## High-frequency microwave signal generation using multi-transverse mode VCSELs subject to two-frequency optical injection |

Optics Express, Vol. 20, Issue 12, pp. 13390-13401 (2012)

http://dx.doi.org/10.1364/OE.20.013390

Acrobat PDF (847 KB)

### Abstract

In this paper we report a new method of photonic generation of microwave signals using a multi-transverse mode VCSEL subject to two-frequency optical injection. Numerical simulations show that double injection locking involving two transverse modes can be obtained in these systems. We show that the higher-order transverse mode is excited with a much larger amplitude than that of the fundamental transverse mode. The comparison with the case of a single-transverse mode VCSEL subject to similar two-frequency optical injection shows that multi-transverse mode operation of the VCSEL enhances the performance of the photonic microwave generation system. Broad tuning ranges, beyond the THz region, and narrow linewidths are demonstrated in our system. The maximum frequency of the generated microwave signals can be substantially increased if multimode VCSELs are used instead of single-mode VCSELs.

© 2012 OSA

## 1. Introduction

2. F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. **24**(12), 4502–4513 (2006). [CrossRef]

10. H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B **29**(4), 867–873 (2012). [CrossRef]

2. F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. **24**(12), 4502–4513 (2006). [CrossRef]

3. C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron. **9**(5), 1386–1393 (2003). [CrossRef]

5. H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. **32**(2), 227–235 (1996). [CrossRef]

11. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. **27**(6), 1402–1409 (1991). [CrossRef]

12. A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. **31**(8), 1423–1431 (1995). [CrossRef]

7. A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. **43**(4), 322–333 (2007). [CrossRef]

10. H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B **29**(4), 867–873 (2012). [CrossRef]

13. A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech. **57**(7), 1850–1858 (2009). [CrossRef]

14. H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express **19**(23), 22437–22442 (2011). [CrossRef] [PubMed]

15. S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron. **40**(2-4), 83–95 (2008). [CrossRef]

19. X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. **17**(5), 1198–1211 (2011). [CrossRef]

21. Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J. **3**(4), 644–650 (2011). [CrossRef]

19. X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. **17**(5), 1198–1211 (2011). [CrossRef]

15. S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron. **40**(2-4), 83–95 (2008). [CrossRef]

19. X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. **17**(5), 1198–1211 (2011). [CrossRef]

**17**(5), 1198–1211 (2011). [CrossRef]

**17**(5), 1198–1211 (2011). [CrossRef]

18. S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett. **31**(15), 2254–2256 (2006). [CrossRef] [PubMed]

21. Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J. **3**(4), 644–650 (2011). [CrossRef]

21. Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J. **3**(4), 644–650 (2011). [CrossRef]

**3**(4), 644–650 (2011). [CrossRef]

**3**(4), 644–650 (2011). [CrossRef]

**3**(4), 644–650 (2011). [CrossRef]

**17**(5), 1198–1211 (2011). [CrossRef]

**17**(5), 1198–1211 (2011). [CrossRef]

**3**(4), 644–650 (2011). [CrossRef]

7. A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. **43**(4), 322–333 (2007). [CrossRef]

14. H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express **19**(23), 22437–22442 (2011). [CrossRef] [PubMed]

**17**(5), 1198–1211 (2011). [CrossRef]

## 2. Theoretical model

7. A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. **43**(4), 322–333 (2007). [CrossRef]

**43**(4), 322–333 (2007). [CrossRef]

*x*and

*y*will be used to denote the two orthogonal linear polarization directions. The appropriate transverse modes of the structure are the LP

_{mn}modes. Here we treat the case of VCSELs that can operate in the fundamental (LP

_{01}) and in the first order (LP

_{11}) transverse modes. Subscripts 0,1 will be used to denote the LP

_{01}and LP

_{11}modes, respectively. The equations describing the polarization and transverse mode behavior of the VCSEL with a two-frequency injected optical field read as [7

**43**(4), 322–333 (2007). [CrossRef]

*E*and

_{0j}*E*are the complex amplitudes of the LP

_{1j}_{01}and LP

_{11}modes (the subindex

*j*stands for the linear polarization state of the given mode),

*N(r,t)*is the total carrier number,

*n(r,t)*is the difference in the carrier numbers of the two magnetic sublevels, and

*ψ*and

_{0j}*ψ*are the modal intensity profiles of the LP

_{1j}_{01}and LP

_{11}modes obtained by solving the Helmholtz Eq [23

23. A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical-cavity surface emitting lasers,” J. Lightwave Technol. **14**(9), 2062–2068 (1996). [CrossRef]

*κ*is the relative loss of the LP

_{r}_{11}mode with respect to the LP

_{01}mode. It determines the value of the injection current at which the LP

_{11}mode begins lasing.

*I(r)*represents a uniform current injection over a circular disc of 6

*μm*radius, and then

*I(r) = I*if

*r<6 μm*, and

*I(r) = 0*, elsewhere. The normal gain normalized to the threshold gain,

*g*, and

_{ij}(i = 0,1, j = x, y)*g*are given by

_{ijk}(i = 0,1; jk = xy,yx)## 3. Two-frequency optically injected single-mode VCSELs

*κ*= 10 to assure LP

_{r}_{01,x}mode operation. Results are given in terms of the separation between the frequencies of the two master lasers,

*Δf = (ω*, the frequency detuning of ML1 with respect to the frequency of the LP

_{2}-ω_{1})/(2π)_{01,x}mode,

*Δν*, and the injection strength

*κ*. We show in Fig. 1(a) the dynamical evolution of a free-running single-transverse mode VCSEL when switched-on at time

_{s}*t*>0 with a

*I =*1.8

*I*bias current value. The VCSEL emits in the steady state in the LP

_{th}_{01,x}mode with a single peaked RF spectrum appearing at the relaxation oscillation frequency. Spectra are calculated after a transient time of 14 ns.

*κ*= 10

_{s}^{−2},

*Δf*= 100 GHz, and with the frequency of ML1 just at the LP

_{01,x}mode frequency. An almost sinusoidal time trace is obtained for the power of LP

_{01,x}mode, that is the only mode with nonnegligible power. The frequency of this sinusoidal modulation is

*Δf.*The optical spectrum consists of two well defined peaks at the ML1 and ML2 optical frequencies and the RF spectrum has a very narrow peak at

*Δf,*the frequency separation between ML2 and ML1. This situation is similar to the double injection locking that has been obtained using a single mode DFB laser subject to dual-beam injection [21

**3**(4), 644–650 (2011). [CrossRef]

## 4. Two-frequency optically injected multi-transverse mode VCSELs

*κ*to a smaller value (

_{r}*κ*= 1.022) for which both transverse modes have rather similar losses. Results obtained for the solitary multimode VCSEL (

_{r}*κ*=

_{s}*κ*are plotted in Fig. 2(a) . In this case the VCSEL shows a steady-state in which both transverse modes, LP

_{c}= 0)_{01}and LP

_{11}, are excited in the

*x*-direction. The steady-state total power in Fig. 2(a) is 1.7, a similar value to the value, 2.1, that was obtained for Fig. 1(a). The power in the LP

_{11,x}mode is only slightly larger than that of LP

_{01,x.}Fig. 2(a) shows that the

*x*-polarized RF spectrum has two peaks that appear due to the multi-transverse mode character of the VCSEL [26

26. A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. **40**(6), 597–606 (2004). [CrossRef]

_{01,x}and LP

_{11,x}, similar to the separation between LP

_{01,y}and LP

_{11,y}, is around 63 GHz.

*Δf*, and

*Δν*are equal to those considered in the single-transverse mode case (Fig. 1(b)). In this way we can compare the performance of microwave generating systems using single and multi-transverse mode VCSELs. Similarly to Fig. 1(b), Fig. 2(b) also shows the double injection locking phenomenon. Again, two well defined peaks at the frequencies of ML1 and ML2 are observed in the

*x*-polarized optical spectrum resulting in a RF spectrum with a narrow peak at the

*Δf*frequency. But Fig. 2(b) also shows an interesting and novel feature when compared to Fig. 1(b): the high-order transverse mode LP

_{11,x}is excited with a much larger amplitude than that of the LP

_{01,x}mode. The power of both transverse modes oscillate with a phase difference near π/2. In this way the variation of the total power is nearly sinusoidal, as shown in the time traces and RF spectrum of Fig. 2(b). Interestingly, the amplitude of the total power is much larger than the one obtained with the equivalent single-transverse mode VCSEL case illustrated in Fig. 1(b). This shows that the amplitude of the microwave signal generated by two-frequency optical injection is enhanced if multi-transverse mode operation in the VCSEL is considered instead single-transverse mode operation.

## 5. Comparison between single and multi-transverse mode cases

*Δf*and with similar conditions to those of Fig. 2(b). Sinusoidal time traces are obtained for the power of LP

_{01,x}, LP

_{11,x}modes and total power. The amplitude of the oscillations decreases as

*Δf*increases. We have also included the time trace corresponding to the single-transverse mode VCSEL to show that the enhancement due to multi-mode operation is maintained. We show in Fig. 4(a) the peak-to-peak amplitude of the total power as a function of

*Δf*. Results for single and multi-transverse mode VCSELs, A

_{sm}and A

_{mm}respectively, are included. Also results for two injection strength levels are shown. All the cases reported in this fig. have an almost sinusoidal variation of the total power. Peak-to-peak amplitudes decrease as

*Δf*increases. An increase of the injection strength

*κ*leads to larger peak-to-peak amplitudes for both, single and multi-transverse mode cases. This is also illustrated in Fig. 3(b) in which

_{s}*κ*is increased with respect to Fig. 3(a). For all the values of

_{s}*Δf*and

*κ*the amplitude of the oscillation obtained with multi-transverse mode VCSELs is larger than that obtained for single-transverse mode VCSELs as it is shown in Fig. 4(a). This enhancement is quantified in Fig. 4(b), in which the ratio between peak-to-peak amplitudes of the total power obtained for multi and single-mode devices, A

_{s}_{mm}/A

_{sm}, is plotted as a function of

*Δf*. A maximum value of 2.6 is obtained for

*κ*= 10

_{s}^{−2}at

*Δf =*63.4 GHz, value that is very near the transverse mode separation. A not so well defined maximum is obtained for

*κ*= 3 10

_{s}^{−2}at

*Δf =*100 GHz. These values are near the 63 GHz transverse mode separation indicating that maximum enhancement is obtained when the optical frequencies of ML1 and ML2 are close to the frequencies of the free-running LP

_{01,x}, and LP

_{11,x}modes, respectively.

*Δf*occur in the microwave region (<300 GHz). In Fig. 4 we have also considered a

*Δf*range that goes beyond the microwave range. In this region the generated radiation has appreciable amplitude that increases as

*κ*is increased. The amplitude of this modulation slightly decreases when

_{s}*Δf*is in the THz region. An example of the dynamical evolution obtained for

*Δf*= 500 GHz, a value larger than those of the microwave region, is shown in Fig. 5(a) . Single and multimode VCSELs are able to respond at 500 GHz with appreciable amplitudes. The response of multimode VCSELs is such that the power of both transverse modes oscillates nearly in phase.

_{mm}and A

_{sm}on the injection strength

*κ*. Results are also given in terms of the injection ratio defined as the ratio of the injected optical power by the

_{s}*m*-master laser, (

*P*+

_{inj,0m}*P*) versus the output power of the free-running multimode VCSEL. Both A

_{inj,1m}_{mm}and A

_{sm}increase with

*κ*. Double injection locking is observed when

_{s}*κ*is larger than 2.5 10

_{s}^{−3}and 2.9 10

^{−3}for single and multimode VCSELs, respectively.

*κ*= 10

_{s}^{−2}that is due to a sudden change of the phase difference between the power time series of both transverse modes: that phase difference is near π if

*κ*≤9 10

_{s}^{−3}and changes to a value near π/2 at

*κ*= 10

_{s}^{−2}. Above the

*κ*value for which the step in A

_{s}_{mm}is observed, the ratio A

_{mm}/A

_{sm}, has an almost constant value of 2.6, as it is shown in Fig. 6(b).

_{mm}and A

_{sm}on the injection strength

*κ*for two different values of

_{c}*κ*. Both A

_{s}_{mm}and A

_{sm}increase with

*κ*. Note that all amplitudes vanish when

_{c}*κ*0. For the single-mode VCSEL with double injection this means that the VCSEL recovers the locked state with single-frequency optical injection characterized by a constant value of the power. For the two-mode VCSEL the situation can be explained as follows. If only injection from ML1 (ML2) with no coupling to the LP

_{c}→_{11,x}(LP

_{01,x}) mode is considered, for instance

*κ*= 3 10

_{01}^{−2},

*κ*=

_{12}= κ_{c}*0*(

*κ*= 3 10

_{12}^{−2},

*κ*=

_{01}= κ_{c}*0*) the optical spectrum of the VCSEL consists on a single peak at the ML1 (ML2) frequency, the power of LP

_{01,x}(LP

_{11,x}) is constant and the RF spectrum is flat. If injection from ML1 and ML2 is considered such that

*κ*=

_{01}*κ*3 10

_{12}=^{−2},

*κ*=

_{c}*0*, the optical spectrum of the VCSEL consists on two peaks at the ML1 and ML2 frequencies, the powers of both modes, LP

_{01,x}and LP

_{11,x}, are constant and the RF spectrum keeps on being flat. A nonzero value of

*κ*is enough for the RF spectrum to develop a peak and for both modes to oscillate at the

_{c}*Δf*frequency. This shows that the reason for the transverse modes power oscillations is the nonzero value of the

*κ*injection strength.

_{c}*κ*, A

_{s}_{mm}> A

_{sm}. However, for

*κ*= 10

_{s}^{−2}, A

_{mm}≤A

_{sm}until the curve for multi-transverse mode VCSELs has a small step near

*κ*= 0.42. This step is again due to a sudden change of the phase difference between the power time series of both transverse modes: that phase difference is near π if

_{c}/κ_{s}*κ*/

_{c}*κ*≤0.4 and changes to a value near π/2 at

_{s}*κ*/

_{c}*κ*= 0.45. Figure 7(b) shows the ratio A

_{s}_{mm}/A

_{sm}corresponding to data of Fig. 7(a). Larger enhancement of A

_{mm}with respect to A

_{sm}can be obtained when

*κ*is small providing that

_{c}*κ*is large enough. This situation is illustrated in Fig. 5(b) for which a value of A

_{s}_{mm}/A

_{sm}= 4.3 is reached.

_{mm}and A

_{sm}on the bias current of the VCSEL is analyzed in Fig. 8(a) . Both quantities increase with the bias current. However the ratio A

_{mm}/A

_{sm}slightly decrease in a linear way with

*I*. For instance, when

*κ*= 3 10

_{s}^{−2}, it goes from 2.6 at

*I/I*1.2 to 2.2 at

_{th}=*I/I*8. We have also analyzed the effect of the frequency detuning, Δν, on the dynamics of the system. Dynamics obtained for the multimode case when Δν = 5 GHz and Δν = −5 GHz are very similar to those obtained when Δν = 0 GHz, providing that the system is in the double injection locked regime. This indicates that there is an appreciable range of Δν for which the enhancement of the amplitude of the generated microwave signal due to high-order transverse mode excitation does not depend on the Δν value. The relative phase between the power time series corresponding to the LP

_{th}=_{01,x}and LP

_{11,x}modes in the double-injection locked multi-transverse mode VCSEL can change depending on the injection conditions. Comparison between Fig. 3(a) and Fig. 3(b) indicates that it decreases as the value of the

*κ*injection strength increases.

_{s}27. S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. **282**(12), 2367–2379 (2009). [CrossRef]

**3**(4), 644–650 (2011). [CrossRef]

**3**(4), 644–650 (2011). [CrossRef]

*Δf*.

## 6. Discussion and conclusions

28. J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. **33**(5), 765–783 (1997). [CrossRef]

*I/I*1.8, A

_{th}=_{mm}(mW) = 0.235A

_{mm}(a.u.). For the conditions of Fig. 2(b) this corresponds to a 1.1 mW peak-to-peak amplitude for 1.17 mW of power injected by each ML.

*y*-polarized transverse modes has been negligible because we have considered an optical injection that is parallel to the

*x*-polarization of the solitary VCSEL. Preliminary work using an extension of this model to consider orthogonally polarized optical injection indicates that the results obtained in this work are maintained. This result is of interest to show that the proposed microwave signal generation system is independent on the polarization of the master lasers. In our calculations we have assumed that the

*κ*parameter that represents the “crossed” injection strength between transverse modes of different order is equal for LP

_{c}_{01}injected into LP

_{11}and for LP

_{11}injected into LP

_{01}mode. Since this is a simplification in our model, future work is intended to know if the results obtained in this work are maintained when asymmetric “crossed” injection strengths are considered. Also in our calculations we have considered a high value of the

*γ*parameter such that the results of the simulations should be the same if the carrier difference

_{s}*n*is set equal to 0 (i.e., if integration of the equations with only the total carrier density is performed). Future work is also planned to investigate the influence of smaller values of the

*γ*parameter, and hence of the spin of the carriers on our results.

_{s}*Δf*

_{max,sm}, such that A

_{sm}>A if

*Δf <Δf*

_{max,sm}. We also calculate the corresponding quantity for the multimode VCSEL,

*Δf*

_{max,mm}, given by A

_{mm}>A if

*Δf <Δf*

_{max,mm}. Figure 9 shows the results for A = 4 a.u. as a function of the injection strength or the injection ratio. The maximum frequency increases significantly when using multimode VCSELs instead of single-mode VCSELs. For instance the maximum frequency increases from 193 GHz to 578 GHz for an injection ratio of 14 dB.

**17**(5), 1198–1211 (2011). [CrossRef]

## Acknowledgments

## References and links

1. | J. Ohtsubo, |

2. | F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. |

3. | C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron. |

4. | D. Parekh, X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express |

5. | H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. |

6. | J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. |

7. | A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. |

8. | A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron. |

9. | A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron. |

10. | H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B |

11. | C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. |

12. | A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. |

13. | A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech. |

14. | H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express |

15. | S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron. |

16. | S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber transmission from an optically injected semiconductor laser in period-one state,” Proc. SPIE |

17. | S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. |

18. | S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett. |

19. | X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. |

20. | X. Q. Qi and J. M. Liu, “Dynamics scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron. |

21. | Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J. |

22. | Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE |

23. | A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical-cavity surface emitting lasers,” J. Lightwave Technol. |

24. | A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE |

25. | J. Y. Law, G. H. M. vanTartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclassic. Opt. J. Eu. Opt. Soc. Part B |

26. | A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. |

27. | S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun. |

28. | J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. |

**OCIS Codes**

(140.3520) Lasers and laser optics : Lasers, injection-locked

(140.5960) Lasers and laser optics : Semiconductor lasers

(250.7260) Optoelectronics : Vertical cavity surface emitting lasers

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: March 23, 2012

Revised Manuscript: April 13, 2012

Manuscript Accepted: April 18, 2012

Published: May 30, 2012

**Citation**

A. Quirce and A. Valle, "High-frequency microwave signal generation using multi-transverse mode VCSELs subject to two-frequency optical injection," Opt. Express **20**, 13390-13401 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-13390

Sort: Year | Journal | Reset

### References

- J. Ohtsubo, Semiconductor Lasers. Stability, Instability and Chaos, Springer Series in Optical Sciences (Springer, 2007).
- F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol.24(12), 4502–4513 (2006). [CrossRef]
- C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron.9(5), 1386–1393 (2003). [CrossRef]
- D. Parekh, X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express16(26), 21582–21586 (2008). [CrossRef] [PubMed]
- H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron.32(2), 227–235 (1996). [CrossRef]
- J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.42(2), 198–207 (2006). [CrossRef]
- A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron.43(4), 322–333 (2007). [CrossRef]
- A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010). [CrossRef]
- A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012). [CrossRef]
- H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B29(4), 867–873 (2012). [CrossRef]
- C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991). [CrossRef]
- A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron.31(8), 1423–1431 (1995). [CrossRef]
- A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009). [CrossRef]
- H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express19(23), 22437–22442 (2011). [CrossRef] [PubMed]
- S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron.40(2-4), 83–95 (2008). [CrossRef]
- S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber transmission from an optically injected semiconductor laser in period-one state,” Proc. SPIE6468,46811–46811 (2007).
- S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron.46(3), 421–428 (2010). [CrossRef]
- S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett.31(15), 2254–2256 (2006). [CrossRef] [PubMed]
- X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron.17(5), 1198–1211 (2011). [CrossRef]
- X. Q. Qi and J. M. Liu, “Dynamics scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron.47(6), 762–769 (2011). [CrossRef]
- Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J.3(4), 644–650 (2011). [CrossRef]
- Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE7936,793609 (2011).
- A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical-cavity surface emitting lasers,” J. Lightwave Technol.14(9), 2062–2068 (1996). [CrossRef]
- A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE3283,280–291 (1998).
- J. Y. Law, G. H. M. vanTartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclassic. Opt. J. Eu. Opt. Soc. Part B9(5), 737–747 (1997). [CrossRef]
- A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.40(6), 597–606 (2004). [CrossRef]
- S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun.282(12), 2367–2379 (2009). [CrossRef]
- J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.33(5), 765–783 (1997). [CrossRef]

## 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.