Present and future of terahertz integrated photonic devices

Traditional terahertz systems, dealing with radiation from 300 GHz to 10 THz, are bulky, in stark contrast with microwave systems (a few tens or hundreds of gigahertz). This stems from the periphery (equipment and cabling) of both detectors and emitters rather than the active core. Their bulkiness represents a clear hindrance to their broad deployment in the strategic areas shown in Fig. 1, where they would otherwise bring important advantages. For example, terahertz communication systems¹ are supposed to transport more information per second compared to microwaves, but terahertz transmitters and receivers need to have a low footprint, be cheap, and be mass-manufacturable. In sensing, terahertz systems have the ability to image through optically opaque media without inducing ionization, in clear contrast to x-rays, but they need to be high-speed, high-resolution, and turn-key. In manufacturing, terahertz imaging² can complement visible imaging and reveal both the compositional and morphological properties of products,^3,4 but it needs to contain a large number of pixels of small dimensions (<100 µm). In environmental monitoring and medical applications,⁵ terahertz waves can detect water in vivo, e.g., in plants or human tissue, since the water has strong resonances in the terahertz, but they should be compatible with small samples that have sub-100 µm thicknesses. In quantum sciences, terahertz waves are key to selectively accessing otherwise inaccessible matter excitations like roto-vibrational modes, electronic transitions, e.g., in two-dimensional electron gases, or transitions between Rydberg states,^6–8 but terahertz sources need to be seamlessly integrated with these systems, which have extremely low dimensionality. In astronomy, terahertz local oscillators are suited to detect oxygen in the universe,^9,10 but they should be light enough to be mounted on satellites or planes orbiting the earth at altitudes where atmospheric absorption does not weaken signals from outer space. Finally, also in wearables, in the context of the internet of things, the requirements for compactness and low cost are extremely stringent.

Instead, at optical frequencies, miniaturization has been a powerful resource. Integrated platforms are ubiquitous for photonic applications, e.g., in frequency combs,^17–19 computing,^20,21 sensing,^22,23 and quantum science.^24–26 Adding microwave and terahertz to the photonic palette further enriches the variety of demonstrated components. On the source side, narrowband high-frequency waves are a crucial requirement when exploiting the coherent, parametric driving of sum- and difference frequency generation, Rabi oscillations, or electrical injection locking. Examples of photonic devices that rely on this principle are modulators,^27,28 electro-optic frequency combs,^19,29,30 photonic molecules,^31–33 driven light–matter systems,³⁴ the distribution and locking of time, and atomic clocks.^35,36 On the contrary, broadband pulses are applied to switch elementary excitations on picosecond time scales. Examples thereof include the application of π-pulses to excite a quantum system into a superposition or a well-defined state.³⁷ On the detector side, the metrology of microwaves downstream from a photonic chip is highly relevant. Examples are stabilization and locking schemes that require an in-loop characterization of noise (such as timing jitter and repetition rate drift) and then its control in real-time. So far, the bulk of applications have been restricted to microwaves, not yet reaching terahertz. For example, to the best of our knowledge, electro-optic frequency combs have been demonstrated up to several tens of gigahertz.³⁸ To reach higher repetition rates, demonstrations have resorted to modulation-induced instabilities to force pulse generation at the second and third harmonics of the fundamental repetition rate.³⁹ 

Given the rich palette of components that rely on optical-electronic interplay, it is worthwhile asking the question, Where do these microwave signals come from, and how are they detected? Currently, microwave and terahertz signals stem, most of the time, from an external instrument. This requires them to be guided along coaxial cables and then applied to miniaturized photonic chips via RF probes. When guiding along cables becomes utterly impractical—as is the case in the terahertz, where standard cables are lossy, rigid, hollow, and very thin—the only alternative left is to broadcast the wave into free space and then recollect it by, e.g., horns or printed antennas at the receiver. However, in this case, water absorption may strongly attenuate the terahertz signal, depending on its frequency.⁴⁰ Once they arrive at the receiver, the waves may be sent further to monitoring electronics such as a vector network analyzer. This modular approach has important advantages. It allows us to combine state-of-the-art all-electronic equipment with microwave chips that have low dimensionality. It comes at the price of high insertion losses, which significantly worsen at higher frequencies, and absorption losses in free space. Furthermore, the power output of all-electronic sources is drastically decreasing toward the terahertz (the typical cutoff features a 20 dB/decade slope, characteristic of RC-type low-pass filters).

More recently, the success of platforms like silicon-on-insulator, hybrid silicon-organic, silicon nitride, diamond, or lithium niobate has inoculated the idea that these platforms would be sufficiently viable for the generation and detection of terahertz waves. While “RF photonics” is by now an established term that represents the research that utilizes optical carriers to generate and detect microwaves, “THz photonics” is similarly in its beginnings. This question has been pursued with a triple focus: first, the hallmark properties of photonics such as ultra-low-noise could be translated to the generation of terahertz waves by exploring coherent processes; second, miniaturization could enable more efficient devices; and, finally, making the need for cables obsolete by generating terahertz waves directly on the chip, right next to the optical components that utilize them. The aim would be to reduce propagation losses by keeping distances short and increasing end-to-end injection efficiency.

As a result, the focus started increasing on various photonic technologies, in particular those that exhibit the second and third-order nonlinearities of χ⁽²⁾ and χ⁽³⁾ or semiconductors, e.g., indium gallium arsenide, as a viable path to realize appreciable terahertz components inside miniaturized waveguides. These would thereby cohabit with photonics. The goal of the current perspective is threefold: 1. to sketch—by virtue of contrast—the principles of state-of-the-art terahertz generation and detection in χ⁽²⁾, χ⁽³⁾ and semiconducting photonic integrated circuits (PICs); 2. to argue that the potential success of miniaturization of terahertz-optical chips strictly relies on a few fundamental properties of these employed platforms: losses, dispersion, and nonlinearities; and 3. to outline the most pressing questions ahead. Our central hypothesis is that concerted efforts are necessary along the following lines to make the transition from bulk to on-chip terahertz photonics a possible and worthwhile enterprise:

1. optimized multi-physics co-design of optical and terahertz properties (such as losses, power, linewidth, efficiency, power consumption, and dissipation) of miniaturized chips,

2. in-line control of the dispersion, spectrum, and temporal properties of the optical and telecom laser light necessary for the operation of the hybrid terahertz-optical chips and,

3. system-level design, including complex chip-scale architectures, ideally on large-scale wafers with efficient coupling in-and-out as well as out-of-chip pre- and post-conditioning of both terahertz and optical counterparts.

Current approaches for the generation of terahertz waves inside photonic integrated circuits rely mainly on the following three distinct principles, summarized in Fig. 2:

1. χ⁽²⁾-driven non-linear down-conversion (optical rectification) inside PICs: an optical pulse containing a broadband spectrum is rectified as it propagates along a transparent nonlinear waveguide. A terahertz antenna patterned around the waveguide efficiently emits the terahertz wave that is generated in the portion of the waveguide enclosed by the antenna and that matches in frequency the resonance and the bandwidth of the antenna. The antenna design determines the direction in which the terahertz is emitted. The maximal emission bandwidth is limited by the chirp of the pump pulse, phase matching, and absorption.

   The bulk polarization induced by optical rectification can be derived as⁴¹ 

   $P0(2)(Ω)=12ε0χ(2)(Ω,ω0)(E0*E0*)(Ω),$

   (1)

   where χ⁽²⁾(Ω, ω₀) is the effective second order nonlinear susceptibility relevant for optical rectification at a pump frequency ω₀ and does not change significantly in the frequency range (ω₀ − Ω, ω₀ + Ω).
   Using the Fourier transform of laser intensity, $Iop(Ω)=ε0n(ω0)c2(E0*E0*)(Ω)$⁠, this polarization (along the z-axis) can be rewritten as

   $P0(2)(Ω)=χ(2)(Ω,ω0)n(ω0)cIop(Ω),$

   (2)

   where n(ω₀) and c are the refractive index of the interaction medium at the pump frequency and speed of light, respectively. The generated terahertz field (generated by solving non-linear Maxwell’s equation in the frequency domain) is

   $|ETHz(Ω)|=μ0χ(2)(Ω,ω0)n(ω0)(n(Ω)+ng)Iop(Ω)Ωleff(Ω),$

   (3)

   where $leff(Ω)=exp(−iΩn(Ω)cL)−exp(−iΩngcL)iΩc(n(Ω)−ng)$ is the effective generation length, and L is the geometric interaction length. The L-dependence of the generated electric field comes directly from l_eff(Ω), and it is strongly dependent on the material dispersion because of n(Ω) − n_g; n(Ω) and n_g are the refractive index at the terahertz frequency and the group refractive index at the pump frequency, respectively.

   Clearly, employing materials with a large second-order susceptibility and a large interaction length between the optical and terahertz fields (assuming l_eff ∼ L) can maximize the generated terahertz field through χ⁽²⁾-driven nonlinearity.

2. χ⁽³⁾-driven generation of optical Kerr combs in PICs, followed by subsequent optical-terahertz conversion at a photodiode (e.g., a uni-traveling carrier photodiode): a continuous-wave beam is sent through a high-Q on-chip resonator where a frequency comb is generated through four-wave mixing. The obtained broadband spectrum is then sent to a photodiode that is typically connected downstream from the photonic chip. The photodiode then performs the optical-to-terahertz transduction through its photocurrent. This approach is limited by the RC-time constant of the photodiode. The efficiency of the generated terahertz power depends on the carrier properties and the response time of the photodiode.

   The generated photocurrent from the optical excitation driven by mixing two continuous waves (with optical intensities I_op1 and I_op2) with a frequency difference of Ω = ω₁ − ω₂ at a photoconductive material (photomixing) can be expressed as⁴² 

   $IPC(t)=τcμeEbiasIop1+Iop2+2Iop1Iop21+Ω2τc2cos(Ωt+ϕ),$

   (4)

   where ϕ = tan⁻¹(Ωτ_c). τ_c, μ_e, and E_bias are carrier lifetime, carrier mobility, and the bias field, respectively. The radiated terahertz field from this oscillating photocurrent is proportional to its derivative $(ETHz∝dIPCdt)$⁠, and the radiated terahertz power at frequency Ω is

   $PTHz(Ω)=2RAEbias2Iop1Iop2τc2μe21+Ω2τc2,$

   (5)

   where R_A is the radiation resistance. For a Hertzian dipole, R_A is equal to $80π2(dλ)2$⁠, where d is the length of the dipole and λ is the free space wavelength. Therefore, high-power terahertz radiation via photomixing requires high optical intensities, a large bias field, and a high-mobility material.

3. Photoconduction directly on-chip inside semiconducting PICs: optical pulses from an external fiber-based source are guided on-chip toward a heterogeneously integrated semiconducting patch that is surrounded by a terahertz antenna. At this patch, which is purposefully designed to contain many defects, generated photocarriers build up an ultrafast current. The defects then decelerate the carriers, which leads to a terahertz waveform that is generated locally and efficiently emitted by the antenna. The maximal bandwidth is determined by the properties of the defects.

   The time-dependent photocurrent in this case is the convolution of the optical pulse envelope and the impulse response of the photoconductive material. Considering the optical pulse is a Gaussian with a pulse duration of $2ln2τp$⁠, the photocurrent can be expressed as⁴² 

   $IPC(t)=π2μeEbiasIop0expτp24τc2−tτc⋅erfcτp2τc−tτp−expτp24τcs2−tτcs⋅erfcτp2τcs−tτp,$

   (6)

   where τ_s, τ_c, μ_e, E_bias, and $Iop0$ are momentum relaxation time, carrier lifetime, carrier mobility, bias field, and optical intensity, respectively. Erfc is the complementary error function $erfc(x)=1−erf(x)=2π∫x∞⁡exp(−t2)dt$ and $τcs−1=τc−1+τs−1$⁠. Similar to the previous part, the radiated terahertz field from the photocurrent is proportional to its derivative $(ETHz∝dIPCdt)$⁠.

   It should be pointed out that the photoconductive antennas can also operate under continuous wave pumping and have shown emitters up to a 3.5 THz bandwidth.^46,47

   Two fundamental properties make the above-mentioned approaches viable for seamless terahertz generation alongside photonics. On the one hand, the mismatch between the wavelength of terahertz radiation (a few tens to thousands of micrometers) and the one of optical radiation (around 1 μm) is a coincidental match that allows the patterning of efficient terahertz cavities (antennas or LC resonators) in the immediate vicinity of photonic structures quasi-independently. In this spirit, for example, on-chip, rib, or slot waveguides can be routed into the gap formed by two electrodes of a metallic antenna, where the generation and extraction of a terahertz wave actually happen. This allows a two-step optimization in which the optical fields remain tightly confined to the core of the waveguides, thus fully exploiting the nonlinearity within, while the properties of the extracted terahertz fields (e.g., the farfield pattern, the center frequency, the linewidth) are directly dependent on the antenna dimensions as well as on the spectral and phase characteristics of the optical light. On the other hand, the photonic circuit can be assembled from individual components that are linked via passive waveguides. In this way, the optical rectification, photoconduction, or terahertz generation may be localized far from other components that may, for example, fulfill the purpose of preconditioning the optical beams, e.g., by generating chip-scale Kerr combs.

4. We present an overview of state-of-the-art devices for terahertz generation in integrated photonic circuits in Table I. Photoconduction has been demonstrated in silicon waveguides using Germanium photoconductive antennas,⁴⁸ in indium phosphide waveguides using indium phosphide/indium gallium arsenide uni-traveling carrier photodiodes,^49–51 and in other platforms (not shown in the table) such as aluminum gallium arsenide waveguides using low-temperature grown gallium arsenide photoconductive antennas.⁵² Optical rectification, on the other hand, has been a valuable alternative to reaching high terahertz frequencies. Early attempts demonstrated terahertz emission up to 6 THz⁵³ from a metal-infused waveguide in bulk lithium niobate. More recently, the low optical loss of the thin film lithium niobate platform⁵⁴ provided access to both the nanoscale design of waveguides and printed antennas and the macroscale design of the entire circuit. These offered unprecedented control over the synthesis of terahertz waveforms up to 680 GHz (3-dB cutoff of 400 GHz), including their phase, amplitude, polarization, and farfield of the emitted radiation. In the case of χ⁽³⁾ generation techniques, micro-resonator frequency combs in silicon nitride have been successfully employed in combination with out-of-chip uni-traveling carrier photodiodes to generate ultra-low noise RF carriers in the X and K bands,¹⁸ but also at 331⁴³ or 560 GHz.⁵⁵ Kerr combs have also been used with out-of-chip photoconductive antennas to generate terahertz waves up to 2.3 THz.⁴⁵ To date, to the best of our knowledge, a demonstration of heterogeneous integration of the uni-traveling carrier photodiode or the photoconductive antenna directly with a Kerr comb is missing. This may only be a matter of time since there have been several demonstrations of uni-traveling carrier photodiodes or other high-frequency photodiodes being integrated with photonic circuits, for example, indium gallium arsenide/indium phosphide-based uni-traveling carrier photodiodes with lithium niobate waveguides using SU-8 as a bonding layer (3-dB bandwidth of 80 GHz),⁵⁶ Germanium diodes integrated with Silicon waveguides (3-dB bandwidth of 265 GHz),⁵⁷ or Graphene photodiodes with plasmonic waveguides (3-dB bandwidth of 110 GHz).⁵⁸ In addition, it seems that efficient emission is rather limited to the sub-terahertz regime since both the P-doped/intrinsic/N-doped semiconductor photodiode and the uni-traveling carrier photodiode feature a strong decay of 20 dB per decade in the power of emitted terahertz at frequencies above about 300 GHz,^50,59,60 due to their intrinsic RC time constant. Nevertheless, they have been employed as transceivers in an optical communication link at 300 GHz.⁶¹ 

Current approaches for the detection of terahertz waves inside integrated photonic circuits rely mainly on the following two distinct principles, summarized in Fig. 3:

1. χ⁽²⁾-driven electro-optic sampling in miniaturized interferometers: a terahertz wave is shone onto a chip-scale antenna, which collects and confines it to the antenna gap. Optical nonlinear waveguides pass through this gap. Here, the terahertz wave introduces a refractive index change in the waveguide material that is proportional to the in-gap terahertz electric field. A femtosecond pulse traverses the antenna gap and experiences a phase delay that is directly proportional to the introduced refractive index change. By geometry, the duration when the two waves meet is a fraction of a terahertz period, thereby limiting the detection to a sub-terahertz cycle time window. The phase delay is transformed into an intensity modulation, which can conveniently be measured by a photodiode downstream from the photonic chip.

   In the case of integrated electro-optic terahertz detection with a Mach–Zehnder configuration, the intensity modulation is expressed as⁶³ 

   $ΔI(t)=Ipr33nopt2lintΩETHz(t)ΓcngFEc,$

   (7)

   where I_p, r₃₃, n_opt, l_int, Γ_c, and FE are probe intensity, electro-optic coefficient, the refractive index at the probe frequency, interaction length, mode overlap between the terahertz and optical beam, and field enhancement, respectively. Sensitive terahertz detection with a high modulation efficiency, $η=ΔIIp$⁠, requires waveguide materials with a high electro-optic coefficient and large refractive index at optical frequencies, a high group refractive index, and antennas with a large interaction length, a high mode overlap with the optical field propagating through the waveguides, and a large field enhancement.

2. Photoconduction-based detection: a photoconductive material is pumped by a femtosecond laser pulse above its bandgap, creating free carriers. A terahertz antenna is patterned on top of the photoconductive material. It collects and confines the terahertz wave to the gap. The wave acts as a drive voltage and accelerates the generated carriers toward the contacts, where a current can be read out. By geometry, the read-out current is directly proportional to the amount of generated photocarriers and to the in-gap terahertz electric field at the moment when the probe pulse arrives. It can therefore be used to retrieve the terahertz transient on sub-cycle temporal scales.

   For a photoconductive detector, one can drive the terahertz electric field as⁶⁴ 

   $IPCD(τ)=μ0ePGT12λhcΣ∫−∞+∞ETHz(t)Φ(t−τ)dt,$

   (8)

   where Φ(t), T₁₂, P_G, h, and Σ are the temporal evolution of the conductivity response of the semiconductor, the Fresnel transmission coefficient for laser at wavelength λ, the average power entering the semiconductor substrate of the photoconductive switch, Planck’s constant, and the standard deviation of the laser Gaussian spatial profile, respectively. Routing the probe pulse via waveguides to the antenna gap (which has dimensions of a few micrometers) is crucial to delivering maximal power to the photoconductive material, especially when such a spot size would be difficult to achieve using free-space focusing optics.

Two fundamental properties make the above-mentioned approaches viable for seamless terahertz detection by photonics. On the one hand, careful engineering of the cross-section of on-chip waveguides (and therefore their group velocity dispersion) allows femtosecond pulses to travel with very low temporal broadening along a few millimeters of total relevant waveguide lengths until the antenna gap where the detection happens. This aspect is crucial, as the temporal resolution of the field measurement is equal to the temporal width of the femtosecond pulse at the location of detection. On the other hand, terahertz antennas allow for the confinement of terahertz fields to highly subwavelength antenna gaps. This confinement increases the local amplitude of the terahertz wave by a factor of 100–1000 compared to free space. This introduces, in the case of χ⁽²⁾-based detection, a large refractive index change inside the nonlinear waveguide and, in the case of photoconduction, a large photocurrent.

We present an overview of state-of-the-art devices for terahertz detection in PICs in Table II. Co-integration of optical waveguides and terahertz antennas has been leveraged to achieve highly efficient detection of terahertz waves in a desired band (e.g., 300, 500, or 700 GHz),⁶⁵ with a maximal frequency demonstrated so far of 2.5 THz⁶³ using on-chip hybrid silicon-organic waveguides that exploit a strong χ⁽²⁾ nonlinearity in organic molecules in combination with strongly confining plasmonic slots and silicon-on-insulator waveguides. In parallel, waveguide-coupled photoconductive detectors using indium gallium arsenide phosphide/indium phosphide passive waveguides and iron-doped indium gallium arsenide photoconductive antennas were shown to have an improved responsivity of up to 2 THz compared to free-space illuminated photoconductive antennas, with a total detection bandwidth of up to 4 THz.⁶⁶ Moreover, several demonstrations of high-frequency photodiodes being integrated with photonic circuits such as germanium diodes integrated with silicon waveguides (3-dB bandwidth of 265 GHz)⁵⁷ or graphene photodiodes with plasmonic waveguides (3-dB bandwidth of 110 GHz)⁵⁸ are among the state-of-the-art devices for terahertz detection.

We note that various other miniaturized terahertz detection and generation schemes have been reported in the literature, and in this perspective, we focus only on those that have been shown to work in integrated photonic circuits.

Notwithstanding the currently undergoing research efforts summarized in Secs. II and III, we foresee that fundamental properties will play a major role in the successful deployment of terahertz photonics by integrated circuits.

Many of the benefits of integrated photonics are rooted in the possibility of propagating optical pulses with extremely low loss along waveguides that can be several millimeters to centimeters in length. This is essential, both in schemes that employ several parallel waveguides (e.g., as is the case of on-chip interferometers), one single long waveguide (e.g., when several antennas are pumped subsequently), or where high-Q resonators are an absolute requirement (e.g., in the generation of Kerr combs). In this respect, silicon-on-insulator, lithium niobate, and silicon nitride have excellent properties. For example, while organics suffer from high losses of 250 dB/mm in plasmonic waveguides, these can be significantly reduced to 0.2–2 dB/mm in slot waveguides.^67,68 Lithium niobate rib waveguides feature losses below 0.7 dB/cm. This is the case even when antennas with a gap width of 3 μm were patterned around the waveguides. Losses below 0.01 dB/cm can be achieved for gaps larger than 6–7 μm.⁵⁴ Silicon nitride, on the other hand, reaches record quality factors.⁶⁹ Indium phosphide has a large optical gain and is mainly used in PIC telecommunication as a semiconductor optical amplifier; however, indium phosphide-based waveguides compared to silicon nitride have a much higher propagation loss (2–0.4 dB/cm) and bend radius (0.1 mm).⁷⁰ 

In the same spirit, terahertz losses on-chip can hamper the widespread use of terahertz photonics. Coincidentally, both hybrid silicon-organic and lithium niobate use high-resistivity silicon as a substrate that has excellent transparency in the terahertz.⁷¹ However, lithium niobate is known to have strong phonon resonances in the terahertz.^72,73 Here, the highly sub-terahertz-wavelength thickness of thin film lithium niobate comes in handy since the generation and detection of the terahertz waves happen just below the surface of the chip. This minimizes any propagation through the lossy material. Still, several fundamental questions need to be addressed. For example, if and to what extent the phonons present in these thin films limit the maximal bandwidth of detection and generation on-chip. In strong contrast to lithium niobate, organic materials have already been demonstrated in a neat form to generate extremely broadband terahertz radiation featuring no spectral gaps⁷⁴ otherwise present, e.g., in semiconductors that have strong phonon resonances in the terahertz. However, organic systems can also inherit a strong terahertz absorption if embedded into a polymer matrix, e.g., for purposes of achieving thick layers [organic molecules mixed with polymethylmethacrylate (PMMA) can have losses of about 60 dB/cm at 1 THz⁷⁵]. In this context, exploration of other polymers that are low-loss in the terahertz (such as benzocyclobutene) may be envisioned. This is, however, not straightforward, as the interaction between the molecule and the polymer matrix plays a role in the achieved electro-optic coefficients and long-term stability at high temperatures.⁷⁶ In scenarios where thin layers of only a few hundred nanometers are sufficient, neat chromophore films are typically recommended to minimize terahertz absorption (see Refs. 63 and 65).

Besides the waveguides, the material losses in terahertz antennas and electrodes restrict the performance of the photonic devices. Ohmic losses increase in metals at high frequencies due to the skin effect. The skin depth of a conductor is the distance below its surface where the current density reaches 1/e of its value at the surface. The skin depth is inversely proportional to the square root of frequency and falls below 100 nm at 1 THz in gold, silver, copper, and aluminum.^77,78 Hence, their conductivity significantly drops at a thickness comparable to/smaller than the skin’s depth. For instance, the conductivity of an 85 nm gold film drops to 33% (12%) of its bulk conductivity at room temperature (at 77 K).⁷⁹ Employing alternative conductive materials^80,81 such as dielectrics,^82,83 transparent conducting oxides,⁸⁴ and graphene⁸⁵ or nano/micro-structuring the pads to steer and control the current^28,86 are ideas worth considering to circumvent the total losses of a photonic terahertz-optical chip.

With the possibility to propagate optical and terahertz waves with minimal loss on-chip, perhaps the biggest advantage of integrated waveguides over bulk media is that they allow for engineering the dispersion. For instance, tailoring their geometrical parameters, such as width, height, etching depth, etc., can alter the effective index to take values between the one of the core and cladding (e.g., at 1550 nm, between ∼2.3 and 1.5 in lithium niobate–silica waveguides, ∼1.87 and 1.5 in organic–silica waveguides, and ∼2 and 1.5 in silicon nitride–silica waveguides). Interested readers can find here the refractive index of lithium niobate,⁸⁷ the organic molecule JRD1 in PMMA,⁸⁸ the organic salts 4-N,N-dimethylamino-4′-N′-methyl-stilbazolium tosylate (DAST)^89,90 and 4-N,N-dimethylamino-4′-N′-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS),^91,92 or silicon nitride.⁹³ The effective index is directly linked to phase matching, and its control allows the suppression of unwanted nonlinear processes and the optimization of terahertz generation and detection. In addition, the group velocity dispersion can be changed, e.g., in lithium niobate, up to a few hundred of $ps2mm$⁠, two orders of magnitude larger than the intrinsic material dispersion in the bulk.⁹⁴ This can be exploited to introduce chirp or compress pulses. The maximal bandwidth of detection and generation of terahertz waves can thereby be optimized since it is strictly related to the pulse width over the entire length of the interaction. Furthermore, dispersion control has been largely exploited in various on-chip platforms for Kerr combs, supercontinuum generation,^95,96 solitons formation,^97,98 femtosecond pulse generation,⁹⁹ etc.

In the context of the dispersion of the terahertz wave, the detailed antenna geometry influences its group delay.⁵⁴ 

In general, materials with high nonlinear coefficients are recommended as they maximize conversion efficiency. However, for the terahertz, exploration of the materials with the largest nonlinearities was only partially possible. In Table III, we report the nonlinear coefficients of platforms for integrated photonics. At the top of the table, we report—for comparison—the most prominent materials for terahertz, zinc telluride and gallium phosphide. Visibly, they have quite low nonlinearities. Their advantage is that they allow high optical powers and have favorable phase-matching properties when used with femtosecond lasers at 780 or 1064 nm—two equally important considerations when maximizing the efficiency of a nonlinear process. Materials with higher nonlinearities like lithium niobate feature extreme phase mismatch (the terahertz refractive index is much larger than the optical one due to the strong phonon resonances). In this respect, integrated circuits overcome the limitations of bulk crystals: waveguide engineering can improve phase matching, and chip-scale resonators recirculate the input optical power as a means to increase the total conversion efficiency.

The most prevalent materials for second-order optical processes for terahertz generation and detection in PICs are hybrid silicon-organic^63,65 and lithium niobate.⁵⁴ As shown in the table, organic molecules have among the highest nonlinearities. These demonstrations have leveraged either the d₃₃ or the r₃₃, the strongest ones in both hybrid silicon-organic and lithium niobate. However, exploration of other components of the electro-optic tensor is possible since crystals with other cuts are available (x- and z-cut). Alternatively, electric field poling^114,115 can be employed to orient the crystal in a desired direction. In addition, they have been shown to work at cryogenic temperatures.^68,116

In the context of Kerr combs, silicon nitride and aluminum nitride are among the most mature material platforms. Interestingly, however, silicon nitride also does not have the highest nonlinearity. The lower optical loss of chip-scale ring resonators compared to other platforms nevertheless positioned them in the leading position because of the overall superior efficiency of four-wave mixing. For example, finesses above 600 were demonstrated in this material.⁶⁹ 

From a more fundamental point of view, we foresee that the biggest challenge to tackle is the generation of high-power terahertz radiation. This is irrespective of the material or principle used. The small cross-section of waveguides imposes a limit on the in-device intensity before other nonlinear effects start to dominate. This, in turn, limits the total pulse energy and, thereby, the maximal number of terahertz sources that can be generated. Workarounds need to foster a more efficient depletion of the pump, e.g., by using long or parallel waveguides or high-Q resonators.

The hybrid terahertz-optical platforms discussed earlier allow—for the first time—compact devices that transduce terahertz waves back and forth to telecom waves, departing from titanium sapphire laser wavelengths. This is promising because fiber technologies are rich and performant in this range. However, their wide adoption critically requires further integration efforts both at the component level and at the system level. The most pressing questions we foresee toward this goal are: 1. how to efficiently generate, distribute, guide, and collect terahertz waves inside miniaturized chips; 2. how to make terahertz systems more streamlined, e.g., using low-loss fiber-to-chip, laser-to-chip, and chip-to-photodiode interfaces for a seamless in-line integration of the photonic chip with, e.g., upstream semiconductor laser diodes, miniaturized pulsed lasers, as well as downstream high-frequency photodiodes; and 3. how to further enhance the compatibility of χ⁽²⁾ and χ⁽³⁾ integrated platforms with other material platforms such as semiconducting or superconducting materials that would bring further advantages.

We believe that a wide adoption of integrated terahertz technologies will stem from two future developments: 1. miniaturization as a driver for optimized operation of custom-cut detectors and emitters; and 2. their further integration into systems that uniquely depend either on small form factors and/or on high-density packaging of entire circuits that are simply unaccessible in bulk optical systems. While the former would allow to minimize the terahertz loss on-chip, increase the maximal bandwidth, and ensure the delivery of maximal power from a source to a detector, thereby enabling a power-efficient chip, the latter would—by mere merit of dimensionality—benefit the many applications that require compactness and an ultra-low price per piece without exception: consumer electronics, the internet of things, communications, and remote sensing.

We showcase in Fig. 4(a) the component-level milestones we deem most central toward the realization of future hybrid terahertz-optical systems. Integrated sources could bypass the need for bulky lasers provided they could co-exist in-line with terahertz emitters and detectors similar to the ones highlighted in the previous sections. Integrated pulse generators (pulsed sources) could enable on-chip electro-optic sampling and broadband terahertz field generation. Going one step further, integrated photodetectors would be very handy for a fast and compact read-out of the up-converted optical light. This would bypass the need for out-of-chip coupling, which typically introduces significant optical loss. For all applications requiring femtosecond pulses, in-line compressors will need to counteract the built-in dispersion in a customized way across the various parts of the chip, e.g., through low-loss waveguides with engineered group velocity dispersion. Finally, on-chip terahertz waveguides could distribute terahertz signals on-chip to the optical components that need them.

Closing the loop, we look back at the big areas of interest for terahertz science displayed in Fig. 1. Clearly, these component-level developments will benefit all areas. In Fig. 4(b), we showcase exemplarily a few use cases. In the area of terahertz wireless communication, integration of the continuous wave sources on the same chip as the optical-to-terahertz transducers and, in parallel, integration of the optical amplifiers and the photodetectors together with the terahertz-to-optical converters are the main steps toward compact, low-cost, and high-speed wireless links.¹¹⁷ In the area of broadband terahertz spectroscopy, integrated pulsed sources may be explored for the generation of broadband terahertz light from the tip of a waveguide and its further detection after interaction with a specimen. Furthermore, the scalability of integrated circuits from a single-pixel detector to a multi-pixel detector could open applications in coherent hyperspectral imaging. However, many daunting challenges need to be solved beyond the already difficult task of scalability. For example, optical amplifiers on-chip appear essential in this case to ensure sufficient terahertz power per pixel.

Encouraging is the fact that hybrid/heterogeneous integration has been a clear priority in the field of photonics,¹¹⁸ and several integration efforts are worth mentioning as they could benefit the terahertz equally well. Hybrid integration, i.e., bringing two or several devices from different material platforms into a single package (via transfer printing, photonic wire-bonding, or flip-chip techniques), has provided the possibility of integrating sources, amplifiers, and detectors on silicon or lithium niobate chips.^{56,99,119–124} Hybrid integration is appealing for lab-scale and pilot-scale manufacturing; however, its challenging alignment and assembly hinder its implementation for mass production. Instead, heterogeneous integration, i.e., combining various materials into a single chip (via direct growth, deposition, or wafer/die bonding), is highly suited for mass manufacturing in foundries. Several high-performance devices have been reported via heterogeneous integration,^57,125–128 mainly for silicon photonics, including a recently reported fully integrated 800 Gbps silicon photonics transmitter with eight heterogeneously integrated distributed feedback lasers.¹²⁹ Although heterogeneous integration is potentially highly attractive for high-volume production, its ultra-clean interface requirement and high-cost fabrication make it challenging on the research lab-scale at the moment.

Terahertz integrated photonics based on χ⁽²⁾ and χ⁽³⁾ nonlinearities and photoconduction is, at present, an exciting and rapidly evolving young field. The simplicity of most designs discussed here is a potential advantage for the near-term adoption of integrated terahertz-optical chips; already, the combination of simple nonlinear waveguides with terahertz antennas enables relatively profound measurement schemes or custom-tailored terahertz radiation. In the long-term, we foresee that important questions will revolve around interfacing these simple building blocks with further photonic structures, as shown in Fig. 4, and revealing the limits in terms of power, linewidth, bandwidth, tunability, and dynamic control of the system as a whole.

On a final note, miniaturization has also been pursued with increasing success in detectors and emitters that operate based on principles not covered in this article, such as intersubband transitions in semiconductor heterostructures (e.g., quantum cascade lasers have been recently integrated into a polymer waveguide platform^130–132) or the inverse spin-Hall effect (spintronic emitters have been patterned on the tip of an optical fiber¹³³). Altogether, these research efforts signal a broad interest in compact, robust, and scalable hybrid optical-terahertz chips.

S.R. and I.-C.B.-C. acknowledge funding from the Swiss National Science Foundation under PRIMA Grant No. 201547.

The authors have no conflicts to disclose.

S.R. and I.-C.B.-C. contributed equally to this work.

Shima Rajabali: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Ileana-Cristina Benea-Chelmus: Conceptualization (equal); Funding acquisition (lead); Investigation (lead); Methodology (equal); Project administration (lead); Supervision (lead); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.