Abstract

Theory and simulations demonstrate that photoactive layers placed in vertical-cavity surface-emitting laser (VCSEL) cavities eliminate the power modulation during laser switch-on. As is well known, this power modulation is caused by the increasing rate of carrier depletion that occurs with increasing photon flux (dN/dt)/P<0, inducing cavity relaxation oscillations. The presence of photoactive layers with appropriately chosen parameters reverses the sign: (dN/dt)/P>0, which means a decreasing depletion rate with increasing laser power. The relaxation frequency then becomes pure imaginary, and the laser cavity behaves as an overdamped oscillator that asymptotes to the final steady state without power modulation or spiking. A flat frequency response over order(s)-of-magnitude higher bandwidth is predicted under direct VCSEL modulation.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Y. Lau and A. Yariv, “Ultra-high-speed semiconductor lasers,” IEEE J. Quantum Electron. 21, 121 (1985).
    [CrossRef]
  2. K. Petermann, in Laser Diode Modulation and Noise (Kluwer Academic, Tokyo, 1988), Chaps. 4–9.
  3. Y. Lam, J. P. Loehr, and J. Singh, IEEE J. Quantum Electron. 29, 42 (1993).
    [CrossRef]
  4. J. W. Scott, B. J. Thibeault, C. J. Mahon, L. A. Coldren, and F. H. Peters, “High modulation efficiency of intracavity contacted vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 65, 1483 (1994).
    [CrossRef]
  5. S. Riyopoulos, “Elimination of transient vertical-cavity surface-emitting laser oscillations using photoactive feedback,” Appl. Phys. Lett. 24, 768 (1999).
  6. S. Riyopoulos, “Stable single-mode vertical-cavity surface-emitting laser with a photoresistive aperture,” Opt. Lett. 24, 768 (1999); “Single-mode vertical-cavity surface-emitting laser operation via photocurrent feedback,” in Vertical-Cavity Surface-Emitting Lasers III, K. K. Choquette and C. Lei, eds., Proc. SPIE 3627, 193 (1999).
    [CrossRef]
  7. W. W. Chow and S. W. Koch, in Fundamentals of Semiconductor Lasers (Springer-Verlag, New York, 1999), Chap. 8.
  8. R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “Transport limits in high speed quantum well lasers: theory and experiment,” Quantum Electron. 28, 1990 (1992).
    [CrossRef]

1999 (1)

S. Riyopoulos, “Elimination of transient vertical-cavity surface-emitting laser oscillations using photoactive feedback,” Appl. Phys. Lett. 24, 768 (1999).

1994 (1)

J. W. Scott, B. J. Thibeault, C. J. Mahon, L. A. Coldren, and F. H. Peters, “High modulation efficiency of intracavity contacted vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 65, 1483 (1994).
[CrossRef]

1993 (1)

Y. Lam, J. P. Loehr, and J. Singh, IEEE J. Quantum Electron. 29, 42 (1993).
[CrossRef]

1992 (1)

R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “Transport limits in high speed quantum well lasers: theory and experiment,” Quantum Electron. 28, 1990 (1992).
[CrossRef]

1985 (1)

K. Y. Lau and A. Yariv, “Ultra-high-speed semiconductor lasers,” IEEE J. Quantum Electron. 21, 121 (1985).
[CrossRef]

Bowers, J. E.

R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “Transport limits in high speed quantum well lasers: theory and experiment,” Quantum Electron. 28, 1990 (1992).
[CrossRef]

Coldren, L. A.

J. W. Scott, B. J. Thibeault, C. J. Mahon, L. A. Coldren, and F. H. Peters, “High modulation efficiency of intracavity contacted vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 65, 1483 (1994).
[CrossRef]

Fukushima, T.

R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “Transport limits in high speed quantum well lasers: theory and experiment,” Quantum Electron. 28, 1990 (1992).
[CrossRef]

Geels, R. S.

R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “Transport limits in high speed quantum well lasers: theory and experiment,” Quantum Electron. 28, 1990 (1992).
[CrossRef]

Ishikawa, M.

R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “Transport limits in high speed quantum well lasers: theory and experiment,” Quantum Electron. 28, 1990 (1992).
[CrossRef]

Lam, Y.

Y. Lam, J. P. Loehr, and J. Singh, IEEE J. Quantum Electron. 29, 42 (1993).
[CrossRef]

Lau, K. Y.

K. Y. Lau and A. Yariv, “Ultra-high-speed semiconductor lasers,” IEEE J. Quantum Electron. 21, 121 (1985).
[CrossRef]

Loehr, J. P.

Y. Lam, J. P. Loehr, and J. Singh, IEEE J. Quantum Electron. 29, 42 (1993).
[CrossRef]

Mahon, C. J.

J. W. Scott, B. J. Thibeault, C. J. Mahon, L. A. Coldren, and F. H. Peters, “High modulation efficiency of intracavity contacted vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 65, 1483 (1994).
[CrossRef]

Nagarajan, R.

R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “Transport limits in high speed quantum well lasers: theory and experiment,” Quantum Electron. 28, 1990 (1992).
[CrossRef]

Peters, F. H.

J. W. Scott, B. J. Thibeault, C. J. Mahon, L. A. Coldren, and F. H. Peters, “High modulation efficiency of intracavity contacted vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 65, 1483 (1994).
[CrossRef]

Riyopoulos, S.

S. Riyopoulos, “Elimination of transient vertical-cavity surface-emitting laser oscillations using photoactive feedback,” Appl. Phys. Lett. 24, 768 (1999).

Scott, J. W.

J. W. Scott, B. J. Thibeault, C. J. Mahon, L. A. Coldren, and F. H. Peters, “High modulation efficiency of intracavity contacted vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 65, 1483 (1994).
[CrossRef]

Singh, J.

Y. Lam, J. P. Loehr, and J. Singh, IEEE J. Quantum Electron. 29, 42 (1993).
[CrossRef]

Thibeault, B. J.

J. W. Scott, B. J. Thibeault, C. J. Mahon, L. A. Coldren, and F. H. Peters, “High modulation efficiency of intracavity contacted vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 65, 1483 (1994).
[CrossRef]

Yariv, A.

K. Y. Lau and A. Yariv, “Ultra-high-speed semiconductor lasers,” IEEE J. Quantum Electron. 21, 121 (1985).
[CrossRef]

Appl. Phys. Lett. (2)

J. W. Scott, B. J. Thibeault, C. J. Mahon, L. A. Coldren, and F. H. Peters, “High modulation efficiency of intracavity contacted vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 65, 1483 (1994).
[CrossRef]

S. Riyopoulos, “Elimination of transient vertical-cavity surface-emitting laser oscillations using photoactive feedback,” Appl. Phys. Lett. 24, 768 (1999).

IEEE J. Quantum Electron. (2)

K. Y. Lau and A. Yariv, “Ultra-high-speed semiconductor lasers,” IEEE J. Quantum Electron. 21, 121 (1985).
[CrossRef]

Y. Lam, J. P. Loehr, and J. Singh, IEEE J. Quantum Electron. 29, 42 (1993).
[CrossRef]

Quantum Electron. (1)

R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “Transport limits in high speed quantum well lasers: theory and experiment,” Quantum Electron. 28, 1990 (1992).
[CrossRef]

Other (3)

K. Petermann, in Laser Diode Modulation and Noise (Kluwer Academic, Tokyo, 1988), Chaps. 4–9.

S. Riyopoulos, “Stable single-mode vertical-cavity surface-emitting laser with a photoresistive aperture,” Opt. Lett. 24, 768 (1999); “Single-mode vertical-cavity surface-emitting laser operation via photocurrent feedback,” in Vertical-Cavity Surface-Emitting Lasers III, K. K. Choquette and C. Lei, eds., Proc. SPIE 3627, 193 (1999).
[CrossRef]

W. W. Chow and S. W. Koch, in Fundamentals of Semiconductor Lasers (Springer-Verlag, New York, 1999), Chap. 8.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Typical transient response of VCSEL light output P=Iω and carrier density N under square-pulse bias turned on at t=0. Local maxima of P fall at the maxima of the derivative dN/dt, demonstrating the out-of-phase evolution of these quantities.

Fig. 2
Fig. 2

Illustration of a mesa-structured VCSEL cavity with symmetrically placed photoactive layers. w0 marks the waist of the paraxial radiation envelope.

Fig. 3
Fig. 3

(a) Photoresistance versus photocarrier density for various carrier mobilities, (b) junction current versus photocarrier density for various bias voltages.

Fig. 4
Fig. 4

Suppression and elimination of relaxation oscillations in the idealized P–I–N case (a) with no photoactive material present, (b) with two 100-nm photoactive layers placed as in Fig. 2, (c) with a third photoactive layer placed λ/2 farther apart. The curves correspond to various bias currents as marked. See text for parameters.

Fig. 5
Fig. 5

Elimination of relaxation oscillations with realistic diode parameters (a) with no photoactive material present, (b) with two 100-nm photoactive layers placed as in Fig. 2. The curves correspond to various bias currents as marked. See text for parameters.

Fig. 6
Fig. 6

Frequency response (magnitude of transfer function) for typical VCSEL without photoactive layers for (a) γ=γ=3.3×108, R=0.9994 and (b) γ=γ=4×109, R=0.996. Here f=ω/2π.

Fig. 7
Fig. 7

Plots of the |ωR*s|/ωR ratio versus laser power for (a) various doped-to-intrinsic carrier density ratios ND/ni at R=0.996 and (b) various R for ND/ni=40.

Fig. 8
Fig. 8

Frequency response (magnitude of transfer function) for a VCSEL with photoactive layers for (a) γ=γ=3.3×108, R=0.9994 and (b) γ=γ=4×109. R=0.996. The parameter eJR/κT is kept fixed. See text for the rest of the parameters.

Fig. 9
Fig. 9

Phase shift versus frequency (argument of the transfer function) for a VCSEL (a) without photoactive layers and (b) with photoactive layers. Same parameters as in Figs. 6(a) and 8(a), respectively.

Tables (2)

Tables Icon

Table 1 Parameter Values with Idealized P–I–N

Tables Icon

Table 2 Parameter Values with Realistic P–I–N

Equations (48)

Equations on this page are rendered with MathJax. Learn more.

dNdt=Jed-BN2-γcN-σ(N-Ng)I,
1vgdIdt=σζ(N-Ng)I-αI+S,
N0=Ng+ασζ=Nth,
I0=Λ-N0(σ/γc)(N0-Ng)=γcζα(Λ-Ng).
ddtδNδI=ANNANIAINAIIδNδI=λδNδI,
ANNN˙N0=-γc-σI0,
ANIN˙I0=-σ(N0-Ng)=-αζ.
AINI˙N0=vgσζI0,
AIII˙Io=vgσζ(No-Ng)-vgα=0.
λ±=½(-ANN±i-4ANIAIN-A2NN)Γ±iωR,
ωR-4ANIAIN/2=vgI0σα.
ωR1τeτp (J/Jth)-11-(Ng/Nth).
J=i0expe(V-Jρ-Jρs)2κT-1=I0Aexpe(V-IR-IRs)2κT-1.
ρ=1enμ.
np=χ1+χND,χ=IUk2 cos2(kzp) σγc,
N˙I0=JI0 1ed-σ(N0-Ng),
Jnp=Jρdρdnp=eJρ2κTJnp.
JI=JnpdnpdI=JnpσγζND.
JI=eJρ2κTJnpσγζND,
NI0=eJρ2κTJednpσγζND-σ(N0-Ng).
eIR2κTNDniΛN0-Ngσσγγζ>1.
ddtδNδI=ANNANIAINAIIδNδI+δJ/ed0exp(iωt).
δNδI=δJed-iωΓ-iωR exp(iωt)-ω2-2iΓω+ωR2+Γ2.
R(ω)δI(ω)δJ(ω)=1edΓ-iωR-ω2-2iΓω+ωR2+Γ2,
|R(ω)|=Γ2+ωR2(ω2-ωR2-Γ2)2+4Γ2ω2
H(ω)=11-ω2/ωR2-2i(ωΓ/ωR2)=11-ω2/ωR2+iωτe(1/ωR2τe2+τp/τe).
|ωR*|2=vgσI0eJρ2κTJedσγNDniζζ-α.
|R(ω)|=Γ+|ωR*|(ω2+|ωR*|2-Γ2)2+4Γ2ω2,
H(ω)=11+ω2/|ωR*|2+2i(ωΓ/|ωR*|2).
Δω2=(|ωR*|2+Γ2)2+(|ωR*|2-Γ2)2-(|ωR*|2+Γ2).
|ωR*|ωR=eJρ2κTJedγσαNDniζζ-1eIR2κTγγσσΛNth-NgNDniζ.
φ(ω)=tan-12Γωω2-(ωR2+Γ2),
φ(ω)=tan-12Γωω2+(|ωR*|2-Γ2).
ddtX=AX+F,
XδNδI,FδJed10exp(iωt),
AANNANIAINAII.
e1,2=1AIN/λ1,2
R10=e1,R01=e2,
R=11A1N/λ1AIN/λ2,
R-1=1AIN(λ2-1-λ1-1)AIN/λ2-1-AIN/λ11.
ddtX=AX+F,
F=RF=δJed1AIN/λ1exp(iωt),
A=RAR-1=λ100λ2.
X=δJedt ds exp(iωs)exp[λ1(t-s)]AINλ1t ds exp(iωs)exp[λ2(t-s)]=δJed1-iω+λ1AINλ11-iω+λ2.
δNδI=R-1X=R-1 δJed1-iω+λ1AINλ11-iω+λ2exp(iωt),
δN(t)δI(t)=δI/edAIN(λ2-1-λ1-1)×AINλ2-1-iω+λ1-AINλ1-1-iω+λ2-AINλ1-1-iω+λ1+AINλ1-1-iω+λ2exp(iωt).
δN(ω)δI(ω)=δJ/ed(-iω+λ1)(-iω+λ2)-iωλ2.
δN(ω)δI(ω)=δJ/ed-ω2-2iΓω+ωR2+Γ2-iωΓ-iωR.

Metrics