Characteristics of ARROW VCSELs under External Optical Feedback

Transcription

1 Characteristics of ARROW VCSELs under External Optical Feedback S.F. Yu and N.S. Chen School of EEE Nanyang Technological University August

2 Contents Introduction Simulation Models Simulation Result New Design Approach Conclusion

3 IntroductionARROW VCSELs with External Reflector External Reflector Feedback External round trip delay time τext p+ layer P-DBR etch-stop layer Spacer layer Active layer First cladding layer Second cladding layer... Second growth First growth n-dbr n-substrate n n n3 d n s n d n s n3 d n 3

4 Introduction-What is ARROW? Effective Refractive index st cladding layer Lateral fields st cladding layer Reflectors r d nd cladding layer s d s d nd cladding layer The reflectors are designed so that only the fundamental leaky mode is in resonance. Other higher order fields are then have high radiation losses.

5 Introduction-What is ARROW? fundamental mode.. Zoom. Field-intensity Field-intensity st order mode Zoom. r (um) nd order mode.... r (um) r (um) Field-intensity Field-intensity 5.7 3rd order mode. Core Region: d. st cladding Layer:. nd cladding Layer:. r (um) 5.7 s d 5

6 Advantages of ARROW Suppress high-order transverse leaky modes Control modal polarization Eliminate secondary pulsation Influence the effects of optical feedback?

7 Optical Field Analysis Model Transfer Matrix Method for ARROW in Cylindrical Structure E+ = E ψ r = r = E+ EN+ Ei++ Ei+ E3+ E+ EN = EN+ E n r= r E3 E n. Ei + Ei n3 3 r3 ri. EN ni ni+ nn nn i i+ N N ri+ Cross sectional view rn rn r 7

8 Transfer Matrix Method Wave Equation: Solution: ( ) n k + β r + o i r r r r φ [ ψ i = ] ψ i = E i + H v() ( β i r ) + E i H v( ) ( β i r ) exp( ± jm φ ) ( ) () where H v, H v : vth order of the Hankel functions of the first and second kind If m= ψi Ei + H v() (β i r ) H v( ) (β i r ) ψ i = β i H v( ) (β i r ) H v(+) (β i r ) β i H v( ) (β i r ) H v( +) (β i r ) E i r N ψn tm tm ψ N ψ TM = = i tm i = r= tm j β Nψ N r > r j β Nψ N r > r { where Eigenequations: βi = } ( N k n i n eff { ) } N η ( n eff ) tm + j β N tm =

9 Rate Equations for ARROW VCSELs with External Feedback Photon Density S m t = v g ( Γz g m α m ζ m ) S m + β sp Γz Bsp N Ref Phase S,m ( t ) = k ext τ L [ + Ref S, m (t ) S m ( t ) S m ( t τ ext ) cos( θ m ( t )) ] φ m t = α H v g Γz g m g th, m + Ref φ, m (t ) Ref φ,m (t ) = k ext τ L_ S m (t τ ext ) / S m (t ) sin( θ m (t )), Carrier N N N N J (r, t ) N i = D + + D + v g ( N ) ψ g i S m t r r φ qd τn m =, r r i=c,s Auxiliary Equations : Carrier induced index change λ an δ n (r, t ) = α H Γz N (r,t) π N c 9

10 Two Possible Designs Radiation Loss (cm-) Method : Minimum threshold current (lowest radiation loss for the fundamental transverse leaky-mode Method : Maximum Radiation Loss Margin (RLM) Improved RLM ~cm- Method selection Method selection s (µm)

11 Minimum Threshold Design Bifurcation diagram for an ARROW VCSEL with external feedback designed in the minimum threshod approach (d=m, s=.um, d=um) Power (mw) 5 3 (a) - Kext J=.5 ka/cm -3 A 3 3 B 3 Time(ns) 5 A - Kext J=7 ka/cm 3 Time (ns) 5 B (b) -3 (c) - Kext J=.5 ka/cm ¾Low critical feedback strength at low injection current ¾Higher order transverse leaky-mode is excited at high injection current

12 Maximum Radiation Loss Margin Design Power (mw) Bifurcation diagram for an ARROW VCSEL with external feedback designed in the maximum RLM approach (d=m, s=.µm, d=3.9µm) 5 3 (a) - -3 (b) Kext J=5. ka/cm - -3 Kext J=. ka/cm (c) - -3 Kext J=7. ka/cm ¾Higher radiation loss increases kcrit ωr = ν g (ζ m + α m )S m g m / N kcrit = τ L ωr / + α H ¾Large RLM suppresses higher order transverse leaky-modes

13 Comparison of the Sensitivity The comparison of the Kcrit versus total output power for ARROW VCSELs designed by the two approaches Max RLM design Kcrit ( -) Total Power(mW) 9 Minimum Threshold Design 3

14 Conclusion ARROW can be used to suppress higher order bifurcations and chaos in VCSELs due to the structure s characteristic of strong mode discrimination The design of ARROW with maximum radiation loss margin can stabilize high-power single-mode operation of VCSELs under the influence of strong external optical feedback. Large radiation loss margin suppresses the excitation of higher order modes at high output powers The increase in radiation loss of the fundamental mode reduces its sensitivity to optical feedback and delay the onset of chaos