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Many molecules have strong and characteristic rotational and vibrational transitions at terahertz (THz) frequencies, which makes this frequency range unique for applications in spectroscopic sensing of chemical and biological species. Here, we propose a broadband THz sensor based on arrays of single-mode QCLs, which could be utilized for sensing of the refractive-index of solids or liquids in reflection geometry. The proposed scheme does not require expensive THz detectors and consists of no movable parts. A recently developed antenna-feedback geometry is utilized to enhance optical coupling between two single-mode QCLs, which facilitates optical downconversion of the THz frequency signal to microwave regime. Arrays of THz QCLs emitting at discrete frequencies could be utilized to provide more than 2 THz of spectral coverage to realize a broadband, low-cost, and portable THz sensor.
© 2015 Optical Society of America
1. Introduction
1.1. Applications of THz sensing, existing techniques, and challenges
It has long been known that the THz/far-infrared region of the spectrum (ν ~ 1 – 10 THz, λ ∼ 30 − 300 μm, photon energy hν ∼ 4 − 40 meV) is ideal in many ways for chemical and biological sensing, imaging, and spectroscopy [1]. Many molecular species have very strong characteristic THz rotational and ro-vibrational transitions (both inter and intra-molecular), and hence could be “fingerprinted” with THz spectroscopy. While the vibrational modes that show up in infrared (IR) or MIR are usually localized within specific regions of a molecule, the THz modes involve collective motions of all atoms in a molecular structure, and hence each vibrational mode has a distinct spectral signature unlike in IR. THz sensing could be applied to cell biology [2] for example, since biomolecular THz spectra changes when they are bound in various ways to water molecules, due to a change in their conformation and function. The extreme sensitivity of THz to solid forms of materials and the presence or absence of water in these materials has obvious applications in process engineering, crystal engineering, pharmaceutical quality control and identification of counterfeit drugs. Currently, all THz spectroscopy is done with non-linear THz sources that generate low average THz power of the order of 10 μW that makes these systems very complex and expensive. Because of low source power and high THz attenuation in liquids (of the order of 100 − 1000 cm−1 [3]), liquid-phase THz spectroscopy is significantly more challenging, and therefore considerably underdeveloped.
1.2. Existing QCL based optical sensors
Laser based chemical sensors can be realized in a large number of modalities, and sense the absorption or refractive-index of the analyte at a single or range of frequencies. For gas sensing, absorption spectroscopy is most common, however, chemicals in condensed and liquid phase are sensed using evanescent-wave techniques that affords sensitive detection with small sample volumes. For spectroscopic evanescent-wave sensing of liquid and solids, however, more complex techniques such as attenuated total reflectance infrared spectroscopy (ATR-IR), or scattering-type scanning near-field optical microscopy (s-SNOM) are often utilized. In gaseous phase, tunable-diode and intracavity laser absorption spectroscopy (TDLAS and ICLAS) respectively are commonly used techniques. Photoacoustic spectroscopy (PAS) can be used for gases, solids, or liquids. Most of these techniques require, either a broadly tunable laser source with single-mode operation and good beam quality, or need a high-power broadband source in combination with a spectrometer. MIR QCLs have now reached a level of maturity that MIR sensors based on most of the above mentioned techniques have recently been demonstrated, such as s-SNOM, PAS, ICLAS. Simpler liquid-phase sensors based on direct absorption have also been demonstrated [4, 5]. Development of THz QCL based sensors, however, is far from where MIR QCL based sensors stand because of the challenges associated with cryogenic cooling, and lack of methods for electrical tuning owing to the microcavity configuration of metal-metal cavities used for THz QCLs. Only few reports for absorption based sensors with THz QCLs have been published, such as the recent result in [6]. A quartz enhanced photo-acoustic sensor employing a single-mode quantum cascade laser for gas sensing purpose is another example of QCL based sensor [7, 8]. As opposed to chemical sensing, some work has been reported toward development of THz radar imaging with QCLs [9,10].
1.3. Overview of the proposed scheme
THz QCLs [11, 12] are required to be cryogenically cooled although they can now operate above 160 K when designed to emit in the frequency range of ν ~ 2 – 5 THz. For sensor development, stable frequency and high average power mandates single-mode cw operation. However, such THz QCLs can only operate up to temperatures of 80 – 100 K and the cw power output is of the order of 1 mW above liquid-Nitrogen temperature. THz QCLs have additional challenges. Their cavities confine the optical mode in sub-wavelength dimensions and hence the commonly used external-cavity tuning technique is not applicable with the low-loss metallic cavities. The lack of electrical methods to tune frequency and low output power make it difficult to devise a sensing scheme with THz QCLs based on intensity interrogation because of challenges related to interference and noise, and more so when spectroscopic sensing is desired by utilizing an array of single-mode QCLs that operate at different frequencies, which will then involve challenges with beam combining and intensity calibration.
This work seeks to overcome the aforementioned limitations of present THz QCLs and proposes a scheme to realize highly practical and affordable, yet sensitive and functional THz spectroscopic sensor instrument with a small footprint for condensed or liquid-phase sensing with small sample volumes. The key idea is to utilize pairs of single-mode distributed-feedback (DFB) THz QCLs at an array of frequencies. One QCL of each pair (i. e. the sensing QCL) then probes the complex refractive-index of the analyte in reflection mode. Depending on the sensitivity desired, the analyte could very well be present at a distance of few meters from the cryocooler in which QCLs are mounted. The reflected signal couples back into the lasing cavity and thus shifts its resonant-frequency. The shift in the resonant frequency is indicative of the refractive index of the analyte, and is down-converted to microwave regime by mixing the optical mode of the sensing QCL with another reference QCL using intracavity frequency mixing [13]. The recently demonstrated antenna-DFB scheme [14] is utilized to enable strong optical coupling of reference and sensing QCLs, which would otherwise be very weak due to the micro-cavity geometry of metal-metal THz QCL cavities. Frequency interrogation (i. e. measurement in frequency shift due to analyte) is inherently immune to noise and interference but typically requires a spectrometer. However, the fact that “electronic” mixing still works at THz frequencies, integrated/on-chip mixing is possible without the need of expensive photonic components. This could be used to efficiently down-convert the sensed THz signal to microwave frequency region. Hence, all that is needed to record the sensed data is a microwave spectrum analyzer working below 5 GHz, and a low-cost handheld spectrum analyzer would work appropriately. The need for expensive THz detectors as well as a THz spectrometer is completely eliminated, whereas the functionality attained can be similar to other advanced spectroscopy techniques.
2. Description of proposed sensing scheme
2.1. DFB cavities radiating in different directions
The best performing THz QCLs are implemented in parallel-plate metallic cavities [17] similar to microstrip transmission lines at microwave frequencies, owing to low optical loss in metals at long wavelengths [18]. Whereas metallic ridge cavities are excellent for THz mode-confinement, their spectral and modal characteristics make it difficult to implement many techniques that are used for conventional diode lasers. First, such lasers excite several lateral and longitudinal modes simultaneously, invariably leading to multi-mode lasing across the gain bandwidth, which is typically up to 0.5 THz around the designed frequency. Second, THz QCLs with such ridge-cavities have very poor diffractive beam patterns due to the sub-wavelength dimension of the emitting facets [19]. To achieve single-mode lasing and radiation in a narrow beam, distributed-feedback (DFB) has been implemented in various ways by implementing periodic photonic structures lithographically in such cavities. Different types of DFB THz QCLs have been developed such as the ones with a first-order [20], second-order [15], third-order [21] gratings respectively.
The proposed work requires to implement a pair of coupled DFB lasers that emit at almost similar frequency (within lithographic variations that could result in a frequency difference of few GHz). One QCL will be termed as the sensing QCL and the other as the reference QCL. There are two primary requirements. First, the two DFBs should lead to emission in different directions. This is because the sensing QCL emits radiation towards analyte, a fraction of which is then reflected back into the same cavity and hence alters the resonant frequency of the QCL as a function of the complex refractive-index of the analyte. The resonant-frequency of the second QCL should, however, remain unaffected by the presence of the analyte, and hence it should radiate in a different direction. The second requirement is that both QCL cavities need to have strong optical coupling. This aspect is discussed in the subsequent section. For the proposed sensor, we choose to implement a second-order DFB cavity similar to that in [15] and an antenna-DFB cavity similar to that in [14]. The schematic and optical mode-shapes of the lowest-loss DFB resonant-cavity mode for each of the cavities are shown in Fig. 1. The emission from the second-order DFB QCL is in surface-normal (z) direction whereas the emission from the antenna-DFB QCL is in the end-fire (x) direction.
Fig. 1 Second-order DFB and Antenna DFB metallic cavities for single-mode THz QCLs emitting in different directions. (a) Three-dimensional schematic of a conventional second-order DFB THz QCL [15] in which the second-order Bragg diffraction from a periodic grating in the top-metal cladding leads to distributed-feedback inside the cavity for a wavelength of the mode such that λGaAs ≡ λ0/nGaAs ≈ Λ where Λ is the lithographically introduced grating period and λ0 is the free-space wavelength of the resonantly excited DFB mode. The dominant TM polarized (Ez) electric-field for the (designed) lowest-loss second-order DFB resonant mode is plotted along x, calculated using a finite-element electromagnetic solver [16]. (b) Similar schematic of an antenna-DFB cavity that was recently demonstrated [14]. For a grating period Λ, a mode with λ0 = (nGaAs +1)Λ is excited for air as the surrounding medium. This periodicity couples a surface-plasmon mode propagating in air on top of the metal-cladding of the laser cavity, to the guided field inside the cavity such that a large fraction of standing-wave exists as evanescent-field on top of the cladding. The dominant TM polarized (Ez) electric-field for the (designed) lowest-loss antenna DFB resonant-mode is plotted along x.
2.2. Strong optical coupling between longitudinally adjacent DFB cavities
In the proposed scheme, the shift in resonant-frequency of the sensing THz QCL is recorded, which is then indicative of the refractive-index of the analyte at that frequency. As shown subsequently, this shift in the resonant frequency is of the order of ~ 1 – 1000 MHz, and hence could be measured by a microwave spectrum analyzer so long as frequency could be downconverted to a microwave regime. The reference THz QCL serves the required purpose of downconversion. The optical field from the sensing QCL is coupled strongly to the reference QCL, by aligning the cavities longitudinally on the mask. As the field leaks into the adjoining coupled cavity, intracavity non-linear mixing in the QCL gain medium produces a microwave difference frequency signal, that could then be extracted from the bias terminals of each QCL, or could even be picked from a free-standing coaxial connector inside the vacuum dewar inside which the QCLs are mounted for cooling. This is because the microwave signal thus generated will also be radiated from each of the QCL cavities inside the cryocooler dewar compartment.
In the proposed sensing scheme, one of the cavities is a second-order DFB cavity and the other is an antenna-DFB cavity. As described later, either of the cavities could be utilized as a sensing cavity, and then the other one becomes the reference cavity. The primary reason for choosing antenna-DFB scheme instead of some other DFB scheme (such as first-order DFB [20, 22] or third-order DFB [21]) is that a large fraction of the optical field exists as standing-wave on top of the antenna-DFB cavity, that significantly enhances the coupling efficiency into the adjoining coupled cavity. While the longitudinal absorbing regions [23] (as illustrated in Fig. 1(b)) are needed for correct operation of the antenna-DFB cavity, they are not to be used for the second-order DFB cavity to enhance coupling. This is because for optical field to couple from antenna-DFB to second-order DFB cavity (and vice-versa), the second-order DFB cavity must radiate from its end-facets as well, which will not happen if absorbing regions are utilized. For this reason, the phase of reflection from the end-facets needs to be taken into account for design of second-order DFB cavity as in [15].
For the coupling calculation, the length of antenna DFB and second-order DFB were chosen to be 1.3 mm and 0.6 mm respectively and the cavities were separated by 100 μm. The choice of these dimensions and cavity-spacing is somewhat arbitrary and hence flexible. However, the shorter the length of the second-order DFB cavity, the greater is the coupling because larger field exists at its end-facets. The center frequencies between antenna DFB and second-order DFB was detuned by 0.8 GHz by choice of grating periods for simulation. Note that the difference in frequency of reference and sensing QCLs needs to be known beforehand, but need not be a certain value for each pair of QCLs (so long as it is less than 5 GHz for it to be measurable by a low-cost microwave spectrum analyzer). The sensing data is the shift in the resonant-frequency of the sensing QCL when analyte is introduced. As shown in Fig. 2 the field coupling from antenna DFB to second-order DFB is significant. Although it is difficult to estimate the non-linear conversion efficiency, it is well known that strong intracavity mixing occurs in THz QCL cavities [13, 24]. A microwave-signal produced as a result of the intracavity mixing (designed to be < 5 GHz) will appear on the biasing terminal of both DFB cavities, although it will be stronger on the biasing terminal of the second-order DFB QCL because of the larger coupled field inside second-order DFB cavity compared to the antenna-DFB cavity. This microwave signal can be extracted by a bias-T in the external coaxial connectors of the cryocooler. Alternatively, an open coaxial connector could be placed inside the cryocooler compartment that will pick up the radiated microwave signal in the compartment.
Fig. 2 Coupling between sensing cavity and reference DFB cavities. Finite-element simulation for demonstrating the optical coupling between sensing and reference DFB cavity. The results from a finite-element two-dimensional simulation (assuming cavities of infinite width) are shown. The optical field for the lowest-loss resonant-cavity modes for respective cavities are plotted along the length of the cavities. The cavities are aligned longitudinally (i. e. in x direction) with a spacing of 100 μm between the end-facets. The antenna-DFB cavity is ∼ 1.3 mm long and is designed with grating period Λ = 21 μm, with absorbing regions of length 40 μm at both ends (see the schematic in Fig. 1). The second-order DFB cavity is ∼ 0.6 mm in length and is designed with Λ = 26.6 μm, without any absorbing regions. For the chosen grating periods, the resonant-modes for each cavity occur at frequencies separated by ∼ 0.8 GHz. The TM field |Ez| is extracted from the center location of cavity’s height and is plotted as a function of longitudinal dimension. (a) When the mode is localized within the antenna-DFB, significant field couples in to the second-order DFB cavity. The peak amplitude of the electric-field in second-order DFB cavity is ~ 15% of that in the antenna-DFB cavity. (b) When the mode is localized within the second-order DFB cavity, its coupling to antenna DFB is smaller at ∼ 8%, but still significant.
2.3. Sensing architecture
A surface-emitting second-order DFB QCL in combination with antenna-DFB QCL placed face-to-face forms the vital element of proposed sensor architecture, which is described in Fig. 3. Each pair of DFB QCLs will be designed with proper geometry and grating period so that their nominal emission frequency is almost the same. However, taking standard fabrication/lithographic variations into account, it is expected that the lasing frequency of the two QCLs in each pair could be within few GHz of each other. An array of single-mode DFB THz QCLs on a semiconductor chip of typical dimension 2 mm × 2 mm will be mounted inside a Stirling cryocooler that is cooled down to ∼ 70 K. This will allow operation of QCLs in continuous-wave (cw), which is possible for present active-region designs. Note that multiple such chips with QCLs processed from different active regions could be simultaneously mounted, with the capacity to cover the entire THz spectral region in which cw operation above ∼ 60 K is available for single-mode QCLs, which is approximately the frequency region of 2 – 4.5 THz. Relatively low-cost cryocoolers, such as the Cryotel GT model from Sunpower, Inc., are now available with relatively modest electrical-power requirements and small weight that can allow operation with a portable setup.
Fig. 3 Proposed architecture of the THz sensor instrument. Two sensing schemes are possible: (a) In this scheme, antenna-DFB QCL emitting in the end-fire direction works as a sensing cavity while surface-emitting second-order DFB acts as a reference cavity. The radiation from the sensing QCL is partially reflected back into the cavity, and the amplitude and phase of the reflected wave changes the resonant-frequency of the sensing QCL according to the complex refractive index of the analyte. Since emission from the second-order DFB is in surface-normal direction, the resonant-frequency of reference QCL is not impacted by the properties of the analyte. (b) In this scheme, the second-order DFB QCL works as a sensing cavity while antenna-DFB QCL works as reference cavity. For this reason, the analyte is now to be placed vertically above the second-order DFB QCLs. The remainder of the operation with this scheme is similar to (a); however, the response characteristics for this scheme are different than that of the antenna-DFB scheme as discussed in main text.
‘n’ pairs of sensing and reference QCLs will be designed for emission at discrete frequencies fn by lithographically implementing the appropriate grating periods. QCLs will be located on chip such that only the sensing QCL out of each pair will be affected by analyte during operation. The analyte in condensed or liquid phase will be placed outside the dewar in a channel or vial made of a material such as high-density polyethylene (HDPE) or polymethylpentene (TPX) with low THz absorption. Similarly, the dewar’s window will be made of TPX or HDPE. The resonant-frequency of n-th sensing QCL depends sensitively on the complex refractive-index of the analyte at frequency fn. THz field from sensing and reference QCLs are mixed in the QCL cavities itself. For intracavity mixing, cavities are placed adjacent to each other longitudinally and are kept electrically isolated. The microwave beat signal (generally in an order of GHz) will be relayed outside the dewar and can be extracted by a bias-T in the external coaxial connector and measured by microwave spectrum analyzer. The frequency of the microwave signal from n-th pair of QCLs is representative of the refractive-index of the analyte at frequency fn. Each pair of QCLs could be electrically cycled and hence, the dielectric response of the analyte could be measured at the entire range of frequencies in which the QCLs are implemented for broadband sensing. The speed of cycling through the spectral range is dependent on measurement speed of the microwave spectrum analyzer, and the entire measurement could potentially be done within a time-frame of couple of seconds for scheme consisting of tens of pairs of DFB QCLs. Finally, sensing of the analyte in a standoff scheme is also possible because of the reflection mode sensing scheme. The scheme shown in Fig. 3(a) is more amenable in this situation because antenna-DFBs emit radiation in an extremely narrow beam (~5 × 5° [14]), and hence, relatively high-sensitivity should be obtainable for distances in the range of few meters. However, note that, as shown subsequently, sensitivity calculations were performed for the case in which analyte is placed in proximity of the cryocooler. The finite-element model used for numerical calculations in this work cannot estimate the results for standoff-sensing due to memory limitations for full-wave electromagnetic modeling of large geometries.
3. Result and discussion
3.1. Finite-element simulations of the sensing-scheme
The frequency shift of the sensing QCL due to the presence of analyte contains information about the THz response of the analyte due to its complex refractive index. To measure the frequency shift accurately, without the need of a high-resolution THz spectrometer and a sensitive THz detector, the frequency of the sensing QCL could be downconverted to a microwave beat signal by mixing it with optical field of a reference QCL.The amplitude of the microwave signal does not contain any useful information, and hence this scheme is insensitive to intensity fluctuations in the DFB QCLs. Finite-element simulation of a sensing-DFB QCL in presence of analyte for realistic dimensions corresponding to the sensing architecture in Fig. 3 are presented in Fig. 4.
Fig. 4 Finite-element simulations of the sensing scheme. Electric field intensity for the resonant-cavity DFB mode (which is also the lowest loss mode, and hence the lasing mode) is plotted. The electric-field reduces by an order of magnitude at the interface of the TPX/analyte boundary from its value inside the laser’s cavity, and thereafter it decays rapidly (within a distance of few hundred microns) in the analyte. The dewar’s TPX window is assumed to be 0.3 mm thick with a refractive index of 1.46. (a) Antenna-DFB cavity (1.4 mm long) with grating period, Λ = 21 μm (emitting at 3.21 THz) is used as a sensing QCL. The grating period is chosen arbitrarily to show a typical simulation result. Analyte is placed 1 mm away from the facet of antenna-DFB QCL in the longitudinal direction. (b) Second-order surface-emitting DFB cavity (0.6 mm long) with grating period, Λ = 27 μm (emitting at 3.18 THz) is used as a sensing QCL. Emitted far-field beam pattern of second-order DFB has two lobes for the structure used in this simulation. Single lobed far-field pattern can be achieved by introducing a 180° phase-shifter at the center of the cavity [15]. Analyte is placed at a vertical distance of 0.8 mm from the surface of the second-order DFB QCL.
When antenna DFB is utilized as sensing QCL, the distance between DFB facet to TPX window of dewar is assumed to be 1mm while TPX window thickness is taken as 300 um. For the case second order DFB acting as sensing QCL, the distance between DFB surface to TPX window of dewar is assumed to be 0.5 mm while TPX window thickness is kept as 300 um. In both cases analyte are assumed to be placed on the surface of TPX window. The QCL cavity is enlarged by a dashed red line at the bottom of the geometry since its height is very small compared to the scale of the simulated geometry. The simulation is illustrated in two-dimensions which should be a good approximation for the fundamental lateral mode propagation that is preferentially excited [15]. The sensing scheme presented here is applicable to analytes with volume as small as 1 mm3. Also, it is suitable for solids and liquids alike, even though liquids absorb THz radiation strongly. For example, water has THz attenuation in the range of ∼ 200 cm−1 at room-temperature [3], which would make absorption spectroscopy through liquid samples prohibitively challenging. However, the proposed sensing scheme does not require light to propagate through a lossy analyte; instead reflection happens at analyte/TPX interface which attributes to the shift in resonant-frequency of the sensing QCL. This fact makes this sensing scheme highly sensitive even for very loss materials at THz regime. For the same reason, the scheme could be utilized for standoff sensing and spectroscopic detection as well, especially when antenna-DFB is the sensing QCL because of its very narrow beam pattern [14], which will lead to little loss in intensity even for meter-scale distances from the cryocooler.
3.2. Sensor performance and detection sensitivity
The shift in resonant-frequency under external optical feedback for Fabry-Pérot cavities could be modeled by Lang-Kobayashi theory [29]. The resonant-frequency shift is a function of both the amplitude and the phase of the reflected wave as illustrated in Fig. 5. In a strong feedback regime, carrier density fluctuations could lead to shift in refractive index of the active medium that causes further changes in the resonant-frequencies. Complex nonlinear dynamics of laser system under optical feedback of a Fabry-Pérot cavity could be calculated analytically. For THz DFB QCLs with metallic gratings, optical feedback not only happens at end-facets but also from every aperture in the top metal cladding. Second order THz DFB QCLs emits THz wave from the surface and analyte is supposed to be placed above the DFB cavity. The reflected THz wave is coupled back into metallic cavity primarily from each aperture instead of end-facets. In this case lasing oscillation is along longitudinal (x) direction while optical feedback happens in vertical (z) direction as shown in Fig. 4(b). This inherent difference make quantitative modeling of DFB laser dynamics based on the Lang-Kobayashi theory beyond scope of this paper. However Lang-Kobayashi theory provides useful qualitative insight about the optical feedback regime. The optical feedback level is measured by feedback parameter C [29], it can be calculated as:
where α is the QCL linewidth enhancement factor, L is the separation between laser facet and analyte, l is the QCL cavity length, n is the cavity refractive index and factor κ is given by: where A is total power attenuation in the external cavity, Rext is the power reflectivity of the analyte which is determined by its dielectrc constant, and R1 is the reflectivity of the cavity’s output-facet as illustrated in Fig. 5. The coefficient ε ≤ 1 is introduced to account for possible mode overlap mismatch between back-reflected light and the lasing mode. THz QCL linewidth enhancement factor has been measured experimentally [30], and is found to be less than 0.5. For our calculation we assume it as 0.5. Output facet reflectivity R1 is taken as 0.8 [18] due to subwavelength confinement of metal-metal cavity. In antenna-DFB case, laser cavity is 1.4 mm long while distance between analyte and output facet is 1.3 mm. In second order DFB case, laser cavity is only 0.6 mm long and the distance between laser surface to analyte is 0.8 mm. Thus feedback parameter C is 0.02 and 0.03 for antenna-DFB and second-order DFB respectively, when mismatch coefficient ε is assumed to be 0.5. In reality, ε will be much smaller since there is a large modal mismatch between guided and propagating waves for THz QCLs with metal-metal cavities, which is also the reason for high end-facet reflectivities. Even under variation of reflected optical geometry in the QCL laser array, that is to say distance between laser facet to analyte depends on particular position of a QCL cavity in the array, feedback parameter remains significantly less than 0.1 for all scenarios. This fact indicates that proposed sensing scheme will operate in a very weak feedback regime for all cases.Fig. 5 Fabry-Pérot QCL cavity under external optical feedback. Symbol R1 represents the internal reflectivity at the end-facets and ϕ1 indicates the change in phase for the reflected wave. In presence of an external reflector (analyte) placed outside one of the end-facets, its effect on the cavity can be modeled with a superposition of an additional reflected-wave with reflectivity R2 and phase ϕ2 at the corresponding facet (in the week feedback regime). The feedback-oscillation condition for the cavity is now modified by both R2 and phase ϕ2, and hence, the resonant-frequency of the cavity is dependent on the phase and amplitude of the field coupled back into the cavity due to the the external feedback mechanism.
Since it is difficult to obtain analytical estimation, or intuitive interpretation of the resonant-frequency shift for DFB cavity, finite-element simulations are needed to calculate the expected shift in the resonant-frequency of the sensing QCL as a function of the analyte’s refractive-index. Owing to the weak feedback regime, the resonant-frequency of the DFB QCL cavity is primarily shifted due to changes in feedback oscillation condition, rather than carrier dynamics and related change in the refractive index of the DFB cavity due to the active gain medium. Hence, finite-element simulation should capture such a shift in the resonant-frequency very accurately.
A systematic study of resonant-frequency shift corresponding to analyte’s refractive-index (when assumed to be real) is performed for both second-order and antenna-DFB sensing schemes. The sensing QCL cavity is designed to excite a resonant-cavity mode at ~ 3 THz (chosen arbitrarily). When the analyte’s refractive index is increased from 1 to 5, resonant-frequency of the antenna-DFB sensing cavity is shifted by ∼ 440 MHz while resonant-frequency of a second-order DFB sensing cavity is shifted by ∼ 320 MHz. Note that the frequency-tuning will occur as a function of amplitude and phase of the wave reflected from the analyte, and hence, will be a function of the complex refractive index of the analyte. However, to show proof of concept and to estimate sensitivities, the refractive index was kept real without loss in generality. The computed plots are shown in Fig. 6. To explain sensitivity of the sensing scheme, a slope δ f/(δnr/nr) ≡ δ f/RIU can be defined where δ f is the shift in resonant-frequency, and δnr/nr is often-termed as the refractive-index unit (RIU), or the fractional change in the refractive index. For the second-order DFB as sensing QCL, δ f/RIU ranges from 100 – 250 MHz, whereas for the antenna-DFB as sensing QCL, δ f/RIU ranges from 150 – 500 MHz approximately depending on operating frequency of the sensing QCL.
Fig. 6 Sensor output as a function of analyte’s refractive-index. The THz sensor relays a microwave beat signal at its output port, the frequency of which determines the effect of the analyte on the sensing DFB QCLs and is a measure of the complex refractive index of the analyte at the lasing frequency of the QCL. The figure shows the computed shift in the resonant-frequency of a sensing QCL operating at ~ 3 THz as a function of the refractive index of the analyte. The imaginary part of the index is kept 0. However, similar result would be obtained if the imaginary part of the index was changed instead. In general, the shift in the resonant-frequency is a function of the complex refractive index. (a) Simulation geometry is exactly same as it in Fig. 4(a) in which the antenna-DFB is the sensing cavity. Real part of analyte’s refractive index is changed from 1 to 5 while the imaginary part is kept as 0. When the refractive index is 5, the resonant-frequency of the antenna-DFB mode is shifted by ∼ 410 MHz compared to the case when the analyte’s refractive index is unity. (b) Second-order DFB is used as sensing cavity and simulation geometry is exactly same as that in Fig. 4(b). When the analyte’s refractive index is 5 the resonant-frequency of the antenna-DFB mode is shifted by ∼ 330 MHz compared to the case when the analyte’s refractive index is unity.
The ultimate sensitivity of the proposed scheme will be determined by the linewidth of the THz QCLs being used for sensing. Linewidth of free-running QCLs is typically in the range of 1 − 10 MHz [25, 26] when electrical or thermal instabilities are not corrected; however, when the frequency is stabilized (which could be done by locking the frequency of the QCL to a microwave reference oscillator [27]), a long-term linewidth of the order of 10 kHz could be achieved. It may be noted that both the reference and sensing QCLs could potentially be biased using the same voltage-supply (because they are from the same active region, and will have similar threshold characteristics), and hence, most likely the linewidth of the microwave beat signal will be significantly smaller than free-running linewidth of individual QCLs because of cross-correlation in frequency jitter of each of the QCLs. For very high-resolution measurements, the THz QCLs could be phased-locked (as opposed to frequency locked) to a microwave reference oscillator, in which case output THz linewidth of the QCL mimics the linewidth of the microwave reference and a linewidth of the order of ∼ 10 Hz could be achieved [28]. The simulation results from Fig. 6 suggest that that ppm (part-per-million) RIU level sensitivity might be obtainable if the linewidth of the beat signal is in the kHz range. For frequency and phase-locked QCLs, even better sensitivities could perhaps be realized.
Laser-based refractive-index sensors that do obtain very high sensitivities and can detect better than ppm RIU (fractional change in refractive index) are typically based on optical- resonance effect of coupled-cavities, and hence are “narrowband” sensors that often target a specific resonance feature of the analyte at a single frequency [31]. In contrast, the proposed sensor can obtain the simulated performance over a broad range of frequencies, only limited by the availability of QCLs at the desired frequency. For specific frequencies, phase-locked QCLs could significantly better the sensitivity by additional three orders of magnitude; however, that will most likely be practically feasible for a few frequencies only rather than a broad range of frequencies due to more complicated set-up for phase-locking. It is also important to know that frequency and phase-locking of QCLs can be done with an all-microwave setup that requires commonly available microwave components, and hence still keeps the cost of the proposed THz sensor instrument low.
To illustrate an example of sensing the imaginary part of refractive index of an analyte, the frequency-shift for sensing QCLs is estimated for ice-water as analyte, and is plotted for ice-water at different temperatures in Fig. 7. According to [3], permittivity of ice at 2.5THz is 3.15 – 0.4906i, 3.15 – 0.4544i, 3.15 – 0.4187i respectively for −15°C, −30°C, −60°C. Figure 7 shows the resonant-frequency shift for antenna-DFB and second-order DFB sensing QCLs for these three cases. The minimum resolution for the computed resonant-frequency of the QCL by the finite-element solver was ~ 1 MHz, hence no data is computed at smaller ranges. However, as long as the intrinsic linewidth of the beat-signal is smaller than ~1 MHz this sensing scheme could detect much smaller changes in complex refractive-index of the analyte.
Fig. 7 Computed sensor output for ice-water at different temperatures at 2.5 THz. As an illustration of the sensing scheme, the geometry described in Fig. 4 is used for obtaining the output of the sensing scheme. For the simulations, the grating period of the sensing QCL cavity is chosen to excite a resonant-cavity mode at 2.5 THz. As shown in [3], imaginary part of complex permittivity for ice-water varies from 0.4187 to 0.4906 for the shown range of temperatures, the real part remains as 3.15 at all temperatures. When second-order DFB is used as sensing cavity, its resonant frequency is shifted by 16 MHz when ice-water’s temperature decreases from −15°C to −60°C. The shift of resonant-frequency for an antenna-DFB sensing QCL for the same parameters is smaller, and is computed to be 5 MHz.
4. Conclusions
In conclusion, here we propose and investigate a novel THz QCL-based spectroscopic sensing scheme, that can probe the complex refractive index of an analyte at a broad range of THz frequencies. The analyte could be in condensed or liquid-phase, may have large THz absorption, and be located in ambient conditions. The analyte does not require any preparation for sensing, even ultrasmall volumes of the analyte could be sensed effectively.The broadband THz sensor consisting of arrays of single-mode QCLs cooled inside a portable Stirling cryocooler could be realized, in which the output signals are microwave frequencies corresponding to each QCL, that are proportional to the shift in the resonant-frequency of the respective single-mode QCLs in presence of the analyte. The proposed scheme could therefore be used for spectroscopic identification and detection of chemical and biological samples, with the potential of standoff sensing and detection as well. No THz detectors or movable parts are required, because the active region of the QCL acts by itself as a non-linear detection medium. The sensing scheme is inherently immune to intensity fluctuations of laser’s output or other interference effects because it relies on measurement of the shift in the resonant-frequency of the QCLs. Better than ppm RIU (refractive-index unit) sensitivities could be attained across the broad-frequency range. The sensing scheme is general and versatile, and could potentially be applied to semiconductor lasers operating at shorter wavelengths as well.
Acknowledgments
This material is based upon work supported by the United States National Science Foundation under Grant Nos. ECCS 1128562, ECCS 1351142, and ECCS 1437168.
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