OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 13 — Jun. 23, 2008
  • pp: 9519–9527
« Show journal navigation

Transverse spatial structure of a high Fresnel number Vertical External Cavity Surface Emitting Laser

X. Hachair, S. Barbay, T. Elsass, I. Sagnes, and R. Kuszelewicz  »View Author Affiliations


Optics Express, Vol. 16, Issue 13, pp. 9519-9527 (2008)
http://dx.doi.org/10.1364/OE.16.009519


View Full Text Article

Acrobat PDF (388 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The transverse spatial structure of an optically-pumped, Vertical External Cavity Surface Emitting Laser is investigated experimentally. The Fresnel number of the laser cavity is controlled with an intracavity lens. We show how the emission profile changes when passing from a low to a high Fresnel number configuration and analyze the RF spectrum of the total laser intensity. Though the laser operates in a multi-longitudinal mode configuration, the transverse profile of the laser emission shows well organized patterns.

© 2008 Optical Society of America

1. Introduction

Vertical External Cavity Surface Emitting Laser (VECSEL) are laser sources of growing importance because they combine the advantages of semiconductor surface emitting lasers and of high-power solid-state lasers. One end of the cavity is composed of a semiconductor gain medium grown on a high reflectivity Bragg mirror and the other end is closed by a usually spherical, high reflectivity dielectric mirror. The extent of the cavities allows for many longitudinal modes inside the gain curve. Thus, VECSELs are less sensitive to temperature effects than monolithic cavities and can be driven at higher pumping, which allows for high output powers. When combined with an intracavity saturable absorber mirror, VECSELs can be operated in the mode-locked regime to deliver ultra-fast pulses in the sub-picosecond range [1

1. U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003). [CrossRef] [PubMed]

, 2

2. U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429, 67–120 (2006). [CrossRef]

] with possibly a high repetition rate. In many applications though, operation in the single fundamental transverse mode is sought together with a high output power. This is potentially a problem since higher order transverse mode can then be excited. In addition, if one wishes to control the repetition rate of pulses in the mode-locked regime, further constraints are imposed on the cavity design parameters and it may become difficult to remain in this regime. On the other hand, it is sometimes desirable to operate the laser in a highly multi-transverse mode regime. This is the case for studies on pattern formation in lasers, and more specifically for localized structures in lasers ([3

3. N. N. Rosanov and N. V. Fedorov, “Diffraction switching waves and autosolitons in a saturable-absorber laser,” Optik. Spectrosk. 72, 1394 (1992).

, 4

4. V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Spatial soliton laser: Localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582 (1997). [CrossRef]

, 5

5. M. Bache, F. Prati, G. Tissoni, R. Kheradmand, L. Lugiato, I. Protsenko, and M. Brambilla, “Cavity soliton laser based on VCSEL with saturable absorber,” Appl. Phys. B pp. 913–920 (2005). [CrossRef]

]). Localized structures in cavities, also called cavity solitons, are independently controllable spots in the transverse plane of a system [6

6. S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödel, M. Miller, and R. Jäger, “Cavity solitons work as pixels in semiconductors,” Nature 419, 699–702 (2002). [CrossRef] [PubMed]

, 7

7. S. Barbay, Y. Ménesguen, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, “Incoherent and coherent writing and erasure of cavity solitons in an optically pumped semiconductor amplifier,” Opt. Lett. 31, 1504–1506 (2006). [CrossRef] [PubMed]

]. Light localization in these systems can be viewed as the result of the transverse mode locking of a great number of modes. The present study was initiated in this context, but we wish to stress that transverse mode selection in VECSELs may be of great interest in other research fields too.

Pattern formation and transverse mode selection in lasers have already been the subject of many studies (see e.g. [8

8. F. T. Arecchi, S. Boccaletti, and P. L. Ramazza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999). [CrossRef]

] for a review). Leaving aside the dynamical aspects, it has been shown that the emitted pattern is the result of a complex interplay between the cavity geometry, the boundary conditions, the material gain and its nonlinearities. In semiconductor materials, a lot of studies have taken place in Vertical Cavity Surface Emitting Lasers VCSELs ([9

9. C. Chang-Hasnain, M. Orenstein, A. Von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 57, 218–221 (1990). [CrossRef]

, 10

10. J. Scheuer and M. Orenstein, “Optical Vortices Crystals: Spontaneous Generation in Nonlinear Semiconductor Microcavities,” Science 285(5425), 230–233 (1999). [CrossRef] [PubMed]

, 11

11. S. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern Formation in the Transverse Section of a Laser with a Large Fresnel Number,” Phys. Rev. Lett. 82, 1434 (1999). [CrossRef]

, 12

12. I. V. Babushkin, N. A. Loiko, and T. Ackemann, “Eigenmodes and symmetry selection mechanisms in circular large-aperture vertical-cavity surface-emitting lasers,” Phys. Rev. E 69, 066,205 (2004). [CrossRef]

, 13

13. T. T. Ackemann, S. Barland, M. Cara, S. Balle, R. Jäger, M. Grabherr, M. Miller, and K. J. Ebeling, “Spatial mode structure of bottom-emitting broad-area vertical-cavity surface-emitting lasers,” J. Opt. B: Quantum Semiclass. 2, 406–412 (2000). [CrossRef]

] to cite a few) but very few, to our knowledge, in VECSELs. VCSELs have the advantage of being single longitudinal-mode lasers with a broad range of applications. Transverse mode control can be achieved to a certain extent at the fabrication level through the design of the active zone diameter (e.g. complex transverse structures can be observed in large diameter oxide confined VCSELs or, conversely, fundamental transverse mode emission in large area photonic crystal lasers [14

14. 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]

, 15

15. H. Liu, M. Yan, P. Shum, H. Ghafouri-Shiraz, and D. Liu, “Design and analysis of anti-resonant reflecting photonic crystal VCSEL lasers,” Opt. Express 12, 4269–4274 (2004). [CrossRef] [PubMed]

] or by changing the operating temperature to control the detuning between the gain maximum and the cavity resonance). In other kinds of lasers, multi-transverse mode operation has been reported in solid-state micro-chip lasers [16

16. Y. F. Chen and Y. P. Lan, “Formation of optical vortex lattices in solid-state microchip lasers: spontaneous transverse mode locking,” Phys. Rev. A 64, 063,807 (2001). [CrossRef]

] and in CO2 lasers with an intracavity lens [17

17. C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65, 3124–3127 (1990). [CrossRef] [PubMed]

, 18

18. D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, “Two-dimensional optical lattices in a CO2 laser,” Phys. Rev. A 46, 5955–5958 (1992). [CrossRef] [PubMed]

]. In the latter study, the cavity geometry plays a great role in the laser emission profile through the Fresnel number which controls the cavity aspect ratio and hence diffraction. A very special cavity design is represented by the self-imaging cavity [19

19. J. A. Arnaud, “Degenerate optical cavities,” Appl. Opt. 8, 189–196 (1969). [CrossRef] [PubMed]

], in which the ABCD propagation matrix is unity. In this singular cavity, diffraction due to the propagation inside the cavity is almost completely canceled and is equivalent, from the transverse field point of view, to that of a zero-length planar cavity : such a cavity configuration can theoretically sustain an infinite number of degenerate transverse modes. A self-imaging cavity configuration is not stable in practice and can only be approached. In spite of this, for a cavity with curved mirrors close to a confocal or more generally self-imaging configuration, as stated in [20

20. M. Le Berre, E. Ressayre, and A. Tallet, “Spirals and vortex lattices in quasi-self-imaging divide-by-three optical parametric oscillators,” Phys. Rev E 73, 036220 (2006). [CrossRef]

, 21

21. V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Pattern Formation and Localized Structures in Degenerate Optical Parametric Mixing,” Phys. Rev. Lett. 81, 2236–2239 (1998). [CrossRef]

], the Fourier mode basis is expected to be well adapted to the modes description.

2. Degenerate cavities

One of the simplest degenerate optical cavity is composed of a plane mirror, a lens, and a spherical mirror as considered in [19

19. J. A. Arnaud, “Degenerate optical cavities,” Appl. Opt. 8, 189–196 (1969). [CrossRef] [PubMed]

] and sketched on Fig. 1. The self-imaging positions between these three elements are:

d1*=f+f2R
(1)
L*=2f+f2R+R
(2)

where d*1 is the self-imaging distance between the plane mirror and the lens, L* is the total self-imaging cavity length, R is the end mirror radius of curvature and f the intracavity-lens focal length. We study such a cavity in a nearly degenerate configuration, i.e. where the cavity length or/and the distance between the lens and the plane mirror are close to the self-imaging distances.

Two parameters play an important role for transverse-mode selection. The first one is the Fresnel number N which controls the cavity aspect ratio and hence the number of transverse modes allowed in the cavity, and the second one is the transverse mode spacing ΔνT which governs the coupling strength between the modes of the active cavity and thus the influence of the nonlinearities on the dynamical behavior of the system [18

18. D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, “Two-dimensional optical lattices in a CO2 laser,” Phys. Rev. A 46, 5955–5958 (1992). [CrossRef] [PubMed]

]. N is evaluated by computing the effective Fresnel number Ne as the ratio of the area of the diffracting aperture that limits the system’s transverse dimension to the area of the fundamental Gaussian-mode along the cavity such that:

Ne=minz(d(z)w(z))2
(3)
Fig. 1. Sketch of the near self-imaging cavity composed of a half-VCSEL mirror, a spherical output mirror (radius of curvature R) and an intracavity lens of focal f.

where w(z) is the beam-waist of the fundamental mode along the propagation axis z and d(z) the size of the corresponding diffracting aperture. In our case, the aperture that limits the system is generally the size of the optical pump spot. Hence the Fresnel number is easily evaluated as the ratio of the square of the pump radius to the waist of the fundamental stable mode. In the degenerate configuration, this number can become very large but is then limited by the other optical elements. In our experiment, the Fresnel number can be changed either by moving the optical components of the cavity, by means of an iris inserted inside the cavity or by changing the pump beam diameter. It can be shown [8

8. F. T. Arecchi, S. Boccaletti, and P. L. Ramazza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999). [CrossRef]

] that the number of allowed transverse modes is proportional to N 2 e, whereas the maximum order of an allowed transverse mode in the cavity is proportional to Ne.

3. Experimental set-up and VECSEL structure

The experimental set-up is sketched on Fig. 3. The VECSEL structure is composed of a half-VCSEL closed by a spherical mirror with an intracavity lens L1. The half-VCSEL is grown by Metal Organic Chemical Vapor Deposition (MOCVD) and designed for lasing around 1010nm with an optical pump. It is composed of a high-reflectivity (27.5 pairs) AlAs/GaAs Bragg mirror. On top of the Bragg mirror is a 3.75 λ-thick cavity with five, 7nm-thick compressively strained InGaAs/GaAs quantum wells (QWs). The QWs are distributed such that the carrier densities remain almost equal in all QWs to counteract pump depletion. The number of QWs was optimized to obtain a low laser threshold and a large differential gain at 300 °K, with total cavity losses of about 1 to 1.5%. The half-VCSEL mirror is bonded onto a SiC substrate for better heat removal and lower thermal resistance of the structure. It is maintained at a constant temperature thanks to a Peltier cooler monitored by a control-loop. The intra-cavity lens L1 is anti-reflection coated and has a focal length of 38.1 mm. The spherical mirror has a 75mm radius of curvature and a reflectivity higher than 99% at 1020 nm. Optical pumping is achieved thanks to a high-power, fiber-coupled laser diode delivering up to 35W of optical power around 808nm. The output of the multimode fiber is focused onto the half-VCSEL with a telescope composed of two microscope objectives so as to form a 200µm diameter pump spot. The VECSEL output field and the image of the active zone are captured by two charge-coupled device cameras CCD1 and CCD2. These images will be referred to in the following as far-field and near-field of the laser, although these two planes are not strictly speaking Fourier transforms of one another. However they constitute obvious physical planes of interest since the near-field plane contains the gain medium and acts as the transverse-field limiting element and in the far field, light emitted at the laser output propagates without noticeable change of structure in its transverse profile. The total intensity of the laser is detected thanks to a 90ps rise-time avalanche photodiode (APD) and analyzed on a RF-spectrum analyzer (SA) or a 6GHz bandwidth sampling oscilloscope.

Fig. 2. Plot of the fundamental stable beam-waist size versus d 1 and L=d 1+d 2 for a cavity with f=3.81cm and R=7.5cm. The S point corresponds to a self-imaging cavity.

4. Experimental results

Images recorded at different positions of the intracavity lens and for a fixed total cavity length are displayed on figs.4,5. The pump power is slightly above laser threshold, but we do not note a substantial qualitative change in the emitted spatial structure when the pump is varied within the (limited) available range of optical powers. Let us first focus on the far-field images. As d 1 decreases, the output field evolves from low-order, on-axis patterns to an off-axis, annular structure with azimuthal modulations. This corresponds to a decrease in the diffraction length and hence to passing from a low-Fresnel number to a high-Fresnel number configuration. At low Fresnel numbers, a small order transverse mode appears (typically a Gaussian mode or a doughnut mode as in the two images in the first two columns of Fig. 4). The near-field in this case is very similar in shape to the far-field. When the Fresnel number increases, the near and far-fields display different structures. Whereas the far-field displays an annular structure whose diameter grows with the Fresnel-number, the near field shows a complex structure composed of bright spots. In the far field (output of the VECSEL), off-axis emission is favored when the Fresnel number is high. On-axis emission is then totally suppressed. This behavior is similar to what has been predicted from numerical modeling of the mode distribution in a gain guided VCSEL by [23

23. W. Nakwaski and R. Sarzala, “Transverse modes in gain-guided vertical-cavity surface-emitting lasers,” Opt. Comm. 148, 63–69 (1998). [CrossRef]

], and experimentally confirmed in broad area VCSELs and in oxide confined VCSELs by [24

24. C. Degen, I. Fisher, and W. Elsässer, “Transverse modes in oxide confined VCSELs: Influence of pump profile, spatial hole burning, and thermal effects,” Opt. Express 5, 38–47 (1999). [CrossRef] [PubMed]

, 13

13. T. T. Ackemann, S. Barland, M. Cara, S. Balle, R. Jäger, M. Grabherr, M. Miller, and K. J. Ebeling, “Spatial mode structure of bottom-emitting broad-area vertical-cavity surface-emitting lasers,” J. Opt. B: Quantum Semiclass. 2, 406–412 (2000). [CrossRef]

]. However we are dealing here with an extended cavity with many longitudinal modes. On-axis emission from the cavity modes whose frequency is higher than the one of the gain maximum always compete with off-axis emission of the modes on the other part of the gain. However, since these modes have higher gain, they seem to dominate and suppress on-axis modes. In this context, the annular structure may be understood in terms of a superposition of plane, tilted waves that are equally possible on a whole range of orientations, giving rise to the annular structure. This interpretation is strengthened when looking at the same kind of situation but for a misaligned system (Fig. 5). The rotational symmetry of the system no-longer holds and we recover field structures observed in systems with square boundary conditions (see e.g. [11

11. S. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern Formation in the Transverse Section of a Laser with a Large Fresnel Number,” Phys. Rev. Lett. 82, 1434 (1999). [CrossRef]

]). We are thus able to completely monitor the passage of a system best described in terms of Gaussian transverse modes to a system best described in terms of plane-wave (Fourier) modes. As for the near-field images, as the lens is moved closer to the gain section, we notice that the field structure becomes increasingly complex and contains finer and finer structures.

Fig. 3. Experimental set-up. SM: spherical mirror; CS: Cube splitter; M: Mirror; L1,L2,L3: Lenses; OP: Optical pump; SA: Spectrum analyzer; APD: avalanche photo diode. CCD1,2: CCD cameras.

The same scenario occurs when moving the mirror alone and letting the lens position fixed. Suppose by example that the lens is at the self-imaging position. As the self-imaging cavity is approached (e.g. by decreasing the total cavity length), a similar annular structure whose diameter increases is formed. Emission stops close to the self-imaging point for several reasons. First of all, the self-imaging configuration is only marginally stable and any small deviation from it make the cavity unstable. Hence it is a point that in practice one cannot reach with a laser. Second, since off-axis emission occurs at an increasing angle, the intracavity lens diameter will ultimately limit the possible propagation angle of light in the cavity. When this critical angle is reached, emission stops as we could verify.

Fig. 4. Near-field (upper row) and far-field (lower row) images of the laser for different positions of the intracavity lens : 5.323, 5.306, 5.297 and for a fixed cavity length (⋍18.6 cm). The field of view of the bottom row images is 3.2°.
Fig. 5. Same as Fig. 4 for an intracavity-lens position: 5.246, 5.132cm, 5.087cm. Last image on the right is for a slightly misaligned cavity.

5. Spectral analysis

Fig. 6. Left figure (a) : map of RF-spectra of the total laser intensity for L=18.9cm versus the lens position d 1. The right figure (b) is a zoom around the central peak.
Fig. 7. Beat spectra of the cold cavity modes when varying the lens position. Ten transverse modes are taken into account in this simulation. The beat frequencies are plotted rescaled to the free spectral range spacing of the longitudinal modes ν 0.

6. Conclusion

In conclusion we have shown the transformation and the selection of the transverse structure emitted by a VECSEL with an intracavity lens : from a Gaussian transverse mode structure the field evolves toward a configuration best described in terms of a combination of Fourier modes. This feature is reminiscent of the high-Fresnel number configuration of the system with the novelty here that the system is also highly multimode. Despite this, clear structures are formed with an ordered RF spectrum. A theoretical description of the system is complex and will be undertaken. We note that in a three-mode quasi-self-imaging system, some recent numerical modeling [20

20. M. Le Berre, E. Ressayre, and A. Tallet, “Spirals and vortex lattices in quasi-self-imaging divide-by-three optical parametric oscillators,” Phys. Rev E 73, 036220 (2006). [CrossRef]

] taking into account the full diffraction integral in the cavity exhibited patterns similar to those we obtained. This is encouraging since it underlines the generality of the results presented here and also shows that it may be feasible to model our system with a limited number of longitudinal modes at least as far as transverse patterns are concerned.

This work has been carried out in the framework of the FunFACS European project (www.funfacs.org) and benefited also of the support from the Région Île-de-France.

References and links

1.

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424, 831–838 (2003). [CrossRef] [PubMed]

2.

U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429, 67–120 (2006). [CrossRef]

3.

N. N. Rosanov and N. V. Fedorov, “Diffraction switching waves and autosolitons in a saturable-absorber laser,” Optik. Spectrosk. 72, 1394 (1992).

4.

V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Spatial soliton laser: Localized structures in a laser with a saturable absorber in a self-imaging resonator,” Phys. Rev. A 56, 1582 (1997). [CrossRef]

5.

M. Bache, F. Prati, G. Tissoni, R. Kheradmand, L. Lugiato, I. Protsenko, and M. Brambilla, “Cavity soliton laser based on VCSEL with saturable absorber,” Appl. Phys. B pp. 913–920 (2005). [CrossRef]

6.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödel, M. Miller, and R. Jäger, “Cavity solitons work as pixels in semiconductors,” Nature 419, 699–702 (2002). [CrossRef] [PubMed]

7.

S. Barbay, Y. Ménesguen, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, “Incoherent and coherent writing and erasure of cavity solitons in an optically pumped semiconductor amplifier,” Opt. Lett. 31, 1504–1506 (2006). [CrossRef] [PubMed]

8.

F. T. Arecchi, S. Boccaletti, and P. L. Ramazza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999). [CrossRef]

9.

C. Chang-Hasnain, M. Orenstein, A. Von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 57, 218–221 (1990). [CrossRef]

10.

J. Scheuer and M. Orenstein, “Optical Vortices Crystals: Spontaneous Generation in Nonlinear Semiconductor Microcavities,” Science 285(5425), 230–233 (1999). [CrossRef] [PubMed]

11.

S. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, “Pattern Formation in the Transverse Section of a Laser with a Large Fresnel Number,” Phys. Rev. Lett. 82, 1434 (1999). [CrossRef]

12.

I. V. Babushkin, N. A. Loiko, and T. Ackemann, “Eigenmodes and symmetry selection mechanisms in circular large-aperture vertical-cavity surface-emitting lasers,” Phys. Rev. E 69, 066,205 (2004). [CrossRef]

13.

T. T. Ackemann, S. Barland, M. Cara, S. Balle, R. Jäger, M. Grabherr, M. Miller, and K. J. Ebeling, “Spatial mode structure of bottom-emitting broad-area vertical-cavity surface-emitting lasers,” J. Opt. B: Quantum Semiclass. 2, 406–412 (2000). [CrossRef]

14.

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]

15.

H. Liu, M. Yan, P. Shum, H. Ghafouri-Shiraz, and D. Liu, “Design and analysis of anti-resonant reflecting photonic crystal VCSEL lasers,” Opt. Express 12, 4269–4274 (2004). [CrossRef] [PubMed]

16.

Y. F. Chen and Y. P. Lan, “Formation of optical vortex lattices in solid-state microchip lasers: spontaneous transverse mode locking,” Phys. Rev. A 64, 063,807 (2001). [CrossRef]

17.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65, 3124–3127 (1990). [CrossRef] [PubMed]

18.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, “Two-dimensional optical lattices in a CO2 laser,” Phys. Rev. A 46, 5955–5958 (1992). [CrossRef] [PubMed]

19.

J. A. Arnaud, “Degenerate optical cavities,” Appl. Opt. 8, 189–196 (1969). [CrossRef] [PubMed]

20.

M. Le Berre, E. Ressayre, and A. Tallet, “Spirals and vortex lattices in quasi-self-imaging divide-by-three optical parametric oscillators,” Phys. Rev E 73, 036220 (2006). [CrossRef]

21.

V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Pattern Formation and Localized Structures in Degenerate Optical Parametric Mixing,” Phys. Rev. Lett. 81, 2236–2239 (1998). [CrossRef]

22.

S. Gigan, L. Lopez, N. Treps, A. Maitre, and C. Fabre, “Image transmission through a stable paraxial cavity,” Phys. Rev. A 72, 023,804 (2005). [CrossRef]

23.

W. Nakwaski and R. Sarzala, “Transverse modes in gain-guided vertical-cavity surface-emitting lasers,” Opt. Comm. 148, 63–69 (1998). [CrossRef]

24.

C. Degen, I. Fisher, and W. Elsässer, “Transverse modes in oxide confined VCSELs: Influence of pump profile, spatial hole burning, and thermal effects,” Opt. Express 5, 38–47 (1999). [CrossRef] [PubMed]

25.

A. E. Siegman, “Lasers,” University Science Books, (1986).

OCIS Codes
(140.3410) Lasers and laser optics : Laser resonators
(140.5960) Lasers and laser optics : Semiconductor lasers
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(140.7270) Lasers and laser optics : Vertical emitting lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: February 8, 2008
Revised Manuscript: April 11, 2008
Manuscript Accepted: May 17, 2008
Published: June 13, 2008

Citation
X. Hachair, S. Barbay, T. Elsass, I. Sagnes, and R. Kuszelewicz, "Transverse spatial structure of a high Fresnel number Vertical External Cavity Surface Emitting Laser," Opt. Express 16, 9519-9527 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-13-9519


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. U. Keller, "Recent developments in compact ultrafast lasers," Nature 424, 831-838 (2003). [CrossRef] [PubMed]
  2. U. Keller and A. C. Tropper, "Passively modelocked surface-emitting semiconductor lasers," Phys. Rep. 429, 67-120 (2006). [CrossRef]
  3. N. N. Rosanov and N. V. Fedorov, "Diffraction switching waves and autosolitons in a saturable-absorber laser," Optik.Spectrosk. 72, 1394 (1992).
  4. V. B. Taranenko, K. Staliunas, and C. O. Weiss, "Spatial soliton laser: Localized structures in a laser with a saturable absorber in a self-imaging resonator," Phys. Rev. A 56, 1582 (1997). [CrossRef]
  5. M. Bache, F. Prati, G. Tissoni, R. Kheradmand, L. Lugiato, I. Protsenko, and M. Brambilla, "Cavity soliton laser based on VCSEL with saturable absorber," Appl. Phys. B pp. 913-920 (2005). [CrossRef]
  6. S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödel, M. Miller, and R. Jäger, "Cavity solitons work as pixels in semiconductors," Nature 419, 699-702 (2002). [CrossRef] [PubMed]
  7. S. Barbay, Y. Ménesguen, X. Hachair, L. Leroy, I. Sagnes, and R. Kuszelewicz, "Incoherent and coherent writing and erasure of cavity solitons in an optically pumped semiconductor amplifier," Opt. Lett. 31, 1504-1506 (2006). [CrossRef] [PubMed]
  8. F. T. Arecchi, S. Boccaletti, and P. L. Ramazza, "Pattern formation and competition in nonlinear optics," Phys. Rep. 318, 1-83 (1999). [CrossRef]
  9. C. Chang-Hasnain, M. Orenstein, A. Von Lehmen, L. T. Florez, J. P. Harbison, and N. G. Stoffel, "Transverse mode characteristics of vertical cavity surface-emitting lasers," Appl. Phys. Lett. 57, 218-221 (1990). [CrossRef]
  10. J. Scheuer and M. Orenstein, "Optical Vortices Crystals: Spontaneous Generation in Nonlinear Semiconductor Microcavities," Science 285(5425), 230-233 (1999). [CrossRef] [PubMed]
  11. S. Hegarty, G. Huyet, J. G. McInerney, and K. D. Choquette, "Pattern Formation in the Transverse Section of a Laser with a Large Fresnel Number," Phys. Rev. Lett. 82, 1434 (1999). [CrossRef]
  12. I. V. Babushkin, N. A. Loiko, and T. Ackemann, "Eigenmodes and symmetry selection mechanisms in circular large-aperture vertical-cavity surface-emitting lasers," Phys. Rev. E 69, 066,205 (2004). [CrossRef]
  13. T. T. Ackemann, S. Barland, M. Cara, S. Balle, R. Jäger,M. Grabherr, M. Miller, and K. J. Ebeling, "Spatial mode structure of bottom-emitting broad-area vertical-cavity surface-emitting lasers," J. Opt. B: Quantum Semiclass. 2, 406-412 (2000). [CrossRef]
  14. D. Ohnishi, T. Okano, M. Imada, and S. Noda, "Room temperature continuous wave operation of a surfaceemitting two-dimensional photonic crystal diode laser," Opt. Express 12, 1562-1568 (2004). [CrossRef] [PubMed]
  15. H. Liu, M. Yan, P. Shum, H. Ghafouri-Shiraz, and D. Liu, "Design and analysis of anti-resonant reflecting photonic crystal VCSEL lasers," Opt. Express 12, 4269-4274 (2004). [CrossRef] [PubMed]
  16. Y. F. Chen and Y. P. Lan, "Formation of optical vortex lattices in solid-state microchip lasers: spontaneous transverse mode locking," Phys. Rev. A 64, 063,807 (2001). [CrossRef]
  17. C. Green, G. B. Mindlin, E. J. D???Angelo, H. G. Solari, and J. R. Tredicce, "Spontaneous symmetry breaking in a laser: The experimental side," Phys. Rev. Lett. 65, 3124-3127 (1990). [CrossRef] [PubMed]
  18. D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, "Two-dimensional optical lattices in a CO2 laser," Phys. Rev. A 46, 5955-5958 (1992). [CrossRef] [PubMed]
  19. J. A. Arnaud, "Degenerate optical cavities," Appl. Opt. 8, 189-196 (1969). [CrossRef] [PubMed]
  20. M. Le Berre, E. Ressayre, and A. Tallet, "Spirals and vortex lattices in quasi-self-imaging divide-by-three optical parametric oscillators," Phys. Rev E 73, 036220 (2006). [CrossRef]
  21. V. B. Taranenko, K. Staliunas, and C. O. Weiss, "Pattern Formation and Localized Structures in Degenerate Optical Parametric Mixing," Phys. Rev. Lett. 81, 2236-2239 (1998). [CrossRef]
  22. S. Gigan, L. Lopez, N. Treps, A. Maitre, and C. Fabre, "Image transmission through a stable paraxial cavity," Phys. Rev. A 72, 023,804 (2005). [CrossRef]
  23. W. Nakwaski and R. Sarzala, "Transverse modes in gain-guided vertical-cavity surface-emitting lasers," Opt. Comm. 148, 63-69 (1998). [CrossRef]
  24. C. Degen, I. Fisher, and W. Elsässer, "Transverse modes in oxide confined VCSELs: Influence of pump profile, spatial hole burning, and thermal effects," Opt. Express 5, 38-47 (1999). [CrossRef] [PubMed]
  25. A. E. Siegman, "Lasers," University Science Books, (1986).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited