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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 5 — Mar. 2, 2009
  • pp: 3165–3172
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Dynamics of band-edge photonic crystal lasers

Fabrice Raineri, Alejandro M. Yacomotti, Timothy J. Karle, Richard Hostein, Remy Braive, Alexios Beveratos, Isabelle Sagnes, and Rama Raj  »View Author Affiliations


Optics Express, Vol. 17, Issue 5, pp. 3165-3172 (2009)
http://dx.doi.org/10.1364/OE.17.003165


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Abstract

Band-edge photonic crystal lasers were fabricated and their temporal characteristics were minutely analyzed using a high resolution up-conversion system. The InGaAs/InP photonic crystal laser operates at room temperature at 1.55 μm with turn on time ranging from 17ps to 30ps.

© 2009 Optical Society of America

1. Introduction

All-optical devices are expected to play an important role in the coming decade in the domain of information and communication technology due to their ability to bring efficient solutions to data transmission and processing. In this context, two-dimensional photonic crystals (2DPCs) have kindled interest for their potential use as active photonic devices. PCs [1

1. E. Yablonovitch, “Photonic crystals: What’s in a name?,” OPN 12-13, March 2007.

] are a periodic arrangement of materials with different refractive indices where the periodicity is of the order of the wavelength of light which confers them with exciting possibilities to manipulate light signals within small volumes of materials [2

2. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic crystal slab,” Opt. Express 13, 2678–2687 (2005) [CrossRef] [PubMed]

]. In this work, we have fabricated an InP-based 2DPCs laser bonded with Silicon and explored its temporal capabilities.

In wavelength sized structures -VCSEL’s, micro-cavities and more recently photonic crystal lasers- three parameters have been presented as the pathway to breakthroughs for speed and compactness, namely the cavity quality factor Q, the volume of the resonator and the spontaneous emission rate: the β factor. Considerable effort has been devoted to optimising one or a combination of these factors to obtain a variety of impressive performances in terms of laser threshold, compactness and speed [3–7

3. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]

]. Manipulation of the β factor gives a handle on the spontaneous emission rate to tailor at will, the temporal response of the system. Similarly Q factors have been under scrutiny with the view to reducing threshold power levels. Mode volumes of the order of cubic wavelength have been achieved permitting strong confinement of light in three dimensions [7

7. K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. 88, 211101 (2006). [CrossRef]

]. In semiconductor 2DPC lasers both the β factor and the Q factor are expected to be fairly high with attractive switching speeds with low threshold levels. The highest β factors reported so far are obtained in nanocavity systems [8

8. S. Strauf, K. Henessy, M. T. Rahker, Y. S. Choi, A. Badolato, L C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006). [CrossRef] [PubMed]

,9

9. K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15, 7506–7514 (2007). [CrossRef] [PubMed]

]. To date the fastest laser reported is in a GaAs nanocavity containing InGaAs multiple quantum wells. It operates at 937nm at 100K [6

6. H. Altug, D. Englund, and J. Vuckovic, “Ultrafast photonic crystal nanocavity laser,” Nature Phys. 2, 484–488 (2006). [CrossRef]

] with a modulation speed of more than 100GHz. In the present work, we study the dynamics of the other type of photonic crystal laser which is the band-edge laser. Here, laser emission is obtained in a perfectly periodic system by exploiting the low group velocity modes occurring at the high symmetry points of the band structure [10

10. C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP two-dimensional photonic crystal on silicon: In-plane Bloch mode laser,” Appl. Phys. Lett. 81, 5102–5104 (2002). [CrossRef]

]. These types of lasers are of interest because they favour the emission of higher powers than nanocavities due to their size and they enable more efficient collection as they are highly directional [11

11. D. Ohnishi, T. Okano, M. Imada, and S. Noda, “Room temperature continuous wave operation of a surface emitting two-dimensional photonic crystal diode laser,” Opt. Express 12, 1562–1568 (2004). [CrossRef] [PubMed]

]. Here we report on the temporal properties of 1.55μm InGaAs/InP 2D photonic crystal band edge lasers operating at room temperature. We performed the measurements with an up-conversion technique [12

12. J. Shah, T. C. Damen, B. Deveaud, and D. Block, “Subpicosecond luminescence spectroscopy using sum frequency generation,” Appl. Phys. Lett. 50, 1307–1309 (1987). [CrossRef]

] which gives us the required temporal resolution (150fs) adapted to the short time responses of these types of lasers. Further this has the advantage of being a direct measurement which does not involve deconvolution of the instrumental time resolution- which in the temporal measurements reported so far in photonic crystal laser- is often lower than the temporal characteristics of the system under study. In addition at 1.55μm, streak cameras are of low efficiency and thus, inefficient to measure the dynamics of such lasers. Our photonic crystal laser is integrated onto a Silicon chip rendering the present work potentially relevant in the context of a rapidly developing domain of hybrid structure devices and on-chip high speed data processing systems.

2. Design and fabrication of the PC structure

Fig. 1. (a) Schematic hetero-structure. (b) SEM top image of the PC structure.

3. Laser characterization

First we recorded the reflectivity spectrum of the PC resonance under near-transparency condition for the gain material in order to evaluate the Q factor of the resonator, which is about 10000 [13

13. G. Vecchi, F. Raineri, I. Sagnes, A. Yacomotti, P. Monnier, T. J. Karle, K-H. Lee, R. Braive, L. Le Gratiet, S. Guilet, G. Beaudoin, A. Talneau, S. Bouchoule, A. Levenson, and R. Raj, “Continuous-wave operation of photonic bandedge laser near 1.55 μm on silicon wafer,” Opt. Express 15, 7551–7556 (2007). [CrossRef] [PubMed]

]. Then a study of the laser emission intensity as a function of the pumping intensity was conducted using micro-photoluminescence measurements with excitation pulses of 5ps with 80MHz repetition rate delivered by a Ti-Saph laser emitting at 840 nm. The excitation pulses were focused on the sample by a long working distance optical microscope (NA=0.4). The excitation spot is roughly 5 μm. The emission, from luminescence to laser emission, is collected by the same microscope objective and separated from the pumping laser by means of a dichroic mirror and an antireflection silicon-coated filter. It is then spectrally dispersed by a 0.5m spectrometer and detected by a cooled InGaAs photodiode array.

Fig. 2. Laser intensity is plotted as a function of the pump power (squares: experimental and line: numerical calculation).

In Fig. 2, we plot on a log-log scale (the blue squares) the laser peak power at 1.52μm as a function of the pump intensity. We observe the characteristic S-shaped curve [16

16. E. Kapon, Semiconductor lasers (Academic Press, 1999).

] of the laser emission. The threshold will be derived in section 5 from a fitting procedure. The value we get is 2.3mW. Then, as pump power is increased above 4.2mW (52.5pJ), a saturation of the emitted power is observed.

4. Temporal studies

We record simultaneously the spectral response of the system using a spectrometer with an InGaAs nitrogen cooled photodiode and the temporal response using a β-Barium Borate (BBO) up-conversion crystal followed by a spectrometer and a photo-multiplier. The source used for the temporal studies is a regenerative amplified Ti-Saph laser providing 10μJ, 150fs, 1 kHz repetition rate pulses at 800 nm. The source is divided in two; one branch is used to optically pump the sample at normal incidence on the sample surface with a 10cm focal lens to a spot size of about 50μm. The other branch of the source is used as a gating pulse for the up-conversion system. The surface normal PC laser emission at 1.52μm is collected using the same lens as for optical pumping. A schematic of the experimental set-up is given in Fig. 3.

Fig. 3. Schematics of the experimental set-up. M1, M2, M3 denotes gold mirrors, D1 and D2 dichroic mirrors, BS a 90%–10% beam splitter, L1 a lens of focal distance 10cm, L2 a lens of focal distance 20cm, L3 a lens of focal distance 30cm, F a BG18 low pass filter filtering the light at 0.8μm and 1.5μm and PM a GaP photomultiplier.

The up-conversion system is a nonlinear optical frequency converter [12

12. J. Shah, T. C. Damen, B. Deveaud, and D. Block, “Subpicosecond luminescence spectroscopy using sum frequency generation,” Appl. Phys. Lett. 50, 1307–1309 (1987). [CrossRef]

,17

17. N. Bouché, C. Dupuy, C. Meriadec, K. Streubel, J. Landreau, L. Manin, and R. Raj, “Dynamics of gain in vertical cavity lasers and amplifiers at 1.53 μm using femtosecond photoexcitation,” Appl. Phys. Lett. 73, 2718–2720 (1998) [CrossRef]

], where one can detect IR radiation by taking advantage of the properties of highly efficient photomultiplier detectors at visible wavelengths. This conversion is accomplished by sum-frequency generation between a weak signal (here the laser emission at 1.52μm) and a strong pump (Ti-Saph at 800nm) in the BBO crystal. The intensity of the sum frequency (at 527nm) produced is proportional to the temporal overlap between the pump and the laser signal [18

18. Y. R. Shen, The Principles of nonlinear optics (Wiley Classics Library, 2003).

] and thus proportional to the signal intensity within the ultrashort pump pulse gate, hereto referred to as “gate”. This is recorded as a function of the relative delay giving an accurate representation of the full temporal shape of the signal. The BBO used here is a type I crystal with a thickness of 1mm chosen so as to give a temporal resolution limited only by the pulse duration i.e 150fs. The gate at 800nm and the laser emission at 1.52μm are collinearly incident and focused in the BBO crystal using AR coated lenses of focal distances 30cm and 20cm, respectively for the gate and the signal, giving rise to a sum frequency generation at 527nm. The up-converted signal is sent into a spectrometer and detected by a GaP photomultiplier. The spectrometer is only used as a filter to eliminate the extremely intense second harmonic of the gate at 400nm which is not easily stopped by ordinary filters, as the pump for up-conversion is 105 times the signal. The signal is then sent into a boxcar averager with a 1ms gate triggered at 1 kHz by the laser. The signal is averaged over 3000 pulses. The averaged output signal from the boxcar is passed to a computer and recorded as a function of the delay between the laser emission and the pump pulses.

Fig. 4. (a) Up-converted laser intensity versus temporal delay between gating pulse and laser emission for three different pumping energies (green 260pJ, blue 290 pJ and red 500pJ); squares: experimental values (the lines joining the squares are a guide to the eye). Black lines are the numerical calculations as a result of the fitted parameters in the rate equation model. (b) Laser spectra for three different pumping energies (green 260pJ, blue 290 pJ and red 500pJ).

The up-converted signal is displayed in Fig. 4(a) for three different pump energies. The zero in the x-axis corresponds to the instant when the pump for optically pumping the sample arrives at the sample. This is determined by measuring the up-conversion signal produced by combining the gate and the optical pump of the PC at the BBO crystal. The PC laser intensity is then plotted as a function of the delay (with respect to the measured zero) introduced in the path of the gate. The corresponding spectra of the laser emission are shown in Fig. 4(b). The PC laser response for the lowest energy, 250pJ shows a turn-on time (the interval between the pump and the peak of laser emission) of 30ps and a fall time of 9ps; the emission is at 1520.5nm with Δλ=0.7nm. When the pumping energy is increased to 290pJ the turn on time is 25.4ps and the peak shifts to 1520nm with Δλ=0.9nm; for the highest energy of 500pJ the turn-on time is 17ps, the peak further blue shifts to 1519nm with Δλ=5nm, probably due to a large chirp coming from amplitude-phase coupling in semiconductor active media [19

19. M. Yacomotti, F. Raineri, C. Cojocaru, P. Monnier, J. A. Levenson, and R. Raj, “Nonadiabatic Dynamics of the Electromagnetic Field and Charge Carriers in High-Q Photonic Crystal Resonators,” Phys. Rev. Lett. 96, 093901 (2006). [CrossRef] [PubMed]

].

Fig. 5. Turn-on time as a function of the pump energy, squares: experimental values; line: numerical calculation resulting from the fitting of the experimental data. Fitted parameters: Rth=75.7 pJ; γsp=0.004; τ¯ rad =6.9; ntr=0.46.

For low pumping energies the temporal signal is almost symmetrical whereas for a pumping energy of 500pJ, the fall time stretches over 15ps giving a strongly asymmetric temporal response. In Fig. 5 we plot the complete set of turn on times as a function of the pump energy. There is a clear decrease in the turn on time with respect to the optical excitation level. It is also seen that this decrease hits a limit around 17ps.

5. Discussion

We will now analyse the physics in play behind the characteristics of the temporal response of the low group velocity band-edge lasers. We model the transient response with a set of standard QW laser rate equations [16

16. E. Kapon, Semiconductor lasers (Academic Press, 1999).

]. The equations read:

dSdt=Sτp+Γvgg(N)S+ΓβBN2
(1)
dNdt=NτnrBN2vgg(N)S+R
(2)

where S is the photon density, N is the carrier density in the quantum wells (per unit volume), τp is the photon lifetime, Γ is the optical confinement factor which takes into account the overlap of the mode field with the active region, vg is the group velocity, g(N) = σ (N − Ntr) is the gain in the linear gain model with Ntr the carrier density at transparency and σ=dg/dN the differential gain, β is the spontaneous emission factor, β is the radiative recombination coefficient in the resonator, τnr is the nonradiative carrier recombination lifetime and R is the pumping rate. Variables S and N are adimensionalized and yield the following equations:

dsdt=1τp[s+(nntr)s+γspn2]
(3)
dndt=1τnr[nn2τ̄rad(nntr)s+R(t)Rth(1+ntr)]
(4)

where n = ΓvgστpN, ntr = ΓvgσNtr, s = vgστnrS, τ¯ rad = τradnr, γsp = βτnrrad and τrad = Γσvgτp/B . Note that the carrier normalization constant (Γvgστp)-1 gives the additional carrier density required to take the system from the transparency to the laser regime for β=0. The parameter ntr essentially gives the QW absorption normalised to optical losses. The photon density is normalized to that corresponding to the laser saturation intensity. τrad gives a characteristic time scale for radiative recombination processes. Finally, Rth=(ntr+1)/(ΓMDvgστpτnr) is a normalization factor for the pumping rate, which corresponds to the pumping rate at the laser threshold for β=0 and τ¯ rad ≥ 1. We integrate Eqs. (3)–(4) in time with a 4th order Runge-Kutta algorithm. We model the femtosecond pumping as a gaussian pulse centred at t0 and duration 2τfs,

R(t)=R0τnrexp[(tt0)2/τfs2]τfsπ
(5)

For a sufficiently long time t1 after the pumping pulse (t1-t0>>tfs) almost all the carriers are excited, giving n(t1) ≈ n0 ≡ r(1 + ntr) where r≡R0/Rth is the pumping parameter. A very short pumping pulse as in our case allows approximating the gaussian by a Dirac function, i.e. R(t) = R0τnrδ(t-t0), which yields n(t0+)=n0. We have verified that this kick-like pump accurately approximates the gaussian model of Eq. (5). Depending on the whole set of parameters -namely Rth, τp, τsp, τnr, τrad and ntr - a laser pulse can develop and attain a peak intensity of smax at t=tmax which gives the turn on time Δt=tmax-t0. We have implemented an algorithm which allows the parameters to fit the experimental data by minimizing the distance between the experimental points and Δt(r) for the data shown in Fig. 5. For the fitting procedure we fixed τp to be Q/ω with Q= 10000, which gives τp=8.2ps, and τnr=200ps (in accordance with the previously measured value [20

20. F. Raineri, C. Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal,” App. Phys. Lett. 85, 1880–1882 (2004). [CrossRef]

]). In Fig. 5, we plot the turn on time Δt as a function of pump intensity.

Now we carry out a crosschecking procedure; thus in order to verify the quality of the fit we use the converged parameters γsp, τ¯ rad and ntr obtained from fitting the curve in Fig. 5 and re-inject them into the equations. The remaining parameter Rth is re-scaled to the pump power of the peak intensity data, giving the threshold value in Fig. 2, Rth=2.3mW. The emission intensity is plotted as a function of pump intensity; the result is shown in Fig. 2. It is seen that the experimental values fit in very neatly with those derived from the model. We see that, starting from spontaneous emission level (Fig. 2) to well above the threshold, the experimental points concur with the simulated curve. Above this level of excitation, both in the intensity versus pump intensity (Fig. 2) curve and in the turn-on time dependency on pump energy curve (Fig. 5), the model deviates slightly from the experimental values probably due to gain compression for pump powers > 4.2mW. As a final verification, we plot the calculated temporal response of the laser for the 3 pump energies used on Fig. 4 a). Once again, we observe a very good agreement with the experiments, especially for the change in the shape of the signal with increasing pump powers.

We can now derive the physical parameters from the normalized ones. The fitting procedure yields the values of γsp, τ¯ rad and ntr. Firstly, the spontaneous emission factor can be extracted directly from the relation γsp = βτnrrad giving β=0.03. Next, the group velocity can be obtained though the relation ntr=Γvgτp a, where a is the QW absorption; using a=6000cm-1 from absorption measurements together with a geometrical estimation of the optical confinement factor, Γ=0.2, we obtain vg=5×105 m/s. Finally, an estimation of the carrier density at transparency Ntr~1018 cm-3 allows to obtain a value for the radiative recombination factor: B~3 10-10 cm3/s in accordance with the value reported in literature [21

21. H. Kawagushi, “Optical bistability and chaos in a semiconductor laser with saturable absorber,” Appl. Phys. Lett. 45, 1264–1266 (1984). [CrossRef]

].

Fig. 6. (a) Calculated 2D photonic band diagram of the studied PC. The blue line indicates the slow band where laser emission is obtained. Green dotted lines indicate the air and silica light lines, the guided modes cut-off at the silica light line. (b) Group index calculated for the blue band on Fig 6(a). The red dashed line indicates the extent of the pumped area of 50μm in reciprocal space.

In order to verify the group velocity value which is deduced from our experimental fitting, the guided resonances of the graphite lattice structure were calculated using a Guided Mode Expansion technique [22

22. L C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006). [CrossRef]

], over a range of lattice constants and filling factors. This technique allows us to calculate the complex resonant frequencies of this asymmetric 3D structure (air/InP/Silica) as a function of wavevector. These frequencies (normalised to the 745nm period of the graphite lattice) are displayed in Fig. 6(a) for wavevectors aligned along the Γ-M direction of the lattice. In Fig. 6(b) we plot the group index (c/vg) around the Γ point of the reciprocal lattice. The red dashed vertical line indicates the extent of the pumped area of 50μm in reciprocal space. Note these results compare favourably with 3D fully-vectorial FDTD calculations [23

23. We have used FDTD Solutions, www.lumerical.com.

], which included the lower metal mirror/bonding layer. The simulation shows that the group index is about 380 corresponding to a group velocity of 7.9×105m.s-1. This value is of the same order of magnitude as the one found by fitting the experimental measurements further validating the quality of the fit.

6. Conclusion

In summary, we have carried out, for the first time, to our knowledge an accurate measurement of the temporal characteristics of a band-edge PC laser with graphite lattice, integrated on a silicon chip and operating in the telecom range at room temperature. The temporal response has been obtained with a precision of about 150fs using an up-conversion technique. It has been observed that the combination of a fairly high value of β(0.03) and a fairly low group velocity (5×105m.s-1) gives the possibility of obtaining lasing in very small structures with a modulation capacity of 30GHz. The fast response and the low threshold powers obtained indicate that these types of lasers will perfectly fit in their role of source in an all optical photonic circuits with the possibility of integrating these devices on silicon platforms.

Acknowledgments

This work has been done in the framework of the Joint Research Activity on InP membrane of the FP6 Network of Excellence ePIXnet and ICT FP7 HISTORIC European project.

References and links

1.

E. Yablonovitch, “Photonic crystals: What’s in a name?,” OPN 12-13, March 2007.

2.

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic crystal slab,” Opt. Express 13, 2678–2687 (2005) [CrossRef] [PubMed]

3.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]

4.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP two-dimensional photonic crystal on silicon: In-plane Bloch mode laser,” Appl. Phys. Lett. 81, 5102–5104 (2002). [CrossRef]

5.

M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express 14, 6308–6315 (2006). [CrossRef] [PubMed]

6.

H. Altug, D. Englund, and J. Vuckovic, “Ultrafast photonic crystal nanocavity laser,” Nature Phys. 2, 484–488 (2006). [CrossRef]

7.

K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. 88, 211101 (2006). [CrossRef]

8.

S. Strauf, K. Henessy, M. T. Rahker, Y. S. Choi, A. Badolato, L C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006). [CrossRef] [PubMed]

9.

K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15, 7506–7514 (2007). [CrossRef] [PubMed]

10.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP two-dimensional photonic crystal on silicon: In-plane Bloch mode laser,” Appl. Phys. Lett. 81, 5102–5104 (2002). [CrossRef]

11.

D. Ohnishi, T. Okano, M. Imada, and S. Noda, “Room temperature continuous wave operation of a surface emitting two-dimensional photonic crystal diode laser,” Opt. Express 12, 1562–1568 (2004). [CrossRef] [PubMed]

12.

J. Shah, T. C. Damen, B. Deveaud, and D. Block, “Subpicosecond luminescence spectroscopy using sum frequency generation,” Appl. Phys. Lett. 50, 1307–1309 (1987). [CrossRef]

13.

G. Vecchi, F. Raineri, I. Sagnes, A. Yacomotti, P. Monnier, T. J. Karle, K-H. Lee, R. Braive, L. Le Gratiet, S. Guilet, G. Beaudoin, A. Talneau, S. Bouchoule, A. Levenson, and R. Raj, “Continuous-wave operation of photonic bandedge laser near 1.55 μm on silicon wafer,” Opt. Express 15, 7551–7556 (2007). [CrossRef] [PubMed]

14.

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “Surface emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006). [CrossRef]

15.

K.-H. Lee, S. Guilet, G. Patriarche, I. Sagnes, and A. Talneau, “Smooth sidewall in InP-based photonic crystal membrane etched by N2-based inductive coupled plasma,” J. Vac. Sci. Technol. B 26, 1326–1333 (2008). [CrossRef]

16.

E. Kapon, Semiconductor lasers (Academic Press, 1999).

17.

N. Bouché, C. Dupuy, C. Meriadec, K. Streubel, J. Landreau, L. Manin, and R. Raj, “Dynamics of gain in vertical cavity lasers and amplifiers at 1.53 μm using femtosecond photoexcitation,” Appl. Phys. Lett. 73, 2718–2720 (1998) [CrossRef]

18.

Y. R. Shen, The Principles of nonlinear optics (Wiley Classics Library, 2003).

19.

M. Yacomotti, F. Raineri, C. Cojocaru, P. Monnier, J. A. Levenson, and R. Raj, “Nonadiabatic Dynamics of the Electromagnetic Field and Charge Carriers in High-Q Photonic Crystal Resonators,” Phys. Rev. Lett. 96, 093901 (2006). [CrossRef] [PubMed]

20.

F. Raineri, C. Cojocaru, P. Monnier, A. Levenson, R. Raj, C. Seassal, X. Letartre, and P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear response in a two-dimensional InP-based photonic crystal,” App. Phys. Lett. 85, 1880–1882 (2004). [CrossRef]

21.

H. Kawagushi, “Optical bistability and chaos in a semiconductor laser with saturable absorber,” Appl. Phys. Lett. 45, 1264–1266 (1984). [CrossRef]

22.

L C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006). [CrossRef]

23.

We have used FDTD Solutions, www.lumerical.com.

OCIS Codes
(140.3460) Lasers and laser optics : Lasers
(230.5298) Optical devices : Photonic crystals

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: November 5, 2008
Revised Manuscript: December 13, 2008
Manuscript Accepted: December 15, 2008
Published: February 17, 2009

Citation
Fabrice Raineri, Alejandro M. Yacomotti, Timothy J. Karle, Richard Hostein, Remy Braive, Alexios Beveratos, Isabelle Sagnes, and Rama Raj, "Dynamics of band-edge photonic crystal lasers," Opt. Express 17, 3165-3172 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3165


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References

  1. E. Yablonovitch, "Photonic crystals: What’s in a name?," OPN 12-13, March 2007.
  2. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic crystal slab," Opt. Express 13, 2678-2687 (2005) [CrossRef] [PubMed]
  3. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999). [CrossRef] [PubMed]
  4. C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Hollinger, E. Jalaguier, S. Pocas, and B. Aspar, "InP two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002). [CrossRef]
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