coherent anti stokes raman spectroscopycoherent anti stokes raman spectroscopy

& Xie, X. S.) (CRC Press, Boca Raton, US 2012). The evolution of electronic structure in few-layer graphene revealed by optical spectroscopy. In this report we propose a novel use of nonlinear Raman spectroscopy as a sensor of local nano-environment . Sidorov-Biryukov, D. A. et al. CAS Coherent anti-Stokes Raman scattering microscopy: overcoming technical Opt. The corresponding susceptibility (3) ( 4; 1 . (1) and the nonlinear polarization obtained from Eqs. 1a, when the energy difference between the two photons matches a phonon energy (PS=v), the interaction of the laser pulses and the sample results in the generation of vibrational coherences4, at variance with impulsive anti-Stokes spontaneous Raman (IARS) which generates vibrational population16,17,18,19. Commun. The sensitivity of the coherent Raman spectroscopy may be further enhanced by using plasmonic nanoparticles so as to allow surface-enhanced coherent anti-Stokes Raman scattering (SECARS) [15, 17, 18, 33-39].This very sensitive technique can be used to detect extremely small amounts of molecules. Chem. The sensitivity in many CARS experiments is not limited by the detection of CARS photons but rather by the distinction between the resonant and non-resonant part of the CARS signal. If the frequency difference, 1 2, is equal to the frequency of a Raman-active rotational or vibrational transition R, then the efficiency of wave mixing is enhanced and signals at A = 21 2 (anti-Stokes) and S = 22 1 (Stokes) are produced by wave mixing due to the nonlinear polarization of the medium. Brocious, J. In the case of real levels, resonance enhancement occurs20. (1). If there is a Raman resonance at 1 2 =, an amplified signal is detected at the anti-Stokes frequency 1 + (see Figure 5 ). Gu, T. et al. By Fourier transform, the fields can be expressed in the frequency domain as \(\hat E_{\mathrm{P}}(\omega ,{\mathrm{\Delta }}T) = {\int}_{ - \infty }^{ + \infty } E_{\mathrm{P}}(t,{\mathrm{\Delta }}T)e^{i\omega t}dt\) and \(\hat E_{\mathrm{S}}(\omega ,0) = {\int}_{ - \infty }^{ + \infty } E_{\mathrm{S}}(t,0)e^{i\omega t}dt\), which can be used to calculate \(P_{{\mathrm{CARS}}}^{(3)}(\omega ,\Delta T)\) as20,53. Cui, M. et al. This method probes dynamical processes with chemical selectivity based on vibration spectroscopy. Sandro Heuke and . Time-resolved coherent anti-Stokes Raman scattering with a femtosecond soliton output of a photonic-crystal fiber. Nat. Phonon anharmonicities in graphite and graphene. a, c Normalized \(\Re (P_{{\mathrm{CARS}}}^{(3)})\), \(\Im (P_{{\mathrm{CARS}}}^{(3)})\), and \(\Re (P_{{\mathrm{NRVB}}}^{(3)})\), \(\Im (P_{{\mathrm{NRVB}}}^{(3)})\). After drying, PMMA is removed in acetone leaving SLG on glass. Coherent anti-Stokes Raman spectroscopy (CARS) is a non- linear process in which the energy difference of a pair of incoming photons matches the energy of the vibrational mode of a molecular bond of interest. Lett. Opt. Camp, C. H. Jr & Cicerone, M. T. Chemically sensitive bioimaging with coherent Raman scattering. Nanotechnol. 17, 34473451 (2017). This temperature dependence makes CARS a popular technique for monitoring the temperature of hot gases and flames. The membrane is subsequently lifted with the target substrate. Nature 490, 235239 (2012). In our experiments, c corresponds to the G phonon at q ~ 0, b and d indicate the vibrational ground state, |e, 0, and the first vibrational excited level, |e, 1, with respect to the excited electronic state |e (* band). 1 schematically illustrate the CARS and NVRB processes20. 4df. Coherent Anti-Stokes Raman Spectroscopy | SpringerLink 4e, f as function of NRVB/CARS, validating the resonance-dominated scenario. Coherent Anti Stokes Raman Spectroscopy In a typical CARS experiment in a liquid or a solid, the applied laser power of the pump and Stokes laser (104-105W) generates an output power of up to 1W, while conventional Raman scattering would give a collected signal power of 104W with the same lasers. 11, 5339 (2011). Opt. Production and processing of graphene and 2d crystals. @article{osti_1033507, title = {Coherent Anti-Stokes Raman Scattering Spectroscopy of Single Molecules in Solution}, author = {Sunney Xie, Wei Min, Chris Freudiger, Sijia Lu}, abstractNote = {During this funding period, we have developed two breakthrough techniques. If material is not included in the articles Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. Mukamel, S. Principles of Nonlinear Optical Spectroscopy. 326, 7479 (2014). J. Opt. Nature 459, 820823 (2009). Finally, we introduce the applications of . (1), (19), and (20). Coherent anti-Stokes Raman spectroscopy (CARS) - Encyclopedia Britannica Electronic resonances in broadband stimulated Raman spectroscopy. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Chemical imaging of tissue in vivo with video-rate coherent anti-stokes raman scattering microscopy. 1, 883909 (2008). developed the modeling and carried out the numerical simulations with contribution from A.V. The energy level diagrams in Fig. A dichroic mirror is used to combine the two beams, whose relative temporal delay is tuned with an optical delay line. Proc. Hence the dispersion effect is negligible. CARS is used for species selective microscopy and combustion diagnostics. Hendry, E. et al. Nature Communications Coherent Anti Stokes Raman Spectroscopy Spectrum Spontaneous Raman spectroscopy is a powerful characterization tool for graphene research. CARS-based detectors for roadside bombs are under development. Opt. This complete solution from Newport includes detailed information on set up, alignment and components used to help researchers save valuable time and resources. Probing graphene grain boundaries with optical microscopy. The same combination of optical fields used for CARS can generate another FWM signal, a nonvibrationally resonant background (NVRB)2, Fig. Natl Acad. ISSN 2041-1723 (online). In comparison to traditional Raman spectroscopy/imaging, CARS generates signals that are typically orders-of-magnitude stronger, enabling high . From Eqs. With development of high-peak-power pulsed dye laser in 1970s, CARS became potentially attractive for non destructive in situ measurements of species' concentrations and temperature in flames. Batignani, G. et al., Genuine Dynamics vs Cross Phase Modulation Artifacts in Femtosecond Stimulated Raman Spectroscopy. led the research project, conceived with A.C.F. Virga, A., Ferrante, C., Batignani, G. et al. The vibrationally resonant contribution I can be isolated by subtracting from the I2 FWM signal at \(\tilde \nu _2 - \tilde \nu _{\mathrm{P}}\sim \tilde \nu _{\mathrm{G}}\), the NRVB obtained by linear interpolation of the spectral intensities measured at the two frequencies at the opposite sides of vibrational resonance. Here, we use pulses with duration t~1ps, since this allows us to scan the inter-pulse delay across the vibrational dephasing time to suppress the NVRB cross section more than the vibrational contribution, while minimizing the spectral broadening due to the finite pulse duration \(1/\delta t \sim 15\,{\mathrm{cm}}^{ - 1}\)20. For example, CARS can be used to determine the composition and local temperatures in flames and plasmas. The visibility of the flakes is limited by the noise of the detector and bythe substrate (3). We experimentally demonstrate and theoretically describe how the inter-pulse delay, T (Fig. }$$, \(A_{{\mathrm{S}}/{\mathrm{P}}}(\omega ,C) = A_{{\mathrm{S}}/{\mathrm{P}}}(\omega )e^{( - iC\omega ^2)}\), $$\begin{array}{*{20}{l}} {P_{{\mathrm{CARS}}}^{(3)}(t, \Delta t)} {\hskip-6pt}\hfill & \propto \hfill & {\hskip-6pt}{\left( i \right)^3n_{{\mathrm{CARS}}}\mu _{ba}\mu _{cb}\mu _{cd}\mu _{ad}\mathop {\int}\limits_0^\infty d \tau _3\mathop {\int}\limits_0^\infty d \tau _2\mathop {\int}\limits_0^\infty d \tau _1} \hfill \\ {} \hfill & {} \hfill & {}{ \times A_{\mathrm{P}} (t - \tau _1 - \tau _2 - \tau _3,{\mathrm{\Delta }}t)A_{\mathrm{S}}^ \ast (t - \tau _2 - \tau _3 ,0)A_{\mathrm{P}}(t - \tau _3,{\mathrm{\Delta }}t)} \hfill \\ {} \hfill & {} \hfill & {}{ \times e^{ - i\omega _{\mathrm{P}}(t - \tau _1 - \tau _2 - \tau _3,{\mathrm{\Delta }}t)}e^{ + i\omega _{\mathrm{S}}(t - {\tau _2} - {\tau _3} )}e^{ - i\omega _{\mathrm{P}}(t - \tau _3)} } \hfill \\ {} \hfill & {} \hfill & {}{ \times e^{ - i\bar \omega _{ba}\tau _1}e^{ - i\bar \omega _{ca}\tau _2}e^{ - i\bar \omega _{da}\tau _3},} \hfill \end{array}$$, $$\begin{array}{*{20}{l}} {P_{{\mathrm{NVRB}}}^{(3)}(t, \Delta T)} \hfill & \propto \hfill & {\left( i \right)^3n_{{\mathrm{NVRB}}}|\mu _{ea}|^4{\int}_0^\infty d\tau _3{\int}_0^\infty d\tau _2{\int}_0^\infty d\tau _1} \hfill \\ {} \hfill & {} \hfill & { \times A_{\mathrm{P}} (t - \tau _1 - \tau _2 - \tau _3, \Delta t)A_{\mathrm{P}}(t - \tau _2 - \tau _3, \Delta t)} \hfill \\ {} \hfill & {} \hfill & { \times A_{\mathrm{S}}^ \ast (t - \tau _3,0) e^{ - i\omega _{\mathrm{P}}(t - \tau _1 - \tau _2 - \tau _3)}e^{ - i\omega _{\mathrm{P}}(t - \tau _2 - \tau _3)}} \hfill \\ {} \hfill & {} \hfill & {\times e^{ + i\omega _{\mathrm{S}}(t - \tau _3)}e^{ - i\bar \omega _{ea}\tau _1}e^{ - i\bar \omega _{ea}\tau _2}e^{ - i\bar \omega _{ea}\tau _3}}, \hfill \end{array}$$, \(\bar \omega _{ij} = \omega _i - \omega _j - i\gamma _{ij}\), $$P^{(3)}(\omega ) = \mathop {\int}\limits_{ - \infty }^\infty {P^{(3)}} (t)e^{i\omega t}dt.$$, $$\begin{array}{l}P_{{\mathrm{CARS}}}^{(3)}(\omega ) \propto \eta _{{\kern 1pt} {\mathrm{CARS}}}\left( i \right)^3\mathop {\int}\limits_{ - \infty }^{ - \infty } d t\,e^{i\omega t}\mathop {\int}\limits_0^\infty d \tau _3\mathop {\int}\limits_0^\infty d \tau _2\mathop {\int}\limits_0^\infty d \tau _1 \\ \times \mathop {\int}\limits_{ - \infty }^\infty d \omega _1\mathop {\int}\limits_{ - \infty }^\infty d \omega _2\mathop {\int}\limits_{ - \infty }^\infty d \omega _3\hat A_{\mathrm{P}}(\omega _1,\Delta T)\hat A_{\mathrm{S}}^ \ast (\omega _2,0) \hat A_{\mathrm{P}}(\omega _3,\Delta T) \\ \times e^{ - i(\omega _{\mathrm{P}} + \omega _1)(t - \tau _1 - \tau _2 - \tau _3)}e^{ + i(\omega _{\mathrm{S}} + \omega _2)(t - \tau _2 - \tau _3)}\\ \times e^{ - i(\omega _{\mathrm{P}} + \omega _3)(t - \tau _3)}e^{ - i\bar \omega _{ba}\tau _1}e^{ - i\bar \omega _{ca}\tau _2}e^{ - i\bar \omega _{da}\tau _3},\end{array}$$, $$\begin{array}{l}P_{{\mathrm{CARS}}}^{(3)}(\omega , \Delta T) \propto - \eta _{{\mathrm{CARS}}}\mathop {\int}\limits_{ - \infty }^\infty d \omega _1\mathop {\int}\limits_{ - \infty }^\infty d \omega _2\mathop {\int}\limits_{ - \infty }^\infty d \omega _3 \\ \times \delta (\omega - 2\omega _{\mathrm{P}} + \omega _{\mathrm{S}} + \omega _1 - \omega _2 + \omega _3)\\ \times \frac{{\hat A_{\mathrm{P}}(\omega _1,\Delta t)\hat A_{\mathrm{S}}^ \ast (\omega _2,0)\hat A_{\mathrm{P}}(\omega _3,\Delta t)}}{{(\omega _P + \omega _1 - \bar \omega _{ba})(\omega _P - \omega _S + \omega _1 - \omega _2 - \bar \omega _{ca})(2\omega _{\mathrm{P}} - \omega _{\mathrm{S}} + \omega _1 - \omega _2 + \omega _3 - \bar \omega _{da})}},\end{array}$$, $$\delta (\omega - 2\omega _{\mathrm{P}} + \omega _{\mathrm{S}} - \omega _1 + \omega _2 - \omega _3) = \mathop {\int}\limits_{ - \infty }^\infty {e^{i(\omega - 2\omega _{\mathrm{P}} + \omega _{\mathrm{S}} - \omega _1 + \omega _2 - \omega _3)t}} ,$$, $$\begin{array}{l}P_{{\mathrm{CARS}}}^{(3)}(\omega ,{\mathrm{\Delta }}T) \propto - \eta _{{\mathrm{CARS}}}{\int}_{ - \infty }^\infty d\omega _1{\int}_{ - \infty }^\infty d\omega _3\\ \times \frac{{\hat A_{\mathrm{P}}(\omega _3,\Delta T)\hat A_{\mathrm{P}}(\omega _1,\Delta T)\hat A_{\mathrm{S}}^ \ast (2\omega _{\mathrm{P}} - \omega _{\mathrm{S}} - \omega + \omega _3 + \omega _1,0)}}{{\left( {\omega _{\mathrm{P}} + \omega _3 - \bar \omega _{ba}} \right)\left( {\omega - \omega _{\mathrm{P}} - \omega _1 - \bar \omega _{ca}} \right)\left( {\omega - \bar \omega _{da}} \right)}}.\end{array}$$, $$\begin{array}{l}P_{{\mathrm{NRVB}}}^{(3)}(\omega ,\Delta T) \propto - \eta _{{\mathrm{NVRB}}}{\int}_{ - \infty }^\infty d\omega _1{\int}_{ - \infty }^\infty d\omega _2\\ \times\frac{{\hat A_{\mathrm{P}}(\omega _1,\Delta T)\hat A_{\mathrm{P}}(\omega _2,\Delta T)\hat A_{\mathrm{S}}^ \ast (2\omega _{\mathrm{P}} - \omega _{\mathrm{S}} - \omega + \omega _1 + \omega _2,0)}}{{\left( {\omega _{\mathrm{P}} + \omega _1 - \bar \omega _{ea}} \right)\left( {2\omega _{\mathrm{P}} + \omega _1 + \omega _2 - \bar \omega _{ea}} \right)\left( {\omega - \bar \omega _{ea}} \right)}}.\end{array}$$, https://doi.org/10.1038/s41467-019-11165-1. Nat. 12, 54955499 (2012). The primary disadvantage of the technique is the need for laser sources with excellent intensity stabilization. (19) and (20). Concentrations of paramagnetic species as low as 109 molecules per cubic centimetre have been observed. B 76, 064304 (2007). = \mathop {\sum}\limits_{i = P,S} {[\hat A_i(t,{\mathrm{\Delta }}t_i)e^{ - i\omega _it} + c.c.]}{. Nature Communications (Nat Commun) prepared and characterized the samples; A.V., C.F., G.B., A.C.F., G.C. In SLG and FLG the FWM signal arises from the imaginary (non dispersive) CARS susceptibility, and it is amplified by its NVRB (third term in Eq. 105, 097401 (2010). The marriage of coherent Raman scattering imaging and advanced - Nature Chemphyschem 8, 21562170 (2007). Mak, K. F. et al. Our exfoliated FLG are Bernal stacked, as also confirmed by the measured 2D peak shape in SR10,11. In the second branch (FemtoFiber pro TNIR), the amplified laser passes through a nonlinear fiber, wherein a supercontinuum (SC) output is generated. Coherent Anti-Stokes Raman Spectroscopy J.-P. Taran Conference paper 317 Accesses 8 Citations Part of the Springer Series in Optical Sciences book series (SSOS,volume 7) Abstract The use of coherent anti-Stokes Raman scattering (CARS) has revolutionized the field of Raman scattering. Google Scholar. Coherent anti-Stokes Raman scattering (CARS) microscopy is a label-free chemical imaging modality capable of interrogating local molecular composition, concentration, and even orientation. Correspondence to This leads to a signal that, under the electronically resonant regime, becomes20. Additional Metadata SAND Number. Nat. The corresponding contrast C is also reported. From: Advances in Quantum Chemistry, 2012 About this page Nonlinear Raman Spectroscopy, Applications Direct observation of a widely tunable bandgap in bilayer graphene. Opt. Volkmer, A. et al. ACS Photonics6, 492 (2019). Marangoni, M. et al. Coherent Anti-Stokes Raman Spectroscopy CARS is a spectroscopic method which relies on three photons in order to probe a multilevel quantum system formed by Raman active vibrational modes in a molecule. Google Scholar. 9, 263 (2014). Chem. Molecules that have one or more unpaired electrons will possess permanent magnetic moments. B 19, 13631375 (2002). g, h Intensity profiles along the scanning paths in and out of a FLG flake as highlighted in (a, c, e) by dashed and full lines, respectively. Lett. Stimulated coherent anti-Stokes Raman spectroscopy (CARS - PNAS Mater. (14) can be written as. Chem. Krauss, G. et al. Electron-electron interactions and doping dependence of the two-phonon Raman intensity in graphene. Resonant Raman spectroscopy of twisted multilayer graphene. Nano. The maximum of the signal, when the dispersive contribution is dominant, can be frequency shifted from the phonon frequency. Nat. SLG is subsequently transferred on a glass substrate by a wet method. Wu, R. et al. (5) and (6), considering45,47 ba=da=ea=10fs, ca=FWHM(G)/2=6cm1. Coherent anti-Stokes scattering is known since study of nonlinear phenomena of crystal structures by Mark and Terhune [4] in 1965. Spontaneous and coherent anti-Stokes Raman spectroscopy of human gastrocnemius muscle biopsies in CH-stretching region for discrimination of peripheral artery disease. 3, unambiguously indicates the presence of electronic resonance in SLG and Bernal FLG. Coherent antiStokes Raman spectroscopy offers significant advantages over standard incoherent Raman spectroscopy. Science 316, 265268 (2007). 1a, b. Consequently, \(P^{(3)} \propto E_{\mathrm{P}}^2E_{\mathrm{S}}^ \ast\), where * indicates the complex conjugate. Background-free broadband CARS spectroscopy from a 1MHz ytterbium laser. Coherent anti-Stokes Raman scattering microscopy for polymers For SLG, the linear dispersion of the massless Dirac Fermions makes the response always electronically resonant. The emerging applications and advancements of Raman spectroscopy in Nano. b, d, f Intensity histograms of (a, c, e). Phys. A more quantitative picture can be derived from Eqs. The data in Fig. Coherent Anti-Stokes Resonance Raman Spectroscopy - an overview | ScienceDirect Topics Coherent Anti-Stokes Resonance Raman Spectroscopy For such systems, resonance CARS spectroscopy is a suitable tool to obtain resonance Raman information via the anti-Stokes, coherent spectroscopic method. volume10, Articlenumber:3658 (2019) Coherent anti-Stokes Raman spectroscopy (CARS) has been shown to be one of the most powerful experimental methodologies for obtaining vibrational information from both stable and transient molecular species. 5b, d, f. In Fig. This paper is a brief overview to coherent anti- Stokes Raman spectroscopic technique and introduces the strengths and barriers to its use all based on the interpretation of simple. Rev. CARS spectra of a FLG and b SLG as a function of Raman shift \(\left( {\tilde \nu - \tilde \nu _{\mathrm{P}}} \right)\) at different T between the beams at tunable S and fixed P. Anal. 2022 Oct 14;37028221136124. doi: 10.1177/00037028221136124. The general principle is embodied in Figure 11, with the substitution of an electric field for the magnetic field. 37. Article Monacelli, L. et al., Manipulating Impulsive Stimulated Raman Spectroscopy with a Chirped Probe Pulse, J. Phys. In the CARS method two strong collinear laser beams at frequencies 1 and 2 (1 > 2) irradiate a sample. Femtosecond Coherent Anti-Stokes Raman Spectroscopy in a Cold-Flow Hypersonic Wind Tunnel for Simultaneous Pressure and Temperature Measurements. This method has made it possible to identify radicals observed in interstellar space and to provide spectral detail for them. In the presence of a temporal delay between PP and SP, their electric fields can be written as3: \(E_{\mathrm{P}}(t,{\mathrm{\Delta }}T) = A_{\mathrm{P}}(t,{\mathrm{\Delta }}T)e^{ - i\omega _{\mathrm{P}}t}\) and \(E_{\mathrm{S}}(t,0) = A_{\mathrm{S}}(t,0)e^{ - i\omega _{\mathrm{S}}t}\), where AP/S(t, T) indicates the PP/SP temporal envelope. 1c). 36. It is sensitive to the same vibrational signatures of molecules as seen in Raman spectroscopy, typically the nuclear vibrations of chemical bonds. Coherent Raman spectro-imaging with laser frequency combs Express 19, 1514315148 (2011). Coherent antiStokes Raman microspectroscopy using spectral focusing Appl. Colormaps in b, e generalize a, d for different NVRB/CARS, as for Eqs. Our Coherent Anti-Stokes Raman Scattering Microspectrometer solution is designed to integrate with Ti:Sapphire femtosecond oscillators to perform CARS Microspectroscopy related experiments. Nat Commun 10, 3658 (2019). Therefore, the FWM signals are quadratic with respect to the pump power and linear with respect to the Stokes power. The bulk crystal is exfoliated on Nitto Denko tape. The total FWM signal is collected with an optical multichannel analyzer (OMA, Photon Control SPM-002-E). For T>2ps, while the total FWM signal decreases by nearly two orders of magnitude, the dip observed for FLG at T ~0ps evolves into a Raman peak shape at the G-phonon energy. The corresponding effect on the CARS profile is a slight intensity modification, below 5% for chirp as large as 104fs2. Single-layer graphene (SLG) has a high nonlinear third-order susceptibility: |(3)| ~1010 e.s.u. NVRB, lacking vibrational specificity, can also originate from the glass substrate outside the FLG flake \(\left( {\overline I _{\mathrm{s}} \gg 0} \right)\), as indicated by the scanning profile in Fig. 4ac. Raman spectroscopy of graphene under ultrafast laser excitation. This enhanced signal level can greatly reduce the time necessary to record a spectrum. Soc. Chem. ; D.D.F. While spontaneous Raman (SR) scattering is an incoherent signal20, since the phases of the electromagnetic fields emitted by individual scatterers are uncorrelated20, in CARS, atomic vibrations are coherently stimulated, i.e., atoms oscillate with the same phase4, potentially leading to a signal enhancement of several orders of magnitude depending on incident power and scatterer density21,22. Phys. Pestov, D. et al. To assess data reproducibility we repeated the CARS measurements (scanning S) finding no appreciable changes. designed and built the CARS setup; A.V. This can be read out by the third field interaction within the phonon dephasing time, ~1ps45 (indicated, for a representative CARS event, by the third dot in Fig. Proc. 3. Similarly, the vibrationally resonant FWM, I2, originating from concurrent CARS and NVRB processes (Fig. Thank you for visiting nature.com. Phys. Ultrabroadband background-free coherent anti-Stokes Raman scattering microscopy based on a compact Er:fiber laser system. 34, 773775 (2009). Nonequilibrium dynamics of photoexcited electrons in graphene: collinear scattering, Auger processes, and the impact of screening. This method is useful for the determination of the dipole moment and structure of species whose rotational transitions fall above the microwave region. (5) and (6), allows us to extract the ratio between the third-order nonlinear susceptibilities for CARS and NVRB, \(\frac{{|\chi _{{\mathrm{CARS}}}^{(3)}|}}{{|\chi _{{\mathrm{NRVB}}}^{(3)}|}}\sim 1.3\), at the G-phonon resonance. However, in performing resonance CARS spectroscopy in solids one must realize that this technique results in a fairly complicated arrangement between the sample and the coherent beams. Khurgin, J. This ratio, combined with Eqs. . Koivistoinen, J. et al. \hfill \\ {} \hfill & {} \hfill & {\left. The images or other third party material in this article are included in the articles Creative Commons license, unless indicated otherwise in a credit line to the material.