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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 21396–21403
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Single step measurement of optical transmitters Henry factor using sinusoidal optical phase modulations

J.-G. Provost, A. Martinez, A. Shen, and A. Ramdane  »View Author Affiliations


Optics Express, Vol. 19, Issue 22, pp. 21396-21403 (2011)
http://dx.doi.org/10.1364/OE.19.021396


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Abstract

Measurement of the Henry factor over large optical bandwidth is carried out in a single step without any filtering, using a technique based on the sinusoidal phase modulation method. This fast technique was successfully applied to a directly modulated Fabry Perot laser to obtain simultaneously the linewidth enhancement factor (LEF) of 14 longitudinal modes. It is also well suited for electro-absorption modulators (EAM) for which the α-factor is determined over 15 nm optical bandwidth. A very good agreement is found with the well established fiber transfer function method.

© 2011 OSA

1. Introduction

The phase-amplitude coupling factor or Henry factor [1

1. C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982). [CrossRef]

] is a fundamental parameter that determines many important characteristics of an optical transmitter for fiber optics communication. The existence of the so called Henry factor, or linewidth enhancement factor (LEF), induces a linewidth broadening of longitudinal modes of the transmitter. When the optical intensity of the emitter is modulated, this results in a frequency modulation (so called ‘chirp’) that interacts with the fiber chromatic dispersion and sets an upper limit to the product squared bit rate times propagation length. This parameter also determines the resistance to optical feedback of lasers [2

2. N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988). [CrossRef]

]. Different methods have been devised to measure the α-factor and their use depends on the type of transmitter, consisting either of a directly modulated laser or an external modulator. The Hakki-Paoli method can only be applied to Fabry-Perot (FP) lasers and it gives the LEF only below threshold. Recently a method based on the linewidth power ratio was proposed to determine the LEF of a FP laser above threshold [3

3. A. Villafranca, A. Villafranca, G. Giuliani, and I. Garces, “Mode-resolved measurements of the linewidth enhancement factor of a Fabry–Pérot laser,” IEEE Photon. Technol. Lett. 21(17), 1256–1258 (2009). [CrossRef]

], however it does not give the LEF versus injection current and cannot be applied to external modulators. Another technique relies on optical injection locking but does not provide a direct measurement of the LEF [4

4. G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett. 13(5), 430–432 (2001). [CrossRef]

,5

5. Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004). [CrossRef]

]. Similarly to the linewidth power ratio method, the optical injection locking technique is only applicable to laser but not to external optical modulators. The RF current modulation method enables to determine the LEF but it applies to only one optical carrier at a time [6

6. C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42(4), 328–330 (1983). [CrossRef]

]. The well established fiber transfer function (FTF) method [7

7. F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993). [CrossRef]

,8

8. R. C. Srinivasan and J. C. Cartledge, “On using fiber transfer functions to characterize laser chirp and fiber dispersion,” IEEE Photon. Technol. Lett. 7(11), 1327–1329 (1995). [CrossRef]

] exploits the interaction between the chirp and the fiber chromatic dispersion but it requires to filter out each individual longitudinal mode in the case of multimode Fabry-Perot lasers. It is therefore highly desirable to have a relevant, fast and direct method to simultaneously measure the LEF of multiple longitudinal modes of an optical transmitter.

In this paper, we present a novel technique based on the sinusoidal optical phase modulation method [9

9. I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32(17), 2538–2540 (2007). [CrossRef] [PubMed]

] to extract directly, simultaneously and together with a high sensitivity the LEF of each longitudinal mode of FP lasers. A simple expression is derived that yields both the value and the sign of the LEF. Moreover, the extraction is fast because it is a non-iterative method. This technique was successfully applied to a directly modulated FP laser to measure simultaneously the LEF of 14 longitudinal modes covering the FP optical spectrum. We also applied our method to an electro-absorption modulator (EAM) to determine the α-factor over 15 nm optical bandwidth and a very good agreement is found with the FTF method. As shown later, we stress here that this technique is adapted for even larger optical bandwidth.

2. Principle and experimental set-up

In small signal modulation regime, the complex amplitude of the spectral components at the output of the device under test (laser or external modulator), by keeping only the first order components for a mmodulation index, can be written [7

7. F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993). [CrossRef]

]:
{A1=I0m(1+jαH)4A0=I0A+1=I0m(1+jαH)4
(1)
where αH is the LEF to be measured and I0 the power of the optical carrier. In the case of a directly modulated laser, the modulation frequency fm must be high enough so as to be able to write [10

10. R. Schimpe, J. E. Bowers, and T. L. Koch, “Characterization of frequency response of 1.5 µm InGaAsP DFB laser diode and InGaAs pin photodiode by heterodyne measurement technique,” Electron. Lett. 22(9), 453–454 (1986). [CrossRef]

]:
2βm=αH
(2)
where β is the frequency modulation index. Moreover, in the case of a multimode laser, these expressions can be independently written for each mode, and consequently, they can be treated separately in order to extract the value of Henry factor of the corresponding mode. If we are able to measure the complex spectrum corresponding to A1 or A+1, the extraction of the value of αH is straightforward:

αH=Im(A±1)/Re(A±1)
(3)

For a decade or so, several methods have been proposed to determine the complete temporal response of short pulses (i.e. both the amplitude and the phase) used in optical telecommunications [9

9. I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32(17), 2538–2540 (2007). [CrossRef] [PubMed]

, 11

11. J. Debeau, B. Kowalski, and R. Boittin, “Simple method for the complete characterization of an optical pulse,” Opt. Lett. 23(22), 1784–1786 (1998). [CrossRef] [PubMed]

18

18. D. A. Reid, S. G. Murdoch, and L. P. Barry, “Stepped-heterodyne optical complex spectrum analyzer,” Opt. Express 18(19), 19724–19731 (2010). [CrossRef] [PubMed]

]. These results are obtained in the temporal domain by fast Fourier transform of the complex spectrum measured with one of these techniques [9

9. I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32(17), 2538–2540 (2007). [CrossRef] [PubMed]

, 11

11. J. Debeau, B. Kowalski, and R. Boittin, “Simple method for the complete characterization of an optical pulse,” Opt. Lett. 23(22), 1784–1786 (1998). [CrossRef] [PubMed]

18

18. D. A. Reid, S. G. Murdoch, and L. P. Barry, “Stepped-heterodyne optical complex spectrum analyzer,” Opt. Express 18(19), 19724–19731 (2010). [CrossRef] [PubMed]

]. Among these methods, we have chosen the one that relies on the sinusoidal modulation of the phase of the signal under test [9

9. I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32(17), 2538–2540 (2007). [CrossRef] [PubMed]

] because it offers several advantages: easy implementation, high sensitivity, use of an electrical signal equivalent to that of the modulation of the device under test (DUT), and direct algorithm (i.e. non-iterative method) for obtaining the complex spectrum of the transmitter.

Figure 1
Fig. 1 Schematics of the experimental set-up based on sinusoidal optical phase modulation technique to measure the phase-amplitude coupling factor. EOS: External Optical Source, DUT: Device Under Test, ODL: Optical Delay Line, PM: Phase Modulator, OSA Optical Spectrum Analyzer, BT: Bias Tee, RFPS: RF Power Splitter
represents a schematics of the experimental set-up of this technique. The DUT is modulated by a sine wave supplied by a RF generator at a modulation frequency fm . An RF variable attenuator allows the control of the modulation index m so as to keep it within the small signal modulation regime. The optical signal to analyze is sent to a fiber coupled LiNbO3 phase modulator that is also modulated at fm by the same oscillator. The inherent large optical bandwidth of LiNbO3 phase modulator is well suited to measure the Henry factor of devices exhibiting smaller optical bandwidth, e.g. electroabsorption modulator. An optical delay line is placed between the DUT and the phase modulator in order to control the delay between the optical and electrical signals at the input of the phase modulator. Instead of making use of a delay line in the optical domain, a RF phase shifter could be used on one of the electrical paths as in reference [9

9. I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32(17), 2538–2540 (2007). [CrossRef] [PubMed]

]. The signal at the output of the modulator is sent to an optical spectrum analyzer (OSA) whose resolution and dynamic range are suitable to resolve the optical carrier and the modulation sidebands. As indicated in [9

9. I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32(17), 2538–2540 (2007). [CrossRef] [PubMed]

], the method relies on the measurement of 4 optical spectra corresponding to 4 different delays equally spaced by 1/(4fm).

Instead of using the general formalism developed in [9

9. I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32(17), 2538–2540 (2007). [CrossRef] [PubMed]

] we modified it to the specific case of our signals given by (1). The optical signal at the output of the component can be written as:
E(t)=A1expj{Ωtωmt}+A0expj{Ωt}+A+1expj{Ωt+ωmt}
(4)
where Ω/2π is the frequency of the optical carrier and ωm=2πfm . At the output of the phase modulator, we have:
S(t)=E(tk4fm)exp(jφ(t))whereφ(t)=ψcos(ωmt+ϕ0)
(5)
with: ψ is the amplitude of the phase modulation, k(=0,1,2or3) is an integer depending on the optical delay, corresponding to 4 different optical delays and ϕ0 is the phase at the origin (for k = 0) between the modulation of the optical signal and the RF signal at the input of the phase modulator.

In the spectral domain, at the optical frequency (Ωωm)/2π, by assuming a low phase modulation amplitude ψ (typically few tenth of radians) and keeping the only three first terms of the Fourier series development of exp(jφ(t)) (i.e. the DC, +ωm and ωm terms), the electric field has the following expression:
S˜k(Ωωm)=[A1J0(ψ)exp(jkπ2)+jA0J1(ψ)exp(jϕ0)]exp(jΩωmkπ2)
(6)
where J0 and J1are Bessel functions of the first kind.

The spectral intensity measured by the OSA will be:

I1k=|A1|2J0(ψ)2+A02J1(ψ)2+2A0J0(ψ)J1(ψ)Im[A1expj(kπ2+ϕ0)]
(7)

A similar calculation done for (Ω+ωm)/2π shows that:

I+1k=|A+1|2J0(ψ)2+A02J1(ψ)2+2A0J0(ψ)J1(ψ)Im[A+1expj(kπ2+ϕ0)]
(8)

Then, we define two quantities:
Q1=(I11I13)+j(I10I12)Q+1=(I+11+I+13)+j(I+10I+12)
(9)
And we obtain:

A1expjϕ0=Q14A0J0(ψ)J1(ψ)A+1expjϕ0=Q+14A0J0(ψ)J1(ψ)
(10)

Finally, in our case, according to (1), as A1=A+1, from (3), we can deduce:

αH=Im(Q1Q+1)Re(Q1Q+1)
(11)

3. Results for Fabry Perot lasers

Figure 2
Fig. 2 Measurement of the αH of each longitudinal modes of a FP laser. The inset shows the emission spectrum in a linear scale.
shows the results of the measurements of αH as a function of different longitudinal modes of the device under test for two different bias currents. The active region of this laser consists of 9 layers of InAs QDashes embedded in 40 nm thick InGaAsP (Q1.17) barriers [19

19. G.-H. Duan, A. Shen, A. Akrout, F. Van Dijk, F. Lelarge, F. Pommereau, O. LeGouezigou, J.-G. Provost, H. Gariah, F. Blache, F. Mallecot, K. Merghem, A. Martinez, and A. Ramdane, “High performance InP-based quantum dash semiconductor mode-locked lasers for optical communications,” Bell Labs Tech. J. 14(3), 63–84 (2009). [CrossRef]

]. The modulation frequency is 12 GHz and the applied RF power yields a modulation index m of about 2.5%. The inset shows the emission spectrum in a linear scale.

Compared to methods based on RF current modulation [6

6. C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42(4), 328–330 (1983). [CrossRef]

] or the fiber transfer function (FTF) [7

7. F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993). [CrossRef]

], our proposed technique is fast because it does not require filtering out each individual mode. Besides, for lower power modes, the FTF technique requires to perform high number of averages [3

3. A. Villafranca, A. Villafranca, G. Giuliani, and I. Garces, “Mode-resolved measurements of the linewidth enhancement factor of a Fabry–Pérot laser,” IEEE Photon. Technol. Lett. 21(17), 1256–1258 (2009). [CrossRef]

] which implies time consuming. Moreover, our method allows to characterize the Henry factor of FP lasers against current, unlike the linewidth power ratio technique which yields an average value over the current [3

3. A. Villafranca, A. Villafranca, G. Giuliani, and I. Garces, “Mode-resolved measurements of the linewidth enhancement factor of a Fabry–Pérot laser,” IEEE Photon. Technol. Lett. 21(17), 1256–1258 (2009). [CrossRef]

].

4. Results for electroabsorption modulators

Our method is also suitable to determine the chirp of external modulators. This is especially important if one aims at implementing an integrated laser with an electro-absorption modulator (EAM) that enables transmission beyond the chromatic dispersion limit for example. Usually the chirping behaviour of the EAM is predicted by measuring the absorption spectrum versus bias values and using Kramers-Krönig integrals: the best operating point is deduced from the Henry factor versus wavelength detunings from the excitonic peak [22

22. D. Delprat, A. Ramdane, A. Ougazzaden, H. Nakajima, and M. Carré, “Integrated multiquantum well distributed feedback laser-electroabsorption modulator with a negative chirp for zero bias voltage,” Electron. Lett. 33(1), 53–54 (1997). [CrossRef]

]. The sinusoidal phase modulation method is very attractive because it allows a simple and direct measurement of the chirp of an EAM versus wavelength.

Therefore, we now applied our method to an optical transmitter that consists of an electroabsorption modulator with an external laser. We generally make use of a tunable laser diode at the input of the EAM in order to make this type of measurements. Here, we prefer to take advantage of the wide optical spectrum of the previously tested FP laser (~15 nm) so as to use it as a simple continuous source. The objective is to exploit all the different longitudinal modes independently in order to get a measurement of αH as a function of the wavelength by making only 4 spectral measurements. The EAM we test here consists of a AlGaInAs/GaInAs structure with 10 QW [23

23. J.-G. Provost, C. Kazmierski, F. Blache, and J. Decobert, “High Extinction Ratio Picosecond Pulses at 40 GHz Rate over 40 nm with an AlGaInAs EAM Characterises by a Spectrogram Acquisition Method,” Proceedings of European Conference on Optical Communication (ECOC) 2005, paper Tu1.5.5 (2005)

].

Figure 4
Fig. 4 Simultaneous measurement of the αH of an EAM over 15 nm optical bandwidth for two different voltages.
depicts the measurement of αH for two bias voltages (−1.0 and −1.6 V). The RF signal is at 10 GHz and its incident power on the DUT equals – 15 dBm only, which illustrates the sensitivity of the method. For - 1.6V, we notice that αH becomes negative for wavelength smaller than 1562 nm.

We finally applied our method to determine the αH of the transmitter as a function of voltage for a given wavelength and compare the results with the FTF method (Fig. 5
Fig. 5 Comparison of the fiber transfer function method and our proposed technique for the measurement of αH of an EAM.
.). A very good agreement between these two curves over a large span of αH [ + 8 to −10] permits to validate this new technique.

For all results presented in this paper, the incident RF power on the phase modulator is + 4 dBm which leads to a value ψ of 0.30 rad. For RF powers leading to ψ0.6 rad, we observed differences that are no more negligible (more than 5% deviation between the FTF method and our method). This is attributed to the approximation by the only three first terms of the Fourier series development of exp(jφ(t)) done in part 2 which is no more valid under higher amplitude phase modulation.

This is further illustrated in Fig. 6
Fig. 6 Determination of the EAM Henry factor versus the amplitude of the phase modulation ψ (bias voltage −2.2 V).
which shows the accuracy of the method for amplitude phase modulation ψ as low as 0.06 rad at a fixed bias voltage. Variation of the measured Henry factor for ψ in the range of 0.06-0.4 is less than ± 2%. A typical value of 0.30 rad for ψis consequently a good trade-off between accuracy and sensitivity for this method.

5. Conclusion

In conclusion, we present a novel method based on sinusoidal phase modulation to determine the Henry factor of FP lasers without extracting each individual mode using a band pass filter. We also applied our method to determine the chirp of an EAM versus the wavelength over more than 15 nm optical bandwidth. This method yields very good agreement with the well-established fiber transfer function technique. It is furthermore capable of analyzing very wide optical bandwidth devices as it is only limited by the phase modulator optical response (typically few tens of nm). This technique will be of great interest for e.g. the characterizations of WDM systems such as optical frequency combs where each channel is independently modulated.

Acknowledgements

The authors would like to thank C. Kazmierski and F. Lelarge for providing the EAM and QDash laser respectively.

References and links

1.

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982). [CrossRef]

2.

N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron. 24(7), 1242–1247 (1988). [CrossRef]

3.

A. Villafranca, A. Villafranca, G. Giuliani, and I. Garces, “Mode-resolved measurements of the linewidth enhancement factor of a Fabry–Pérot laser,” IEEE Photon. Technol. Lett. 21(17), 1256–1258 (2009). [CrossRef]

4.

G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett. 13(5), 430–432 (2001). [CrossRef]

5.

Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett. 16(4), 990–992 (2004). [CrossRef]

6.

C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42(4), 328–330 (1983). [CrossRef]

7.

F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol. 11(12), 1937–1940 (1993). [CrossRef]

8.

R. C. Srinivasan and J. C. Cartledge, “On using fiber transfer functions to characterize laser chirp and fiber dispersion,” IEEE Photon. Technol. Lett. 7(11), 1327–1329 (1995). [CrossRef]

9.

I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32(17), 2538–2540 (2007). [CrossRef] [PubMed]

10.

R. Schimpe, J. E. Bowers, and T. L. Koch, “Characterization of frequency response of 1.5 µm InGaAsP DFB laser diode and InGaAs pin photodiode by heterodyne measurement technique,” Electron. Lett. 22(9), 453–454 (1986). [CrossRef]

11.

J. Debeau, B. Kowalski, and R. Boittin, “Simple method for the complete characterization of an optical pulse,” Opt. Lett. 23(22), 1784–1786 (1998). [CrossRef] [PubMed]

12.

M. Kwakernaak, R. Schreieck, A. Neiger, H. Jäckel, E. Gini, and W. Vogt, “Spectral phase measurement of mode-locked diode laser pulses by beating sidebands generated by electrooptical mixing,” IEEE Photon. Technol. Lett. 12(12), 1677–1679 (2000). [CrossRef]

13.

C. Dorrer and I. Kang, “Simultaneous temporal characterization of telecommunication optical pulses and modulators by use of spectrograms,” Opt. Lett. 27(15), 1315–1317 (2002). [CrossRef] [PubMed]

14.

P. Kockaert, M. Haelterman, P. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quantum Electron. 10(1), 206–212 (2004). [CrossRef]

15.

C. Gosset, J. Renaudier, G.-H. Duan, G. Aubin, and J.-L. Oudar, “Phase and amplitude characterization of a 40-GHz self-pulsating DBR laser based on autocorrelation analysis,” J. Lightwave Technol. 24(2), 970–975 (2006). [CrossRef]

16.

Y. Ozeki, S. Takasaka, and M. Sakano, “Electrooptic spectral shearing interferometry using a Mach-Zehnder modulator with a bias voltage sweeper,” IEEE Photon. Technol. Lett. 18(8), 911–913 (2006). [CrossRef]

17.

J. Bromage, C. Dorrer, I. A. Begishev, N. G. Usechak, and J. D. Zuegel, “Highly sensitive, single-shot characterization for pulse widths from 0.4 to 85 ps using electro-optic shearing interferometry,” Opt. Lett. 31(23), 3523–3525 (2006). [CrossRef] [PubMed]

18.

D. A. Reid, S. G. Murdoch, and L. P. Barry, “Stepped-heterodyne optical complex spectrum analyzer,” Opt. Express 18(19), 19724–19731 (2010). [CrossRef] [PubMed]

19.

G.-H. Duan, A. Shen, A. Akrout, F. Van Dijk, F. Lelarge, F. Pommereau, O. LeGouezigou, J.-G. Provost, H. Gariah, F. Blache, F. Mallecot, K. Merghem, A. Martinez, and A. Ramdane, “High performance InP-based quantum dash semiconductor mode-locked lasers for optical communications,” Bell Labs Tech. J. 14(3), 63–84 (2009). [CrossRef]

20.

B. Riou, N. Trenado, F. Grillot, F. Mallecot, V. Colson, M. F. Martineau, B. Thédrez, L. Silvestre, D. Meichenin, K. Merghem, and A. Ramdane, “High Performance Strained-Layer InGaAsP/InP Laser With Low Linewidth Enhancement Factor Over 30 nm,” Proceedings of European Conference on Optical Communication (ECOC) 2003, paper We4.P.85, Rimini, Italy, (2003).

21.

F. Lelarge, B. Dagens, J. Renaudier, R. Brenot, A. Accard, F. van Dijk, D. Make, O. Le Gouezigou, J.-G. Provost, F. Poingt, J. Landreau, O. Drisse, E. Derouin, B. Rousseau, F. Pommereau, and G.-H. Duan, “Recent advances on InAs/InP quantum dash based semiconductor lasers and optical amplifiers operating at 1.55 μm,” IEEE J. Sel. Top. Quantum Electron. 13(1), 111–124 (2007). [CrossRef]

22.

D. Delprat, A. Ramdane, A. Ougazzaden, H. Nakajima, and M. Carré, “Integrated multiquantum well distributed feedback laser-electroabsorption modulator with a negative chirp for zero bias voltage,” Electron. Lett. 33(1), 53–54 (1997). [CrossRef]

23.

J.-G. Provost, C. Kazmierski, F. Blache, and J. Decobert, “High Extinction Ratio Picosecond Pulses at 40 GHz Rate over 40 nm with an AlGaInAs EAM Characterises by a Spectrogram Acquisition Method,” Proceedings of European Conference on Optical Communication (ECOC) 2005, paper Tu1.5.5 (2005)

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.5060) Instrumentation, measurement, and metrology : Phase modulation

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: August 5, 2011
Revised Manuscript: September 2, 2011
Manuscript Accepted: September 6, 2011
Published: October 13, 2011

Citation
J.-G. Provost, A. Martinez, A. Shen, and A. Ramdane, "Single step measurement of optical transmitters Henry factor using sinusoidal optical phase modulations," Opt. Express 19, 21396-21403 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-21396


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References

  1. C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron.18(2), 259–264 (1982). [CrossRef]
  2. N. Schunk and K. Petermann, “Numerical analysis of the feedback regimes for a single-mode semiconductor laser with external feedback,” IEEE J. Quantum Electron.24(7), 1242–1247 (1988). [CrossRef]
  3. A. Villafranca, A. Villafranca, G. Giuliani, and I. Garces, “Mode-resolved measurements of the linewidth enhancement factor of a Fabry–Pérot laser,” IEEE Photon. Technol. Lett.21(17), 1256–1258 (2009). [CrossRef]
  4. G. Liu, X. Jin, and S. L. Chuang, “Measurement of linewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett.13(5), 430–432 (2001). [CrossRef]
  5. Y. Yu, G. Giuliani, and S. Donati, “Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect,” IEEE Photon. Technol. Lett.16(4), 990–992 (2004). [CrossRef]
  6. C. Harder, K. Vahala, and A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett.42(4), 328–330 (1983). [CrossRef]
  7. F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol.11(12), 1937–1940 (1993). [CrossRef]
  8. R. C. Srinivasan and J. C. Cartledge, “On using fiber transfer functions to characterize laser chirp and fiber dispersion,” IEEE Photon. Technol. Lett.7(11), 1327–1329 (1995). [CrossRef]
  9. I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett.32(17), 2538–2540 (2007). [CrossRef] [PubMed]
  10. R. Schimpe, J. E. Bowers, and T. L. Koch, “Characterization of frequency response of 1.5 µm InGaAsP DFB laser diode and InGaAs pin photodiode by heterodyne measurement technique,” Electron. Lett.22(9), 453–454 (1986). [CrossRef]
  11. J. Debeau, B. Kowalski, and R. Boittin, “Simple method for the complete characterization of an optical pulse,” Opt. Lett.23(22), 1784–1786 (1998). [CrossRef] [PubMed]
  12. M. Kwakernaak, R. Schreieck, A. Neiger, H. Jäckel, E. Gini, and W. Vogt, “Spectral phase measurement of mode-locked diode laser pulses by beating sidebands generated by electrooptical mixing,” IEEE Photon. Technol. Lett.12(12), 1677–1679 (2000). [CrossRef]
  13. C. Dorrer and I. Kang, “Simultaneous temporal characterization of telecommunication optical pulses and modulators by use of spectrograms,” Opt. Lett.27(15), 1315–1317 (2002). [CrossRef] [PubMed]
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