AlGaA

s laser

InGa

N la

ser

Ith

0

5

10

15

20

25

30Em

itted

pow

erP

(mW

)

10 20 30 40 50 60Injection current I (mA)

Figure 3 The 119871-119868 characteristics of the InGaN and AlGaAs laserdiodes

AlGaAs laser

InGaN laser

0 4 8 12 16 20Emitted power P (mW)

minus170

minus160

minus150

minus140

minus130

minus120

minus110

minus100

minus90

LF-R

IN (d

BH

z)

Figure 4 Variation of LF-RIN as a function of the emitted power 119875

Therefore this relation predicts that the quantum noise inthe 410 nm InGaN laser is nearly 83 dB higher than that inthe AlGaAs laser This result fits the experimental finding byMatsuoka et al [11] on 410 nm InGaN and 830 nm AlGaAslasers with almost identical structure design and operationcharacteristics [11] It is worth noting that the correspondingvariation of the quantum noise level with the current ratio119868119868th reveals much smaller differences between both laserswhich agrees also with the experimental results in [11]

Figure 5 compares the simulated spectrum of RIN ofboth lasers when 119875 = 5mW As shown in the figure theInGaN laser reveals RIN spectra higher than those of theAlGaAs laser On the other hand the position of theenhanced resonance peak of the InGaN laser occurs at arelaxation frequency lower than that of the AlGaAs laser

43 Influence of Gain Saturation on RIN The gain sup-pression is a critical property of the lasing medium andcontrols most of the dynamics and operation characteristics

InGaN laser

minus160

minus140

minus120

minus100

RIN

(dB

Hz)


AlGaAs laser

P = 5mW

Figure 5 The spectra of RIN of InGaN and AlGaAs lasers when119875 = 5mW

minus171

minus170

minus169

RIN

(dB

Hz)

00 05 10 15 20 25 30Gain suppression ratio BcBc0

I = 5Ith

Figure 6 Influence of gain suppression factor on the LF-RIN levelwhen 119868 = 5119868th

of semiconductor lasers Influence of the nonlinear gainsuppression 119866

119873119871on the quantum noise of the InGaN laser

is illustrated in Figure 6 when 119868 = 5119868th The gain suppressionis varied by varying 119861

119888relative to the set value in Table 1 119861

1198880

The figure shows that the increase in119866119873119871

results in a decreasein the LF-RIN level within 1 dBHz The variation 119866

119873119871

was found not to affect the position of the resonance peakof the RIN spectrum (ie the relaxation frequency) Thissuppression in the amplitude of intensity fluctuations agreeswith the prediction by Abdulrhmann et al [27] in InGaAsPlasers

The spectral gain suppression is a nonlinear effect Inits most exact description the optical gain is expressed asan infinite perturbation expansion of the field intensity [24]Yamada and Suematsu [25] showed that within the normaloperation of semiconductor lasers the gain suppression haspartial homogeneous spectral broadening Therefore thegain of semiconductor lasers is usually described by thethird-order perturbation form in (2) [25] In semiconductorlasers with high power emission the gain suppressionbecomes inhomogeneously broadened [25] and the infinite


20 25 30 35 40

minus170

minus168

minus166

minus164

minus162

minus160

minus158

minus156

minus154

Gain form (9)

Gain form (2)

LF-R

IN (d

BH

z)

Injection current IIth

Figure 7 Dependence of LF-RIN on the injection current 119868119868th ofInGaN lasers under partial homogeneous gain broadening (form(2)) and inhomogeneous gain broadening (form (9))

gain expansion in [23] is reduced to the following formdeveloped by Agrawal [28]

119866 =119866119871

radic1 + 120576119878where 120576 = 119861

119888

119881

119886120585 (9)

Here we examine the validity of this gain suppression tomodel the noise properties of the present InGaN laserReplacing form (2) of the partial homogeneous gain suppres-sion with form (9) of the inhomogeneous gain suppressionwas found not to change the 119871-119868 characteristics In Figure 7we compare the obtained noise properties of the InGaN laserby those obtained when applying the form in (9) As shownin the figure the inhomogeneous gain broadening littleoverestimates the RIN level in the regime of high injectioncurrents the difference is just within 4 dB

5 Conclusions

We modeled and simulated the noise properties of the blue-violet InGaN laser diodes We compared the RIN results withthose of the AlGaAs lasers since both lasers are the mostrepresentative light sources in the high-density disc systemsAlso we examined the influence of the gain suppressionon RIN The results showed that the RIN spectra are flatin the low-frequency regime RIN is suppressed remarkablywith the increase in the injection current up to 119868 sim 16119868thbeyond which the decrease in LF-RIN becomes within05 dBHz This increase in the injection level is associatedalso with an increase in the relaxation oscillation peaktowards higher frequenciesThe simulated noise results are ingood agreement with the experimental data reported inliterature The RIN level in the InGaN laser is nearly 9 dBhigher than that of the AlGaAs laser A big contributor to thishigher RIN is the inverse proportionality of RIN on the thirdpower of the emission wavelength The increase in the gainsuppression was found to decrease the quantum noise within1 dBHz Describing the gain suppression by the form of

inhomogeneous gain broadening was found to induce 4 dBoverestimation of the RIN level

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publishing of this paper

Acknowledgment

This work was funded by the Deanship of Scientific Research(DSR) King Abdulaziz University Jeddah under Grant no(130 - 474 - D1435)The author therefore acknowledges withthanks DSR technical and financial support

References

[1] J Piprek Nitride Semiconductor Devices Wiley-VCH Wein-heim Germany 2007

[2] S Nakamura S Pearton and G Fasol The Blue Laser DiodeSpringer Berlin Germany 2nd edition 2000

[3] S Nakamura M Senoh S Nagahama et al ldquoOptical gain andcarrier lifetime of InGaN multi-quantum well structure laserdiodesrdquo Applied Physics Letters vol 69 no 11 pp 1568ndash15701996

[4] T Takeuchi H Takeuchi S Sota H Sakai H Amano and IAkasaki ldquoOptical properties of strained AlGaN and GaInN onGaNrdquo Japanese Journal of Applied Physics vol 36 no 2 ppL177ndashL179 1997

[5] T Kobayashi F Nakamura K Naganuma et al ldquoRoom-temperature continuous-wave operation of GaInNGaN multi-quantumwell laser dioderdquo Electronics Letters vol 34 no 15 pp1494ndash1495 1998

[6] A Kuramata S Kubota R Soejima K Domen K Horino andT Tanahashi ldquoRoom-temperature continuous wave operationof InGaN laser diodes with vertical conducting structure on SiCsubstraterdquo Japanese Journal of Applied Physics vol 37 no 11 ppL1373ndashL1375 1998

[7] M Kuramoto C Sasaoka Y Hisanaga et al ldquoRoom-temper-ature continuous-wave operation of InGaN multi-quantum-well laser diodes grown on an n-GaN substrate with a backsiden-contactrdquo Japanese Journal of Applied Physics vol 38 part 2pp L184ndashL186 1999

[8] M Kneissl D P Bour C G van de Walle et al ldquoRoom-temperature continuous wave operation of InGaNrdquoMoldavianJournal of the Physical Sciences vol 5 pp 153ndash170 2006

[9] M Ahmed M Yamada and M Saito ldquoNumerical modeling ofintensity andphase noise in semiconductor lasersrdquo IEEE Journalof Quantum Electronics vol 37 no 12 pp 1600ndash1610 2001

[10] M Yamada ldquoVariation of intensity noise and frequency noisewith the spontaneous emission factor in semiconductor lasersrdquoIEEE Journal of QuantumElectronics vol 30 no 7 pp 1511ndash15191994

[11] K Matsuoka K Saeki E Teraoka M Yamada and Y Kuwa-mura ldquoQuantum noise and feed-back noise in blue-violetInGaN semiconductor lasersrdquo IEICE Transactions on Electron-ics vol E89-C no 3 pp 437ndash439 2006

[12] M Ahmed ldquoNumerical characterization of intensity and fre-quency fluctuations associated with mode hopping and single-mode jittering in semiconductor lasersrdquo Physica D vol 176 no3-4 pp 212ndash236 2003


[13] M Ahmed ldquoSpectral lineshape and noise of semiconductorlasers under analog intensity modulationrdquo Journal of Physics DApplied Physics vol 41 Article ID 175104 10 pages 2008

[14] S Abdulrhmann M Ahmed andM Yamada ldquoA newmodel ofanalysis of semiconductor laser dynamics under strong opticalfeedback in fiber communication systemsrdquo inThe InternationalSociety for Optical Engineering Physics and Simulation of Opto-electronic Devices XI vol 4986 of Proceedings of SPIE pp 490ndash501 January 2003

[15] AW Smith and J A Armstrong ldquoIntensity noise inmultimodeGaAs laser emissionrdquo IBM Journal of Research and Develop-ment vol 10 pp 225ndash232 1966

[16] C H Henry ldquoPhase noise in semiconductor lasersrdquo Journal ofLightwave Technology vol 4 no 3 pp 298ndash311 1986

[17] G P Agrawal N AOlsson andN KDutta ldquoEffect of fiber-far-end reflections on intensity and phase noise in InGaAsP semi-conductor lasersrdquoApplied Physics Letters vol 45 no 6 pp 597ndash599 1984

[18] G P Agrawal ldquoNoise in semiconductor lasers and its impact onoptical communication systemsrdquo in Laser Noise Proceedings ofSPIE pp 224ndash235 November 1990

[19] G P Agrawal ldquoEffect of nonlinear gain on intensity noise insingle-mode semiconductor lasersrdquo Electronics Letters vol 27no 3 pp 232ndash234 1991

[20] M YamadaW Ishimori H Sakaguchi andM Ahmed ldquoTime-dependent measurement of the mode competition phenomenaamong longitudinal modes in long-wavelength Lasersrdquo IEEEJournal of Quantum Electronics vol 39 no 12 pp 1548ndash15542003

[21] M Ahmed ldquoNumerical approach to field fluctuations and spec-tral lineshape in InGaAsP laser diodesrdquo International Journalof Numerical Modelling Electronic Networks Devices and Fieldsvol 17 no 2 pp 147ndash163 2004

[22] C Masoller C Cabeza and A S Schifino ldquoEffect of the non-linear gain in the visibility of a semiconductor laser withincoherent feedback in the coherence collapsed regimerdquo IEEEJournal of Quantum Electronics vol 31 pp 1022ndash1028 1995

[23] R Abdullah ldquoThe influence of gain suppression on dynamiccharacteristics of violet InGaN laser diodesrdquoOptik vol 125 pp580ndash582 2014

[24] M Ahmed and M Yamada ldquoAn infinite order perturbationapproach to gain calculation in injection semiconductor lasersrdquoJournal of Applied Physics vol 84 no 6 pp 3004ndash3015 1998

[25] M Yamada and Y Suematsu ldquoAnalysis of gain suppression inundoped injection lasersrdquo Journal of Applied Physics vol 52 no4 pp 2653ndash2664 1981

[26] M Ahmed ldquoNumerical characterization of intensity and fre-quency fluctuations associated with mode hopping and single-mode jittering in semiconductor lasersrdquo Physica D NonlinearPhenomena vol 176 no 3-4 pp 212ndash236 2003

[27] S Abdulrhmann M Ahmed and M Yamada ldquoInfluence ofnonlinear gain and nonradiative recombination on the quan-tum noise in InGaAsP semiconductor lasersrdquo Optical Reviewvol 9 no 6 pp 260ndash268 2002

[28] G P Agrawal ldquoEffect of gain nonlinearities on period doublingand chaos in directly modulated semiconductor lasersrdquoAppliedPhysics Letters vol 49 no 16 pp 1013ndash1015 1986

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to partial homogeneous broadening of gain [25] Instead thenonlinear gain expression should include higher-order termsfrom the infinite gain expansion in terms of the electric fieldintensity to account for the case of high power emission [23]

In this paper we introduce modeling and simulation onthe spectral properties of RIN in the blue-violet InGaN laserdiode The studies are based on appropriate modeling of therate equations and intensive computer simulations of the laserdynamics and noise We enhance the novelty of the presentwork by comparing the simulated results with the previouspublications such as in [11] In addition we compare the noiseresults of 410 nm InGaN lasers with those of 830 nm AlGaAslasers Also we study the influence of gain suppression onthe noise properties and compare the noise results whenusing the expressions of inhomogeneous gain broadeningWe show that RIN is suppressed remarkably with the increasein the injection current in the regime near the threshold leveland that the RIN level in the InGaN laser is nearly 9 dBhigher than that of the AlGaAs laser The noise results arecompared with the experimental results in [11] The increasein the gain suppression was found to suppress the quantumnoise within 1 dBHz Finally we point out that the caseof inhomogeneously broadened gain overestimates the RINlevel by about 4 dB in the limit of high power emission

2 Theoretical Model

The noise properties of the InGaN laser are described bysolving the following rate equations of the photon number119878(119905) and injected carriers119873(119905) in the active region at a givencurrent 119868

119889119878

119889119905= (119866 minus 119866th) 119878 +

119886120585

119881119873 + 119865119878 (119905)

119889119873

119889119905=119868

119890minus119873

120591119904

minus 119866119871119878 + 119865119873 (119905)

(1)

where119866 is the optical gain and is composed of linear term119866119871

and nonlinear term 119866119873119871 [25]

119866 = 119866119871minus 119866119873119871119878 (2)

The linear term 119866119871is a linear function of119873 and is character-

ized by the gain slope 119886 and the injected carrier number attransparency119873

119892as [25]

119866119871=119886120585

119881(119873 minus 119873

119892) (3)

whereas the nonlinear gain 119866119873119871

is given in terms of theinjected carrier number119873 as [25]

119866119873119871

= 119861119888 (119873 minus 119873

119904) (4)

where 119861119888 and119873119904 are characteristic parameters of the nonlin-ear gain The influence of the nonlinear gain is to suppressthe optical gain under the threshold gain level 119866th due tothe increase in the photon number 119878 when the laser operatesabove threshold [24] In (3) 120585 is the confinement factor of theoptical field in the active layer whose volume is 119881 The other

parameters in (1) include 119890 as the electron charge and 120591119904as the

electron lifetime due to the spontaneous emission The lastterms 119865

119878(119905) and 119865

119878(119905) are Langevin noise sources with zero

mean values and are added to the equations to account forintrinsic fluctuations in 119878(119905) and119873(119905) respectively [9] Thesenoise sources are assumed to have Gaussian probability dis-tributions and to be 120575-correlated processes [9]The frequencycontent of intensity fluctuations is measured in terms of RINwhich is calculated from the fluctuations 120575119878(119905) = 119878(119905) minus 119878 in119878(119905) where 119878 is the time-average value of 119878(119905) Over a finitetime 119879 RIN is given as [14]

RIN =1

11987821

119879

100381610038161003816100381610038161003816100381610038161003816

int

119879

0

120575119878 (119905) 119890minus1198952120587119891120591

119889120591

100381610038161003816100381610038161003816100381610038161003816

2

(5)

where 119891 is the noise frequencyThe noise performance of thelaser is evaluated also in terms of the average value of the RINcomponents at frequencies lower than 100MHz LF-RINThepower 119875(119905) emitted from the front facet is determined fromthe photon number 119878(119905) as [9]

119875 (119905) =ℎ1198882

2119899119863119871119863120582

(1 minus 119877119891) ln (1119877

119891119877119887)

(1 minus radic119877119891119877119887) (1 minus radic119877119891119877119887)

119878 (119905) (6)

where 120582 is the emission wavelength ℎ is Planckrsquos constantand 119877119891 and 119877119887 are the power reflectivities at the front and theback facets respectively

3 Numerical Calculations

Rates (1) are solved by the 4th order Runge-Kutta methodusing a time integration of Δ119879 = 10 ps At each integrationinstant the noise sources 119865

119878(119905) and 119865

119873(119905) are generated fol-

lowing the technique developed in [14] using two uniformlydistributed random numbers generated by the computerRIN of the total output is calculated from the fast Fouriertransform (FFT) of the time fluctuations 120575119878(119905

119894) via (5) as

follows

RIN =1

1198782

Δ1199052

119879

1003816100381610038161003816FFT [120575119878 (119905119894)]1003816100381610038161003816

2 (7)

In the calculations we assume 410 nmmultiple quantumwell(MQW) InGaN single mode laser with the parameters listedin Table 1 The active region is assumed to contain threequantum wells (QWs) with well thickness barrier thicknessand stripe width of 5 nm 10 nm and 5 120583m respectively Theoptical confinement factor in each quantum well layer is00342

4 Results and Discussion

41 RIN in InGaN Laser Diodes Figure 1 plots the spectralcharacteristics of RIN at different injection levels near abovethreshold (119868 = 101 and 11119868th) above threshold (119868 = 15119868th)and far above threshold (119868 = 30119868th) The RIN spectra are flat(white noise) in the low-frequency regime due to the smallamplitude of the intensity fluctuations and the large signal-to-noise ratio In the high-frequency regime the spectra exhibit






minus12m2

119861119888


119873119892


119873119904






11 sminus1


RIN

(dB

Hz)

minus180

minus160

minus140

minus120

minus100

minus80







TheoryExperiment

LF-R

IN (d

BH

z)

minus160

minus140

minus120

minus100





minus12m2 119899119863=

359119873119892= 189times10

8119873119904= 163times10

8119861119888= 395times10




RIN prop1

12058231198753 (8)


AlGaA

s laser

InGa

N la

ser

Ith

0

5

10

15

20

25

30Em

itted

pow

erP

(mW

)



AlGaAs laser

InGaN laser


minus170

minus160

minus150

minus140

minus130

minus120

minus110

minus100

minus90

LF-R

IN (d

BH

z)





InGaN laser

minus160

minus140

minus120

minus100

RIN

(dB

Hz)


AlGaAs laser

P = 5mW


minus171

minus170

minus169

RIN

(dB

Hz)


I = 5Ith






1198880



119873119871




20 25 30 35 40

minus170

minus168

minus166

minus164

minus162

minus160

minus158

minus156

minus154

Gain form (9)

Gain form (2)

LF-R

IN (d

BH

z)




119866 =119866119871

radic1 + 120576119878where 120576 = 119861

119888

119881

119886120585 (9)


5 Conclusions





Acknowledgment


References



































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








minus12m2

119861119888


119873119892


119873119904






11 sminus1


RIN

(dB

Hz)

minus180

minus160

minus140

minus120

minus100

minus80







TheoryExperiment

LF-R

IN (d

BH

z)

minus160

minus140

minus120

minus100





minus12m2 119899119863=

359119873119892= 189times10

8119873119904= 163times10

8119861119888= 395times10




RIN prop1

12058231198753 (8)


AlGaA

s laser

InGa

N la

ser

Ith

0

5

10

15

20

25

30Em

itted

pow

erP

(mW

)



AlGaAs laser

InGaN laser


minus170

minus160

minus150

minus140

minus130

minus120

minus110

minus100

minus90

LF-R

IN (d

BH

z)





InGaN laser

minus160

minus140

minus120

minus100

RIN

(dB

Hz)


AlGaAs laser

P = 5mW


minus171

minus170

minus169

RIN

(dB

Hz)


I = 5Ith






1198880



119873119871




20 25 30 35 40

minus170

minus168

minus166

minus164

minus162

minus160

minus158

minus156

minus154

Gain form (9)

Gain form (2)

LF-R

IN (d

BH

z)




119866 =119866119871

radic1 + 120576119878where 120576 = 119861

119888

119881

119886120585 (9)


5 Conclusions





Acknowledgment


References



































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




AlGaA

s laser

InGa

N la

ser

Ith

0

5

10

15

20

25

30Em

itted

pow

erP

(mW

)



AlGaAs laser

InGaN laser


minus170

minus160

minus150

minus140

minus130

minus120

minus110

minus100

minus90

LF-R

IN (d

BH

z)





InGaN laser

minus160

minus140

minus120

minus100

RIN

(dB

Hz)


AlGaAs laser

P = 5mW


minus171

minus170

minus169

RIN

(dB

Hz)


I = 5Ith






1198880



119873119871




20 25 30 35 40

minus170

minus168

minus166

minus164

minus162

minus160

minus158

minus156

minus154

Gain form (9)

Gain form (2)

LF-R

IN (d

BH

z)




119866 =119866119871

radic1 + 120576119878where 120576 = 119861

119888

119881

119886120585 (9)


5 Conclusions





Acknowledgment


References



































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




20 25 30 35 40

minus170

minus168

minus166

minus164

minus162

minus160

minus158

minus156

minus154

Gain form (9)

Gain form (2)

LF-R

IN (d

BH

z)




119866 =119866119871

radic1 + 120576119878where 120576 = 119861

119888

119881

119886120585 (9)


5 Conclusions





Acknowledgment


References



































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics

























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



Research Article Theoretical Modeling of Intensity Noise in … · 2019. 7. 31. · Research...

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Transcript of Research Article Theoretical Modeling of Intensity Noise in … · 2019. 7. 31. · Research...