and the wavelength tunability is dependent on the energy difference between the wavefunc- tions created by the applied bias in each case. So, the control over wavelength tuning and the possibility of multi-color emission is limited in single segment QCLs.
As we have seen that the same QCL structure is capable of emitting at different wavelengths under different bias conditions, we propose to segment the QCL cavity into sections and apply different bias in each section to get multi-color output from the same device.
8.4 8.6 8.8 9.0 9.2 0.0
0.5 1.0 1.5
Wavelength (µm)
Mode Gain (norm.)
V1= 60 kV/cm V2= 80 kV/cm
(a)
8.4 8.6 8.8 9.0 9.2
0.0 0.5 1.0 1.5
Wavelength (µm)
Mode Gain (norm.)
V1= 60 kV/cm V2= 50 kV/cm V3= 80 kV/cm
(b)
8.4 8.6 8.8 9 9.2
0.0 0.5 1.0 1.5
Wavelength (µm)
Mode Gain (norm.)
V1= 60 kV/cm V2= 50 kV/cm V3= 55 kV/cm V4= 80 kV/cm
(c)
8.4 8.6 8.8 9.0 9.2
0.0 0.5 1.0 1.5
Wavelength (µm)
Mode Gain (norm.)
V1= 60 kV/cm V2= 50 kV/cm V3= 55 kV/cm V4= 75 kV/cm V5= 80 kV/cm
(d)
Figure 3.11: Output emission modes of (a) 2 segment, (b) 3 segment, (c) 4 segment, and (d) 5 segment 3 mm long QCL cavity divided into segments of equal length separated by 20µm.
conditions, one might consider segmenting the device further. However, widely separated modes suffer from less total gain. In Fig. 3.11, we note that for two segment QCL, widely spaced modes have less gain compared to the others. This is due to their widely separated gain spectra. Each mode suffers considerable loss in each others bias regions and hence the total mode gain suffers.
Figure 3.12 shows the gain spectrum for two conditions when the spectra are widely apart and also when they are close together. The overall gain for the spectra close together will give much greater mode gain than the ones farther apart. So when a QCL with widely separated lasing modes are segmented into many segments the individual modes might not receive enough gain to give useful output. Figure 3.13 shows three different gain spectrums for two sets of bias conditions in a two segment QCL. For the case where the spectrums peaks are separated by an energy less than their linewidth, both modes receive considerable
7 8 9 10 0
10 20 30 40 50
Wavelength (µm) Gain (cm−1 )
V1 = 60 kV/cm V2 = 80 kV/cm G2(λ2)
G1(λ1)
G2(λ1) G
1(λ2) (a)
7 8 9 10
0 10 20 30 40 50
Wavelength (µm) Gain (cm−1 )
V1 = 60 kV/cm V2 = 55 kV/cm G1(λ1)
G2(λ2) G2(λ1)
G1(λ2)
(b)
Figure 3.12: Gain Spectrum overlap of two segment QCL under applied bias of (a)V1 =60 kV/cm,V2=80kV/cm and (b)V1 =60kV/cm,V2=55kV/cm.
gain in both bias regions resulting in the emission of both the modes. However, in the case where gain spectrums peaks are separated by an energy greater than their linewidth, the modes have very low gain in each other’s bias region. In this case, neither of the modes may receive sufficient gain to give useful output.
4 6 8 10
0.0 0.2 0.4 0.6 0.8 1.0
Wavelength ( µm)
Gain (norm.)
G1(λ1)
G1(λ2)
G1(λ3) G2(λ2)
G2(λ
1)
G3(λ1)
G3(λ
3)
∆s < γij
∆s > γ
ij
Figure 3.13: Gain spectrum overlap of two segment QCL under different bias conditions showing the effect of peak energy difference between the peak modes. ∆ s is the energy separation between the peak emission modes andγi jis the linewidth.
Therefore, segmenting the QCL cavity into too many segments are unlikely to yield useful
results. In terms of practical use the number of segments in a QCL cavity will be limited by the structures output characteristics, output mode separation under each bias condition, and the overall gain achieved by individual modes.
Another interesting phenomenon noticed in multi-segment cavity is that a new mode dif- ferent from the output modes of each segment often emerges as the dominant third output mode as shown in Fig. 3.14. Here, the otherwise suppressed mode if the QCL was a single segment cavity receives considerable amount of gain in the interaction of two separately bi- ased segments and hence gets a fair chance at becoming a dominant output emission mode.
7 8 9 10
0 10 20 30 40 50
Wavelength (µm) Gain (cm−1 )
V1= 60 kV/cm V2= 80 kV/cm
λ1 λ2 λ3 (a)
8.4 8.6 8.8 9.0
0.0 0.5 1.0 1.5
Wavelength (µm)
Mode Gain (norm.)
V1= 60 kV/cm V2= 80 kV/cm Third Mode
Figure 3.14: Emergence of a third mode in two segment QCL cavity. (a) Gain received by each mode under each segment. (b)The three modes created.
So far we have discussed QCLs with equal segment lengths. Fig. 3.15 shows the output characteristics of a two segment QCL with segment lengthsaLand(1−a)LwhereLis the total cavity length and ais the percentage of length that a segment covers. The segment lengths i.e. a is varied keeping the two applied biases constant. Here, we notice that for drastically different segment lengths the output emission mode is monochromatic following the light created by the longer length. At comparable segment lengths both the modes gain sufficient gain to be useful outputs. Whether the output will be single mode or multi-mode for variable segment length also depends on the spectrum over-lap and individual gains of
the modes.
0 1
0 1
0 1
0 1
8.4 8.6 8.8 9.0
0 1
Wavelength (µm)
Mode Gain (norm.)
8.4 8.6 8.8 9.0
0 1
Wavelength (µm)
Mode Gain (norm.)
λ1
λ1
λ1
λ1
λ1
λ2 λ2
λ2
λ2 λ2
λ2
λ1 a = 0.3
a = 0.7
a = 0.2
a = 0.5
a = 0.9 a = 0.1
Figure 3.15: Output emission modes for two segment QCL cavity for various segment lengths at applied bias ofV1=45kV/cm andV2 =60kV/cm.
Figure 3.16 shows the tuning of the third dominant mode with segment length variation.
It is found that the third mode closely follows the mode produced by the longer segment.
The third dominant mode in a two-segment QCL can be significantly tuned by changing the segment lengths. However, segment length variation is only possible at the fabrication level. Depending on the intended application and quantum mechanical design of the active region of the QCL, the proper segment length can be determined by using the developed simulation tool in this work prior to fabrication.