High power room-temperature design of terahertz quantum cascade laser based on difference frequency generation

Optik 125 (2014) 979–983

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High power room-temperature design of terahertz quantum cascade laser based on difference frequency generation A. Selkghaffari, A. Rostami ∗ , H. Baghban, M. Dolatyari School of Engineering-Emerging Technologies, University of Tabriz, Tabriz 5166614761, Iran

a r t i c l e

i n f o

Article history: Received 15 March 2013 Accepted 20 July 2013

Keywords: Terahertz Room Temperature Quantum Cascade Laser High Power

a b s t r a c t Terahertz (THz) quantum cascade lasers (QCLs) are key elements for high-power terahertz beam generation for integrated applications. In this study, we design a highly nonlinear THz-QCL active region in order to increase the output power of the device especially at lower THz frequencies based on difference frequency generation (DFG) process. It has been shown that the output power increases for a 3.2 THz structure up to 1.2 ␮W at room temperature in comparison with the reported power of P = 0.3 ␮W in [1]. The mid-IR wavelengths associated with this laser are 1 = 12.12 ␮m and 2 = 13.93 ␮m, which are mixed in a medium with high second-order nonlinearity. A similar approach has been used to design an active region with THz frequency of 1.8 THz. The output power of this structure reaches to 1 ␮W at room temperature where the mid-IR wavelengths are 1 = 12.05 ␮m, 2 = 12.99 ␮m. © 2013 Published by Elsevier GmbH.

1. Introduction Terahertz quantum cascade lasers are the most considering electrically pumped semiconductor lasers in the spectral range of 1–5 THz or the wavelength region from 60 to 300 ␮m [1]. There have been a growing interest in fields using THz waves, for imaging, spectroscopy, communications, signal processing, quantum information, security screening, (bio) chemical detection, remote sensing, nondestructive materials evaluation, astronomy, biology, and medicine [2,3]. Room-temperature operation and efficient output power are the most controversial issues in these fields. The main problem in demonstration of room- temperature THz lasers is the THz energy band gap which is smaller than the energy proportional to ambient temperature. So, all the energy levels will be filled at room temperature and no population inversion will occur. The record operating temperature of 178 K at 3 THz has been reported for THz-QCLs [4]. Recent progresses have led to higher operating temperatures up to 200 K, but through thermoelectric coolers. The maximum operating temperatures of THz QCLs tend to be lower for devices operating at frequencies both higher and lower than ∼3 THz. Because of electron transit time and resistance–capacitance limitations, the power generated by electronic devices is currently well below the milliwatt level for frequencies above 1 THz [3]. Also, photonic devices generating THz radiation at room-temperature are limited to optically pumped gas

∗ Corresponding author. E-mail address: [email protected] (A. Rostami). 0030-4026/$ – see front matter © 2013 Published by Elsevier GmbH. http://dx.doi.org/10.1016/j.ijleo.2013.07.096

lasers, free-electron lasers, and the frequency down-conversion systems that require high-power laser pump sources [5]. These photonic devices are either bulky, provide low power output, or can only operate in pulsed mode. Different approaches may be utilized to improve the temperature performance of THz QCLs [6], including improving the active region designs for existing GaAs/AlGaAs or InGaAs/AlInAs THz QCLs, utilizing new materials systems, and using 0-D heterostructures. In particular, the GaN/AlGaN system has been suggested, because its large LO-phonon energy (about 90 meV) would present a high barrier to thermally activated optical phonon scattering [7]. In this paper we have utilized an integrated optical nonlinearity for difference frequency generation (DFG) into the active region of a dual wavelength mid-IR QCL [8], using band structure engineering of the QCLs active region [9]. Since mid-IR QCLs have been shown to operate at room temperature [10], this approach will lead to room-temperature THz QCL. Using an integrated optical nonlinearity for DFG into the active region [1], output power achieved with silicon lens are 7 ␮W at 80 K, 1 ␮W at 250 K and 300 nW at room temperature. With surface emitting waveguide design, the reported output powers are 1 ␮W at 80 K and 70 nW at 300 K. At first part we have increased output power in comparison with [1] in same output frequency by enhancing the second order nonlinearity through inserting structures with high nonlinearity into the active region of laser. Because of the wide application of low frequency QC terahertz lasers, such as low frequency QC terahertz lasers that has been investigated as a local oscillator in the context of the development of terahertz receivers for the Stratospheric Observatory for Infrared Astronomy (SOFIA) [11], many materials such as explosives and drugs have similar

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spectral features in the 1–2 THz range [12–15]. At second part we have used previous technique but at lower frequency (f = 1.8 THz) and increased output power. At mentioned paper a nonlinear process is used to produce THz radiation which is named Different Frequency Generation (DFG). The main advantage of this approach is its independence of operating temperature. So, room temperature THz QC lasers are achievable. In [1] active region is composed of two parts: Boundto-continuum and Two-phonon-resonant. Bound-to-continuum transition allows us to eliminate confinement of upper state which was done through separating structure into active region and injection/relaxation parts [16]. The upper state is efficiently separated from miniband which is created by chirped superlattice [17,18]. So, the probability of leakage current from upper level to higher states is significantly reduced. Moreover, according to (1), to have a sufficient DFG process a structure with high nonlinearity is needed. According to [19–23], nonlinearity of QC structures in mid and farIR is intrinsically high. So, bound to continuum part is a proper ambient for DFG process. However, high nonlinearity in bound to continuum structures is a consequence of resonance between all interacting fields and intersubband transitions [1]. So, there will be a strong absorption of mid-IR and THz DFG emission. This problem is solved by adding second part to active region. Therefore, we have both efficient DFG process and high power simultaneously [1]. We have increased output power of [1], which introduced previously, by inserting structures with high nonlinearity to active region. According to (1) terahertz power is a function of second order nonlinearity coefficient. So, any increase in (2) will lead to enhancement in the output power. Pω3 =ω1 −ω2 ≈

ω32 8nω1 nω2 nω3 ε0 c

   (2) 2 Pω1 Pω2 2  leff  DFG  3 A

(1)

eff

In (1) Pω1 and Pω2 are mid-IR powers, nω1 , nω2 , nω3 are the refrac(2)

tive indices of waves at ω1 , ω2 and ω3 frequencies, DFG is the second-order nonlinear susceptibility for the DFG process, Aeff is the effective area for the interacting fields and leff is the effective length of interaction. The values of nω1 , nω2 , nω3 are 3.19, 3.17 and 3.2, respectively. leff = 80 ␮m and Aeff = 4 × 103 ␮m2 have been considered based on [9,24].Pω1 and Pω2 are mid-IR powers which can be obtained from (2) in which 0 is power output coupling efficiency, W and L are the width and length of the cavity respectively, Sp is the photon density inside the optical cavity,  p the photon lifetime inside the cavity. ω is the energy associated with appropriate transport. Pmid-IR = 0 ω

WLSp p

(2)

Difference frequency generation DFG is a nonlinear optical process in which two beams at frequencies ω1 and ω2 interact in a medium with an effective second-order nonlinear susceptibility (2) to produce radiation at frequency ω = ω1 − ω2 [8]. The expression for nonlinear susceptibility simplifies to: (2) (ω3 = ω1 − ω2 ) ≈ ×



z12 z23 z31 e3 2 ε0 (ω3 − ω23 + i23 )

N1 − N3 N1 − N2 + (ω1 − ω13 + i31 ) (−ω2 + ω12 + i21 )

Fig. 1. (a) and (b) Schematics view of the THz source based on intracavity DFG in a dual-wavelength mid-IR QCL. The active region generates light output at mid-IR frequencies ω1 and ω2 through the laser action, and light output at a THz frequency ωTHz through the DFG process and the active region components.

A coupled quantum well structure with (2) = 106 pm/V for DFG at 60 ␮m was reported in [22], four orders of magnitude larger than that of traditional nonlinear crystals (LiNbO3 , GaP, GaAs, etc.) [7]. The difference between the value of nonlinearity in [22] and the structure that we have used originates from the value of  , broadening of transition between the states, which is  = 7.5 meV for structure introduced in [1] and  ∼ 1–2 meV for [22]. Although, the calculation of electron transport in a THz QCL is a critical problem, simple rate equations can be used to analyzing coupled electronic and electromagnetic systems. We have three energy levels, so equations number (4)–(6) are clarifying electrons transportation and equations number (7)–(9) are for photons. N3  c 2e2 E32 |z32 |2 dN3 J N3 − − (N3 − N2 ) N = 3 − e 32 31 Np neff cε0 neff Lp 32 ph3 dt − (N3 − N1 )

(3)

where Ni are the population densities in the electron states i = 1, 2 and 3 and ezij , ωij , and  ij are the dipole matrix element, frequency, and broadening of the transition between states i and j, respectively. We have used the parameters according to [1], so the results are completely comparable. Parameters are  ≈ 0.4, ˛wg ≈ 8 cm−1 , and ˛m ≈ 3 cm−1 ,  ij ≈ 7.5 meV, Ne and |(2) | that have been used in calculations. The length of the cavity is 3 mm and the cavity width is about 10 ␮m. Fig. 1 illustrates a schematic of DFG process.

(4)

dN2 J N2 N1  c 2e2 E32 |z32 |2 N3 = 2 + − + +(N3 − N2 ) N e 32 21 21 Np neff cε0 neff Lp 32 ph3 dt − (N3 − N1 )

 c 2e2 E31 |z31 |2 N Np neff cε0 neff Lp 31 ph2

(5)

dN1 N2 N3 N1 N1  c 2e2 E31 |z31 |2 = + − − + (N3 − N1 ) N 21 31 1 21 Np neff cε0 neff Lp 31 ph3 dt + (N2 − N1 )



 c 2e2 E31 |z31 |2 N Np neff cε0 neff Lp 31 ph2

 c 2e2 E21 |z21 |2 N Np neff cε0 neff Lp 21 ph2

(6)

In above equations, J is the density of electronic current (in the direction of electron transport) following through device,  is the injection efficiency of active region, Np is the number of repeated modules in QCL and  is the fraction of optical mode that overlaps with the entire active region. N3 , N2 , N1 are the electron populations associated with intersubband energy levels 3, 2 and 1.  ij are the carriers scattering times between levels i and j, neff is the effective refractive index of the laser mode, Eij are the difference between the eigenvalues of i and j energy levels, zij are the dipole matrix elements of energy levels associated with

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Table 1 Optical parameters for device simulation. Parameters for band structures

Bound-to-continuum at3.2 THz

Two-phonon-resonance at 3.2 THz

Bound-to-continuum at 1.8 THz

Two-phonon-resonance at 1.8 THz

Z32 Z31 Z21  32  31  21

32

31

21  Lp neff

3.225 nm 1.669 nm 11.317 nm 1.74 ps 3.38 ps 1.17 ps 7.5 meV 7.5 meV 7.5 meV 0.4 80 nm 3.2

3.274 nm 0.354 nm 6.127 nm 2.17 ps 12.2 ps 1.78 ps 7.5 meV 7.5 meV 7.5 meV 0.4 80 nm 3.2

2.828 nm 2.48 nm 13.398 nm 2.76 ps 2.48 ps 1.14 ps 7.5 meV 7.5 meV 7.5 meV 0.4 80 nm 3.2

3.176 nm 0.334 nm 6.055 nm 2.41 ps 13.17 ps 1.64 ps 7.5 meV 7.5 meV 7.5 meV 0.4 80 nm 3.2

i and j energy levels and ij is the broadening factor. The sentences which contain Ni parameters denote spontaneous emission and sentences which contain the difference of electrons population (Ni − Nj ) denote stimulated emission.  21 =  12 × exp (E12 /KT) reveals the thermal backfilling transitions time in which,  12 is the reverse transition time between levels number one and two depicted in Fig. 1, E12 is the difference of energy between these levels, k is the Boltzmann constant and T is the operation temperature. These equations are solved for two terahertz frequencies f = 3.2 THz and f = 1.8 THz. The calculated and utilized parameters are listed in Table 1. Eqs. (7)–(9) describe the photons dynamics, including nph1, 2,3 as the number of photons per unit energy (in Joules−1 ) generated into all available cavity modes and  phi as photons lifetimes in the cavity. dNph3 dt dNph2 dt dNph1 dt

= (N3 − N2 )

Nph3  c 2e2 E32 |z32 |2 N − Np neff cε0 neff Lp 32 ph3 ph3

(7)

= (N3 − N1 )

Nph2  c 2e2 E31 |z31 |2 N − Np neff cε0 neff Lp 31 ph2 ph2

(8)

= (N2 − N1 )

Nph1  c 2e2 E21 |z21 |2 N − Np neff cε0 neff Lp 21 ph1 ph1

(9)

At first, we have increased nonlinear susceptibility to |(2) | ≈ 6.51 × 104 pm/V for approximately the same frequency mentioned in [1] (f = 3.2 THz). The rest of mentioned parameters are the same. Active region simulations associated with this frequency, bound to continuum and two phonon resonance, are obtained based on self-consistent solution of effective-mass Schrodinger and Poisson equations. At second part, we have changed working frequency by engineering laser’s active region and approached 1.8 THz. The parameters for this structure are available: according to [1]  ≈ 0.4, ˛wg ≈ 8 cm−1 , and ˛m ≈ 3 cm−1 . Assuming  ij ≈ 7.5 meV, we obtain that N1 − N3 ≈ 1.14 × 1015 cm−3 , N1 − N2 ≈ 1 × 1015 cm−3 and |(2) | ≈ 7.22 × 104 pm/V. The length of the cavity is 3 mm and the cavity width is about 10 ␮m. The output power has increased from P = 0.3 ␮m to P = 1.2 ␮m. The wavelength for Bound-to-continuum and Double-PhononResonance parts are  = 12.12 ␮m and  = 13.93 ␮m respectively. The output power for  = 12.12 ␮m is P = 1.2 W and for  = 13.93 ␮m is P = 0.7 W. Our simulations for terahertz frequency in 3.2 THz with P = 1.2 ␮W are done at room temperature. Figs. 2 and 3 show the band structure of Bound-to-continuum and Two-phononresonant, respectively. Fig. 4 shows the mid-IR output powers for Bound-to-continuum, Two-phonon-resonant structures and output terahertz power for 3.2 THz.

At second part a room temperature quantum cascade terahertz laser based on the mentioned technique is designed at 1.8 THz. All previous process is repeated for this laser. Figs. 5 and 6 show the band structure of Bound-to-continuum and Two-phonon-resonant, respectively. Fig. 7 shows the mid-IR output powers for Bound-tocontinuum, Two-phonon-resonant structures and output terahertz power for 1.8 THz.

Fig. 2. Energy profile of the conduction band edge and the wave functions for Boundto-continuum structure emitting at  = 12.12 ␮m.

Fig. 3. Energy profile of the conduction band edge and the wave functions for Twophonon-resonant structure emitting at  = 13.93 ␮m.

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Fig. 4. Output power for f = 3.2 THz as a function of bias current: upper panel shows the mid-IR output power for Bound-to-continuum at  = 12.12 ␮m, middle panel shows mid-IR output power for Two-phonon-resonant at  = 13.93 ␮m and bottom panel shows Terahertz output power at  = 71.3 ␮m.

Fig. 7. Output power for f = 1.8 THz as a function of bias current: upper panel shows mid-IR output power for Bound-to-continuum at  = 12.05 ␮m, middle panel shows mid-IR output power for Two-phonon-resonant at  = 12.99 ␮m and bottom panel shows terahertz output power at  = 166.55 ␮m.

2. Conclusion We have explained the method that we have utilized to approach room-temperature in quantum cascade terahertz lasers. Because this method is based on the nonlinear feature of quantum wells, we have tried to enhance this property. This goal is achieved by inserting structures with high second order susceptibility to the active region of laser. For first step, we managed to optimize the results in [1]. So, we approximately have doubled the nonlinearity and the output power increased from P = 0.3 ␮w to P = 1.2 ␮w. In this laser, mid-IR wavelengths are 1 = 12.12 ␮m and 2 = 13.93 ␮m. The output terahertz wavelength is  = 71.3 ␮m (f = 3.2 THz). Then, because of the importance of terahertz low frequency application in different places, we have decreased the terahertz frequency from f = 3.2 THz to f = 1.8 THz. Moreover, we have obtained a sufficient output power in the range of microwatt for this laser. All of the simulations are done at room temperature.

Fig. 5. Energy profile of the conduction band edge and the wave functions for Boundto-continuum structure emitting at  = 12.05 ␮m.

Fig. 6. Energy profile of the conduction band edge and the wave functions for Twophonon-resonant structure emitting at  = 12.99 ␮m.

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