in the

We develop a comprehensive theoretical model for the design and analysis of the output characteristics of a multi-segment QCL. A multisegment cavity QCL was found to produce a multicolor output if the modes generated in the segments receive enough gain to overcome the cavity losses.

Quantum Cascade Lasers

The QCL structure was designed through careful band structure engineering to produce periodic arrangements of a unit cell. Since the first demonstration of a successful QCL, remarkable advances have been made in device performance.

Figure 1.2: Schematic illustration of band structure of the supperlattice device proposed by Kazarinov and Suris [2].

Importance of Quantum Cascade Lasers

The resulting transmittance or absorbance spectrum then provides information about the molecular structure of the sample. This makes them an ideal source for many such applications in the mid-infrared region that require relatively high power, small package footprint and low power consumption [15].

Figure 1.4: Spectral absorption signatures for molecular trace gases [1].

Objectives and Organization of Work

The electric field distribution in a multi-segment QCL cavity is also shown, and based on the results, limitations on the number of segments and the length of the QCL cavity are investigated. The change in the QCL output when the number of segments in the cavity, biases applied to the segments and the length of the segments are changed are discussed in detail.

Proposed QCL Structure

Active Region Designs

Lattice Matched Structures

The peak emission mode of this QCL is centered around 8.5 µm[27], while the active region in the other design consists of two wells and the radiative transition occurs diagonally with the peak emission mode centered around 5.5 µm[28]. The simulated conduction band diagram for one period of injector and active region and wave functions of the two QCL structures are shown below in Fig.

Strain Compensated Structure

The active and injection regions of the strain-compensated structure used in our work are grown from In0.61Ga0.39AsQWs and In0.45Al0.55Asbarriers. The strain-compensated structure has a barrier height of 650 meV and is designed to emit in the critical 4.5µm region [1]. In Fig.

Figure 2.4: Conduction band diagram and moduli-squared wave-functions of one period at 65kV/cm applied electric field and 300 K temperature.The structure details are provided in Appendix A: Table A.2.

Cavity Designs

The only wavelength selectivity is from the wavelength dependence of the gain medium and the requirement for an integer number of wavelengths in a cavity round trip. Fabry-P´erot lasers are capable of producing high powers [30], and are typically multi-mode output lasers, which suits our purpose of producing a multi-color output from a multi-segment QCL.

Electric Field Distribution in Multi-Segment QCL

So, while calculating the gain of a 3 mm long QCL with two segments under different bias conditions, we can assume that the cavity is separated into two regions with different constant electric field distribution. The validity of our approximation of the QCL segments under uniform electric field depends on the dimensions of the device, the segments, and the segment spacing. So our unit length must be chosen carefully to assume QCL cavity with uniform electric field distribution in each region and negligible non-uniform region.

As the number of segments increases, the percentage of voids under a non-uniform electric field increases as the segment length and segment separation length ratio decrease.

Figure 2.7: Surface electric potential plot of a two segment QCL with equal segment lengths biased at 60 kV/cm and 80 kV/cm.

Summary

In a multi-segment QCL, the cavity is divided into regions of different electric field distributions defined by the bias applied to that segment. Different segments therefore give rise to different gain spectra and emit light of different wavelengths. The different wavelengths of light propagating in the cavity experience different gain in each segment.

The net modal gain of a mode is determined by considering the effect of all the different gains that the mode experiences as it travels through the different segments.

Gain Modeling

Gain Equation

The peak material gain between two subbands i and j in the conduction band of a QCL with the assumption of Lorentzian line shape is given by [28]. Peak profit can also be expressed in shorter form as. where gc is the gain cross section and Nis is the population inversion parameter given by . The confinement factorΓ refers to the ratio of modal gain to the gain in the active region of the laser.

It depicts the percentage of generated gain that the laser can give as output [31].

Important Gain Parameters

3.5) The confinement factorΓ refers to the ratio between modal gain and gain in the active region of the laser. One and a half periods of the QCL structure consisting of collector, active and injector regions are considered. This implies that the injection rates on either side of the active region are equal.

The procedure is repeated until self-consistency is achieved; i.e. the estimate is sufficiently close to that of the previous iteration.

Figure 3.1: Various levels required for calculation of carrier density.

Gain Spectrum

Modes

Axial Modes

In case of bias change, the effective refractive index can be assumed to be constant. For a multimode quantum cascade or Fabry-P´erot laser, the laser output will be the modes that have gain over the laser cavity losses as shown in Fig. However, as the bias increases, the spectrum narrows and limits the number of modes of oscillation.

In a multi-segment QCL cavity, the modes that persist are the modes supported by the entire cavity, not just the modes supported by each segment.

Modeshape

Overall Gain Modeling

Thus, by applying different bias voltages in different segments of a multi-segment QCL, the laser can be operated to give multiple output wavelengths. Depending on the quantum mechanical design of the QCL active region, the segment lengths and bias conditions can be manipulated to give a wide tuning range and multicolor broadband emission.

Figure 3.5: Schematic illustration of an N segment QCL.

Output Characteristics of Single-Segment QCL

It emits in a range very useful for the detection of trace gases such as CO2, N2O and CO. It can be tuned to detect each molecule separately using a single segment, or all three using three QCL segments. If this mode can be tuned to resonate with the CO2 wavelength, then the same structure can be used to detect all three molecules.

As we have seen that the same QCL structure can emit at different wavelengths under different bias conditions, we propose to segment the QCL cavity into sections and apply different biases in each section to obtain a multi-color output from the same device.

Figure 3.8: Output emission modes of vertical transition single segment QCL under differ- differ-ent bias conditions.

Output Characteristics of Multi-Segment QCL

However, strongly separated modes suffer from lower total gain. 3.11 we note that for a two-segment QCL, the widely spaced modes have lower gain compared to the others. Overlay of the gain spectrum of two QCL segments under different bias conditions showing the effect of the difference in peak energy between the two peak modes. s is the energy separation between the highest emission species and γi ji is the line width. Here we note that for drastically different segment lengths, the output emission mode is monochromatic, following the light produced by the larger length.

The third dominant mode in a two-segment QCL can be significantly tuned by changing the segment lengths.

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 20 µm .

Design of a Multi-Color Multi-Segment QCL

Depending on the intended application and the quantum mechanical design of the active region of the QCL, the appropriate segment length can be determined by using the simulation tool developed in this work prior to fabrication. Analyzing the behavior of a single segment QCL under different applied bias conditions to identify the available emission modes of the device and match them to the required wavelengths needed for molecule detection. Choosing the number of contact metal layer segments to be created on the device based on the number of usable individual modes available and choosing the device length taking into account the ratio of the segment length to the segment separation length.

Fabrication of the device and application of an appropriate bias to obtain the desired output for the detection of multi-molecule detection.

Summary

The number of possible segmentations is also limited by the segment separation length and the segment length ratio due to the significant non-uniformity of the electric field arising in the cavity. Since we have a segmented device, we can attach different thermocouples to different segments to create regions with different refractive indices in the same QCL cavity as shown in Fig. The modes that are supported by all regions are those that are able to hold in the cavity.

So by changing the temperatures in the segments, the stable modes in the cavity can be changed, which allows us to get different wavelengths of emission from the same device.

Figure 4.1: Schematic illustration of an N segment QCL with heat sinks attached.

Effective Refractive Index

In the case of alloy materials, the temperature-dependent band gaps of the components, EAg and EBg, are calculated by Eq. For that purpose, additional model parameters are needed for the higher energy valleys in the respective III-V binaries. The refractive index variation with temperature using the above equations is shown in Fig.??.

From Fig.??, we see that the effective refractive index of both material systems increases almost linearly with increase in temperature.

Table 4.1: Values of E g , 0 , α and β for different materials.

Effects of Segment Temperature Variation

Temperature Tuning in Multi-Segment QCL

To observe the temperature tuning in a multi-segment QCL, we have solved the sustainable modes using Lumerical MODE solutions in the Lumerical FDTD Solutions suite. To model the multi-segment QCL with varying temperature ranges, the cavity is divided into regions with different refractive indices as shown in Fig. As the temperature is varied in one segment while the other is kept fixed at 300 K, mode tuning is observed.

Variation of Segment Temperature keeping Bias Constant

This large difference of 0.6 µm between the wavelengths shows that the same structure can be used to detect multiple trace gases, as the absorption peaks of many gases are separated by only 0.2−0.4 µm.

Variation of Segment Temperature and Bias

Summary

Gini, "Broadband tuning of external cavity coupled-to-continuum quantum cascade lasers," Applied Physics Letters, vol. Belkin, "Mid-infrared quantum cascade lasers with electrical control of the emission frequency," IEEE Journal of Quantum Electronics, vol. Razeghi, "Extended electrical tuning of quantum cascade lasers with digital linked gratings,” Applied Physics Letters , vol.

Harrison, “The role of temperature in quantum-cascade laser waveguides,” Journal of Computational Electronics, vol.

Table A.1: Layer sequence of lattice matched two phonon resonance vertical transition structure starting from active region quantum well.

Schematic illustration of band structure of the supperlattice device pro-

Schematic illustration of band structure of a quantum cascade laser consist-

Spectral absorption signatures for molecular trace gases [1]

Schematic diagram of different layers of a fabricated QCL device

Schematic diagram of proposed segmented QCL

Conduction band diagram and moduli-squared wave-functions of one pe-

Schematic diagram of Fabry-P´erot cavity QCL