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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 25 — Dec. 10, 2007
  • pp: 17392–17400
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Light beam output from diamond-shaped total-internal reflection modes by using intracavity air gaps

Takehiro Fukushima, Susumu Shinohara, and Takahisa Harayama  »View Author Affiliations


Optics Express, Vol. 15, Issue 25, pp. 17392-17400 (2007)
http://dx.doi.org/10.1364/OE.15.017392


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Abstract

We propose a novel method for extracting light beams from diamond-shaped total-internal reflection modes in two-dimensional microcavity laser diodes by the use of intracavity air gaps. By fabricating such a laser diode, we experimentally demonstrate that the direction and longitudinal mode spacing of the output beams are in good accordance with theoretical calculations.

© 2007 Optical Society of America

1. Introduction

Two-dimensional microcavity lasers such as microdisk lasers and microcylinder lasers have received much attention because they can confine light by total internal reflection, and thus serve as low-threshold lasers [1

1. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992). [CrossRef]

3

3. R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996). [CrossRef]

]. Fiber taper waveguides [4

4. T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74, 051802-1–051802-4 (2006). [CrossRef]

,5

5. K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14, 1094–1105 (2006). [CrossRef] [PubMed]

] and linear waveguides [6

6. S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photon. Technol. Lett. 15, 1330–1332 (2003). [CrossRef]

,7

7. J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. D. Cioccio, J.-M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007). [CrossRef] [PubMed]

] are commonly used for extracting light output from microcavity lasers. However, they require precise alignment of the waveguide or sophisticated fabrication processes to achieve efficient evanescent coupling between the microcavity laser and the waveguide. One method that has been proposed to overcome these problems is the introduction of asymmetry to the cavity shape in order to obtain directional emission from the laser cavities [8

8. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997). [CrossRef]

,9

9. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998). [CrossRef] [PubMed]

]. These so-called asymmetric resonant cavities (ARCs), which are smooth deformations of a circular cavity, generate directional emissions by sacrificing the Q factor. Also, it has been proposed to introduce defects and air holes into a perfectly circular cavity to extract directional light output [10

10. V. M. Apalkov and M. E. Raikh, “Directional emission from a microdisk resonator with a linear defect,” Phys. Rev. B 70, 195317-1-195317-6 (2004). [CrossRef]

,11

11. J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73, 031802-1-031802-4 (2006). [CrossRef]

]. Whereas the introduction of such asymmetricities has shown to yield relatively intense and directional light output, it is not clear whether it is possible to obtain the desired quality of light output by the introduction of the asymmetricities.

In this paper, we propose a novel method for extracting well-controlled light output from a high-Q mode in a two-dimensional (2-D) microcavity laser; we employ intracavity air gaps to partially reflect light beams confined inside the cavity by total internal reflection. We designed the shape of the p-electrode contact such that only high-Q modes are excited. Such partial spatial pumping has been demonstrated to excite specific desired modes [12

12. T. Fukushima and T. Harayama, “Stadium and quasi-stadium laser diodes,” IEEE Sel. Top. Quantum Electron. 10, 1039–1051 (2004). [CrossRef]

,13

13. T. Fukushima, T. Harayama, T. Miyasaka, and P. O. Vaccaro, “Morphological dependence of lasing modes in two-dimensional quasi-stadium laser diodes,” J. Opt. Soc. Am. B 21, 935–943 (2004). [CrossRef]

]. In this study, we apply such partial pumping to a high-Q cavity mode confined in the cavity by total internal reflection. In order to extract light output from this high-Q mode, we inserted air gaps inside the cavity. This cavity design enables us to control the direction of light output by varying the angles of the air gaps and the sidewall mirrors. We demonstrate that a 2-D microcavity with intracavity air gaps can be used to output light beams having tailored optical properties.

2. Device design

Figures 1(a)-(c) schematically show the structure of a 2-D microcavity laser diode with intracavity air gaps. The laser diode is fabricated by applying a reactive-ion-etching technique to a graded-index (GRIN) separate-confinement-heterostructure (SCH) single-quantum-well (SQW) GaAs/AlGaAs structure that was grown by metal organic chemical vapor deposition. The laser cavity consists of four curved mirrors. The four corner sections are unpumped to suppress undesired lasing modes and to absorb stray light. Figure 1(d) shows a plot of a diamond-shaped cavity mode; it was numerically calculated using a Gaussian-optical approach [14

14. H. E. Türeci, H. G. L. Schwefel, A. D. Stone, and E. E. Narimanov, “Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities,” Opt. Express 10, 752–776 (2002). [PubMed]

]. The ray trajectory corresponding to this cavity mode strikes the curved mirror at an incident angle of 45°, which is larger than the critical angle (approximately 17.6°). Thus, the optical beams are confined inside the cavity by total internal reflection. In order to excite this diamond-shaped mode, the p-cap layer and the p-electrode contact area were patterned along the mode (see Figs. 1(b) and (c)). Moreover, we inserted air gaps in the middle of the straight-line segments (see Fig. 1(b)) so that the optical beams are partially extracted from the diamond-shaped mode. The p-cap layer and the p-contact area are also formed along the extracted beams to amplify the extracted beams. The p-electrode contact area is coated with the p-electrode metal for current injection. The important device parameters are listed in Table 1.

Next, we explain the design of the air gaps. Figure 2(a) shows an enlargement of region A that is shown in Fig. 1(b). The ray transmitted through the air gap is translated by an amount ΔL, which is given by

ΔL=dcosβ[sin(π4α+β)cos(π4α+β)],
(1)

where d is the width of the air gap, α is the incident angle, β=sin-1(n eff sin α) is the angle of refraction, n eff is the effective refractive index of the laser diode and is determined to be 3.3 from the layer structure of the laser diode. To compensate for this translation, the cavity length is longer than the cavity width by an amount 2ΔL in our design (see Fig. 1(b)). It is speculated that the incident beam undergoes multiple reflections inside the air gap. In this case, the transmittance is maximized and the reflectance is minimized at a wavelength of λ m=2d cosβ/m, where m is an integer. We set d=1.35 µm and m=3, so that the transmittance is maximized at the gain peak wavelength (approximately 862 nm) and d is larger than 1 µm. Figure 3 shows the filtering characteristics of the air gap for p-polarization. Here, N is the number of beams used in the calculation. In the ideal case, namely N=∞, the reflectance becomes zero and the transmittance becomes unity at the wavelength λ m. However, diffraction in the air gap and translation of the ray trajectory due to multiple reflections cause significant coupling loss. Accordingly, N is restricted to a small value so that the reflectance increases and the transmittance decreases.

Fig. 1. Schematic diagram of 2-D microcavity laser diode having intracavity air gaps; (a) device structure; (b) definition of cavity parameters and cap layer shape; (c) contact area shape and electrode metal shape. (d) Diamond-shaped total internal reflection mode calculated using a Gaussian-optical approach [14].

Table 1. Designed values of device parameters

table-icon
View This Table
Fig. 2. Enlarged diagrams of (a) the air gap (Region A) and (b) the output port (Region B). The red lines indicate ray trajectories. The green lines are normal to the interfaces.
Fig. 3. Calculated filtering characteristics of air gap; (a) reflectance and (b) transmittance.

Finally, we explain the orientations of the output beams. Figure 2(b) shows an enlargement of region B shown in Fig. 1(b). The beams propagating along the diamond-shaped trajectory in the clockwise and the counter-clockwise directions are partially reflected at the air gaps. The reflected beams are then transmitted through the sidewall mirrors. The direction θ of the output beams is given by

θ=πφsin1[neffsin(3π4+2αφ)],
(2)

where φ is the angle of the sidewall mirror as shown in Fig. 2(b). The output direction can thus be controlled by the incident angle α and the angle φ of the sidewall mirror. We set the values of these parameters so that θ is approximately zero (α=5° and φ=132° yields θ=0.07°).

3. Fabrication

Figure 4 shows a schematic diagram of the fabrication process for the 2-D microcavity laser diode having intracavity air gaps. The laser diode was fabricated from a metal organic chemical vapor deposition grown material with a 1.5-µm-thick n-Al0.5Ga0.5As lower cladding layer, a 0.2-µm-thick n-AlxGa1-xAs (x=0.5-0.2) graded SCH layer, a 10-nm-thick GaAs SQW layer, a 0.2-µm-thick p-AlxGa1-xAs (x=0.2-0.5) graded SCH layer, a 1.5-µm-thick p-Al0.5Ga0.5As upper cladding layer and a 0.2-µm-thick p-GaAs cap layer.

First, the cap layer was removed everywhere except along the ray trajectory. A 500-nm SiO2 layer was then deposited on the epitaxial wafer. This layer was used as an etching mask and as the insulation between the p-GaAs cap layer and the p-electrode metal outside the contact area. Following that, air gaps were formed deep in the lower cladding layer in order to ensure sufficient reflection. The geometry of the laser cavity was defined by using a 5:1 projection reduction i-line lithography system and a reactive ion etching technique. The contact window was then etched through the SiO2 layer along the ray trajectory, the p-electrode metal AuZnNi/Au was evaporated, and the laser diode was annealed to obtain good ohmic contact. The p-electrode metal was formed over the contact area and part of the surrounding SiO2 layer using a liftoff process. After lapping and polishing the n-GaAs substrate to 100-µm thickness, it was coated with an n-electrode metal AuGeNi/Au and the laser diode was annealed.

Fig. 4. Laser diode fabrication process: (a) etching of p-cap layer; (b) deposition of SiO2 film and formation of air gaps and 2-D laser cavity; (c) formation of p-electrode; (d) lapping, polishing, and formation of n-electrode.

The laser diode was mounted on an AuSn metallized AlN heat sink with p-side up for continuous wave operation at room temperature. Figure 5 shows a scanning electron microscope image of the laser diode. Smooth and vertically etched mirror facets were obtained. Moreover the geometry of the laser cavity was very well defined.

Fig. 5. Scanning electron microscope images of the 2-D laser diode: (a) general view; (b) enlargement of curved mirror; (c) enlargement of air gap.

4. Experiment

The laser diode was tested under continuous wave operation at 25°C. We measured its fundamental lasing characteristics, namely, optical output power as a function of injection current, far-field emission pattern, and lasing spectrum.

Figure 6 shows the optical output power plotted as a function of injection current. Output emitted from a single output port was measured using an optical power meter. The threshold current was evaluated to be 349 mA. Although the laser diode exhibits a high threshold current, a clear onset of lasing was confirmed.

Figure 7 shows the far-field emission patterns of the laser diode at an output power of 8 mW. The laser diode exhibited highly directional emission at an angle of approximately 0°. The far-field emission pattern also exhibits a fringe pattern can be seen in Fig. 7(b). The average angular spacing of the fringe peaks was evaluated to be 0.78°.

Finally the lasing spectrum at the output power 8 mW is shown in Fig. 8. Fig. 8(a) shows that the laser diode lases at 868.8 nm. In Fig. 8(b), we show a magnification of the spectrum data for a narrow wavelength range far from the main peak at 868.8 nm. Fig. 8(b) reveals the longitudinal mode spacing; the average mode spacing of the nine longitudinal modes can be evaluated as 0.11 nm. Since the width of the lasing peak at 868.8 nm is narrower than this mode spacing, we conclude that the peak at 868.8 nm corresponds to a single longitudinal mode.

Fig. 6. Light output power versus injection current characteristics of the 2-D laser diode.
Fig. 7. Far-field emission pattern from the output port: (a) wide angular range; (b) narrow angular range.
Fig. 8. Lasing spectrum of the 2-D laser diode: (a) wide wavelength range; (b) narrow wavelength range far from the main peak at λ=868.8 nm.

5. Discussion

The laser diode exhibited a considerably high threshold current. We conjecture that the increase in the threshold current was mainly caused by two reasons. One reason is the transmission loss at the air gap. As discussed in Section 2, the diffraction of the optical beams in the air gap and translation of the ray trajectory due to multiple reflection result in considerable transmission loss (coupling loss). This loss could be reduced by decreasing the number of air gaps. The other reason is current spreading in the cap layer and upper cladding layer. In our design we set the width W of the cap layer area to 40 µm; this value has not been optimized yet. Current spreading may be suppressed by narrowing the width of the cap layer area. We expect that it will be possible to reduce the threshold current by optimizing the device structure.

In our design the output beam is emitted at an angle of approximately 0°(±0.07°). We confirmed that this direction of the output beam agrees very well with the theoretical value. Next, we discuss the fine fringe pattern in the far-field emission pattern. Assuming that the fringe pattern is caused by the interference between the two beams transmitted through the sidewall mirrors, we derive the theoretically fringe spacing. Figure 9 shows the relationship between the angular difference Δθ of the 0th order and 1st order fringe peaks and the optical path difference Δl=l 2-l 1=λ of the two output beams. Here we assumed that the 0th order fringe peak appears at Δl=0. (x m, y m) are the coordinates of the edge of the curved end mirror and are given by

xm=L2+RR2(Wm2)2,
(3)
ym=Wm2.
(4)
Fig. 9. Relationship between the spacing Δθ of the interference fringe peaks and optical path difference Δl between two output beams.

(x c,y c) are the coordinates of the point of intersection of the sidewall mirror and the trajectory of the ray, and it is given by

xc=xmtan(φπ2)(L4)tan(π42α)+ymL4tan(φπ2)+tan(π42α),
(5)
yc=(xm+L4)tan(φπ2)tan(π42α)+(L4)tan(φπ2)+ymtan(π42α)tan(φπ2)+tan(π42α).
(6)

In the case of the far-field emission pattern, l 1 and l 2 are much longer than 2y c. Therefore, Δl can be expressed by Δl≈2y c sin Δθ. Accordingly, Δθ can be expressed by

Δθsin1[λ(2yc)],
(7)

where λ is the lasing wavelength. By setting λ=868.8 nm, Δθ can be estimated to be Δθ=0.779°. This theoretically derived fringe spacing agrees excellently with the experimentally observed fringe spacing of 0.78°. We thus conclude that the fringe pattern was caused by interference between the two output beams.

Finally, we discuss the lasing wavelength and the longitudinal mode spacing. The lasing wavelength was approximately 7 nm longer than the designed maximum transmission wavelength (approximately 862 nm) of the air gaps. It is speculated that this wavelength shift was caused by a shift of the gain peak due to thermal effects. The finesse of the air gaps is relatively small, as shown in Fig. 3. Accordingly, the lasing wavelength is also affected by the gain profile. The derivation of longitudinal mode spacing for conventional Fabry-Perot laser diodes is given in ref. [15

15. H. C. Casey Jr. and M. B. Panish, Heterostructure Lasers (Academic Press, New York, NY, 1978).

]. We extended the derivation for laser diodes having air gaps. The longitudinal mode spacing of our device can be expressed by

Δλ=λ2neffLs[1(λneff)(dneffdλ)]+La,
(8)

where L s is the path length in the laser diode for one round trip and is given by

Ls=42{L2[dcos(π4α+β)](cosβ)}.
(9)

On the other hand, L a is the path length in the air gaps for one round trip and is given by

La=4dcosβ.
(10)

By using-1.0×104 cm-1 [15

15. H. C. Casey Jr. and M. B. Panish, Heterostructure Lasers (Academic Press, New York, NY, 1978).

] for the quantity dn eff/ and λ=867 nm, the longitudinal mode spacing is estimated to be 0.106 nm. This value agrees with the observed mode spacing 0.11 nm. This provides evidence that the diamond-shaped modes depicted in Fig. 1(d) are excited in the laser diode even when air gaps are present.

6. Conclusion

We proposed and demonstrated a novel method for extracting light beams from total internal reflection modes in a 2-D microcavity laser diode by the use of intracavity air gaps. By using a projection reduction i-line lithography system and a reactive ion etching technique, we fabricated fine microcavity structure with air gaps. In experiments, we succeeded in obtaining output light beams in the direction that we had designed. Moreover, we confirmed that the longitudinal mode spacing and the fringe pattern formed by the interference of the two output beams are in good agreement with theoretical estimates. Our cavity design enables us to control the direction of output beams by varying the angles of air gaps and sidewall mirrors, thus providing a new method for obtaining light beams with tailored properties from a 2-D microcavity laser.

Acknowledgments

The research performed at ATR was supported in part by the National Institute of Information and Communications Technology of Japan. The research performed at Okayama Prefectural University was supported in part by the Ministry of Education, Culture, Sports, Science and Technology under Grant-in-Aid 19560037. The laser diodes were partially fabricated at NTT Advance Technology Corporation.

References and links

1.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992). [CrossRef]

2.

A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, “Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes,” Appl. Phys. Lett. 62, 2021–2023 (1993). [CrossRef]

3.

R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996). [CrossRef]

4.

T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74, 051802-1–051802-4 (2006). [CrossRef]

5.

K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14, 1094–1105 (2006). [CrossRef] [PubMed]

6.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photon. Technol. Lett. 15, 1330–1332 (2003). [CrossRef]

7.

J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. D. Cioccio, J.-M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007). [CrossRef] [PubMed]

8.

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997). [CrossRef]

9.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998). [CrossRef] [PubMed]

10.

V. M. Apalkov and M. E. Raikh, “Directional emission from a microdisk resonator with a linear defect,” Phys. Rev. B 70, 195317-1-195317-6 (2004). [CrossRef]

11.

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73, 031802-1-031802-4 (2006). [CrossRef]

12.

T. Fukushima and T. Harayama, “Stadium and quasi-stadium laser diodes,” IEEE Sel. Top. Quantum Electron. 10, 1039–1051 (2004). [CrossRef]

13.

T. Fukushima, T. Harayama, T. Miyasaka, and P. O. Vaccaro, “Morphological dependence of lasing modes in two-dimensional quasi-stadium laser diodes,” J. Opt. Soc. Am. B 21, 935–943 (2004). [CrossRef]

14.

H. E. Türeci, H. G. L. Schwefel, A. D. Stone, and E. E. Narimanov, “Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities,” Opt. Express 10, 752–776 (2002). [PubMed]

15.

H. C. Casey Jr. and M. B. Panish, Heterostructure Lasers (Academic Press, New York, NY, 1978).

OCIS Codes
(140.2020) Lasers and laser optics : Diode lasers
(140.3410) Lasers and laser optics : Laser resonators
(140.3945) Lasers and laser optics : Microcavities

ToC Category:
Novel Concepts and Theory

History
Original Manuscript: September 24, 2007
Revised Manuscript: October 27, 2007
Manuscript Accepted: November 22, 2007
Published: December 10, 2007

Virtual Issues
Physics and Applications of Microresonators (2007) Optics Express

Citation
Takehiro Fukushima, Susumu Shinohara, and Takahisa Harayama, "Light beam output from diamond-shaped total-internal reflection modes by using intracavity air gaps," Opt. Express 15, 17392-17400 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-17392


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References

  1. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992). [CrossRef]
  2. A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993). [CrossRef]
  3. R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996). [CrossRef]
  4. T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, "Demonstration of an erbium-doped microdisk laser on a silicon chip," Phys. Rev. A 74, 051802-1-051802-4 (2006). [CrossRef]
  5. K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, "Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots," Opt. Express 14, 1094-1105 (2006). [CrossRef] [PubMed]
  6. S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, "Microdisk lasers vertically coupled to output waveguides," IEEE Photon. Technol. Lett. 15, 1330-1332 (2003). [CrossRef]
  7. J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. D. Cioccio, J.-M. Fedeli, C. Lagahe, and R. Baets, "Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on -insulator waveguide circuit," Opt. Express 15, 6744-6749 (2007). [CrossRef] [PubMed]
  8. J. U. Nöckel and A. D. Stone, "Ray and wave chaos in asymmetric resonant optical cavities," Nature 385, 45-47 (1997). [CrossRef]
  9. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998). [CrossRef] [PubMed]
  10. V. M. Apalkov and M. E. Raikh, "Directional emission from a microdisk resonator with a linear defect," Phys. Rev. B 70, 195317-1-195317-6 (2004). [CrossRef]
  11. J. Wiersig and M. Hentschel, "Unidirectional light emission from high-Q modes in optical microcavities," Phys. Rev. A 73, 031802-1-031802-4 (2006). [CrossRef]
  12. T. Fukushima and T. Harayama, "Stadium and quasi-stadium laser diodes," IEEE Sel. Top. Quantum Electron. 10, 1039-1051 (2004). [CrossRef]
  13. T. Fukushima, T. Harayama, T. Miyasaka, and P. O. Vaccaro, "Morphological dependence of lasing modes in two-dimensional quasi-stadium laser diodes," J. Opt. Soc. Am. B 21, 935-943 (2004). [CrossRef]
  14. H. E. Türeci, H. G. L. Schwefel, A. D. Stone, and E. E. Narimanov, "Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities," Opt. Express 10, 752-776 (2002). [PubMed]
  15. H. C. CaseyJr. and M. B. Panish, Heterostructure Lasers (Academic Press, New York, NY, 1978).

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