Abstract

We report a new graphical tool to analyze optical injection-locked vertical-cavity surface-emitting lasers (VCSELs). It predicts the resonant frequency enhancement and cavity mode behavior for both single- and multi- mode VCSELs under injection locking. Calculations based on this model show excellent agreement with experimental results.

© 2012 OSA

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References

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  1. C. J. Chang-Hasnain and X. Zhao, “Ultra-high speed VCSEL modulation by injection locking,” Chapter 6 in Optical Fiber Telecommunication V A, Components and Subsystems, 145–182, edited by I. P. Kaminow, T. Li and A. E. Willner, Academic Press, (2008).
  2. X. Zhao and C. J. Chang-Hasnain, “A new amplifier model for resonance enhancement of optically injection-locked lasers,” IEEE Photon. Technol. Lett. 20(6), 395–397 (2008).
    [CrossRef]
  3. A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron. 39(10), 1196–1204 (2003).
    [CrossRef]
  4. E. K. Lau, H. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44(1), 90–99 (2008).
    [CrossRef]
  5. E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
    [CrossRef]
  6. W. Yang, P. Guo, D. Parekh, and C. J. Chang-Hasnain, “Reflection-mode optical injection locking,” Opt. Express 18(20), 20887–20893 (2010).
    [CrossRef] [PubMed]
  7. L. Chrostowski, X. Zhao, and C. J. Chang-Hasnain, “Microwave performance of optically injection-locked VCSELs,” IEEE Trans. Microw. Theory Tech. 54(2), 788–796 (2006).
    [CrossRef]
  8. 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 16(26), 21582–21586 (2008).
    [CrossRef] [PubMed]
  9. A. Ng'oma, D. Fortusini, D. Parekh, W. Yang, M. Sauer, S. Benjamin, W. Hofmann, M. C. Amann, and C. J. Chang-Hasnain, “Performance of a multi-Gb/s 60 GHz radio over fiber system employing a directly modulated optically injection-locked VCSEL,” J. Lightwave Technol. 28(16), 2436–2444 (2010).
    [CrossRef]
  10. 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]
  11. R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1242–1249 (2011).
    [CrossRef]
  12. A. Hurtado, I. D. Henning, and M. J. Adams, “Different forms of wavelength polarization switching and bistability in a 1.55 microm vertical-cavity surface-emitting laser under orthogonally polarized optical injection,” Opt. Lett. 34(3), 365–367 (2009).
    [CrossRef] [PubMed]
  13. A. Quirce, A. Valle, and L. Pesquera, “Very wide hysteresis cycles in 1550 nm-VCSELs subject to orthogonal optical injection,” IEEE Photon. Technol. Lett. 21(17), 1193–1195 (2009).
    [CrossRef]

2011 (1)

R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

2010 (2)

2009 (3)

A. Hurtado, I. D. Henning, and M. J. Adams, “Different forms of wavelength polarization switching and bistability in a 1.55 microm vertical-cavity surface-emitting laser under orthogonally polarized optical injection,” Opt. Lett. 34(3), 365–367 (2009).
[CrossRef] [PubMed]

A. Quirce, A. Valle, and L. Pesquera, “Very wide hysteresis cycles in 1550 nm-VCSELs subject to orthogonal optical injection,” IEEE Photon. Technol. Lett. 21(17), 1193–1195 (2009).
[CrossRef]

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
[CrossRef]

2008 (3)

X. Zhao and C. J. Chang-Hasnain, “A new amplifier model for resonance enhancement of optically injection-locked lasers,” IEEE Photon. Technol. Lett. 20(6), 395–397 (2008).
[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. Express 16(26), 21582–21586 (2008).
[CrossRef] [PubMed]

E. K. Lau, H. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44(1), 90–99 (2008).
[CrossRef]

2007 (1)

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]

2006 (1)

L. Chrostowski, X. Zhao, and C. J. Chang-Hasnain, “Microwave performance of optically injection-locked VCSELs,” IEEE Trans. Microw. Theory Tech. 54(2), 788–796 (2006).
[CrossRef]

2003 (1)

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron. 39(10), 1196–1204 (2003).
[CrossRef]

Adams, M. J.

R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, “Different forms of wavelength polarization switching and bistability in a 1.55 microm vertical-cavity surface-emitting laser under orthogonally polarized optical injection,” Opt. Lett. 34(3), 365–367 (2009).
[CrossRef] [PubMed]

Al-Seyab, R.

R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

Amann, M. C.

Atsuki, K.

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron. 39(10), 1196–1204 (2003).
[CrossRef]

Benjamin, S.

Chang-Hasnain, C. J.

Chrostowski, L.

L. Chrostowski, X. Zhao, and C. J. Chang-Hasnain, “Microwave performance of optically injection-locked VCSELs,” IEEE Trans. Microw. Theory Tech. 54(2), 788–796 (2006).
[CrossRef]

Fortusini, D.

Gatare, I.

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]

Guo, P.

Henning, I. D.

R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, “Different forms of wavelength polarization switching and bistability in a 1.55 microm vertical-cavity surface-emitting laser under orthogonally polarized optical injection,” Opt. Lett. 34(3), 365–367 (2009).
[CrossRef] [PubMed]

Hofmann, W.

Hurtado, A.

R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, “Different forms of wavelength polarization switching and bistability in a 1.55 microm vertical-cavity surface-emitting laser under orthogonally polarized optical injection,” Opt. Lett. 34(3), 365–367 (2009).
[CrossRef] [PubMed]

Kawashima, K.

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron. 39(10), 1196–1204 (2003).
[CrossRef]

Khan, N. A.

R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

Lau, E. K.

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
[CrossRef]

E. K. Lau, H. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44(1), 90–99 (2008).
[CrossRef]

Murakami, A.

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron. 39(10), 1196–1204 (2003).
[CrossRef]

Ng'oma, A.

Panajotov, K.

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]

Parekh, D.

Pesquera, L.

A. Quirce, A. Valle, and L. Pesquera, “Very wide hysteresis cycles in 1550 nm-VCSELs subject to orthogonal optical injection,” IEEE Photon. Technol. Lett. 21(17), 1193–1195 (2009).
[CrossRef]

Quirce, A.

A. Quirce, A. Valle, and L. Pesquera, “Very wide hysteresis cycles in 1550 nm-VCSELs subject to orthogonal optical injection,” IEEE Photon. Technol. Lett. 21(17), 1193–1195 (2009).
[CrossRef]

Sauer, M.

Schires, K.

R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

Sciamanna, M.

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]

Sung, H.

E. K. Lau, H. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44(1), 90–99 (2008).
[CrossRef]

Valle, A.

A. Quirce, A. Valle, and L. Pesquera, “Very wide hysteresis cycles in 1550 nm-VCSELs subject to orthogonal optical injection,” IEEE Photon. Technol. Lett. 21(17), 1193–1195 (2009).
[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]

Wong, L. J.

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
[CrossRef]

Wu, M. C.

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
[CrossRef]

E. K. Lau, H. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44(1), 90–99 (2008).
[CrossRef]

Yang, W.

Zenteno, L. A.

Zhao, X.

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 16(26), 21582–21586 (2008).
[CrossRef] [PubMed]

X. Zhao and C. J. Chang-Hasnain, “A new amplifier model for resonance enhancement of optically injection-locked lasers,” IEEE Photon. Technol. Lett. 20(6), 395–397 (2008).
[CrossRef]

L. Chrostowski, X. Zhao, and C. J. Chang-Hasnain, “Microwave performance of optically injection-locked VCSELs,” IEEE Trans. Microw. Theory Tech. 54(2), 788–796 (2006).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron. 39(10), 1196–1204 (2003).
[CrossRef]

E. K. Lau, H. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44(1), 90–99 (2008).
[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]

IEEE J. Sel. Top. Quantum Electron. (2)

R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

E. K. Lau, L. J. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

A. Quirce, A. Valle, and L. Pesquera, “Very wide hysteresis cycles in 1550 nm-VCSELs subject to orthogonal optical injection,” IEEE Photon. Technol. Lett. 21(17), 1193–1195 (2009).
[CrossRef]

X. Zhao and C. J. Chang-Hasnain, “A new amplifier model for resonance enhancement of optically injection-locked lasers,” IEEE Photon. Technol. Lett. 20(6), 395–397 (2008).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

L. Chrostowski, X. Zhao, and C. J. Chang-Hasnain, “Microwave performance of optically injection-locked VCSELs,” IEEE Trans. Microw. Theory Tech. 54(2), 788–796 (2006).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (2)

Opt. Lett. (1)

Other (1)

C. J. Chang-Hasnain and X. Zhao, “Ultra-high speed VCSEL modulation by injection locking,” Chapter 6 in Optical Fiber Telecommunication V A, Components and Subsystems, 145–182, edited by I. P. Kaminow, T. Li and A. E. Willner, Academic Press, (2008).

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Figures (6)

Fig. 1
Fig. 1

(a) Ellipse model illustrating the relationship between wavelength detuning Δλ and slave laser cavity shift Δλcavity under OIL, as described in Eq. (1)(2). Only the curve bounded by point a and b on the ellipse represents the steady-state of OIL laser. (b) The ellipse model provides an intuitive visualization of the OIL process and spectra. The origin is set to be λslave0 and the x-axis and y-axis is relabeled into λcavity and λmaster. For each detuning value, a horizontal line y = λmaster intersects y = x and the solid blue curve. The x-coordinates of the two intersecting points represent the optical spectrum of λmaster and λcavity.

Fig. 2
Fig. 2

(a) Analysis of OIL cavity mode behavior under different wavelength detuning Δλ utilizing the ellipse model. Three typical conditions are shown under an injection ratio of 20.9 dB: a. Δλ = −0.66 nm; b. Δλ = 0 nm; c. Δλ = 2.0 nm. (b) The simulation results of small signal frequency response of an OIL-laser under the three typical conditions in (a). For condition a (Δλ = −0.66 nm), the spacing between two wavelengths is 0.93 nm shown in (a), in agreement with the resonance frequency is 116 GHz shown in (b).

Fig. 3
Fig. 3

The size of the ellipse is proportional to injection ratio Rinj. This diagram provides a full map to analyze the OIL-laser behavior under different OIL conditions. The α value is set to 3. The resonance frequency dependence on Rinj is investigated as an example. The four ellipses correspond to four injection ratio: a. Rinj = 16.7 dB; b. Rinj = 17.9 dB; c. Rinj = 18.7 dB; d. Rinj = 19.4 dB. A horizon line corresponds to Δλ = 0.0 nm intercepts with these four ellipse, so that their resonance frequencies can be extracted. For condition a (Rinj = 16.7 dB), the spacing between two wavelengths is 0.68 nm, in agreement with the resonance frequency is 85 GHz.

Fig. 4
Fig. 4

The eccentricity of the ellipse is determined by linewidth enhancement factor. The four ellipses corresponds to different α value: a. α = 1; b. α = 2; c. α = 3; d. α = 4. The injection ratio is 22.7 dB. Asymmetric locking range is seen. In the α = 4 case, the locking range is the most asymmetric one and the eccentricity is the largest for its large α.

Fig. 5
Fig. 5

Ellipse Model for two-mode VCSEL: The master laser, the slave laser’s 1st order mode and fundamental mode move along the solid black, blue and red trace, respectively. The α value is set to 4 and the injection ratio is 19 dB. At y = λmaster = λiii, the locking switches from 1st order mode to fundamental mode. (a) Locking on the 1st order mode. (b) Locking on the fundamental mode.

Fig. 6
Fig. 6

(a) Typical experiment results of optical spectra and small signal frequency response of an OIL-VCSEL. The result of the free-running VCSEL is also plotted for comparison. (b) The measured data (Δλ and Δλcavity) from the spectrum are fitted into ellipses for both polarization modes. Blue ellipse is for the 1st polarization mode and red ellipse is for the 2nd polarization mode.

Tables (1)

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Table 1 Parameters Used in the Model

Equations (10)

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Δ λ c a v = A cos ( Δ ϕ )
Δ λ = B sin ( Δ ϕ + θ 0 )
A = ( k 0 λ s l a v e 0 2 / 2 π c ) S i n j / S 0 α B = ( k 0 λ s l a v e 0 2 / 2 π c ) S i n j / S 0 1 + α 2 θ 0 = tan 1 α
A ( k λ s l a v e 0 2 / 2 π c ) R i n j α B ( k λ s l a v e 0 2 / 2 π c ) R i n j 1 + α 2 θ 0 = tan 1 α
R i n j = P m a s t e r / P s l a v e 0 = S i n j ω V p ( 1 r 2 ) v g 2 L / S f r ω V p τ p α m α m + α i = S i n j S f r v g 2 L τ p α m + α i α m 1 ( 1 r 2 ) S i n j S 0 v g 2 L τ p α m + α i α m 1 ( 1 r 2 )
Δ λ c a v 2 2 C Δ λ c a v Δ λ + C Δ λ 2 + D = 0
C = α 2 1 + α 2 D = α 2 1 + α 2 ( k λ s l a v e 0 2 / 2 π c ) 2 R i n j
A r e a = π | D | C C 2 = π ( k λ s l a v e 0 2 / 2 π c ) 2 α R i n j
e = 2 1 + 4 α 4 / ( 1 + 4 α 4 + 1 + 2 α 2 )
α = e 4 + ( 2 e 2 ) e 4 + 4 e 2 4 8 ( 1 e 2 )

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