Measurement of gain characteristics of semiconductor lasers by amplified spontaneous emissions from dual facets

M-L Ma; J Wu; Y-Q Ning; F Zhou; M Yang; X Zhang; J Zhang; G-Y Shang

doi:10.1364/OE.21.010335

1. Introduction

Optical gain is an important physical parameter in assessing semiconductor laser performance. Although the gain spectra can be calculated in theory, some problems are always encountered, such as the approximation treatment to some coefficients in equations, because they are difficult to be determined in the calculation. Moreover, the inevitable structure defects of the device resulting from fabrication mean that the gain from completely theoretical calculation represents only an ideal situation of the device performance.

Since the 1970s some methods have been developed to measure the gain of semiconductor lasers and to obtain true gain spectra from actual device operations. The main techniques involve those developed by Hakki-Paoli and Cassidy [1–3], Henry [4], Oster et al [5, 6], Thomson el al [7–12] and Troger [13]. However, there are always several drawbacks in these methods. For instance, Hakki-Paoli’s method requires high spectral resolution of the measurement system [14], in order to resolve the longitudinal modes generated in F-P cavity. This increases the complexity in the experimental determination of the gain. Henry’s technique is based on the calculation of Fermi-level separation and absorption coefficient, and thus, it does not give the gain in absolute units so that the calibration is needed. Moreover, these two techniques are only suited for the small-signal gain measurement below the threshold point. In the Oster’s method, the use of different lengths of contact stripes in the amplified spontaneous emission (ASE) collection leads to the difficulty in ensuring a uniform collection efficiency of the spontaneous emission for every stripe so that the disparity with true gain spectra of the laser diode cannot be avoided. In the Thomson’s approach, the carrier diffusion between segments will inevitably lead to non-uniformity of the carrier distribution in each section, particularly in the case of high current density [15]. This will affect the gain measurement accuracy. In addition, the multi-section structure of the sample requires fairly precise etching processing, and thus increases the difficulty in experimental preparation. With Troger’s approach, the gain can be measured directly using the laser strip. However, the use of an additional light source will bring difficulty in achieving correct light coupling and signal collection between the light source and the diode.

In this paper, we develop a convenient and effective approach to measuring gain spectra of semiconductor lasers. This method is based on the collection of the ASE at dual facets of the laser strip itself. First, the measurement principle is described. Then, transverse-electric (TE) and transverse-magnetic (TM) gain spectra of an unstrained edge-emitting GaAs/AlGaAs single quantum well laser strip with continuous current injection are measured and compared with theoretical gain spectra. Finally, the TE and TM gain-related heavy hole (HH) and light hole (LH) subband structure in valence band of the well regarding different carrier densities and continuous operation of the device are discussed using the gain data.

2. Gain measurement principle

A diagram describing the amplified spontaneous emissions to be measured at dual facets of a laser diode is shown in Fig. 1, where the reflectance of the two facets are designed as R₁ = 0 and R₂ = R, respectively, and R can be any value of reflectivity which can be obtained by coating easily. R₁ is designed as zero to avoid the intra-cavity light feedback at the facet. The ASE₁ collected at R₁-facet of the device consists of two ASE beams. One comes from the direct single-pass ASE beam to the R₁-facet. The other is from the reflected part of the ASE beam by R₂-facet.

Fig. 1 Diagram of gain measurement model based on the ASE collected from dual facets.

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Since these two beams come from the same light source, they are coherently superposed with each other and result in the total intensity of I_ASE1, while the ASE₂ collected at R₂-facet of the device consists only of the transmitted part of the single-pass ASE beam through the R₂-facet, which results in the intensity I_ASE2. Thus, the ASE intensities from the dual facets can be described mathematically as follows, in terms of the optical gain definition and the beam interference.

I_{A S E_{2}} = \int_{0}^{L} I_{s p} e^{G x} (1 - R) \cdot d x .

I_{A S E_{1}} = \int_{0}^{L} I_{s p} [1 + R e^{2 G x} + 2 \sqrt{R} e^{G x} \cdot \cos (2 k x)] e^{G (L - x)} \cdot d x .

where I_sp is the spontaneous emission intensity from the light source, L denotes the length of active region, k is the wave number, G is the modal gain coefficient, and x indicates the light propagation direction. With integrals of Eq. (1) and Eq. (2), the ASE intensities from both facets can be expressed, respectively, as

I_{A S E 2} = \frac{(1 - R) I_{s p}}{G} (e^{G L} - 1) .

I_{A S E 1} = \frac{I_{s p}}{G} (e^{G L} - 1) ({Re}^{G L} + 1) \cdot [1 + \frac{λ \sqrt{R} \cdot G e^{G L}}{2 π \cdot (e^{G L} - 1) (R e^{G L} + 1)} \sin (2 k L)] .

where λ is the wavelength in the gain medium. The calculation shows that the interference term

\frac{λ \sqrt{R} \cdot G e^{G L}}{2 π \cdot (e^{G L} - 1) (R e^{G L} + 1)} \sin (2 k L)

in Eq. (4) ranges between a value of 0 to 10⁻⁵ for any of G and R values with the given L and λ. For G → 0, this result is still correct by using the L′Hospital rule in mathematics. Thus, the interference term can be ignored as a good approximation, and the Eq. (4) is simplified as

I_{A S E 1} = \frac{I_{s p}}{G} (e^{G L} - 1) ({Re}^{G L} + 1) .

By combining Eqs. (3) and (5), the mode gain G can be obtained as

G = \frac{1}{L} \ln \frac{(1 - R) I_{A S E 1} - I_{A S E 2}}{R \cdot I_{A S E 2}} .

3. Experimental preparation and results

The experimental sample for the gain measurement is grown by metal-organic chemical vapor deposition (MOCVD). The active region of the device involves an unstrained 4 nm-thick GaAs single quantum well, which is sandwiched by Al_0.25Ga_0.75As waveguide core with a thickness of 0.145 μm. The cladding layer is 1.2 μm in thickness and the strip length is 1200 μm. On one facet of the sample, the anti-reflectance coating with T = 99.99% is applied, and there is no coating on the other facet. It means that the reflectivity of this facet is determined by the refractive indices of both quantum well and waveguide core materials, which is expressed as

R = {(\frac{n_{A l_{x} G a_{1 - x} A s} - n_{a i r}}{n_{A l_{x} G a_{1 - x} A s} + n_{a i r}})}^{2} .

where

n_{a i r} \approx 1

,

n_{A l_{x} G a_{1 - x} A s}

is determined by Sellmeier equation

n (x, λ) = \sqrt{A + \frac{B}{λ^{2} - C} - D λ^{2}} .

where the coefficients of A, B, C and D are related to Al content in Al_xGa_1-xAs. As the quantum well layer is fairly thin (4 nm), compared with the waveguide core thickness (145 nm), the reflectivity of the facet is mainly determined by the refractive index of the guiding layer. Thus, the reflectance spectrum of the facet is calculated with x = 0.25. Certainly, the reflectivity, R can also be designed by applying a reflectance coating on this facet. Since the light feedback in the cavity is suppressed by the R₁-facet, the injection current is no longer restrained by the threshold point. Thus, the modal gain larger than the threshold can be measured. Using a polarizer, the ASE spectra of TE and TM polarizations are collected at the dual facets with continuous current injection under room temperature. The results are shown in Fig. 2. So the TE and TM gain spectra can be worked out using Eq. (6).

Fig. 2 ASE spectra of TE and TM polarizations measured at dual facets with a continuous current density of 30A·cm⁻² at room temperature.

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Figure 3 shows TE (solid lines) and TM (dash lines) modal gain spectra over a current range of 10 A·cm⁻² - 90A·cm⁻². With the gain spectra at long wavelength side of the band edge in Fig. 3, the internal loss coefficient α can be evaluated to be 2 - 8 cm⁻¹. The peak gain as a function of the current density is plotted in Fig. 4. The results in Figs. 3 and 4 show that TE gains are nearly the same as TM gains at the short wavelength side for low current densities. This at least confirms that there is no strain generated in the quantum well layer from fabrication. It approves the theoretical design of the unstrained GaAs/AlGaAs quantum well. The material gain of the device may be obtained by the modal gain conversion using the relationship of G = Γg - α. With the definition of optical confinement factor [16] and the sample structure parameters given above, the Γ can be estimated to be 0.015.

Fig. 3 Modal gain spectra measured over a current range of 10 A·cm⁻² to 90 A·cm⁻².

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Fig. 4 Peak gain as a function of the current density.

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To analyze the HH and LH subband mixing situation in the valence band under different carrier densities and continuous operation condition with gain data, the theoretical gain curves of TE and TM polarizations are also calculated. The four-band k⋅p model including the valence-band mixing and the Lorentzian broadening is used. Since the injection current level is not too high for the continuous operation of the device concerning thermal effect influence on the gain measurement, the many-body Coulomb interaction is ignored in the gain modeling. The calculated material gains of TE and TM polarizations at room temperature are plotted in Fig. 5. The current densities of 10 A⋅cm⁻³ – 90 A⋅cm⁻³ correspond to the carrier concentrations of N = 1.45 - 4.6 × 10¹⁸ cm⁻³.

Fig. 5 Calculated material gains with various carrier densities.

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The calculated HH and LH subband distribution in the valence band is plotted in Fig. 6. It can be clearly seen from Fig. 6 that there are three subbands of HH1, LH1 and HH2 in order, all of which are near to the top of the valence band for the unstrained structure. In comparison with the theoretical gain curves, the dual peaks in the TE gain curves are corresponding to the electron-hole recombination between the conduction band and the HH1, HH2 subbands, respectively, while the single TM gain peak mainly comes from the electron-hole recombination between the conduction band and the LH1 subband.

Fig. 6 Calculated HH and LH subbands in the unstrained GaAs quantum well for a fixed carrier density.

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Since the gain generated at the long wavelength side is mainly from the electron-hole recombination between the conduction band and the HH1 subband around the wave vector kt = 0, the TE gain will be larger than the TM gain in this region. This can be interpreted by the transition matrix element (TME) theory [16], in which the TME magnitudes of TE and TM polarizations are ${| M |}_{T E}^{2} = {| M |}^{2} / 2$ and ${| M |}_{T M}^{2} = 0$ , respectively, which are corresponding to the electron-hole recombination between the conduction band and the HH1 subband, where ${| M |}^{2}$ is the fixed momentum matrix element and TME is associated with the recombination rate. At the short wavelength side, the TM gain may be larger than the TE gain, as the electron-hole recombination happens mainly between the conduction band and the LH1 subband. In this case, the TME values for TE and TM polarizations are changed to ${| M |}_{T E}^{2} = {| M |}^{2} / 6$ and ${| M |}_{T M}^{2} = 2 {| M |}^{2} / 3$ , respectively.

Some differences between the measured gain spectra and the theoretical result can be seen from Figs. 3 and 5. This should come from two effects. One is the many-body Coulomb interaction in the well, which may cause the gain detuning due to the bandgap reduced. This effect is ignored in the gain modeling. The other is related to the thermal effect induced by continuous current injection, which can lead to self-heating in the device and thermal gain detuning to long wavelength direction and peak gain reduction. This is why the gain curve spaces become smaller at the short wavelength side and larger at the long wavelength side, in comparison with the theoretical gain curves in Fig. 5. The experimental result in Fig. 3 reflects the true gain status for the continuous operation of the device, and thus is meaningful in assessing and examining fabrication defects and performance of the device.

4. Conclusions

A convenient and practical approach to measuring gain polarization characteristics of edge-emitting semiconductor lasers is developed and described in this paper. This method is based on the collection of the amplified spontaneous emissions from dual facets of the device. The gain measurement is carried out using an unstrained GaAs/AlGaAs single quantum well laser strip under the continuous operation and the room temperature. The experimental result is compared with theoretical gain curves. The electron-hole recombination related to the HH and LH subband structure with different injection current levels and continuous operation of the device is analyzed. Since the measured gain spectra reflect the true gain status from the device operation, it is quite useful in assessing and examining the fabrication defects and performance of the device.

Acknowledgments

The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (Grant No. 10974012) and for this work. F. Zhou acknowledges the support from the IUP Innovation Research Award.

References and links

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Measurement of gain characteristics of semiconductor lasers by amplified spontaneous emissions from dual facets

Abstract

1. Introduction

2. Gain measurement principle

3. Experimental preparation and results

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (6)

Equations (8)

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