Figure 3 - uploaded by Jacob B Khurgin
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Dispersion of a) energy and b) velocity in the nonparabolic band (solid lines) and its parabolic approximation (dashed lines).
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Novel materials, with enhanced light–matter interaction capabilities, play an essential role in achieving the lofty goals of nonlinear optics. Recently, epsilon‐near‐zero (ENZ) media have emerged as a promising candidate to enable the enhancement of several nonlinear processes including refractive index modulation and harmonic generation. Here, the...
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Context 1
... m * is the effective mass at k = 0, E gap is the bandgap energy and we have introduced the "nonparabolicity" wavevector k 0 = √ m * E gap ∕2ℏ 2 at which the dispersion changes from "parabolalike" to "linear-like" as shown in Figure 3a, where the energy is measured relative to the bottom of conduction band, wavevectors are normalized to k 0 , and the energy is normalized to E gap ∕2. The velocity, plotted in Figure 3b, is ...
Context 2
... m * is the effective mass at k = 0, E gap is the bandgap energy and we have introduced the "nonparabolicity" wavevector k 0 = √ m * E gap ∕2ℏ 2 at which the dispersion changes from "parabolalike" to "linear-like" as shown in Figure 3a, where the energy is measured relative to the bottom of conduction band, wavevectors are normalized to k 0 , and the energy is normalized to E gap ∕2. The velocity, plotted in Figure 3b, is ...
Context 3
... this we can see two possible avenues from which optical nonlinearities can arise, similar to the ideal two-level system described in Section 2. The first avenue is through an applied electric field which effectively polarizes the conduction band electrons in the nonparabolic band (see (12) and Figure 3b). Note that the expansion of carrier velocity, i.e., conductivity current in (12) is conceptually no different from the expansion of polarization (and displacement current) in (6) and (7), and involves no characteristic time. ...
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Epsilon-near-zero (ENZ) materials that operate in the spectral region where the real part of the permittivity crosses zero have recently emerged as a promising platform for all-optical switching because of the large, optically induced reflectance and transmittance modulation they offer at ultrafast speeds. To gain insights into the ENZ modulation,...
Citations
... attosecond perturbations of bounded electrons) or large (e.g. material phase transitions) with these two attributes typically excluding each other [8]. ...
... On the other hand, hot electron nonlinearities stem from changes of the electrons effective mass [8]. In fact, when pumping a metallic material, the electrons in the conduction band are heated up thus modifying their effective mass which in turn changes the plasma frequency, and ultimately modifies the refractive index. ...
... In this second case, the nonlinearity is no longer directly dependent on the electric field and associated material polarisation, and the underlying process is always "active" thus leading to a unitary scattering cross section. For all these reasons, Eq. 2) implicitly describes the nonlinear optical behaviour of TCOs and justify why they are the best possible approximation to ideal time-varying systems [7] [8]. ...
Transparent conducting oxides are highly doped semiconductors that exhibit favourable characteristics when compared to metals, including reduced material losses, tuneable electronic and optical properties, and enhanced damage thresholds. Recently, the photonic community has renewed its attention towards these materials, recognizing their remarkable nonlinear optical properties in the near-infrared spectrum, a feature previously overlooked despite their long-standing application in photovoltaics and touchscreens. The exceptionally large and ultra-fast change of the refractive index, which can be optically induced in these compounds, extends beyond the boundaries of conventional perturbative analysis and makes this class of materials the closest approximation to a time-varying system, and a unique playground for studying a variety of novel phenomena within the domain of photon acceleration. Here we report the spatio-spectral fission of an ultra-fast pulse trespassing a thin film of aluminium zinc oxide with a non-stationary refractive index. By applying phase conservation to this time-varying layer, our model can account for both space and time refraction and explain in quantitative terms, the spatial separation of both the spectrum and energy. Our findings represent an example of extreme nonlinear phenomena on subwavelength propagation distances and shed light on the nature of several nonlinear effects recently reported not accounting for the full optical field distribution. Our work also provides new important insights into transparent conducting oxides transient optical properties which are critical for the ongoing research in photonic time crystals, on-chip generation of nonclassical states of light, integrated optical neural networks as well as ultra-fast beam steering and frequency division multiplexing
... However, to reach the successful synthesis of PTCs from these materials, two primary challenges remain to be addressed: (i) the high pumping power requirements that could induce thermal degradation of the modulated material [57] and (ii) the inadvertent excitation of a "dynamic-grating" nonlinear effect, potentially hindering the observation of the PTC state [64]. Notwithstanding these obstacles, ongoing research endeavors in this domain persist, and alternative promising methodologies for constructing optical PTCs continue to emerge [65,66]. ...
... It should be noted that the nonlinearities, represented by 2 , in transparent conducting oxides (TCOs) originate differently compared to those in conventional Kerr nonlinear materials. This distinction arises from the non-parabolic dispersion of the conduction band, which leads to a change in the average effective mass of the electron sea due to intraband absorption [64,164]. Significant changes in refractive index Δ / , on the order of 100%, have indeed been observed in these materials [162]. ...
... This oscillation modulates the material's refractive index at the same frequency, thereby offering the potential to form a PTC. However, such effects are typically overshadowed by other more dominant nonlinear phenomena, such as the "slow dynamic grating" [57,64,167]. ...
This tutorial offers a comprehensive overview of photonic time crystals-artificial materials whose electromagnetic properties are periodically modulated in time at scales comparable to the oscillation period of light while remaining spatially uniform. Being the temporal analogs to traditional photonic crystals, photonic time crystals differ in that they exhibit momentum bandgaps instead of energy bandgaps. The energy is not conserved within momentum bandgaps, and eigenmodes with exponentially growing amplitudes exist in the momentum bandgap. Such properties make photonic time crystals a fascinating novel class of artificial materials from a basic science and applied perspective. This tutorial overviews the fundamental electromagnetic equations governing photonic time crystals and explores the groundbreaking physical phenomena they support. Based on these properties, we also oversee a diverse range of applications they unlock. Different material platforms suitable for creating photonic time crystals are discussed and compared. Furthermore, we elaborate on the connections between wave amplification in photonic time crystals and parametric amplification mechanisms in electrical circuits and nonlinear optics. The tutorial will be helpful for readers with physics or engineering backgrounds. It is designed to serve as an introductory guide for beginners and to establish a reference baseline reflecting the current understanding for researchers in the field.
... 48,50 In the case of absorption-driven effects (often the case near a resonance), this leads to the approximation DnðxÞ % aðxÞnðxÞIs=2NU o , where DnðxÞ is the optically induced index change, nðxÞ is the linear refractive index, and aðxÞ is the absorption coefficient all at x, I is excitation irradiance, s is the characteristic time of the nonlinearity (e.g., recombination time), N is the density of states, and U o is the binding energy. 50,58 Other than the irradiance of light I, s is the only parameter in this expression that can be varied by orders of magnitude. This implies that moving to nonlinearities with a longer characteristic time results in a larger nonlinear effect-a well-known effect. ...
... Fast nonlinearities encompass instantaneous (typically sub %1 fs) 127 processes like electronic polarization (virtual transitions) and the collective oscillation of the free electron gas within the conduction band (real transition). 58 They are responsible for driving processes such as harmonic generation. Electronic polarization nonlinearities in semiconductors are well covered in various nonlinear textbooks 48,128 and will not be repeated here. ...
... A. Physical mechanism of fast free-carrier nonlinearity While slow free carrier effects are most often discussed in ENZ literature, a fast free-carrier process in Drude ENZ materials exists at all wavelengths and can dominate the response for hx < (3/4)E g . Khurgin et al. 58 describe this process as the incident energy driving the oscillation of free electrons within a non-parabolic conduction. Under small driving fields, the electrons oscillate predominantly in the parabolic region of the band where the electron velocity grows linearly with momentum-giving rise to a current density J ¼ Àq k v(k,t) that is linear. ...
In the continuously evolving realm of nonlinear optics, epsilon near zero (ENZ) materials have captured significant scientific interest, becoming a compelling focal point over the past decade. During this time, researchers have shown extraordinary demonstrations of nonlinear processes such as unity order index change via intensity dependent refractive index, enhanced second harmonic generation, saturable absorption in ultra-thin films and more recently, frequency shifting via time modulation of permittivity. More recently, remarkable strides have also been made in uncovering the intricacies of ENZ materials' nonlinear optical behavior. This review provides a comprehensive overview of the various types of nonlinearities commonly observed in these systems, with a focus on Drude based homogenous materials. The review emphasizes that while ENZ materials may not significantly surpass the nonlinear capabilities of traditional materials, either in terms of fast or slow nonlinearity, they do offer distinct advantages. These advantages encompass an optimal response time, inherent enhancement of slow light effects, and a broadband characteristic, all encapsulated in a thin film that can be purchased off-the shelf. The review further builds upon this framework and not only identifies key properties of transparent conducting oxides that have so far made them ideal test beds for ENZ nonlinearities, but also brings to light alternate material systems, such as perovskite oxides, that could potentially outperform them. We conclude by reviewing the upcoming concepts of time varying physics with ENZ media and outline key points the research community is working toward.
... The combination with ENZ materials can achieve this goal to some extent. As a kind of metamaterial, ENZ materials possess extraordinary electromagnetic manipulation capabilities, such as electromagnetic wave tunneling effects [27], directional radiation [28], nonlinear effects [29], etc., which can be utilized to enhance molecular fluorescence [30], enhance vortex harmonic radiation [31], and so on. Due to the large field enhancement and uniform phase distribution in ENZ materials, ENZ plasmonic waveguides have recently been used to control the decay rates of emitters and achieve long-time entanglement [32][33][34][35][36][37][38][39]. ...
Two emitters can be entangled by manipulating them through optical fields within a photonic cavity. However, maintaining entanglement for a long time is challenging due to the decoherence of the entangled qubits, primarily caused by cavity loss and atomic decay. Here, we found the entangled dark state between two emitters mediated by a dielectric cavity within epsilon-near-zero (ENZ) materials, ensuring entanglement maintenance over a long time. To obtain the entangled dark state, we derived an effective model with degenerate mode modulation. In the dielectric cavities within ENZ materials, the decay rate of emitters can be regarded as 0, which is the key to achieving the entangled dark state. Meanwhile, the dark state immune to cavity loss exists when two emitters are in symmetric positions in the dielectric cavity. Additionally, by adjusting the emitters to specific asymmetric positions, transient entanglement with higher concurrence can be achieved. By overcoming the decoherence of the entangled qubits, this study demonstrates stable, long-term entanglement with ENZ materials, holding significant importance for applications such as nanodevice design for quantum communication and quantum information processing.
... The decay time is deep in the subpicosecond scale, which agrees with the strong electron-phonon coupling hypothesis [38]. We note that we called this component "fast" to express the timescale (femtosecond), not the physical mechanism related to virtual electronic transitions, as often understood in nonlinear optics [39]. The second component (denoted "2") is related to the occurrence of the second maximum in the time response of the reflectance in the picosecond time scale. ...
Refractory metal nitrides have recently gained attention in various fields of modern photonics due to their cheap and robust production technology, silicon-technology compatibility, high thermal and mechanical resistance, and competitive optical characteristics in comparison to typical plasmonic materials like gold and silver. In this work, we demonstrate that by varying the stoichiometry of sputtered nitride films, both static and ultrafast optical responses of refractory metal nitrides can efficiently be controlled. We further prove that the spectral changes in ultrafast transient response are directly related to the position of the epsilon-near-zero region. At the same time, the analysis of the temporal dynamics allows us to identify three time components: the “fast” femtosecond one, the “moderate” picosecond one, and the “slow” at the nanosecond time scale. We also find out that the non-stoichiometry does not significantly decrease the recovery time of the reflectance value. Our results show the strong electron-phonon coupling and reveal the importance of both the electron and lattice temperature-induced changes in the permittivity near the ENZ region and the thermal origin of the long tail in the transient optical response of refractory nitrides.
... Epsilon-near-zero (ENZ) low-index optical materials exhibit a number of fascinating optical properties, including a dramatic enhancement of nonlinear processes, such as harmonic generation, frequency mixing and conversion, electro-optical modulation, and light-induced refractive index changes. [1][2][3][4][5][6][7][8][9][10] These effects are boosted in sub-wavelength nanostructures across their ENZ spectral regions and provide unprecedented opportunities for classical and quantum information technologies, optical spectroscopy, and sensing. Specifically, indium tin oxide (ITO) degenerate semiconductors have recently attracted a significant interest due to their extreme optical nonlinearity resulting in order-of-unity light-induced refractive index changes with sub-picosecond response time. ...
... Specifically, indium tin oxide (ITO) degenerate semiconductors have recently attracted a significant interest due to their extreme optical nonlinearity resulting in order-of-unity light-induced refractive index changes with sub-picosecond response time. 5,11 A number of impressive ENZ-driven optical nonlinear phenomena and devices have been demonstrated based on ITO nanolayers, including enhanced second-harmonic 12 and third-harmonic frequency generation, 10 ultrafast all-optical modulation, 11 high-efficiency optical time reversal, 9 as well as time-varying and spatiotemporal photonic devices. 7,8,[13][14][15] Moreover, the linear optical dispersion properties of ENZ materials and structures based on ITO can be tuned widely with a zero permittivity wavelength λ ENZ (i.e., the wavelength at which the real part of the permittivity vanishes) that extends from the near-infrared to mid-infrared spectral range, 16,17 enabling the engineering of efficient nonlinear phenomena across multiple wavelengths. ...
In this paper, we introduce a fully non-perturbative approach for the description of the optical nonlinearity of epsilon-near-zero (ENZ) media. In particular, based on the rigorous Feynman path integral method, we develop a dressed Lagrangian field theory for light–matter interactions and discuss its application to dispersive Kerr-like media with order-of-unity light-induced refractive index variations. Specifically, considering the relevant case of Indium Tin Oxide (ITO) nonlinearities, we address the novel regime of non-perturbative refractive index variations in ENZ media and establish that it follows naturally from a scalar field theory with a Born–Infeld Lagrangian. Moreover, we developed a predictive model that includes the intrinsic saturation effects originating from the light-induced modification of the Drude terms in the linear dispersion of ITO materials. Our results extend the Huttner–Barnett–Bechler electrodynamics model to the case of non-perturbative optical Kerr-like media providing an intrinsically nonlinear, field-theoretic framework for understanding the exceptional nonlinearity of ITO materials beyond traditional perturbation theory.
... 17,23,31,32 Transparent conducting oxides (TCOs) belong to the epsilon-nearzero (ENZ) materials, which exhibit large permittivity tunability under applied voltage and/or light illumination. 30,[33][34][35] TCOs exhibit fast switching times and low switching voltages when operating under an electrical switching mechanism, 30,33-35 which is highly advantageous for efficient neuromorphic networks. Furthermore, TCOs are CMOScompatible and produce low optical loss, akin to the SiN platform. ...
... For interband absorption, the energy of the optical pump must be greater than the bandgap of the TCO to excite photocarriers from the valence band to the conduction band. 30,34 As in the case of the electrical switching, the photoexcited carriers lower the permittivity of the TCO via Drude dispersion and move the TCO closer to the ENZ region. On the other hand, intraband absorption with the pump energy lower than the bandgap heats up electrons in the conduction band, which move it toward higher energies. ...
... In our previous papers, we focused on ITOs 28,29 as it is currently the most popular TCO material commonly found in the literature. 30,[33][34][35][43][44][45] However, the family of TCO materials is very broad and, depending on applications and an operation wavelength range, the proper TCO material can be identified. In this paper, we examine first four TCO materials, AZO, GZO, ITO, and In doped CdO, which represent a wide spectrum of ENZ wavelengths ranging from k ¼ 1.0 lm for 6% Ga:ZnO (GZO) through, k ¼ 1.5 lm for ITO, k ¼ 1.82 lm for In:CdO to k ¼ 3.34 lm for 10% Al:ZnO (AZO). ...
Fully CMOS-compatible photonic memory holding devices hold a potential in the development of ultrafast artificial neural networks.
Leveraging the benefits of photonics such as high-bandwidth, low latencies, low-energy interconnect, and high speed, they can overcome the
existing limits of electronic processing. To satisfy all these requirements, a photonic platform is proposed that combines low-loss nitride-rich
silicon as a guide and low-loss transparent conductive oxides as an active material that can provide high nonlinearity and bistability under
both electrical and optical signals.
... Additionally, because nonlinearities in ENZ are non-instantaneous and involve real states (so-called "slow" processes), they should not be compared to instantaneous nonlinearities involving virtual states (so-called "fast" processes), as is common, as they are well-known to be much larger. 89,98 A more appropriate comparison is to similar non-instantaneous process materials, such as semiconductors and metals. Finally, while it is common to quantify nonlinearities via χ (3) , n 2 , or α 2 , these terms imply properties such as linearity with respect to applied irradiance and an instantaneous response. ...
The engineering of the spatial and temporal properties of both the electric permittivity and the refractive index of materials is at the core of photonics. When vanishing to zero, those two variables provide efficient knobs to control light−matter interactions. This Perspective aims at providing an overview of the state of the art and the challenges in emerging research areas where the use of near-zero refractive index and hyperbolic metamaterials is pivotal, in particular, light and thermal emission, nonlinear optics, sensing applications, and time-varying photonics.
... Thirdorder optical nonlinearity can be generally subdivided into nonlinearity caused by bound electrons and free electrons. 35 One of the former is well known as the optical Kerr effect, which is related to virtual processes and not mediated by real transition. 25 On the other hand, real excitation of free electrons takes place and persists over a certain lifetime. ...
... For inorganic ENZ materials, the free-carrier-related nonlinearity is estimated to be about two order of magnitude higher than the Kerr nonlinearity. 35 To understand the ENZ effect in the p-type PEDOT film, we employed the z-scan technique to evaluate the nonlinear optical behavior of EG-modified PEDOT around its ENZ wavelength. Figure 2a shows the used z-scan system, where a TM-polarized light with a Gaussian distribution of light intensity is used to measure the transmittance at different locations along the z-axis. ...
... In general, the free-carrier-related nonlinearity in n-type degenerate ENZ materials is due to the intraband transition of electrons from the conduction band edge. The excited electrons modify the average effective mass of carriers due to the nature of nonparabolic bands 22,35 and thus change the screened plasma frequency ω p . The magnitude of the optical nonlinearity in ENZ materials could be estimated on the basis of the Drude dispersion model as proposed by Secondo et al. 22 ...
... The decay time is deep in the subpicosecond scale, which agrees with the strong electron-phonon coupling hypothesis [38]. We note that we called this component "fast" to express the timescale (femtosecond), not the physical mechanism related to virtual electronic transitions, as often understood in nonlinear optics [39]. The second component (denoted "2") is related to the occurrence of the second maximum in the time response of the reflectance in the pico-second time scale. ...
Refractory metal nitrides have recently gained attention in various fields of modern photonics due to their cheap and robust production technology, silicon-technology compatibility, high thermal and mechanical resistance, and competitive optical characteristics in comparison to typical plasmonic materials like gold and silver. In this work, we demonstrate that by varying the stoichiometry of sputtered nitride films, both static and ultrafast optical responses of refractory metal nitrides can efficiently be controlled. We further prove that the spectral changes in ultrafast transient response are directly related to the position of the epsilon-near-zero region. At the same time, the analysis of the temporal dynamics allows us to identify three time components - the "fast" femtosecond one, the "moderate" picosecond one, and the "slow" at the nanosecond time scale. We also find out that the non-stoichiometry does not significantly decrease the recovery time of the reflectance value. Our results show the strong electron-phonon coupling and reveal the importance of both the electron and lattice temperature-induced changes in the permittivity near the ENZ region and the thermal origin of the long tail in the transient optical response of refractory nitrides.
