Thermal lensing in high power ridge waveguide lasers. H. Wenzel, M. Dallmer and G. Erbert

Transcription

1 Thermal lensing in high power ridge waveguide lasers H. Wenzel, M. Dallmer and G. Erbert

2 Outline motivation and laser structure experimental results theoretical model simulation results conclusions

3 Motivation fundamental spatial mode diode lasers with an output power in the W range of interest for a variety of applications requires narrow lateral waveguide defined by small effective index step to cut off higher order modes at higher output power appearance of instabilities like kinks in light current characteristics beam steering appearance of higher order modes possible reasons: carrier induced index suppression thermal lensing spatial hole burning

4 Schematic cross sectional view of RW devices trench ridge insulator B W p-contact metal residual layer thickness active layer finite trench width = radiation leaks into the outer high-index regions radiation loss rises with mode number = stabilization of th order mode anti index guiding = sensitive to thermal lensing effect x

5 Experimental light current characteristics cavity length L = 3.9 mm ridge width W =.8 µm emission wavelength around λ = 64 nm output power P >.3 W at I = A only small difference in the characteristics for trench widths B = µm and B = 5 µm strong increase of threshold current and decrease of slope efficiency slightly above threshold for B =.5 µm o p tic a l p o w e r P / W.5..5 B / µm c u rre n t I / A 4 3 b ia s U / V

6 Experimental lateral far field intensity profiles B/µm strong dependence of far field profiles on trench width B = 5 µm: much more stable far field compared to B = µm B =.5 µm: double peaked far field, peaks joining around I =.4 A

7 Theoretical model: Optics effective index method for calculating lateral field profile Φ(x) and complex propagation constant β d Φ dx = [ β k ε eff (x) ] Φ(x) boundary conditions dφ dx x= = (even modes) lim Φ(x) e i k ε eff(x c ) β x x far field S FF (Θ) = Φ(x)e k sin(θ)x dx with Re k ε eff(x c ) β > (outgoing wave)

8 Complex effective dielectric function [ ] n ε eff (x) = n eff, eff, + n eff(x) + n N (x) + n T (x) + i g eff(x) k background effective index n eff, built in effective index step n eff (x) step wise constant carrier density dependent part temperature dependent part n N (x) = Γ AZ n N N < n T (x) = n T T (I,x) > step wise constant effective gain g eff (N) step wise constant In the model, ε eff depends on current only via temperature T.

9 Theoretical model: Heat I effective heat conduction equation for lateral relative temperature profile T (x) (temperature difference to heat sink temperature) κ d T = q(x) + γt (x) dx boundary conditions dt dx x= = and lim x T (x) = dissipated power density within active stripe obtained from experimental lightvoltage-current P U I characteristics q(i) = U(I)I P(I) dwl

10 Theoretical model: Heat II temperature relaxation parameter γ determined from the condition W W/ T (x,i ) dx = calculated average temperature within the active stripe [ ] λ [λ(i ) λ()] T temperature rise determined from the experimental wavelength shift dependence of emission wavelength on injection current λ(i) = a + bi + ci

11 Experimental wavelength current characteristics w a v e le n g th λ / n m 8 B / µm c u rre n t I / A parameters of λ(i) and γ determined at I = A B / µm a / nm b / nma c / nma γ / KW m

12 Model parameters parameter value d µm W 3 µm L 39 µm κ 6 WK m n.5 4 K T λ T.45 nmk n eff, 3.33 n eff n N g eff ridge: trench: outside: ridge: -5 4 trench: outside: ridge: cm trench: outside: - cm

13 Model parameters effective-index profiles without and with heating: anti vs. real index guiding parameter value d µm W 3 µm L 39 µm κ 6 WK m n.5 4 K T λ T.45 nmk n eff, 3.33 n eff n N g eff ridge: trench: outside: ridge: -5 4 trench: outside: ridge: cm trench: outside: - cm

14 Calculated lateral far field intensity profiles B/µm same dependence on trench width and current as measured B =.5 µm: far field peaks joining at I =.4 A due to thermal lensing

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16 Measured and calculated near and far field profiles in te n s ity / a.u good agreement for both near and far field profiles despite the simple model used parameters and model o.k.

17 Conclusions thermal lensing contributes significantly to lateral waveguiding in high power narrow stripe lasers for P > W thermal lensing governs lateral waveguiding associated with pronounced far field instabilities visible in the experimental profiles as current is varied possibly caused by coherent superposition of fundamental and higher order modes very stable far field for trench width B = 5 µm minimization of thermal lensing effect crucial for increase of fundamental-spatial mode output power