Low-gain Regime Research Articles

Impact of polarization pulling on optimal spectrometer design for stimulated Brillouin scattering microscopy.

Brillouin spectroscopy has become an important tool for mapping the mechanical properties of biological samples. Recently, stimulated Brillouin scattering (SBS) measurements have emerged in this field as a promising technology for lower noise and higher speed measurements. However, further improvements are fundamentally limited by constraints on the optical power level that can be used in biological samples, which effectively caps the gain and signal-to-noise ratio (SNR) of SBS biological measurements. This limitation is compounded by practical limits on the optical probe power due to detector saturation thresholds. As a result, SBS-based measurements in biological samples have provided minimal improvements (in noise and imaging speed) compared with spontaneous Brillouin microscopy, despite the potential advantages of the nonlinear scattering process. Here, we consider how a SBS spectrometer can circumvent this fundamental trade-off in the low-gain regime by leveraging the polarization dependence of the SBS interaction to effectively filter the signal from the background light via the polarization pulling effect. We present an analytic model of the polarization pulling detection scheme and describe the trade-space unique to Brillouin microscopy applications. We show that an optimized receiver design could provide >25× improvement in SNR compared to a standard SBS receiver in most typical experimental conditions. We then experimentally validate this model using optical fiber as a simplified test bed. With our experimental parameters, we find that the polarization pulling scheme provides 100× higher SNR than a standard SBS receiver, enabling 100× faster measurements in the low-gain regime. Finally, we discuss the potential for this proposed spectrometer design to benefit low-gain spectroscopy applications such as Brillouin microscopy by enabling pixel dwell times as short as 10 μs.

3D small-gain formula allowing strong focusing and harmonic lasing for a ring-based x-ray free electron laser oscillator

We present a detailed derivation of a formula for the small-gain calculation for an x-ray free electron laser oscillator (XFELO) based on a medium-energy (3–4 GeV) storage ring. We found harmonic lasing and strong focusing are essential for this beam energy range. Taking the small-signal low-gain formula developed by Kim and his colleagues, we modified it in such a way that the gain can be calculated without the “no focusing approximation,” and a strong focusing can be applied, as well as harmonic lasing. In this formula, the gain is represented as a product of two factors with one of them depending only on the harmonic number, undulator period, and gap. Using this factor, we show that it is favorable to use harmonic lasing to achieve hard x-ray FEL working in the small-signal low-gain regime with the medium-energy electron beam. Our formula also allows FEL optimization by varying the vertical gradient of the undulator, the vertical dispersion, and the horizontal and vertical focusing, independently. As an example, we applied this formula to study the feasibility of an XFELO option for the National Synchrotron Light Source II (NSLS-II) upgrade. Since a quite high peak current is required for the FEL, collective effects of beam dynamics in medium-energy synchrotrons significantly affect the electron beam parameters. We carried out a multiparameter optimization taking collective effects into account. Note, even though our example is for a ring-based XFELO at 3 to 4 GeV, the formula and, in particular, the approach developed here may be applied to other types of FELs. Published by the American Physical Society 2024

Reconstructing the full modal structure of photonic states by stimulated-emission tomography in the low-gain regime

Stimulated emission tomography (SET) is a powerful and successful technique to both improve the resolution and experimentally simplify the task of determining the modal properties of biphotons. In the present paper we provide a theoretical description of SET valid for any quadratic coupling regime between a nonlinear medium and pump fields generating photons by pairs in the low-gain regime. We use our results to obtain not only information about the associated modal function modulus but also its phase, for any mode, and we discuss the specific case of time-frequency variables as well as the quantities and limitations involved in the measurement resolution.

Classical model of spontaneous parametric down-conversion

We model spontaneous parametric down-conversion (SPDC) as classical difference frequency generation (DFG) of the pump field and a hypothetical stochastic "vacuum" seed field. We analytically show that the second-order spatiotemporal correlations of the field generated from the DFG process replicate those of the signal field from SPDC. Specifically, for low gain, the model is consistent with the quantum calculation of the signal photon's reduced density matrix; and for high gain, the model's predictions are in good agreement with our experimental measurements of the far-field intensity profile, orbital angular momentum spectrum, and wavelength spectrum of the SPDC field for increasing pump strengths. We further theoretically show that the model successfully captures second-order SU(1,1) interference and induced coherence effects in both gain regimes. Intriguingly, the model also correctly predicts the linear scaling of the interference visibility with object transmittance in the low-gain regime -- a feature that is often regarded as a quintessential signature of the nonclassicality of induced coherence. Our model may not only lead to novel fundamental insights into the classical-quantum divide in the context of SPDC and induced coherence, but can also be a useful theoretical tool for numerous experiments and applications based on SPDC.

Theory of two-photon absorption with broadband squeezed vacuum

We present an analytical quantum theoretic model for nonresonant molecular two-photon absorption (TPA) of broadband, spectrally multimode squeezed vacuum, including low-gain (isolated entangled photon pairs) and high-gain (bright squeezed vacuum or BSV) regimes. The results are relevant to the potential use of entangled-light TPA as a spectroscopic and imaging method. We treat the scenario that the exciting light is spatially single mode and is nonresonant with all intermediate molecular states. In the case of high gain, we find that in the case that the linewidth of the final molecular state is much narrower than the bandwidth of the exciting light, bright squeezed vacuum is found to be equally (but no more) effective in driving TPA as is a quasimonochromatic coherent-state (classical) pulse of the same temporal shape, duration, and mean photon number. Therefore, in this case the sought-for advantage of observing TPA at extremely low optical flux is not provided by broadband bright squeezed vacuum. In the opposite case that the final-state linewidth is much broader than the bandwidth of the BSV exciting light, we show that the TPA rate is proportional to the second-order intensity autocorrelation function at zero time delay ${g}^{(2)}(0)$, as expected. We derive and evaluate formulas describing the transition between these two limiting cases, that is, including the regime where the molecular linewidth and optical bandwidth are comparable, as is often the case in experimental studies. We also show that for ${g}^{(2)}(0)$ to reach the idealized form ${g}^{(2)}(0)=3+1/\overline{n}$, with $\overline{n}$ being the mean number of photons per temporal mode, it is required to compensate the dispersion inherent in the nonlinear-optical crystal used to generate the BSV.

Three-Dimensional, Time-Dependent Analysis of High- and Low-Q Free-Electron Laser Oscillators

Free-electron lasers (FELs) have been designed to operate over virtually the entire electromagnetic spectrum, from microwaves through to X-rays, and in a variety of configurations, including amplifiers and oscillators. Oscillators can operate in both the low and high gain regime and are typically used to improve the spatial and temporal coherence of the light generated. We will discuss various FEL oscillators, ranging from systems with high-quality resonators combined with low-gain undulators, to systems with a low-quality resonator combined with a high-gain undulator line. The FEL gain code MINERVA and wavefront propagation code OPC are used to model the FEL interaction within the undulator and the propagation in the remainder of the oscillator, respectively. We will not only include experimental data for the various systems for comparison when available, but also present, for selected cases, how the two codes can be used to study the effect of mirror aberrations and thermal mirror deformation on FEL performance.

Wavelength variable generation and detection of photon pairs in visible and mid-infrared regions via spontaneous parametric downconversion

We report an experimental demonstration of wavelength variable generation and detection of photon pairs in the visible and mid-infrared (MIR) regions over a wide spectral range of 2–5 µm via spontaneous parametric downconversion. Despite the recent increase in interest in such a photon-pair source, there have been few detailed evaluations of emitted photons generated via the downconversion process in the low gain regime, due to the lack of suitable single-photon detectors. By changing the angle of the nonlinear crystal, we continuously tune the phase-matching condition and generate photon pairs as signal photons in the wavelength range of 600–965 nm and idler photons in the wavelength range of 1186–4694 nm. We evaluate the generated photon pairs using single and coincidence counts by superconducting nanowire single-photon detectors up to a wavelength of 2 µm and detect the intensity using an InSb detector with a lock-in detection system up to 5 µm. From this analysis, a pair generation rate of 10 5 s − 1 per mW of pump power is experimentally obtained for this wavelength range. This work provides a basis for the realization of applications such as heralded MIR single-photon sources, infrared imaging, and infrared spectroscopy based on quantum technologies in the MIR region.

Quantum Fourier-Transform Infrared Spectroscopy for Complex Transmittance Measurements

Harnessing the quantum interference of the pair generation processes, infrared quantum spectroscopy, based on nonlinear interferometers with visible-infrared photon-pair sources, enables the extraction of the infrared optical properties of a sample through visible photon detection without the need for an infrared optical source or detector. We develop a theoretical framework for quantum Fourier-transform infrared (QFTIR) spectroscopy. The proposed Fourier analysis method, which fully utilizes the phase information in the interferogram, allows us to determine the complex transmittance and optical constants for a sample in a simple setup without the use of any dispersive optics for spectral selection. In the experimental demonstrations, the transmittance spectrum of a bandpass filter and the refractive index of silica glass are measured in the near-infrared region using QFTIR operated in a low gain regime; these results agree well with the independently measured spectrum using a conventional spectrometer and an value estimated from references. These demonstrations prove the validity and great potential of QFTIR spectroscopy.

Frequency-correlation requirements on the biphoton wave function in an induced-coherence experiment between separate sources

There is renewed interest in using the coherence between beams generated in separate down-converter sources for new applications in imaging, spectroscopy, microscopy and optical coherence tomography (OCT). These schemes make use of continuous wave (CW) pumping in the low parametric gain regime, which produces frequency correlations, and frequency entanglement, between signal-idler pairs generated in each single source. But can induced coherence still be observed if there is no frequency correlation, so the biphoton wavefunction is factorable? We will show that this is the case, and this might be an advantage for OCT applications. High axial resolution requires a large bandwidth. For CW pumping this requires the use of short nonlinear crystals. This is detrimental since short crystals generate small photon fluxes. We show that the use of ultrashort pump pulses allows improving axial resolution even for long crystal that produce higher photon fluxes.

The quantum effects in slow–wave free–electron lasers operating in the low–gain regime

A quantum mechanical treatment is presented to describe slow–wave free–electron lasers (FELs) operating in the low–gain regime. Here, we address the quantum effect of electrons on the FEL operation where each electron is represented as a Gaussian wave packet with an arbitrary width. It is shown that this quantum effect should be described in two different regimes. The first regime is realized when the initial width of the electron wave packet σz0 is comparable to (larger or smaller than) the radiation wavelength λL. In this regime, the gain degrades significantly as σz0 increases and approaches λL. The latter regime is realized when σz0 is quite smaller than λL (i.e., approximately when σz0<λL/3) where the behavior of the gain is opposite to that in the first regime since it decreases with decreasing σz0. Therefore, it is predicted that there is an optimum initial width of the electron wave packet at which the gain is maximum.

Entanglement swapping for generation of heralded time-frequency-entangled photon pairs

Photonic time-frequency entanglement is a promising resource for quantum information processing technologies. We investigate swapping of continuous-variable entanglement in the time-frequency degree of freedom using three-wave mixing in the low-gain regime with the aim of producing heralded biphoton states with high purity and low multi-pair probability. Heralding is achieved by combining one photon from each of two biphoton sources via sum-frequency generation to create a herald photon. We present a realistic model with pulsed pumps, investigate the effects of resolving the frequency of the herald photon, and find that frequency-resolving measurement of the herald photon is necessary to produce high-purity biphotons. We also find a trade-off between the rate of successful entanglement swapping and both the purity and quantified entanglement resource (negativity) of the heralded biphoton state.

Relative-phase and time-delay maps all over the emission cone of hyperentangled photon source

High flux of hyperentangled photons entails collecting the two-photon emission over relatively wide extent in frequency and transverse space within which the photon pairs are simultaneously entangled in multiple degrees of freedom. In this paper, we present a numerical approach to determining the spatial-spectral relative-phase and time-delay maps of hyperentangled photons all over the spontaneous parametric down conversion (SPDC) emission cone. We consider the hyperentangled-photons produced by superimposing noncollinear SPDC emissions of two crossed and coherently-pumped nonlinear crystals. We adopt a vectorial representation for all parameters of concern. This enables us to study special settings such as the self-compensation via oblique pump incidence. While rigorous quantum treatment of SPDC emission requires Gaussian state representation, in low-gain regime (like the case of the study), it is well approximated to the first order to superposition of vacuum and two-photon states. The relative phase and time-delay maps are then calculated between the two-photon wavepackets created along symmetrical locations of the crystals. Assuming monochromatic plane-wave pump field, the mutual signal-idler relations like energy conservation and transverse-momentum conservation define well one of the two-photon with reference to its conjugate. The weaker conservation of longitudinal momentum (due to relatively thin crystals) allows two-photon emission directions coplanar with the pump beam while spreading around the perfect phase-matching direction. While prior works often adopt first-order approximation, it is shown that the relative-phase map is a very well approximated to a quadratic function in the polar angle of the two-photon emission while negligibly varying with the azimuthal angle.

Enhancement of entanglement using cascaded four-wave mixing processes.

A maximal joint quadrature squeezing of -6.8±0.4 dB is experimentally obtained by a scheme of cascaded four-wave mixing (FWM) processes, which gives strong proof about the inseparability or entanglement between output of the twin beams from the system. Here joint quadrature is the difference between the two quadratures of the twin beam output from the cascaded FWM processes. This result is enhanced by about 3.1 dB, compared with the one of the single FWM process. We also study the gain dependence of the entanglement enhancement in this cascaded system. Theoretical predictions with the considerations of the losses in the experiment are also studied, and a similar trend in the low-gain regime can be found between the experimental results and the theoretical predictions. The scheme of cascaded FWM processes, which can be used to improve or even manipulate the degree of the entanglement between the output fields from the single FWM process, may find its applications in the continuous-variable quantum communication protocols.

Narrowband biphoton generation in the group delay regime

We study narrow-band biphoton generation from spontaneous four-wave mixing with electromagnetically induced transparency in a laser cooled atomic ensemble. We compare two formalisms in the interaction and Heisenberg pictures, and find that they agree in the low gain regime but disagree in the high gain regime. We extend both formalisms accounting the non-uniformity in atomic density and the driving laser fields. We find that for a fixed optical depth and a weak and far-detuned pump laser beam, the two-photon waveform is independent of the atomic density distribution. However, the spatial profiles of the two driving laser beams have significant effects on the biphoton temporal waveform. We predict that waveform shaping in time domain can be achieved by controlling the spatial profiles of the driving laser fields.

Kinetic description of a free electron laser with an electromagnetic-wave wiggler and ion-channel guiding by using the Einstein coefficient technique

A theoretical study of electron trajectories and gain in a free electron laser (FEL) with an electromagnetic-wave wiggler and ion-channel guiding is presented based on the Einstein coefficient method. The laser gain in the low-gain regime is obtained for the case of a cold tenuous relativistic electron beam, where the beam plasma frequency is much less than the radiation frequency propagating in this configuration. The resulting gain equation is analyzed numerically over a wide range of system parameters.

Critical behavior of coherence and correlation of counterpropagating twin beams

This work analyzes the temporal coherence and correlation of twin beams generated in a quasi-phase-matched nonlinear crystal in a counterpropagating configuration, ranging from the low-gain regime, where counterpropagating photon pairs are generated spontaneously, to the regime of stimulated pair production, close to the mirrorless optical parametric oscillator threshold. Here, we show a critical divergence of the correlation time and slowing down of quantum fluctuations originating from the feedback mechanism responsible for the MOPO threshold.

Approaching single temporal mode operation in twin beams generated by pulse pumped high gain spontaneous four wave mixing.

By investigating the intensity correlation function, we study the spectral/temporal mode properties of twin beams generated by the pulse-pumped high gain spontaneous four wave mixing (SFWM) in optical fiber from both the theoretical and experimental aspects. The results show that the temporal property depends not only on the phase matching condition and the filters applied in the signal and idler fields, but also on the gain of SFWM. When the gain of SFWM is low, the spectral/temporal mode properties of the twin beams are determined by the phase matching condition and optical filtering and are usually of multi-mode nature, which leads to a value larger than 1 but distinctly smaller than 2 for the normalized intensity correlation function of individual signal/idler beam. However, when the gain of SFWM is very high, we demonstrate the normalized intensity correlation function of individual signal/idler beam approaches to 2, which is a signature of single temporal mode. This is so even if the frequencies of signal and idler fields are highly correlated so that the twin beams have multiple modes in low gain regime. We find that the reason for this behavior is the dominance of the fundamental mode over other higher order modes at high gain. Our investigation is useful for constructing high quality multi-mode squeezed and entangled states by using pulse-pumped spontaneous parametric down-conversion and SFWM.

Development of a dual MCP framing camera for high energy x-rays.

Recently developed diagnostic techniques at LLNL require recording backlit images of extremely dense imploded plasmas using hard x-rays, and demand the detector to be sensitive to photons with energies higher than 50 keV [R. Tommasini et al., Phys. Phys. Plasmas 18, 056309 (2011); G. N. Hall et al., "AXIS: An instrument for imaging Compton radiographs using ARC on the NIF," Rev. Sci. Instrum. (these proceedings)]. To increase the sensitivity in the high energy region, we propose to use a combination of two MCPs. The first MCP is operated in a low gain regime and works as a thick photocathode, and the second MCP works as a high gain electron multiplier. We tested the concept of this dual MCP configuration and succeeded in obtaining a detective quantum efficiency of 4.5% for 59 keV x-rays, 3 times larger than with a single plate of the thickness typically used in NIF framing cameras.

Theory of filtered type-II parametric down-conversion in the continuous-variable domain: Quantifying the impacts of filtering

Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single-photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behavior. A rigorous theoretical description to accurately describe the effects of filtering on PDC, however, is still missing. To date, the theoretical models of filtered PDC are rooted in the discrete-variable domain and only account for filtering in the low gain regime, where only a few photon pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and put forward a simple model, which is able to accurately describe the effects of filtering on PDC in the continuous-variable domain. This developed straightforward theoretical framework enables us to accurately quantify the trade-off between suppression of higher-order modes, reduced purity and lowered Einstein-Podolsky-Rosen (EPR) entanglement, when narrowband filters are applied to multimode type-II PDC.

Kinetic description of a wiggler-pumped ion-channel free-electron laser by applying the Einstein coefficient technique

AbstractA kinetic theory is used to investigate the theory of a free-electron laser with a helical wiggler and an ion channel based on the Einstein coefficient method. The laser gain in the low-gain regime is obtained for the case of a cold tenuous relativistic electron beam, where the beam plasma frequency is much less than the radiation frequency, propagating in this configuration. The resulting gain equation is analyzed numerically over a wide range of system parameters.