## Compact modulated and tunable microdisk laser using vertical coupling and a feedback loop |

Optics Express, Vol. 18, Issue 19, pp. 19612-19625 (2010)

http://dx.doi.org/10.1364/OE.18.019612

Acrobat PDF (1799 KB)

### Abstract

A study of vertical coupling conditions between microdisk based resonators and waveguides is presented using an analytical model. The coupling efficiency optimization is investigated and compared to 3D FDTD computations. We also demonstrate that coupling losses can be exploited to favor high quality factor modes in circular resonators. In addition, we propose to modify the shape of the coupled waveguide to enhance mode selectivity and obtain a very compact structure with mode hoping capacities. Lower thresholds and modulation are also expected.

© 2010 Optical Society of America

## 1. Introduction

1. D. Yang, Y. Li, F. Sun, S. Chen, and J. Yu, “Fabrication of a 4×4 strictly nonblocking SOI switch matrix,” Opt. Commun. **250**, 48–53 (2005). [CrossRef]

8. P. Rojo Romeo, J. Van Campenhout, F. Mandorlo, C. Seassal, X. Letartre, P. Regreny, D. Van Thourhout, R. Baets, L. DiCioccio, and J. Fedeli, “Integration of an Electrically Driven InGaAsP Based Microdisk laser with a Silicon based Passive Photonic Circuit,” Optical Society of America-CLEO/QELS Conference (2007).

9. L. Zhang and E. Hu, “Lasing from InGaAs quantum dots in an injection microdisk,” Appl. Phys. Lett. **82**, 319 (2003). [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]

6. 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]

8. P. Rojo Romeo, J. Van Campenhout, F. Mandorlo, C. Seassal, X. Letartre, P. Regreny, D. Van Thourhout, R. Baets, L. DiCioccio, and J. Fedeli, “Integration of an Electrically Driven InGaAsP Based Microdisk laser with a Silicon based Passive Photonic Circuit,” Optical Society of America-CLEO/QELS Conference (2007).

6. 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]

*l,m,n*) denoting the number of nodes on the radial direction (

*l*), of periods at the edge (azimuthal order

*m*) and of nodes (

*n*) on the height. A 3D semi-analytical model of the WGM [11

11. F. Mandorlo, P. Rojo Romeo, X. Letartre, and P. Viktorovitch, “A simple perturbative analysis for fast design of an electrically pumped micro-disk laser,” Opt. Express **17**, 70–79 (2009). [CrossRef] [PubMed]

*f*

_{(l,m,n)}with an accuracy better than 1

*nm*in a few micrometers radius microdisk at telecom wavelengths. Modes with the same radial

*l*and vertical

*n*orders are very regularly positioned (Fig. 2) in the frequency domain, leading to different combs (denoted

*P*

_{(l,n)}) with a characteristic frequency distance called Free Spectral Range defined as

*FSR*(

*l,n*)=

*f*

_{(l,m,n)}−

*f*

_{(l,m+1,n)}.

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]

*µm*with Q factors limited to few thousands. Since the emission range in quantum wells is higher than the FSR, mode competition occurs between each comb

*P*

_{(l,n)}and between modes from a same comb with different azimuthal orders (Fig. 2). To select a particular WGM, a solution consists in increasing the optical losses of the unwanted ones. This is partially done by the microdisk itself as losses of modes with small

*l*and

*n*are lower [10

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]

*nm*) lead to

*n*≤1 and replacing the inner part of the microdisk by a low index material prevents modes from having high radial orders [13]. Absorption through the top contact can also be profitably used to favor the most confined modes [11

11. F. Mandorlo, P. Rojo Romeo, X. Letartre, and P. Viktorovitch, “A simple perturbative analysis for fast design of an electrically pumped micro-disk laser,” Opt. Express **17**, 70–79 (2009). [CrossRef] [PubMed]

*m*,0) modes, we propose to exploit the vertical coupling between a microdisk and a straight waveguide. We will explain how to efficiently couple modes from the

*P*

_{(0,0)}comb at the expense of those with a higher vertical order. In the second part of this paper, we will increase the azimuthal order sensitivity and demonstrate that controlling the optical index of the waveguide can be advantageously used for mode hoping applications or to adjust the resonant frequency.

## 2. Vertical coupling of a microdisk to a waveguide

11. F. Mandorlo, P. Rojo Romeo, X. Letartre, and P. Viktorovitch, “A simple perturbative analysis for fast design of an electrically pumped micro-disk laser,” Opt. Express **17**, 70–79 (2009). [CrossRef] [PubMed]

14. K. Chiang, “Analysis of the effective-index method for the vector modes of rectangular-core dielectric waveguides,” IEEE Trans. Microwave Theory Tech. **44**, 692–700 (1996). [CrossRef]

*R*(resp. by its axial line) that corresponds to the maximum energy density on the radial direction for

_{eff}*l*=0 (resp. in the cross-section plane). If the center of the waveguide is close enough to the center of the resonator, coupling mainly occurs at two different points (

*A*and

*B*), along a local distance

*L*(Fig. 3).

*x*of the center of the waveguide since it changes the two optical paths from

_{g}*A*to

*B*(i.e. in the resonator and in the waveguide).

### 2.1. Model used for the local coupling efficiency

15. M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injectionlasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. **5**, 673–681 (1999). [CrossRef]

*τ*

^{−1}

_{0}) term will stand for all types of cavity losses (like contact induced ones [11

**17**, 70–79 (2009). [CrossRef] [PubMed]

16. 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]

17. M. Borselli, K. Srinivasan, P. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. **85**, 3693 (2004). [CrossRef]

*η*as the portion of the energy that is transferred from the resonator to the waveguide at each turn of a propagative mode. Thus, if

_{c}*I*represents the energy flux just before the coupling area, an energy Δ

*I*= −

*η*·

_{c}*I*is transferred in the coupling area. For a (

*l,m,n*) propagative WGM, this variation occurs each Δ

*t*=

*FSR*(

*l,n*)

^{−1}. This is the time duration of a lap in the cavity. Then, using the definition of the coupling loss rate

*τ*

^{−1}

*, we get:*

_{c}*η*with the same equations as in [19]:

_{c}*L*=

*R*·(sin(

_{eff}*θ*

_{2})−sin(

*θ*

_{1})) and using a projection of the WGM on the waveguide direction with

*β*(resp.

_{d}*β*) is the propagative constant in the microdisk (resp. waveguide).

_{g}*C*

_{i→j}represents the energy from element

*i*that interferes with element

*j*. It can be expressed using [19]:

*u*corresponds to the distribution of the electromagnetic field along the vertical direction. These functions can be easily approximated using the effective index

_{i,j}*n*for the microdisk (resp.

_{disk}*n*for the waveguide) and height

_{g}*H*, in a cladding material of optical index

_{i}*n*. From these equations, when the waveguide is close to the center of the resonator (

_{clad}*x*~0), the local coupling loss rate

_{g}*τ*

^{−1}

*tends to 0, due to orthogonal propagative vectors.*

_{c}- an effective index adaptation between the two elements;
- an interaction distance which is an odd multiple of the transfer distance
*L*=_{t}*π*/(2*γ′*).

*nm*due to fabrication limitations) and few micrometers radius resonators,

*L*is generally longer than

_{t}*L*, so the contribution of the interfering distance

*L*is maximum when the waveguide is close to the edge of the resonator. On the other hand, index adaptation is obtained at a particular position

*x*equal to:

_{g}^{Adapt}*β*<

_{g}*β*leads to

_{d}*x*<

_{g}^{Adapt}*R*: given that

_{eff}*L*is smaller than

*L*, the maximum coupling efficiency is achieved for

_{t}*x*in the range [

_{g}*x*,

_{g}^{Adapt}*R*].

_{eff}### 2.2. Effective coupling losses of the system

*ϕ*between the two optical paths from

_{AB}*A*to

*B*can be easily estimated:

*τ*′

*)*

_{c}^{−1}, its global quality factor

*Q*and its resonant frequency

_{r}*ω*. Using the Coupled Mode Theory (CMT) [20

_{r}20. C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. **35**, 1322–1331 (1999). [CrossRef]

*ω*can theoretically vary in a range that is only limited by the local coupling loss rate

_{r}*τ*

^{−1}

*and centered around the resonant frequency of the device with no waveguide (*

_{c}*ω*

_{0}). Depending on the relative position between the waveguide and the microdisk

*x*, the phase conditions at the two coupling areas strongly impact the global quality factor

_{g}*Q*which vary:

_{r}### 2.3. Unwanted losses due to the presence of the waveguide

*R*is not far enough from the tangency position of the waveguide (

_{eff}*x*=

_{g}*R*−

*W*/2), we have to take them into account to find the position with the best coupling efficiency since they can significantly increase the total losses of the system. In other words:

_{g}- either
*R*−*R*>_{eff}*W*/2 [Fig. 4(a)]: our model should give a pretty good description of the coupling properties if the unwanted diffraction losses can be neglected._{g} - or
*R*−*R*≲_{eff}*W*/2 [Fig. 4(b)]: both coupling and diffraction losses should increase for_{g}*x*∈[_{g}*R*−*W*/2,_{g}*R*]. FDTD is required to find the position with the best coupling efficiency._{eff}

### 2.4. Analytical results and comparison to FDTD when − > /2

21. Tessa FDTD, http://alioth.debian.org/projects/tessa/

*µm*radius) to ensure that unwanted losses effect are reduced. To reduce spectral densities and ease the post treatment with Harminv [22

22. Harminv, http://ab-initio.mit.edu/harminv/

*µm*wide ring with the same external radius as the wanted microdisk and an adapted excitation source is used.

*TE*(0,45,0) mode of the resonator are represented on Fig. 5. Positions where we get destructive interferences according to the analytical model (Δ

*ϕ*≡

_{AB}*π*, at

*x*~3.46

_{g}*µm*and

*x*~3.68

_{g}*µm*) are in very good agreement with FDTD [Fig. 5(a)]. When inhibiting the energy transfer, losses should be extremely low but FDTD shows that loss rates variations is lower than one decade. For this reason, we can reasonably assume that the difference mainly comes from diffraction losses due to the presence of the waveguide itself. Their existence is confirmed in Fig. 5(b) since the difference between the model and FDTD results increases with

*x*.

_{g}### 2.5. FDTD analysis and model limitations when R−R ≲ W/2

*E*, since:

*e*the electromagnetic energy density and

_{m}*S⃗*the Poynting vector.

*P*(

_{g}*ω*) is proportional to the square of the amplitude

_{r}*a*(

_{g}*ω*) of the guided mode, we only need a local sensor in the waveguide to measure the coupling efficiency. Then, the coupling loss rate (

_{r}*τ*′

*)*

_{c}^{−1}is given by:

*a*(

_{g}*ω*) and ∫

_{r}_{Σ}

*S⃗*(

*ω*)·

_{r}*d⃗s*are easily obtained by application of Harminv [22

22. Harminv, http://ab-initio.mit.edu/harminv/

21. Tessa FDTD, http://alioth.debian.org/projects/tessa/

*τ*′

*)*

_{c}^{−1}for different positions

*x*, maintaining the sensor in the center of the waveguide, far from the interaction area.

_{g}*x*~1.95

_{g}*µm*and FDTD confirms that this position corresponds to a minimum light transfer. A maximum coupling efficiency is obtained at position (a) where

*x*<

_{g}*R*, and we fulfill 2 contradictory conditions corresponding to a maximum transferred energy and a minimum global loss rate. For higher values of

_{eff}*x*, coupling losses are decreasing (red curve) contrary to the total ones (black curve): losses induced by the presence of the waveguide itself are dominating. Consequently, the coupling efficiency is maintained at low values for

_{g}*x*between

_{g}*R*and

_{eff}*R*, and is divided by 10 at position

*x*≈2.35

_{g}*µm*.

*nm*thick III-V membrane) used for the bottom contact (Fig. 1 and inserted picture in Fig. 6), an effective index adaptation between the waveguide and the extended part of WGM in this membrane can also correspond to an interesting coupling condition. This later (referred as (b) in Fig. 6) can compete with the best coupling position with

*x*<

_{g}*R*(a), depending on the distance between the bottom surface of the resonator and the waveguide since it strongly affects the transfer distance

_{eff}*L*.

_{t}### 2.6. Influence of the vertical mode order

**17**, 70–79 (2009). [CrossRef] [PubMed]

*n*≤1 in a

*R*=4

*µm*radius microdisk are displayed in Fig. 7.

*β*<

_{d}*β*for the

_{g}*TE*(0,34,1) mode, the position with destructive interferences (around 2.15

*µm*in Fig. 7) is much farther from

*x*=

_{g}*R*than for the

_{eff}*TE*(0,42−44,0) modes. Their coupling loss rate is maintained at a very high value on a large range of positions

*x*while for the modes of interest, coupling is modulated by the position of the waveguide (range [2.5

_{g},*µm*,

*R*] in Fig. 7). Consequently, having

_{eff}*β*<

_{d}*β*corresponds to a more robust design since a misalignment error at fabrication does not significantly change the coupling efficiency. Unfortunately, such a condition cannot be achieved for the

_{g}*P*

_{(0,0)}comb since the need of doped layers and QWs [10

**26**, 52–63 (2008). [CrossRef]

*β*.

_{d}*TE*(0,

*m*,0) modes is expected as being optimized at position

*x*=

_{g}*R*, but this position competes with

_{eff}*x*= 3.45

_{g}*µm*. In both cases, we get high enough quality factors to reach the lasing regime, while for the higher vertical order ones (green curve in Fig. 7), losses are significantly increased to limit this later to few hundreds.

*TE*(0,

*m*,0) modes. For a given WGM, the effective coupling loss rate (

*τ*′

*)*

_{c}^{−1}depends on the propagative constants: in order to prevent WGMs from coupling to a low effective index waveguided mode with unwanted phase conditions, we suggest to use single mode waveguides.

### 2.7. Conclusion

*R*<3

*µm*), an optimization is required to find the most interesting position.

*x*≲

_{g}*R*ensures much more important coupling losses for modes with a high vertical order, that can be used to increase the selectivity between the

_{eff}*TE*(0,

*m*,0) modes and the

*TE*(0,

*m*,

*n*) ones. This behavior can be strengthened using the top contact of the microdisk [11

**17**, 70–79 (2009). [CrossRef] [PubMed]

*P*

_{(0,0)}), we have almost no dependence on the azimuthal order

*m*and on the wavelength. This behavior comes from too short optical paths between the two effective coupling areas.

## 3. Modulated coupling efficiency and azimuthal order control

*ϕ*, we propose to strongly couple the resonator to the waveguide and to lengthen the optical paths between the two coupling areas (Fig. 8):

_{AB}- in the resonator using two diametrically opposed points;
- using a longer Si waveguide to strengthen the impact of the propagative constant.

*ε*to measure the attenuation of the electromagnetic field between

*A*and

*B*. Results from CMT applied to a propagative mode are very close to the previously presented ones since only the following expressions are changed:

*β*·

_{i}*d*the phase difference induced by the photons travel in each elementary portion of the waveguide (bent parts, straight ones…).

_{i}*ω*and associated quality factor

_{r}*Q*. For low loss waveguided modes (

_{r}*ε*close to 0), variations of these parameters are similar to the case of the vertical coupling studied in the previous part.

*ε*≠ 0) in the Si waveguide ensures optical light in the output waveguide whatever the value of Δ

*ϕ*, since the coupling losses (

_{AB}*τ*′

*)*

_{c}^{−1}cannot be canceled [Eq. (9)], preventing

*Q*from reaching

_{r}*Q*

_{0}. Both a high coupling efficiency and a very high quality factor when Δ

*ϕ*≡

_{AB}*π*are ensured if τ

^{−1}

_{0}≪

*ε*·

*τ*

^{−1}

*.*

_{c}*ϕ*parameter.

_{AB}### 3.1. 2D simulations and optimization with the analytical model

*τ*

^{−1}

*values). This can be achieved using*

_{c}*x*close to

_{g}*R*as explained in the first part. Then, only 2D simulations are required to study the feedback loop influence on the device. In this model, the optical path in the feedback loop is controlled by the length of 2 straight waveguide portions (like in Fig. 8).

_{eff}*m*between 25 and 27 for a 2.5

*µm*radius ring resonator.

### 3.2. Spectral properties depending on the feedback loop length

*P*

_{(l,n)}(with a frequency distance

*FSR*(

*l,n*)) and demonstrate that different regimes can be achieved.

*Q*of a structure based on a 3

_{r}*µm*radius microdisk is given in Fig. 10(d) as a function of the feedback loop length

*Z*. As we need Δ

*ϕ*≡0 to reduce the effective coupling losses and to achieve the lasing regime with a low threshold, we will introduce the comb (in the frequency domain) for which destructive interferences are available (blue combs in Fig. 10). Then, depending on its spacing (that decreases with

_{AB}*Z*) and on the FSR of the resonator, different regimes are available:

- if all
*TE*(0,*m*,0) modes almost share the same phase condition [Fig. 10(c)]. Then the mode with the higher quality factor is changed for a slight optical index modification in the waveguide (by thermal or electrical actuation for instance). Such a feedback loop length is well adapted to mode hoping: for instance, we can switch from*λ*=1.643_{r}*µm*to*λ*=1.490_{r}*µm*changing the optical path (i.e. the optical index) by a few ‰. - if
*M*modes are regularly distributed [Fig. 10(b) with*M*=5]: each mode has a dominating quality factor on a 2*π*/*M*range of Δ*ϕ*. The resonant wavelength can be adjusted still granting a high quality factor contrast between the chosen mode and the other ones. Such values of_{AB}*Z*are quite interesting for wavelength tuning, more particularly for small*M*values, since the margin on Δ*ϕ*is higher._{AB}

- we can adjust the resonant wavelength with a maximum range ~±
*τ*^{−1}_{0}. - we can switch from one resonant wavelength to another one, with a frequency step corresponding to the FSR.

*ϕ*≡

_{AB}*π*).

### 3.3. Tunable laser with a single output waveguide

*A*and

*B*and the parity of the azimuthal order that induces a

*m*·

*π*phase difference in the resonator for two diametrically opposed points. For symmetrical paths, only even (or odd) modes are available at the output of the MMI, depending on the symmetry at the coupling points

*A*and

*B*. Table 2 summarizes the types of interferences at the single output.

- add a Bragg grating at the peripheral of the microdisk [25]. In this case, the feedback loop is used to modulate the light in the waveguide, since there will only be one mode per
25. M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett.

**80**, 2051 (2002). [CrossRef]*P*_{(l,n)}comb in respect to the periodicity of the Bragg grating. This corresponds to a single wavelength operating laser with an extremely compact modulation system (with the feedback loop). - use a local default in the microdisk or in the waveguide to set the phase. Then, depending on the length of the feedback loop, we get a laser with mode hoping, wavelength adjustment or modulation capacities.

*A*and

*B*) and the Y coupler can also be used to modulate the output signal. Meanwhile, switching from even to odd azimuthal order modes with the feedback loop leads to much more compact structures, with a probably higher bandwidth.

## 4. Conclusion

## Acknowledgment

## References and links

1. | D. Yang, Y. Li, F. Sun, S. Chen, and J. Yu, “Fabrication of a 4×4 strictly nonblocking SOI switch matrix,” Opt. Commun. |

2. | I. Kiyat, A. Aydinli, and N. Dagli, “High-Q silicon-on-insulator optical rib waveguide racetrack resonators,” Opt. Express |

3. | A. Kaz´mierczak, W. Bogaerts, D. Van Thourhout, E. Drouard, P. Rojo Romeo, D. Giannone, and F. Gaffiot, “Analysis of silicon on insulator (SOI) optical microring add-drop filter based on waveguide intersections,” Proc. SPIE, 6996, 69960D (2008). [CrossRef] |

4. | L. Vivien, D. Marris-Morini, J. Mangeney, P. Crozat, E. Cassan, S. Laval, J.-M. Fedeli, J. Damlencourt, and Y. Lecunff, “42 GHz waveguide Germanium-on-silicon vertical PIN photodetector,” 5 |

5. | P. Binetti, J. Van Campenhout, X. Leijtens, M. Nikoufard, T. de Vries, Y. Oei, L. Di Cioccio, J. Fedeli, C. Lagahe, and R. Orobtchouk et al., “An optical interconnect layer on silicon,” Proceedings of the 13 |

6. | 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 |

7. | L. Liu, J. VanCampenhout, G. Roelkens, R. Soref, D. VanThourhout, P. Rojo Romeo, P. Regreny, C. Seassal, J. Fedeli, and R. Baets, “Compact optical modulator based on carrier induced gain of an InP-InGaAsP microdisk cavity integrated on SOI,” Proc. SPIE |

8. | P. Rojo Romeo, J. Van Campenhout, F. Mandorlo, C. Seassal, X. Letartre, P. Regreny, D. Van Thourhout, R. Baets, L. DiCioccio, and J. Fedeli, “Integration of an Electrically Driven InGaAsP Based Microdisk laser with a Silicon based Passive Photonic Circuit,” Optical Society of America-CLEO/QELS Conference (2007). |

9. | L. Zhang and E. Hu, “Lasing from InGaAs quantum dots in an injection microdisk,” Appl. Phys. Lett. |

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. | F. Mandorlo, P. Rojo Romeo, X. Letartre, and P. Viktorovitch, “A simple perturbative analysis for fast design of an electrically pumped micro-disk laser,” Opt. Express |

12. | F. Mandorlo, P. Rojo Romeo, X. Letartre, J. Fedeli, and P. Viktorovitch, “Improving contact design for micro-disc based lasers in integrated circuits,” 5 |

13. | F. Mandorlo, J. Fedeli, and P. Rojo Romeo, “Microdisc system with gallery modes for electrically pumped optical sources,” European Patent Office (EPO) Patent EP2 101 380 (2009). |

14. | K. Chiang, “Analysis of the effective-index method for the vector modes of rectangular-core dielectric waveguides,” IEEE Trans. Microwave Theory Tech. |

15. | M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injectionlasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. |

16. | 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 |

17. | M. Borselli, K. Srinivasan, P. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. |

18. | F. Mandorlo, P. Rojo Romeo, X. Letartre, P. Regreny, P. Viktorovitch, J. Fedeli, and P. Grosse, “Contacting InP based micro disk lasers on 200 mm Si wafers,” 20 |

19. | L. Coldren and S. Corzine, |

20. | C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. |

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

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

23. | R. Orobtchouk, S. Jeannot, B. Han, T. Benyattou, J. Fedeli, and P. Mur, “Ultra compact optical link made in amorphous silicon waveguide,” Proc. SPIE |

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

25. | M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(140.5960) Lasers and laser optics : Semiconductor lasers

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: June 9, 2010

Revised Manuscript: July 26, 2010

Manuscript Accepted: August 13, 2010

Published: August 31, 2010

**Citation**

F. Mandorlo, P. Rojo Romeo, X. Letartre, R. Orobtchouk, and P. Viktorovitch, "Compact modulated and tunable
microdisk laser using vertical coupling
and a feedback loop," Opt. Express **18**, 19612-19625 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-19612

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