Alexander Tiu


Lasers

Standing for Light Amplification by Stimulated Emission of Radiation, lasers have become incredibly commonplace in the 21st century. However what is generally less known is that they stem from quantum physical phenomenon. While society has been unable to replicate the weaponisation of laser technology seen in Star Wars or other science fiction movies, lasers still have very important places in the military, as well as other facets of our lives such as hospitals and scanning items at supermarkets. 

Fig 1: Lasers are possible due to fundamental features of quantum physics [1].

The concept and ideas used in lasers has spawned countless variations of them, which all have their unique applications and properties. Here we will look at the Quantum Cascade Laser (QCL), a laser efficient in producing infrared radiation. As its name suggests, they involve a cascading effect in the production of light. This feature allows it to emit in the infrared region of electromagnetic radiation, granting it an important and still expanding role in many industries.

Electron Transitions 
A. Energy Levels 

A fundamental aspect of quantum physics that lasers are based on is the discrete energies of electron levels within an atom [2]

Fig. 2: Left: the Bohr model depicts an atom’s electrons around its positive nucleus. Right: 4 energy levels of hydrogen. Only 4 are shown here for simplicity.

The energy associated with each level represent the amount of energy required to remove an electron from that level (This energy can come in the form of phothons). The electron eventually escapes the electrostatic attraction of the positive nucleus, and the atom ends up with an overal positive charge, i.e. ionisation has occurred. Additionally, no two energy differences between levels within an atom will be the same, as the energies are related by a 1n2 relationship.

B. Stimulated Emission 

The process where electrons decay naturally to produce photons is known as Spontaneous Emission. Spontaneous emission is not induced, and can happen at any time for an electron in an excited state. Stimulated Emission, on the other hand is the controlled process of using light to stimulate electrons in excited states to decay to lower energy levels [3]

An electron in an excited state will emit a photon when they decay to lower states. The energy of this photon is equal to the difference in energy between the excited state and the lower state, obeying the principle of conservation of energy. The electron could either transition to the ground state (interband transition), or to a lower excited state (intersubband transition). The wavelength (λ) and frequency (f) of the photon is determined by E = hf =hcλ, where h is Planck’s constant (6.626 × 1034m2kgs1) [4]

Fig. 3: Illustration of stimulated emission [5].

If photons with the same energy as the desired transition are incident on an electron in an excited state, the perturbations in the electric and magnetic field will induce a decay in energy level. This results in a photon emitted with equal energy and frequency to the incident one, while the incident photon is unaffected. 

Population inversion is a condition which must be achieved in all lasers. This requires more atoms to have electrons in excited states than in ground states, so that the probability of stimulated emission is greater than that of the photons being absorbed to excite ground state electrons. This allows stimulated emission be the dominant process overall. Population inversion is achieved by either optical pumping (with light) or electrical discharge pumping (increasing the temperature). 

C. Non-radiative Transitions 

Transitions from excited to ground states may not always result in the emission of electromagnetic radiation. The energy difference can be emitted in a different way, most commonly vibrations in the lattice structure and ultimately lost as heat energy. These are known as non-radiative transitions [6]

When it comes to lasers and photonics, non-radiative transitions inhibit efficiency, as not all the energy is being transferred to the electromagnetic radiation. However, quantum cascade lasers make use of non-radiative transitions, as the process doesn’t require all the transitions to emit electromagnetic radiation, as we’ll see in the section on Structure

Quantum Cascade Lasers 
A. Why are they useful? 

There are countless applications for each part of the electromagnetic spectrum. Standard lasers typically have wavelengths of visible light (400-700nm) [7] and ultraviolet radiation (100-400nm) [8]. Lasers that emit infrared radiation also exist, already used in medical fields and in the military. 

Quantum cascade lasers are one of the forms of lasers that emit in the infrared range, particularly the mid-infrared (3-50µm). What distinguishes them from standard infrared lasers is their high efficiency, as several photons can be produced by a single electron. 

Quantum cascade lasers are able to emit infrared because, as the higher energy levels have smaller differences in energy between them, transitions in the higher levels can produce photons with low enough energy to be in the infrared range. The process in which electrons transition from their current excited state to a lower excited state, instead of its ground state, is called intersubband transitions. This is the key feature of quantum cascade lasers.

B. Structure 

The basic idea QCLs is that an electron decaying in the higher energy level within a quantum well. Then the electron decays again to a lower energy level via a non-radiative transition. Ultimately, the electron move onto the next well, in a process known as resonant tunneling, via a voltage applied across the device, already entering in that quantum well’s excited state, and decay by the same amount as the first time, emitting a photon of equal energy to the original. The process repeats, and the result is multiple photons all of the same frequency, after initially only having to excite a single electron [9]

In terms of the composition, QCLs are made up of alternating layers of semi-conductor material. The alternating layers of atoms (generally Indium Gallium Arsenide and Alluminium Indium Arsenide, although other variations exist) form the quantum wells required for the electron energies to be quantised. 

Resonant Tunneling 

In QCLs, electrons need to move from one quantum well to the next, entering the same excited state in the next well as they started in the previous. For example, they start in n=3, transition down to n=1, then enter the next well at the n=3 level. This is done via resonant tunneling, a special form of quantum tunneling. 

But how can the electron essentially re-excite itself? The answer is that it doesn’t. However if the potential barriers (boundaries of the quantum wells) can be setup in a way that allows for this process to happen without needing to excite the electron again. Adjusting the height of the barriers will change the quantised energies inside the well, and this is as depicted below. 

Fig. 4: The effect of adjusting the potential barriers to allow resonant tunneling to take place.

On the left hand side, the energies have not been aligned and thus the electron in the n=1 energy level cannot tunnel to the n=3 level of the next well. Whereas on the right hand side, resonant tunneling occurs and the electron can move from well to well. For the quantum cascade lasers, how these barriers are setup is dependent on the superlattice itself and depends on the wavelength of laser light desired. Generally these barriers are controlled by voltages across the laser device.

Full Process 
Fig. 5: General process of quantum cascade lasers. Adapted from [10].

Figure 5 illustrates the cascade process after an electron has entered an excited state. These energy levels are just examples, while in reality they vary depending on the materials of the laser, and the wavelength desired.

1) An electron in an excited state will decay to a lower excited state, emitting a photon whose energy is equal to the difference in energy between those states. 

2) Electron decays again to a lower state, via a non-radiative transition. This does not release a photon, instead transferring the energy via vibrations in the lattice. 

3) Electron tunnels to next quantum well, via resonant tunneling. 

4) Process repeats, producing many photons of the same energy and frequency. 

Applications 

Aside from the monochromatic electromagnetic radiation they can provide, another reason quantum cascade lasers are sought after is their efficiency. As one stimulated emission will lead to many more, they naturally have much higher efficiency than standard lasers. 

As quantum cascade lasers allow for efficient production of monochromatic electromagnetic radiation in the infrared range, they have a wide range of applications which continues to widen.

Fig. 6: QCLs have a lot of important military applications, such as comabint heat seeking missiles [11].

As mentioned, the military can make great use of QCLs [12]. Heat-seeking missiles are weapons that are guided by strong sources of infrared radiation. QCLs can be used to combat these missiles, as its infrared radiation from the laser will make the missile unable to see its actual target [11]. This is similar to trying to hear someone speak when the music in the room is deafeningly loud. 

QCLs can be used to combat improvised explosive devices (IEDs) as well [13]. IEDs tend to be composed of material that absorbs infrared radiation, and thus QCLs will be able to detect the presence of IEDs in many situations. QCLs are also also useful in detecting gases, of which there are many applications [14] [15]. As QCLs will have a defined wavelength, they can be used to determine the wavelengths of infrared that a gas will absorb, creating a profile of the gas’ infrared absorption spectrum. This allows for their use in detecting gases in the atmosphere, and breath analysers. In general, this opens up more options for infrared spectroscopy, and is used very often in the field of chemistry. However, as the structure is quite complex, they are considerably more expensive to make than other laser varients. Nonetheless their traits of high efficiency and having infrared wavelength are very desirable, and hopefully once we perfect the technique they will be seen in many more industries.


References

[1] Cover Image: Christopher S. Baird. What makes the light waves in laser light parallel? Science Questions with Surprising Answers, Dec 2012. Available from: https://wtamu.edu/∼cbaird/sq/2012/12/20/what-makes-the-light-waves-in-laser-light-parallel/.

[2] Jeremy Tatum. The bohr model of hydrogen-like atoms. LibreTexts, Dec 2020. Available from: https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Book%3A_Stellar_Atmospheres_(Tatum)/07%3A_Atomic_Spectroscopy/7.04%3A_The_Bohr_Model_of_Hydrogen-like_Atoms

[3] Tom Weideman. Lasers. LibreTexts, May 2020. Available from: https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9HE_-_Modern_Physics/06%3A_Emission_and_Absorption_of_Photons/6.3%3A_Lasers

[4] Encyclopædia Britannica. Planck’s constant. Encyclopædia Britannica, Dec 2019. Available from: https://www.britannica.com/science/Plancks-constant.

[5] Thomas Edwards. How a laser works. UAF, 2011. Available from: http://ffden-2.phys.uaf.edu/212_spring2011.web.dir/Thomas_Edwards/How%20Lasers%20Work.html.

[6] Dr. Rudiger Paschotta. Non-radiative transitions. RP Photonics, Oct 2008. Available from: https://www.rp-photonics.com/non_radiative_transitions.html

[7] National Aeronautics and Science Mission Directorate Space Administration. Visible light. Nasa Science, 2010. Available from: https://science.nasa.gov/ems/09_visiblelight

[8] World Health Organization. Radiation: Ultraviolet (uv) radiation. World Health Organization, Mar 2016. Available from: https://www.who.int/news-room/q-a-detail/radiation-ultraviolet-(uv)

[9] Magdalena Wojtaszek. Superlattices as building blocks for quantum cascade lasers: a theoretical analysis of superlattice states. University of Groningen, Jun 2008. Available from: https://www.rug.nl/research/zernike/education/topmasternanoscience/ns190wojtaszek.pdf.

[10] Stefan Birner. 1d tutorial simple quantum cascade structure. nextnano. Available from: https://www.nextnano.de/nextnano3/tutorial/1Dtutorial_QCL_simple.htm

[11] Eric Takeuchi. Quantum cascade laser (qcl) technology. Sitrep, Q4 2017. Available from: https://www.leonardodrs.com/sitrep/q4-2017-defensive-protection-systems-and-technologies/to-protect-with-light/.

[12] Michael S. Walker. Quantum fuzz: the strange true makeup of everything around us. Prometheus Books, 2017.

[13] Wavelength Electronics. Quantum cascade laser basics. Wavelength Electronics, Apr 2013. Available from: https://www.teamwavelength.com/quantum-cascade-laser-basics/

[14] M. Hannemann, A. Antufjew, K. Borgmann, F. Hempel, T. Ittermann, S. Welzel, K. D. Weltmann, H. Volzke, and ¨ J. Ropcke. Influence of age and sex in exhaled breath samples investigated by means of infrared laser absorption ¨ spectroscopy. Journal of Breath Research, 5(2):027101, Jun 2011. 

[15] Erwan Normand and Iain Howieson. Quantum-cascade lasers: Quantum-cascade lasers enable gas-sensing technology. Laser Focus World, Jan 2007. Available from: https://archive.vn/20130127164107/http://www.laserfocusworld.com/display article/ 289410/12/none/none/Feat/QUANTUM-CASCADE-LASERS:-Quantum-cascade-lasers-enable-gas-sensing-technology.