## A simple perturbative analysis for fast design of an electrically pumped micro-disk laser

Optics Express, Vol. 17, Issue 1, pp. 70-79 (2009)

http://dx.doi.org/10.1364/OE.17.000070

Acrobat PDF (236 KB)

### Abstract

A perturbative analysis is proposed to estimate optical losses for electrically pumped micro-disk lasers. The optical field interaction with the electrical contacts and the optimization of their implementation is investigated. Our model shows a good agreement with 3D Finite Difference Time Domain (FDTD) computation and can be used for designing contacts for thin micro-disks, with a considerably reduced calculation time.We also demonstrate that losses induced by the contacts can be exploited to select the optical mode of a micro-laser.

© 2009 Optical Society of America

## 1. Introduction

1. J. Brasseur, P. Roos, K. Repasky, and J. Carlsten, “Characterization of a continuous-wave Raman laser in *H*_{2},” J . Opt. Soc. Am. B **16**, 1305–1312 (1999). [CrossRef]

2. H. Park, A. Fang, S. Kodama, and J. Bowers, “Hybrid silicon evanescent laser fabricated with a silicon waveguide and III-V offset quantum wells,” Opt. Express **13**, 9460–9464 (2005). [CrossRef] [PubMed]

3. A. Fang, H. Park, R. Jones, O. Cohen, M. Paniccia, and J. Bowers, “A continuous-wave hybrid AlGaInAs-silicon evanescent laser,” IEEE Photon. Technol. Lett. **18**, 1143–1145 (2006). [CrossRef]

4. R. Ushigome, M. Fujita, A. Sakai, T. Baba, and Y. Kokubun, “GaInAsP microdisk injection laser with benzocyclobutene polymer cladding and its athermal effect,” Jpn. J. Appl. Phys **41**, 6364–6369 (2002). [CrossRef]

*μm*) and low power consumption (threshold below 50

*μW*) [5

5. M. Fujita, R. Ushigome, and T. Baba, “Continuous wave lasing in GaInAsP microdisk injection laser withthreshold current of 40 *μ*A,” Electron. Lett. **36**, 790–791 (2000). [CrossRef]

6. J. Van Campenhout, P. Rojo-Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Di Cioccio, J. Fedeli, and R. Baets, “Electrically injected thin-film InGaAsP microdisk lasers integrated on a Si-wafer,” 2006 Annual Symposium of the IEEE/LEOS Benelux Chapter, 30/11/2006-1/12/2006, Eindhoven, the Netherlands/Molina Vazquez, J; Verdurmen, E; van den Boom, H; Leijtens, X; Koonen, A.-2006-ISBN 90-6144-989-8 (2006).

7. P. Rojo Romeo, J. Van Campenhout, P. Regreny, A. Kazmierczak, C. Seassal, X. Letartre, G. Hollinger, D. Van Thourhout, R. Baets, and J. Fedeli et al., “Heterogeneous integration of electrically driven microdisk based laser sources for optical interconnects and photonic ICs,” Opt. Express **14**, 3864–3871 (2006). [CrossRef] [PubMed]

8. J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. 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]

10. J. Van Campenhout, P. Rojo-Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Cioccio, J. Fedeli, and R. Baets, “Design and Optimization of Electrically Injected InP-Based Microdisk Lasers Integrated on and Coupled to a SOI Waveguide Circuit,” J. Lightwave Technol. **26**, 52–63 (2008). [CrossRef]

10. J. Van Campenhout, P. Rojo-Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Cioccio, J. Fedeli, and R. Baets, “Design and Optimization of Electrically Injected InP-Based Microdisk Lasers Integrated on and Coupled to a SOI Waveguide Circuit,” J. Lightwave Technol. **26**, 52–63 (2008). [CrossRef]

## 2. Description of the model

*μm*when not annealed. Moreover, this material can be used with standard Si equipments, and may act as an intermediate medium between standard metalization for Si processes and InP, without using gold based contacts.

*R*, thickness

*H*) made of a high optical index material (

*n*) in a lower index cladding medium (

_{disk}*n*), like silica. The top contact can be divided into 2 elementary volumes (see Fig. 2):

_{clad}- the “via” which contacts the central area of the disk, and allows carriers injection from the top surface. The smaller is the radius
*R*of this via, the smaller are the absorption losses in the conductive material and the greater is the global Q factor...but, at the same time, the electrical injection becomes less efficient._{c} - the “tab” (thickness
*H*) which is separated from the WGM by silica (distance_{m}*H*). Δ_{c}*L*can be used for misalignment compensation in fabrication.

*H*and

_{c}*R*.

_{c}*l,m,n*), that respectively correspond to the number of nodes along the

*r*axis, the number of periods on the circumference, and the number of nodes on the

*z*axis. For symmetry reasons, we will focus on a separated variables problem to describe the field in the

*r*≤

*R*area using cylindrical coordinates. Such approximation is commonly used to study thin micro-disks [11

11. M. Chin, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. **75**, 3302 (1994). [CrossRef]

*r*>

*R*. In each homogeneous region of the structure, the electric field obey the d’Alembert vectorial equation given by:

*n*is the index of the considered medium and

_{i}*k*the wavenumber. In our model, we consider a perfect TE mode neglecting the vertical component of the electric field. Then, the equation 1 in cylindrical coordinates can be solved:

*U*is a linear combination of Bessel functions of the first kind (

_{m}*J*and

_{m}*Y*) and

_{m}*E*(

*z*) the solution of the electric field for a TE mode of effective index

*n*guided in the corresponding infinite membrane. Continuity conditions are automatically satisfied at

_{eff}*z*= ±

*H*/2 for both the electric field

*E*⃗ and the magnetic induction

*H*⃗, obtained from the Faraday’s law. Unfortunately, the 5 equations corresponding to continuity conditions at

*r*=

*R*have no trivial solution, except if setting aside the

*θ*component of

*H*⃗ (then we get 2 redundant equations) and the

*z*equation from the d’Alembert for

*r*>

*R*. This limitation proves that a separated variables problem only returns an approximation of a WGM. Then, the resonant wavelength

*λ*can be easily computed [12] since the equations 3 lead to solve the 2D solution of an infinite cylinder of the same index

_{res}*n*in a medium of index

_{eff}*n*. For better results, effective index is not considered as a constant parameter, but is adjusted according to the wavelength.

_{clad}*N*

^{2}

_{Disk}=

*n*

_{disk}^{2}-

*n*

_{eff}^{2}and

*N*

_{clad}^{2}=

*n*

_{eff}^{2}-

*n*

_{clad}^{2}and coefficients (

*j,y*) to satisfy continuity conditions at

*r*=

*R*. The given expression of

*E*(

*z*) corresponds to even values of

*n*: replace

*cos*functions by

*sin*ones for odd values and preserve continuity conditions at

*z*= +

*H*/2 changing if necessary the sign of the expression when |

*z*| >

*H*/2.

*θ*and

*z*components. This model takes the most from two 2D models thanks to the use of both separated variable functions and continuity conditions. Last, the cladding material influence on wavelength is taken into account since the E-field is not trivial at the

*r*=

*R*boundary [13

13. N. Frateschi and A. Levi, “The spectrum of microdisk lasers,” J. Appl. Phys. **80**, 644 (1996). [CrossRef]

*θ*) energy density

*e*

_{<θ>}as a function of

*z*and

*r*:

*ε*

_{2D}equal to

*n*

_{eff}^{2}since

*r*<

*R*, and

*ε*

_{3D}equal to

*n*

_{disk}^{2},

*n*

_{clad}^{2}or

*n*

_{cont}^{2}, depending on the value of

*z*. Then, by integration of

*e*

_{<θ>}, we can easily obtain the energy in our system without contacts,

*E*. Two kinds of losses are considered: first, the optical intrinsic losses

_{tot}*τ*

_{o}^{-1}due to the diffraction at the edge of the micro-disk, and absorption losses in the electrical contact which will be calculated using its contained electromagnetic energy

*E*, associated to a loss rate

_{cont}*τ*

_{a}^{-1}. This loss rate is proportional to the absorption constant of the contact medium

*α*

_{0}since

*τ*

_{a}^{-1}=

*α*

_{0}∙

*v*with

_{g}*v*the photons group velocity in this material. Then we can link the energy and global losses

_{g}*τ*

^{-1}with:

*τ*

_{c}^{-1}are given by:

*r*<

*R*, absorption losses should be under estimated, but the strong confinement of WGM should ensure a quite good estimation if the real part of the index for the top contact is close to that of the cladding material.

*R*) and the distance between the tab and the membrane (

_{c}*H*), we compared our model to 3D FDTD calculations (TESSA [14

_{c}14. Tessa FDTD: http://alioth.debian.org/projects/tessa/ .

15. Harminv: http://ab-initio.mit.edu/harminv/.

*τ*

_{c}^{-1}are estimated from the loss rate difference between with (

*τ*

^{-1}) and without the contact (

*τ*

_{o}^{-1}).

## 3. Application of the model to a contacted micro-disk laser

### 3.1. Influence of the top contact

8. J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. 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]

10. J. Van Campenhout, P. Rojo-Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Cioccio, J. Fedeli, and R. Baets, “Design and Optimization of Electrically Injected InP-Based Microdisk Lasers Integrated on and Coupled to a SOI Waveguide Circuit,” J. Lightwave Technol. **26**, 52–63 (2008). [CrossRef]

*R*,

*H*,

*H*and Δ

_{m}*L*are set to respectively 2.5

*μm*, 0.55

*μm*, 0.9

*μm*and 0.5

*μm*. The following results only concern the (0,26,0) mode at 1.51

*μm*wavelength for

*n*= 1.44 (silica),

_{clad}*n*= 3.17 (InP) and an ITO based top contact, with an absorption constant

_{disk}*α*

_{0}= 1.83 × 10

^{6}

*m*

^{-1}.

*z*, as derived from FDTD simulations and from our model are shown in Fig. 3. Outside of the resonator, the effective index approximation of our model results in a slower decay of the field and we can consider that losses through the top contact should be over estimated with our model. For |

*z*| < 500

*nm*, we can observe a good agreement.

*R*as simulated by FDTD (dots) and as derived from our analytical model (bold blue line). It is possible to separate tab losses from the via ones and for a given distance

_{c}*H*, optical losses occur mainly in the tab (resp. the via) if

_{c}*R*is smaller (resp. larger) than a characteristic value (~1.58

_{c}*μm*in Fig. 4). It is observed that there is no need to reduce further beyond 1.7

*μm*the via radius, since intrinsic losses become dominant, and the top contact is uselessly too small.

*H*can lead to very high loss level, more particularly due to interactions in the portion 2 (Fig. 2). The impact of

_{c}*H*on optical losses is shown in Fig. 5, using again FDTD simulation and the present model. When contact losses dominate the intrinsic losses of the contact free micro-disk, the discrepancy between FDTD and our model increases when the tab to micro-disk distance reduces. For quality factors higher than 10 000, our model lead to an over-estimation of the contact to membrane distance from 60

_{c}*nm*to 25

*nm*.

*H*,

_{c}*R*) for which top contact losses do not affect too much the global losses. With such a condition,

_{c}*R*values are limited by

_{c}*R*which gives the maximum acceptable radius of the via and corresponds to

_{c}^{max}*H*=∞. A simple way to choose these 2 parameters consists in getting comparable losses in the tab and the via. Last, we will compensate misalignment between the micro-disk and the via during fabrication choosing a smaller value of

_{c}*R*if necessary. On the contrary, we can keep the computed

_{c}*H*value since this parameter is over-estimated.

_{c}### 3.2. The fully contacted structure

6. J. Van Campenhout, P. Rojo-Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Di Cioccio, J. Fedeli, and R. Baets, “Electrically injected thin-film InGaAsP microdisk lasers integrated on a Si-wafer,” 2006 Annual Symposium of the IEEE/LEOS Benelux Chapter, 30/11/2006-1/12/2006, Eindhoven, the Netherlands/Molina Vazquez, J; Verdurmen, E; van den Boom, H; Leijtens, X; Koonen, A.-2006-ISBN 90-6144-989-8 (2006).

7. P. Rojo Romeo, J. Van Campenhout, P. Regreny, A. Kazmierczak, C. Seassal, X. Letartre, G. Hollinger, D. Van Thourhout, R. Baets, and J. Fedeli et al., “Heterogeneous integration of electrically driven microdisk based laser sources for optical interconnects and photonic ICs,” Opt. Express **14**, 3864–3871 (2006). [CrossRef] [PubMed]

*nm*thick slab and a 550

*nm*III-V membrane, FDTD results show that quality factors are limited to around 30 000. Bigger structures (thicker membranes or larger radius) are less affected by the bottom contact [7

7. P. Rojo Romeo, J. Van Campenhout, P. Regreny, A. Kazmierczak, C. Seassal, X. Letartre, G. Hollinger, D. Van Thourhout, R. Baets, and J. Fedeli et al., “Heterogeneous integration of electrically driven microdisk based laser sources for optical interconnects and photonic ICs,” Opt. Express **14**, 3864–3871 (2006). [CrossRef] [PubMed]

^{5}are theoretically reachable. The FDTD field distribution in Fig. 6 shows that the WGM extends laterally into the slab over a few wavelengths distance, which is obviously very different from the perfect micro-disk. Then, at position

*r*>

*R*, it is expected that the top contact absorbs additional photons.

*E*(

*z*) functions in the micro-disk and in the slab are normalized with respect to the field inside the micro-disk. The effective index approximation still shows a good agreement with FDTD simulations in both regions. Only the greatest positive values of

*z*show a slight disparity. For negative values of

*z*(i.e.

*z*< -600

*nm*in our case), losses induced by the slab can dominate the disk ones due to a lower confinement of the field. For this reason, it is necessary to increase the distance between the bottom face of the micro-disk and underlying high index materials like the substrate. It is also observed that for high values of

*H*(

_{c}*z*> 0), the intensity of the field that meets the contact is close over the micro-disk (diamonds in Fig. 7) and in the

*r*>

*R*region (triangles in Fig. 7). We can deduce that the shape and size of the top contact when (

*r*>

*R*) can significantly affect the contact induced losses.

*R*, the difference between our model and FDTD almost reaches one decade, and the crossing point between tab and via losses is lower for FDTD (~ 1.35

_{c}*μm*) than for our model (~ 1.53

*μm*), that means that the WGM is also less confined in the plane (

*e*⃗

_{r},

*e*⃗

_{θ}).

### 3.3. Mode selection induced by contact losses

*l,m,n*) can compete to reach lasing regime, especially if quality factors are close and spectral overlaps between the optical mode and the gain are similar. Low threshold is expected when the chosen WGM quality factor for lasing is significantly larger than that of other modes. In the following, we show that top contacts can be used to get significantly different quality factors between the mode chosen for lasing and other ones. Table 1 gives orders and effective index of different modes computed as explained in section 2, with

*λ*around 1.55

_{res}*μm*.

*m*,0) modes correspond to lower intrinsic losses, the (0,25,0) mode will be considered as the desired mode because of its wavelength close to 1.55

*μm*. For all the modes mentioned in table 1, we estimate losses using our model with

*α*

_{0}= 1.83 × 10

^{6}

*m*

^{-1}(ITO) and

*n*= 1.52. Only the (0,19,1) mode has a

_{cont}*n*value significantly different from the other solutions. As we can see in Fig. 10, this leads to an important shift in losses for this particular mode when studying

_{eff}*H*, due to a lower vertical confinement. Increasing the radial mode number (

_{c}*l*) slightly increases losses.

*n*from ~ 2.99 to 2.37) also leads to a significant increase of losses with a difference of more than one decade.

_{eff}*m*, 0) family modes and the distance from the WGM,

*H*, to select (

_{c}*l*,

*m*,0) modes. Both via and tab contributes to a deep quality factor contrast between the (0,

*m*,0) family modes and the other ones. A numeric application with our model for

*R*=1.8

_{c}*μm*,

*H*=0.40

_{c}*μm*and the parameters of part 3.1 shows that quality factors are limited to 5 300 except for the desired mode which should reach 46 000. In comparison, FDTD simulations leads to similar quality factors: respectively 5 400 and 56 000.

## 4. Conclusion

*m*,0) modes can be favored by considerably lowering associated losses (1 decade or more), still granting very high quality factors (typically more than 50 000).

## Acknowledgment

## References and links

1. | J. Brasseur, P. Roos, K. Repasky, and J. Carlsten, “Characterization of a continuous-wave Raman laser in |

2. | H. Park, A. Fang, S. Kodama, and J. Bowers, “Hybrid silicon evanescent laser fabricated with a silicon waveguide and III-V offset quantum wells,” Opt. Express |

3. | A. Fang, H. Park, R. Jones, O. Cohen, M. Paniccia, and J. Bowers, “A continuous-wave hybrid AlGaInAs-silicon evanescent laser,” IEEE Photon. Technol. Lett. |

4. | R. Ushigome, M. Fujita, A. Sakai, T. Baba, and Y. Kokubun, “GaInAsP microdisk injection laser with benzocyclobutene polymer cladding and its athermal effect,” Jpn. J. Appl. Phys |

5. | M. Fujita, R. Ushigome, and T. Baba, “Continuous wave lasing in GaInAsP microdisk injection laser withthreshold current of 40 |

6. | J. Van Campenhout, P. Rojo-Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Di Cioccio, J. Fedeli, and R. Baets, “Electrically injected thin-film InGaAsP microdisk lasers integrated on a Si-wafer,” 2006 Annual Symposium of the IEEE/LEOS Benelux Chapter, 30/11/2006-1/12/2006, Eindhoven, the Netherlands/Molina Vazquez, J; Verdurmen, E; van den Boom, H; Leijtens, X; Koonen, A.-2006-ISBN 90-6144-989-8 (2006). |

7. | P. Rojo Romeo, J. Van Campenhout, P. Regreny, A. Kazmierczak, C. Seassal, X. Letartre, G. Hollinger, D. Van Thourhout, R. Baets, and J. Fedeli et al., “Heterogeneous integration of electrically driven microdisk based laser sources for optical interconnects and photonic ICs,” Opt. Express |

8. | J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express |

9. | J. Fedeli, L. Di Cioccio, D. Marris-Morini, L. Vivien, R. Orobtchouk, P. Rojo-Romeo, C. Seassal, and F. Mandorlo, “Development of silicon photonics devices using microelectronic tools for the integration on top of a CMOS wafer,” Adv. Opt. Technol. |

10. | J. Van Campenhout, P. Rojo-Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Cioccio, J. Fedeli, and R. Baets, “Design and Optimization of Electrically Injected InP-Based Microdisk Lasers Integrated on and Coupled to a SOI Waveguide Circuit,” J. Lightwave Technol. |

11. | M. Chin, “Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes,” J. Appl. Phys. |

12. | K. P. Huy, “Etude de micro structures utilisant le guidage réfractif à fort confinement de la lumiére,” Ph.D. dissertation, Institut de Microélectronique, Electromagnétisme et Photonique (2005). |

13. | N. Frateschi and A. Levi, “The spectrum of microdisk lasers,” J. Appl. Phys. |

14. | Tessa FDTD: http://alioth.debian.org/projects/tessa/ . |

15. | Harminv: http://ab-initio.mit.edu/harminv/. |

**OCIS Codes**

(140.5960) Lasers and laser optics : Semiconductor lasers

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: September 15, 2008

Revised Manuscript: November 7, 2008

Manuscript Accepted: November 9, 2008

Published: December 22, 2008

**Citation**

Fabien Mandorlo, Pedro Rojo Romeo, Xavier Letartre, and Pierre Viktorovitch, "A simple perturbative analysis for fast design of an electrically pumped
micro-disk laser," Opt. Express **17**, 70-79 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-1-70

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### References

- J. Brasseur, P. Roos, K. Repasky, and J. Carlsten, "Characterization of a continuous-wave Raman laser in H2," J. Opt. Soc. Am. B 16, 1305-1312 (1999). [CrossRef]
- H. Park, A. Fang, S. Kodama, and J. Bowers, "Hybrid silicon evanescent laser fabricated with a silicon waveguide and III-V offset quantum wells," Opt. Express 13, 9460-9464 (2005). [CrossRef] [PubMed]
- A. Fang, H. Park, R. Jones, O. Cohen, M. Paniccia, and J. Bowers, "A continuous-wave hybrid AlGaInAs-silicon evanescent laser," IEEE Photon. Technol. Lett. 18, 1143-1145 (2006). [CrossRef]
- R. Ushigome, M. Fujita, A. Sakai, T. Baba, and Y. Kokubun, "GaInAsP microdisk injection laser with benzocyclobutene polymer cladding and its athermal effect," Jpn. J. Appl. Phys 41, 6364-6369 (2002). [CrossRef]
- M. Fujita, R. Ushigome, and T. Baba, "Continuous wave lasing in GaInAsP microdisk injection laser withthreshold current of 40 ?A," Electron. Lett. 36, 790-791 (2000). [CrossRef]
- J. Van Campenhout, P. Rojo-Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Di Cioccio, J. Fedeli, and R. Baets, "Electrically injected thin-film InGaAsP microdisk lasers integrated on a Si-wafer," 2006 Annual Symposium of the IEEE/LEOS Benelux Chapter, 30/11/2006-1/12/2006, Eindhoven, the Netherlands/Molina Vazquez, J; Verdurmen, E; van den Boom, H; Leijtens, X; Koonen, A.-2006-ISBN 90-6144-989-8 (2006).
- P. Rojo Romeo, J. Van Campenhout, P. Regreny, A. Kazmierczak, C. Seassal, X. Letartre, G. Hollinger, D. Van Thourhout, R. Baets, J. Fedeli et al., "Heterogeneous integration of electrically driven microdisk based laser sources for optical interconnects and photonic ICs," Opt. Express 14, 3864-3871 (2006). [CrossRef] [PubMed]
- J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. 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]
- J. Fedeli, L. Di Cioccio, D. Marris-Morini, L. Vivien, R. Orobtchouk, P. Rojo-Romeo, C. Seassal, and F. Mandorlo, "Development of silicon photonics devices using microelectronic tools for the integration on top of a CMOS wafer," Adv. Opt. Technol. 15 (2008).
- J. Van Campenhout, P. Rojo-Romeo, D. Van Thourhout, C. Seassal, P. Regreny, L. Cioccio, J. Fedeli, and R. Baets, "Design and Optimization of Electrically Injected InP-Based Microdisk Lasers Integrated on and Coupled to a SOI Waveguide Circuit," J. Lightwave Technol. 26, 52-63 (2008). [CrossRef]
- M. Chin, "Estimation of the spontaneous emission factor for microdisk lasers via the approximation of whispering gallery modes," J. Appl. Phys. 75, 3302 (1994). [CrossRef]
- K. P. Huy, "Etude de micro structures utilisant le guidage réfractifá fort confinement de la lumiére," Ph.D. dissertation, Institut de Microélectronique, Electromagnétisme et Photonique (2005).
- N. Frateschi and A. Levi, "The spectrum of microdisk lasers," J. Appl. Phys. 80, 644 (1996). [CrossRef]
- TessaFDTD : http://alioth.debian.org/projects/tessa/.
- Harminv: http://ab-initio.mit.edu/harminv/.

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