Temperature dependent gain characteristics by a Nd: yttrium

Figure 3.13 shows the photoluminescence spectra of the GaN-based VCSEL under different pumping power levels at 80 K. Above the threshold condition, only one lasing mode at about 407 nm dominates. The Hakki-Paoli method is one of the most common method to extract net optical gain from amplified spontaneous emission (ASE) spectra.

Therefore, the optical gain can be therefore estimated using the Hakki-Paoli [5.14 pig]

method to analyze these multiple cavity modes from the photoluminescence spectra below the threshold condition. To derive the net optical gain, we first consider a semiconductor laser in a Fabry-Perot cavity. The reflectivities of the two mirrors are R1

and R2, respectively. Now, a field P1 incident on mirror 1 and the amplitude of the reflected wave is R1^1/2F1. This first reflection travels towards morror 2 with a propagation constant k-j (α /2), where αi i is the internal loss per unit length. When a wave bounces back and forth in a Fabry-Perot cavity, its amplitude after one round trip of distance 2L has to remain at least the same to obtain gain. When the multiple reflections interfere constructively and destructive, the total incident field in a single mode are

⎪⎪

The maximum and minimum intensities with spectral measurements of Fabry-Perot modes in the cavity are I⁺ and I^-, respectively. Therefore, αi can be obtained from Eq. (3.1)

( ) ( ) _{( )}

(3.2) whereλ is the wavelength at which the cavity modes are being measured. Confinement factor of the laser structure is estimated as Γ = 0.7% by calculating the spatial overlap between the optical field and MQWs layers in the VCSEL cavity, da is the thickness of ten quantum wells, I⁺ and I^- are the maximum and minimum PL intensities for each cavity mode obtained from the measured PL spectra, R1 and R2 are DBRs reflectivities which are 99% and 98%, respectively, αi is the average internal loss of the cavity, which is dominated by the absorption of thick GaN layer and was set to be 42 cm^-1 at room temperature [3.8] and L is the cavity length. Under different pumping levels, the I⁺ and I -would vary and the individual gain for each cavity modes can be obtained from the eq.

(3.2). The gain spectra of the VCSEL under different pumping power levels at 80 K are shown in Figure 3.14. Each data point was calculated from the corresponding cavity mode in Figure 3.13. The gain curves show an increasing trend as the pumping intensity increases and the gain bandwidth keeps broadening. In addition, the mode peaks blue shift due to the increase of the optical gain. At 80k, the peak gain of 2.2×10³ cm-1 was obtained at threshold condition with a carrier density of 6.8×10¹⁹ cm-³. The gain spectra under different temperature (at 150K, 220K and 300K) were also obtained with the same measurement and calculation method, respectively. The pumping carrier density dependence of the peak gain of the lasing mode (at about 407 nm) is plotted in Figure 3.15 for different measurement temperature. Here the carrier density in QWs was estimated from the power density of the pumping laser assuming that the pumping light

( ) ( )

with the emission wavelength of 355 nm has experienced a 60% transmission through the SiO /Ta O2 2 5 DBR layers and undergone a 98% absorption in the thick GaN layer with a absorption coefficient of 10⁴ cm^-1 [3.9]. At 80k, the threshold carrier density was estimated to be about 6.8×10¹⁹ cm^-3. The figure shows that the carrier density required to reach a given gain increases with increasing temperature and we can observe the gain increase more rapidly as a function of the injected carrier density at lower temperature. It could be resulted from several reasons: (1) The ratio of radiative to nonradiative recombination is lower at high temperature than that at low temperature. (2) The carrier overflow becomes pronounced at higher temperatures resulting in less radiative recombination in the MQWs and consequently a lower gain [3.10]. (3) The main cause is the broadening of Fermi occupation probability function which spreads carriers over a larger energy range for a given overall carrier density. The result is a lower spectral concentration of inverted carriers, which leads to a broadening of the gain spectrum.

Semiconductor lasers exhibit a strong variation of refractive index and optical gain when injected carrier concentration changes. The parameter describing this dependency is called linewidth enhancement factor (α-factor) [3.11]. It is an important parameter of semiconductor lasers, such as laser linewidth and chirp. We can estimate the linewidth enhancement factor from the ASE spectra below the threshold condition [3.12]. The α-factor is the ratio of the change of the refractive index (n) with carrier density (N) respect to the change in optical gain with carrier density and can be expressed by

dg d L

λ λ α π

= 2Δ

(3.3)

where Δλ is the cavity mode spacing, L is the cavity length, dλ is the wavelength shift

density (N). Hence, the α-factor can be obtained from the emission spectra under different pumping power levels below the threshold from Eq. (3.3). The estimated α-factors under different temperature are shown in Figure 3.16. At the lasing mode, the α-factors decrease as the ever-declining temperature. The α values increase as the increasing temperature owing to the increment of carrier density in the QWs. For the lasing mode, the α-factors varied from 4.3 to 0.6 as the temperature varied from 300K to 80K. In comparison to the InGaN/GaN edge emitting laser structure that the α value varies between 2.5 and 10 [3.13], the linewidth enhancement factor in the GaN-based VCSEL structure is smaller.