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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8401–8408
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Realization of pure frequency modulation of DFB laser via combined optical and electrical tuning

Chao Tian, I-Chun Anderson Chen, Seong-Wook Park, and Rainer Martini  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8401-8408 (2013)
http://dx.doi.org/10.1364/OE.21.008401


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Abstract

In this paper we present a novel approach to convert AM signal into FM signal in semiconductor lasers via off resonance optical pumping and report on experimental results obtained with a commercial DFB laser. Aside of demonstrating discrete and fast frequency modulation, we achieve pure frequency modulation through combination with electrical modulation suppressing the associated amplitude modulation, which is detrimental to application such as spectroscopy and communication.

© 2013 OSA

1. Introduction

Direct amplitude modulation (AM) of semiconductor laser remains the primary method of data transmission through existing optical networks due to its simplicity and low cost. However, such systems inevitably suffer from undesirable frequency response, such as chirping and side band modulation, which affects signal fidelity and limits data through-put. Moreover, AM communication is also highly sensitive to time varying absorption, scattering, and scintillation which directly influences the bit-error rate, and especially pronounced in free space communication networks. In contrast, frequency modulated (FM) transmission is the preferred methodology as bandwidths can be dramatically increased using unique transmission architectures, and is practically immune to environmental influences. However, controlled high speed variation of the emission frequency for a semiconductor laser is much harder to achieve; hence much less common. An even greater challenge is to realize pure FM modulation without the typical amplitude modulation, which not only improves signal fidelity but also quasi doubles the bandwidth of existing communication channels by enabling simultaneous AM and FM transmissions. Pioneering work reported by L. Thévenaz [1

1. L. Thévenaz, D. Alasia, S. Le Floch, and J. Troger, “Generation of high-quality signals for optical sensing using DFB lasers injection locking,” in Second European Workshop on Optical Fiber Sensors, 5502, 556–559, (2004). [CrossRef]

] in which injection locking was used to stabilize and tune the wavelength of a slave laser operating at constant optical power. Yet such an approach proves impractical for commercial applications because large wavelength shifts are unfeasible, requires specialized lasers, and demands a complex detection for sensitive detection. Other approaches have reported ultra-fast wavelength tuning of DBR lasers via quantum confined Stark effect [2

2. M. Pantouvaki and C. P. Liu, “Monolithically Integrated QCSE-tuned InGaAsP MQW ridge waveguide DBR laser,” IEEE International Conference on Indium Phosphide and Related Materials Conference Proceedings72–74. (IEEE, 2006). [CrossRef]

, 3

3. M. Pantouvaki, C.C. Renaud, P. Cannard, M.J. Robertson, R. Gwilliam, and A.J. Seeds, “Fast tunable InGaAsP DBR laser using quantum-confined stark-effect-induced refractive index change,” IEEE J. Sel. Top. Quant. 13(5), 1112–1121 (2007).

], which has accomplished 7 nm tuning range within 2 ns. Though this would be an ideal solution, our presented methodology represents another robust and inexpensive method of integrating AM and FM modulation with readily available commercial components; in contrast to custom fabricated monolithically integrated systems.

First demonstrated for mid-infrared Quantum Cascade lasers (QCLs) [4

4. G. Chen, R. Martini, S.- Park, C. G. Bethea, I.-C. A. Chen, P. D. Grant, R. Dudek, and H. C. Liu, “Optically induced fast wavelength modulation in a quantum cascade laser,” Appl. Phys. Lett. 97(1), 011102 (2010). [CrossRef]

], we introduce a very simple but highly promising FM scheme of non-resonant optical coupling that is applied to standard semiconductor lasers. While the experimental setup appears similar, it is fundamentally different from resonant carrier injection locking, and avoids the stringent demands on the properties of the slave and master lasers. Furthermore utilizing a combination of non-resonant optical and classical electrical modulation, we offer a low cost pure FM solution of existing system with moderate tuning range and fast tuning speed; opening possibilities to bandwidth enhancement even for existing fiber optic communication systems. While the modulation principle of this technique can be applied to any form of semiconductor laser, it is demonstrated here using a commercial DFB laser.

2. Principles

To understand the mechanism of non-resonant optical modulation we first revisit the theoretical background. The AM response caused by optical injection had been studied extensively in [5

5. T. Keating, X. Jin, S. L. Chuang, and K. Hess, “Temperature dependence of electrical and optical modulation responses of quantum-well lasers,” IEEE J. Quantum Electron. 35(10), 1526–1534 (1999). [CrossRef]

], especially for small signal injection. Within this framework, the modulation scheme proposed here can be understood as generation of additional charge carriers within the active region. Therefore the low-frequency roll-off due to the transport and parasitic effects are removed via all optical modulation. However, the behavior of the laser diode changes when optical injection is raised to the same magnitude as electrical injection. First, we analyze the dynamic effect of carrier concentration on the laser emission below threshold. It is widely accepted that frequency and output power of a semiconductor laser are closely connected since real and imaginary part of refractive index are linked by the Kramers-Kronig relation [6

6. C. H. Henry; “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Elect. 18(2), 259–264 (1982).

]. If carrier induced effects are considered alone, refractive index change of semiconductor is attributed to a combination of bandgap filling, bandgap shrinkage, and free carrier absorption [7

7. B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26(1), 113–122 (1990). [CrossRef]

]. Theoretical calculation shows a decrease in refractive index as carrier concentration increases, which can be verified through the blue shift of amplified spontaneous emission spectrum observed in semiconductor laser devices [8

8. J. K. Sheu, G. C. Chi, Y. K. Su, C. C. Liu, C. M. Chang, W. C. Hung, and M. J. Jou, “Luminescence of an InGaN/GaN multiple quantum well light-emitting diode,” Solid-State Electron. 44(6), 1055–1058 (2000). [CrossRef]

].

The situation changes when laser current is above threshold, in which case bandgap filling loses its significance since the energy of the electrons is pinned to Fermi energy [9

9. D. Sands, Diode Lasers, (Taylor & Francis, 2004).

]. On one hand, insertion of carriers well above the bandgap starts a relaxation process via phonon scattering, and thereby heat up the laser. The resulting change in lattice constant of semiconductor will lead to a red shift in the emission wavelength [10

10. M. Kondow, T. Kitatani, K. Nakahara, and T. Tanaka, “Temperature dependence of lasing wavelength in a GaInNAs laser diode,” IEEE Photonic Tech. L. 12(7), 777–779 (2000). [CrossRef]

]. On the other hand, the free carrier population does not remain constant for example through the here suggested non-resonant optical modulation. The spatial distribution of carrier is altered instead of Fermi energy, and hence refractive index of device can be varied as well. This phenomenon is known as free carrier absorption or plasma effect [11

11. H. C. Casey Jr and F. Stem, “Concentration-dependent absorption and spontaneous emission of heavily doped GaAs,” J. Appl. Phys. 47(2), 631–643 (1976). [CrossRef]

], and described through the following equation:
Δn=(e2λ28π2c2ε0n)(Nme+Pmh),
(1)
where Δn is the variation of real part of refractive index, n denotes the index of refraction, λ the wavelength, N, P are the carrier density of electrons and holes, respectively, and me, mh are their effective masses. This refractive index change is directly proportional to carrier concentration and allows for very fast wavelength modulation, which makes it clearly distinguishable from the above mentioned heat associated red-shift. It has been recently observed as a blue shift of center wavelength in corresponding modulation scheme applied to mid-infrared quantum cascade laser [4

4. G. Chen, R. Martini, S.- Park, C. G. Bethea, I.-C. A. Chen, P. D. Grant, R. Dudek, and H. C. Liu, “Optically induced fast wavelength modulation in a quantum cascade laser,” Appl. Phys. Lett. 97(1), 011102 (2010). [CrossRef]

].

To determine the effect on the emission of a DFB laser we performed a simple theoretical calculation based on a coupled wave analysis used in [12

12. S. Hansmann, “Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures,” IEEE J. Quantum Electron. 28(11), 2589–2595 (1992). [CrossRef]

, 13

13. T. Makino and J. Glinski, “Transfer matrix analysis of the amplified spontaneous emission of DFB semiconductor laser amplifiers,” IEEE J. Quantum Electron. 24(8), 1507–1518 (1988). [CrossRef]

]. The simple periodical structure is expected to create two equally strong modes on each edge of stop band, and when driven above threshold, one of them (typically with the longer wavelength [12

12. S. Hansmann, “Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures,” IEEE J. Quantum Electron. 28(11), 2589–2595 (1992). [CrossRef]

],) will start lasing and hence suppress the other. Nevertheless, introduction of optical pumping will reduce the effective refractive index within periodical structure and should lead to a switch of the dominant mode from right edge (long wavelength) to left edge (short wavelength), allowing for the desired fast frequency modulation of the laser.

As the modulation is clearly different from electrical modulation, different dependencies in amplitude and wavelength response are expected. As a consequence we suggest the possibility to compensate for unwanted side effects through combination of both. For example a variation in amplitude caused by a rise in current can be compensated by carefully tuning the variation of the optical pump power, while keeping the emission power constant. However, as the frequency response associated with the variation of current will differ from the frequency response due to the variation of optical pump power, they will not compensate each other, resulting in a frequency tuning of the laser without change in the emission power. Hence to demonstrate this possibility of FM without AM through combination of off resonance optical pumping and electrical current variation, we have to examine the individual responses first.

3. Experiment

We selected a commercially available 1550nm DFB laser (line width<1 MHz) mounted on a heat sink held constant at 20° C.

3.1 AM and FM response caused by current modulation

3.2 Optical tuning of spontaneous emission spectrum

To compare the effect of off-resonant optical modulation with electrical modulation, we construct a set-up that resembles a slave-master scheme, yet using two lasers with clearly separated wavelengths.

Figure 2
Fig. 2 Experimental setup. The emission from the a secondary “pump” laser is focused on to the front facet of a DFB laser (“signal”), whose emission power and spectrum is monitored.
shows the setup, where a “pump” laser is used in place of a “master” and a “signal” laser replaces the “slave”, respectively. As the restrictions are far more relaxed compared to a master-slave setup, we are able to use a multi-mode Fabry-Perot laser as pump laser, centered at 1310 nm (which is well above the bandgap of the signal laser), and whose current can be modulated by function generator. It should be noted, that there are nearly no requirements on emission wavelength and linewidth of the pump laser as long as it can create charge carriers within the active part of the signal laser. Its optical output is injected into the signal DFB’s front facet, which is the same DFB laser studied before. In contrast to the master-slave configuration, there is no specific requirement on the reflectivity or coating of the signal laser, allowing us to a standard commercially available laser in the position of the “slave” laser. Pump (1310 nm) and signal (1550 nm) beams are combined by a JDS WDM coupler, which ensures reliable optical isolation to avoid back reflection into the pump laser as well as ensuring detection of only the signal laser’s emission. Again the emission power and frequency of the signal laser is monitored using a power meter and an optical spectrum analyzer.

In analogy to electrical modulation, we first examine the response of the signal laser under non-resonant optical modulation, starting with its behavior below threshold current.

In the left part of Fig. 3
Fig. 3 Spontaneous emission influenced by optical injection. Left (a-d): Emission spectrum of 1550 nm DFB laser driven below threshold (1.5 mA drive current) for increasing optical pumping intensities. Right (e): Intensity of the observed peaks plotted against the optical pumping intensity identifying the switching behavior.
the amplified spontaneous emission spectrum of the signal laser is shown for increasing intensities injected from the pump laser. The frames show a typical spontaneous emission spectrum of DFB laser with two dominant modes (A and B), whereby mode A starts lasing above threshold corresponding to the measurement in Fig. 1. However, keeping the current below threshold while introducing external optical pumping, we observe first comparable amplitude growth for both modes (frame b), yet with further growth the plasma effect reduces the real part of refractive index, and hence varies the periodical structure. In agreement with the simulation discussed above such an index shift will favor mode B over mode A, which is evident in the following frames – starting with (frame c). It should be noted that the total gain is still growing due to the additional optically injected carriers contributing to the overall gain in the laser. Eventually, mode B becomes the dominant mode (frame d) and lasing emission would start at the shorter wavelength of mode B if the signal laser would be driven above threshold. This switch of dominant mode by off resonant optical pumping is clarified in the right hand side of Fig. 3, where the amplitude of the two modes is plotted against the injected optical intensity, identifying the switching point to be around 4 mW. It should be noted, that below 3.5 mW of optical pump power no clear shift in the wavelength occurs, hence the efficiency of the optical pumping drastically increases above this value. As mentioned above, these results agree very well with simulated spectrum obtained using transfer matrix method [12

12. S. Hansmann, “Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures,” IEEE J. Quantum Electron. 28(11), 2589–2595 (1992). [CrossRef]

, 13

13. T. Makino and J. Glinski, “Transfer matrix analysis of the amplified spontaneous emission of DFB semiconductor laser amplifiers,” IEEE J. Quantum Electron. 24(8), 1507–1518 (1988). [CrossRef]

], and the real refractive index change can be estimated to be around −0.04 causing the mode switching.

3.3 Optical tuning of stimulated emission spectrum

Next, we investigate the effect of the non-resonant optical tuning when DFB laser is driven above threshold. Normally the carrier concentration should be capped to the threshold due to stimulated emission. However, the existence of spatial hole-burning will allow us still to change the carrier distribution within the cavity and hence effect emission power and wavelength as discussed above.

In Fig. 4
Fig. 4 Bistability of DFB mode under optical pumping. Emission wavelength (red) and power (blue) of the signal laser plotted vs. optical pump power, the switch between the two modes happens at 5.16 mW.
we plotted output power (blue) and center wavelength (red) of the signal DFB laser’s emission at 12mA as a function of optically pump power. In agreement with Fig. 1, we expect an emission power of 75 μW at 1550.84 nm (mode A). For optical pump powers below 3.5 mW we observe only small changes in emission frequency as well as in emission power in agreement with the observation below threshold. However, above 4 mW pump power, we observe a strong rise of the emission intensity with increasing pump power (20.1 μW/mW), which remains nearly constant up to the maximal measured pump power. In addition the laser switches from mode A to mode B at 5.16 mW optical pump power, which is slightly higher, compared to the observation below threshold, which we attribute to the enhanced recombination of the optically generated charges by stimulated emission process. It should also be noted that the emission frequency shows an additional red-shift afterwards at a rate of 35.5 pm/μW.

In order to prove that the optical modulation can tune the DFB laser fast and discrete between these two modes, the pump laser was modulated by a 500 kHz sine signal centered at the pump laser’s threshold with peak emission power of 12.7 mW, which is far beyond switch point at 5.16 mW. The signal laser emission intensity mirrors the pump laser intensity due to its roughly linear response above 4 mW pump power, showing a half cycle sine wave, which is recorded as the top waveform in Fig. 5
Fig. 5 Optically induced mode switching measured with photo detector. The top graph shows the emission of signal laser without filter, the lower graph shows the emission of the signal laser after a band pass filter aligned with mode A. The dashed blue line shows estimated switch point.
.

As the optical pump power is way above the threshold of the mode jump, the DFB should also switch between the two modes in each half cycle. To resolve the wavelength shift, a tunable filter is aligned to mode A that effectively demodulates the FM signal and the obtained signal is shown in the bottom part of Fig. 5. It is obvious that the emission jumps between the two modes whenever the pump laser passes the switching power level and a frequency modulation of the laser is achieved, showing a good bistability yet still with an associated variation in the emission intensity. It should be pointed out, that the speed of this switching process was limited by rise time of the used current sources and not by the modulation scheme.

3.4 Pure FM signal

Based on the measurements shown in Fig. 4, a variation of the optical pump power from 4.5 to 6 mW results the DFB laser’s emission wavelength to blue jump by 1.42 nm and its intensity to rise from 94.5 to 118 μW. Yet according to Fig. 1, decreasing the drive current by 2 mA (from 14 mA to 12 mA) will cause the emission intensity to drop by the same amount, yet shift the emission wavelength by less than 0.014 nm. As suggested above, doing both as the same time, such current variation could cancel the intensity fluctuation caused by the optical modulation, therefore leaving a pure FM signal or – if combined in the opposite mode – generate an enhanced AM and FM modulation. This combination or cancellation approach allowing for compensation or enhancement of separate modulations is fundamentally applicable for any semiconductor laser – including continuous tunable lasers– as long as the non-resonant optical and electrical modulations exhibit different amplitude and frequency responses. Three function generators are used in order to synchronize two modulations. The first one produces AM signal to modulate current of signal DFB laser, and meanwhile triggers the second function generator; then the second one generates a pulse with tunable pulse width, which acts as a delay line, for its falling edge is used to trigger the third function generator; eventually the third function generator controls the current of pump laser and therefore the strength of optical modulation. The duty circle of pulse signal is tunable from 1% to 99%, resulting in a delay from 0 to 2π.

Figure 6
Fig. 6 Pure FM modulation generated with combined optical and electrical modulation. Frame (a) illustrates the modulation to be transmitted; frame (b) and (c) show the signal laser emission if the non-resonant optical and electrical modulations are used to enhance (b) or compensate each other – which lead to compensation of amplitude modulation (c). Frame (d) and (e) show emission from (c) with an additional filter tuned either to mode A (d) or mode B (e) – illustrating the presence of FM without AM.
shows the experimental verification of this scheme: Pump laser and signal laser are both modulated by square waves at 1 kHz as illustrated in frame (a). If the modulations are selected to enhance each other (i.e. optically non-resonant and electrical modulations are in phase and achieving higher intensity at the same time), a single square wave is observed in the emission of the signal laser (frame b). If one modulation is delayed by 180 degree phase difference, the electrical modulation will compensate the intensity variations stemming from off-resonant optical modulation. Hence, the emission intensity of signal laser remains constant except for some residual kinks at transition points, as shown in frame (c), and hence de facto the AM is suppressed. The residual kinks are attributed to deviations in the square waves due to different rise time in the current sources for example, more sophisticated adjustment should allow for better suppression.

In order to prove the presence of frequency modulation, a band pass filter (1.27 nm FWHM) is placed in front of detector. The signal shown in frame (d) is recovered when the center filter wavelength is tuned to the shorter wavelength and aligned with mode B; if the center wavelength is tuned to align with mode A, the signal shown in frame (e) is observed, showing the inverted square wave. This clearly demonstrates that the laser is switching between the two modes and the signal is encoded via FM. In connection with the constant amplitude observed in the unfiltered signal (shown in frame (c)), this is to prove that the signal was transmitted as a pure FM signal with a wavelength shift of 1.42 nm.

4. Conclusions

We introduce off-resonant optical modulation as a new way to transfer AM signal at one wavelength into FM signal at another wavelength using a standard semiconductor laser, with very low technical restriction to signal and even lesser to the pump laser. Optically controlled switching between different modes were observed below and above threshold operation and used to demonstrate fast switching between the modes via pure optical modulation. We introduced a new scheme to generate pure frequency modulation through combination of off-resonant optical and synchronized electrical modulation, where the amplitude modulation could be suppressed and a pure frequency modulation was demonstrated for the first time. The information carried by a discrete wavelength shift was recovered with an optical pass filter while constant emission intensity was recorded. This concept can easily be expanded to allow for transmission of AM and FM signal at the same time within same channel, principally allowing for an increase in the transmission bandwidth.

While all of these experiments were performed using a NIR DFB laser, the fundamental concept can be applied for all kind of semiconductor lasers including continuously tunable lasers. While the bandwidth of the experimental observed modulation is restricted by our equipment, it is fundamentally only limited by the carrier dynamics and can lead to high GHz modulation rate.

Acknowledgment

The authors would like to thank Clyde Bethea and Tao Yang for the useful discussion and experimental assistance.

References and links

1.

L. Thévenaz, D. Alasia, S. Le Floch, and J. Troger, “Generation of high-quality signals for optical sensing using DFB lasers injection locking,” in Second European Workshop on Optical Fiber Sensors, 5502, 556–559, (2004). [CrossRef]

2.

M. Pantouvaki and C. P. Liu, “Monolithically Integrated QCSE-tuned InGaAsP MQW ridge waveguide DBR laser,” IEEE International Conference on Indium Phosphide and Related Materials Conference Proceedings72–74. (IEEE, 2006). [CrossRef]

3.

M. Pantouvaki, C.C. Renaud, P. Cannard, M.J. Robertson, R. Gwilliam, and A.J. Seeds, “Fast tunable InGaAsP DBR laser using quantum-confined stark-effect-induced refractive index change,” IEEE J. Sel. Top. Quant. 13(5), 1112–1121 (2007).

4.

G. Chen, R. Martini, S.- Park, C. G. Bethea, I.-C. A. Chen, P. D. Grant, R. Dudek, and H. C. Liu, “Optically induced fast wavelength modulation in a quantum cascade laser,” Appl. Phys. Lett. 97(1), 011102 (2010). [CrossRef]

5.

T. Keating, X. Jin, S. L. Chuang, and K. Hess, “Temperature dependence of electrical and optical modulation responses of quantum-well lasers,” IEEE J. Quantum Electron. 35(10), 1526–1534 (1999). [CrossRef]

6.

C. H. Henry; “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Elect. 18(2), 259–264 (1982).

7.

B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron. 26(1), 113–122 (1990). [CrossRef]

8.

J. K. Sheu, G. C. Chi, Y. K. Su, C. C. Liu, C. M. Chang, W. C. Hung, and M. J. Jou, “Luminescence of an InGaN/GaN multiple quantum well light-emitting diode,” Solid-State Electron. 44(6), 1055–1058 (2000). [CrossRef]

9.

D. Sands, Diode Lasers, (Taylor & Francis, 2004).

10.

M. Kondow, T. Kitatani, K. Nakahara, and T. Tanaka, “Temperature dependence of lasing wavelength in a GaInNAs laser diode,” IEEE Photonic Tech. L. 12(7), 777–779 (2000). [CrossRef]

11.

H. C. Casey Jr and F. Stem, “Concentration-dependent absorption and spontaneous emission of heavily doped GaAs,” J. Appl. Phys. 47(2), 631–643 (1976). [CrossRef]

12.

S. Hansmann, “Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures,” IEEE J. Quantum Electron. 28(11), 2589–2595 (1992). [CrossRef]

13.

T. Makino and J. Glinski, “Transfer matrix analysis of the amplified spontaneous emission of DFB semiconductor laser amplifiers,” IEEE J. Quantum Electron. 24(8), 1507–1518 (1988). [CrossRef]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(140.0140) Lasers and laser optics : Lasers and laser optics

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 14, 2013
Revised Manuscript: March 7, 2013
Manuscript Accepted: March 7, 2013
Published: March 29, 2013

Citation
Chao Tian, I-Chun Anderson Chen, Seong-Wook Park, and Rainer Martini, "Realization of pure frequency modulation of DFB laser via combined optical and electrical tuning," Opt. Express 21, 8401-8408 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8401


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References

  1. L. Thévenaz, D. Alasia, S. Le Floch, and J. Troger, “Generation of high-quality signals for optical sensing using DFB lasers injection locking,” in Second European Workshop on Optical Fiber Sensors, 5502, 556–559, (2004). [CrossRef]
  2. M. Pantouvaki and C. P. Liu, “Monolithically Integrated QCSE-tuned InGaAsP MQW ridge waveguide DBR laser,” IEEE International Conference on Indium Phosphide and Related Materials Conference Proceedings72–74. (IEEE, 2006). [CrossRef]
  3. M. Pantouvaki, C.C. Renaud, P. Cannard, M.J. Robertson, R. Gwilliam, and A.J. Seeds, “Fast tunable InGaAsP DBR laser using quantum-confined stark-effect-induced refractive index change,” IEEE J. Sel. Top. Quant.13(5), 1112–1121 (2007).
  4. G. Chen, R. Martini, S.- Park, C. G. Bethea, I.-C. A. Chen, P. D. Grant, R. Dudek, and H. C. Liu, “Optically induced fast wavelength modulation in a quantum cascade laser,” Appl. Phys. Lett.97(1), 011102 (2010). [CrossRef]
  5. T. Keating, X. Jin, S. L. Chuang, and K. Hess, “Temperature dependence of electrical and optical modulation responses of quantum-well lasers,” IEEE J. Quantum Electron.35(10), 1526–1534 (1999). [CrossRef]
  6. C. H. Henry; “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Elect.18(2), 259–264 (1982).
  7. B. R. Bennett, R. A. Soref, and J. A. Del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quantum Electron.26(1), 113–122 (1990). [CrossRef]
  8. J. K. Sheu, G. C. Chi, Y. K. Su, C. C. Liu, C. M. Chang, W. C. Hung, and M. J. Jou, “Luminescence of an InGaN/GaN multiple quantum well light-emitting diode,” Solid-State Electron.44(6), 1055–1058 (2000). [CrossRef]
  9. D. Sands, Diode Lasers, (Taylor & Francis, 2004).
  10. M. Kondow, T. Kitatani, K. Nakahara, and T. Tanaka, “Temperature dependence of lasing wavelength in a GaInNAs laser diode,” IEEE Photonic Tech. L.12(7), 777–779 (2000). [CrossRef]
  11. H. C. Casey and F. Stem, “Concentration-dependent absorption and spontaneous emission of heavily doped GaAs,” J. Appl. Phys.47(2), 631–643 (1976). [CrossRef]
  12. S. Hansmann, “Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures,” IEEE J. Quantum Electron.28(11), 2589–2595 (1992). [CrossRef]
  13. T. Makino and J. Glinski, “Transfer matrix analysis of the amplified spontaneous emission of DFB semiconductor laser amplifiers,” IEEE J. Quantum Electron.24(8), 1507–1518 (1988). [CrossRef]

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