Abstract

The conversion of a photon’s frequency has long been a key application area of nonlinear optics. It has been discussed how a slow temporal variation of a material’s refractive index can lead to the adiabatic frequency shift (AFS) of a pulse spectrum. Such a rigid spectral change has relevant technological implications, for example, in ultrafast signal processing. Here, we investigate the AFS process in epsilon-near-zero (ENZ) materials and show that the frequency shift can be achieved in a shorter length if operating in the vicinity of ${\rm Re}\{{\varepsilon _r}\}\; = \;{0}$. We also predict that, if the refractive index is induced by an intense optical pulse, the frequency shift is more efficient for a pump at the ENZ wavelength. Remarkably, we show that these effects are a consequence of the slow propagation speed of pulses at the ENZ wavelength. Our theoretical predictions are validated by experiments obtained for the AFS of optical pulses incident upon aluminum zinc oxide thin films at ENZ. Our results indicate that transparent metal oxides operating near the ENZ point are good candidates for future frequency conversion schemes.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2019 (6)

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1 (2019).
[Crossref]

Y. Yang, J. Lu, A. Manjavacas, T. S. Luk, H. Liu, K. Kelley, J.-P. Maria, E. L. Runnerstrom, M. B. Sinclair, S. Ghimire, and I. Brener, “High-harmonic generation from an epsilon-near-zero material,” Nat. Phys. 15, 1022 (2019).
[Crossref]

H. Wang, K. Du, C. Jiang, Z. Yang, L. Ren, W. Zhang, S. J. Chua, and T. Mei, “Extended Drude Model for Intraband-Transition-Induced Optical Nonlinearity,” Phys. Rev. Appl. 11, 064062 (2019).
[Crossref]

N. Kinsey and J. Khurgin, “Nonlinear epsilon-near-zero materials explained: opinion,” Opt. Mater. Express 9, 2793–2796 (2019).
[Crossref]

N. Kinsey, C. DeVault, A. Boltasseva, and V. M. Shalaev, “Near-zero-index materials for photonics,” Nat. Rev. Mater. 4, 742–760 (2019).
[Crossref]

O. Reshef, I. De Leon, M. Z. Alam, and R. W. Boyd, “Nonlinear optical effects in epsilon-near-zero media,” Nat. Rev. Mater. 4, 535 (2019).
[Crossref]

2018 (3)

M. Z. Alam, S. A. Schulz, J. Upham, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material,” Nat. Photonics 12, 79–83 (2018).
[Crossref]

E. G. Carnemolla, L. Caspani, C. DeVault, M. Clerici, S. Vezzoli, V. Bruno, V. M. Shalaev, D. Faccio, A. Boltasseva, and M. Ferrera, “Degenerate optical nonlinear enhancement in epsilon-near-zero transparent conducting oxides,” Opt. Mater. Express 8, 3392–3400 (2018).
[Crossref]

S. Vezzoli, V. Bruno, C. DeVault, T. Roger, V. M. Shalaev, A. Boltasseva, M. Ferrera, M. Clerici, A. Dubietis, and D. Faccio, “Optical time reversal from time-dependent epsilon-near-zero media,” Phys. Rev. Lett. 120, 043902 (2018).
[Crossref]

2017 (2)

M. Clerici, N. Kinsey, C. DeVault, J. Kim, E. G. Carnemolla, L. Caspani, A. Shaltout, D. Faccio, V. M. Shalaev, A. Boltasseva, and M. Ferrera, “Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation,” Nat. Commun. 8, 1 (2017).
[Crossref]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–159 (2017).
[Crossref]

2016 (3)

R. M. Kaipurath, M. Pietrzyk, L. Caspani, T. Roger, M. Clerici, C. Rizza, A. Ciattoni, A. Di Falco, and D. Faccio, “Optically induced metal-to-dielectric transition in epsilon-near-zero metamaterials,” Sci. Rep. 6, 27700 (2016).
[Crossref]

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced Nonlinear Refractive Index in ε-Near-Zero Materials,” Phys. Rev. Lett. 116, 233901 (2016).
[Crossref]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352, 795–797 (2016).
[Crossref]

2015 (1)

2014 (1)

A. M. Mahmoud and N. Engheta, “Wave-matter interactions in epsilon-andmu- near-zero structures,” Nat. Commun. 5, 1 (2014).
[Crossref]

2013 (1)

2010 (1)

2009 (1)

T. Tanabe, M. Notomi, H. Taniyama, and E. Kuramochi, “Dynamic Release of Trapped Light from an Ultrahigh-Q Nanocavity via Adiabatic Frequency Tuning,” Phys. Rev. Lett. 102, 043907 (2009).
[Crossref]

2007 (2)

2006 (1)

M. Notomi and S. Mitsugi, “Wavelength conversion via dynamic refractive index tuning of a cavity,” Phys. Rev. A 73, 051803 (2006).
[Crossref]

2005 (2)

2003 (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[Crossref]

1979 (1)

J. Mendonça, “Nonlinear interactions of wave packets,” J. Plasma Phys. 22, 15–26 (1979).
[Crossref]

Alam, M. Z.

O. Reshef, I. De Leon, M. Z. Alam, and R. W. Boyd, “Nonlinear optical effects in epsilon-near-zero media,” Nat. Rev. Mater. 4, 535 (2019).
[Crossref]

M. Z. Alam, S. A. Schulz, J. Upham, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material,” Nat. Photonics 12, 79–83 (2018).
[Crossref]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352, 795–797 (2016).
[Crossref]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[Crossref]

Boltasseva, A.

N. Kinsey, C. DeVault, A. Boltasseva, and V. M. Shalaev, “Near-zero-index materials for photonics,” Nat. Rev. Mater. 4, 742–760 (2019).
[Crossref]

S. Vezzoli, V. Bruno, C. DeVault, T. Roger, V. M. Shalaev, A. Boltasseva, M. Ferrera, M. Clerici, A. Dubietis, and D. Faccio, “Optical time reversal from time-dependent epsilon-near-zero media,” Phys. Rev. Lett. 120, 043902 (2018).
[Crossref]

E. G. Carnemolla, L. Caspani, C. DeVault, M. Clerici, S. Vezzoli, V. Bruno, V. M. Shalaev, D. Faccio, A. Boltasseva, and M. Ferrera, “Degenerate optical nonlinear enhancement in epsilon-near-zero transparent conducting oxides,” Opt. Mater. Express 8, 3392–3400 (2018).
[Crossref]

M. Clerici, N. Kinsey, C. DeVault, J. Kim, E. G. Carnemolla, L. Caspani, A. Shaltout, D. Faccio, V. M. Shalaev, A. Boltasseva, and M. Ferrera, “Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation,” Nat. Commun. 8, 1 (2017).
[Crossref]

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced Nonlinear Refractive Index in ε-Near-Zero Materials,” Phys. Rev. Lett. 116, 233901 (2016).
[Crossref]

N. Kinsey, C. DeVault, J. Kim, M. Ferrera, V. M. Shalaev, and A. Boltasseva, “Epsilon-near-zero Al-doped ZnO for ultrafast switching at telecom wavelengths,” Optica 2, 616–622 (2015).
[Crossref]

A. Shaltout, M. Clerici, N. Kinsey, R. P. M. Kaipurath, J. Kim, E. G. Carnemolla, D. Faccio, A. Boltasseva, V. M. Shalaev, and M. Ferrera, “Doppler-shift emulation using highly time-refracting TCO layer,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FF2D.6.

Boyd, R. W.

O. Reshef, I. De Leon, M. Z. Alam, and R. W. Boyd, “Nonlinear optical effects in epsilon-near-zero media,” Nat. Rev. Mater. 4, 535 (2019).
[Crossref]

M. Z. Alam, S. A. Schulz, J. Upham, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material,” Nat. Photonics 12, 79–83 (2018).
[Crossref]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352, 795–797 (2016).
[Crossref]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[Crossref]

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Brener, I.

Y. Yang, J. Lu, A. Manjavacas, T. S. Luk, H. Liu, K. Kelley, J.-P. Maria, E. L. Runnerstrom, M. B. Sinclair, S. Ghimire, and I. Brener, “High-harmonic generation from an epsilon-near-zero material,” Nat. Phys. 15, 1022 (2019).
[Crossref]

Bruno, V.

S. Vezzoli, V. Bruno, C. DeVault, T. Roger, V. M. Shalaev, A. Boltasseva, M. Ferrera, M. Clerici, A. Dubietis, and D. Faccio, “Optical time reversal from time-dependent epsilon-near-zero media,” Phys. Rev. Lett. 120, 043902 (2018).
[Crossref]

E. G. Carnemolla, L. Caspani, C. DeVault, M. Clerici, S. Vezzoli, V. Bruno, V. M. Shalaev, D. Faccio, A. Boltasseva, and M. Ferrera, “Degenerate optical nonlinear enhancement in epsilon-near-zero transparent conducting oxides,” Opt. Mater. Express 8, 3392–3400 (2018).
[Crossref]

Carnemolla, E. G.

E. G. Carnemolla, L. Caspani, C. DeVault, M. Clerici, S. Vezzoli, V. Bruno, V. M. Shalaev, D. Faccio, A. Boltasseva, and M. Ferrera, “Degenerate optical nonlinear enhancement in epsilon-near-zero transparent conducting oxides,” Opt. Mater. Express 8, 3392–3400 (2018).
[Crossref]

M. Clerici, N. Kinsey, C. DeVault, J. Kim, E. G. Carnemolla, L. Caspani, A. Shaltout, D. Faccio, V. M. Shalaev, A. Boltasseva, and M. Ferrera, “Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation,” Nat. Commun. 8, 1 (2017).
[Crossref]

A. Shaltout, M. Clerici, N. Kinsey, R. P. M. Kaipurath, J. Kim, E. G. Carnemolla, D. Faccio, A. Boltasseva, V. M. Shalaev, and M. Ferrera, “Doppler-shift emulation using highly time-refracting TCO layer,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FF2D.6.

Caspani, L.

E. G. Carnemolla, L. Caspani, C. DeVault, M. Clerici, S. Vezzoli, V. Bruno, V. M. Shalaev, D. Faccio, A. Boltasseva, and M. Ferrera, “Degenerate optical nonlinear enhancement in epsilon-near-zero transparent conducting oxides,” Opt. Mater. Express 8, 3392–3400 (2018).
[Crossref]

M. Clerici, N. Kinsey, C. DeVault, J. Kim, E. G. Carnemolla, L. Caspani, A. Shaltout, D. Faccio, V. M. Shalaev, A. Boltasseva, and M. Ferrera, “Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation,” Nat. Commun. 8, 1 (2017).
[Crossref]

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced Nonlinear Refractive Index in ε-Near-Zero Materials,” Phys. Rev. Lett. 116, 233901 (2016).
[Crossref]

R. M. Kaipurath, M. Pietrzyk, L. Caspani, T. Roger, M. Clerici, C. Rizza, A. Ciattoni, A. Di Falco, and D. Faccio, “Optically induced metal-to-dielectric transition in epsilon-near-zero metamaterials,” Sci. Rep. 6, 27700 (2016).
[Crossref]

Chowdhury, E.

M. R. Shcherbakov, K. Werner, Z. Fan, N. Talisa, E. Chowdhury, and G. Shvets, “Photon acceleration and tunable broadband harmonics generation in nonlinear time-dependent metasurfaces,” Nat. Commun. 10, 1 (2019).
[Crossref]

Chua, S. J.

H. Wang, K. Du, C. Jiang, Z. Yang, L. Ren, W. Zhang, S. J. Chua, and T. Mei, “Extended Drude Model for Intraband-Transition-Induced Optical Nonlinearity,” Phys. Rev. Appl. 11, 064062 (2019).
[Crossref]

Ciattoni, A.

R. M. Kaipurath, M. Pietrzyk, L. Caspani, T. Roger, M. Clerici, C. Rizza, A. Ciattoni, A. Di Falco, and D. Faccio, “Optically induced metal-to-dielectric transition in epsilon-near-zero metamaterials,” Sci. Rep. 6, 27700 (2016).
[Crossref]

Clerici, M.

S. Vezzoli, V. Bruno, C. DeVault, T. Roger, V. M. Shalaev, A. Boltasseva, M. Ferrera, M. Clerici, A. Dubietis, and D. Faccio, “Optical time reversal from time-dependent epsilon-near-zero media,” Phys. Rev. Lett. 120, 043902 (2018).
[Crossref]

E. G. Carnemolla, L. Caspani, C. DeVault, M. Clerici, S. Vezzoli, V. Bruno, V. M. Shalaev, D. Faccio, A. Boltasseva, and M. Ferrera, “Degenerate optical nonlinear enhancement in epsilon-near-zero transparent conducting oxides,” Opt. Mater. Express 8, 3392–3400 (2018).
[Crossref]

M. Clerici, N. Kinsey, C. DeVault, J. Kim, E. G. Carnemolla, L. Caspani, A. Shaltout, D. Faccio, V. M. Shalaev, A. Boltasseva, and M. Ferrera, “Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation,” Nat. Commun. 8, 1 (2017).
[Crossref]

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced Nonlinear Refractive Index in ε-Near-Zero Materials,” Phys. Rev. Lett. 116, 233901 (2016).
[Crossref]

R. M. Kaipurath, M. Pietrzyk, L. Caspani, T. Roger, M. Clerici, C. Rizza, A. Ciattoni, A. Di Falco, and D. Faccio, “Optically induced metal-to-dielectric transition in epsilon-near-zero metamaterials,” Sci. Rep. 6, 27700 (2016).
[Crossref]

A. Shaltout, M. Clerici, N. Kinsey, R. P. M. Kaipurath, J. Kim, E. G. Carnemolla, D. Faccio, A. Boltasseva, V. M. Shalaev, and M. Ferrera, “Doppler-shift emulation using highly time-refracting TCO layer,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FF2D.6.

De Leon, I.

O. Reshef, I. De Leon, M. Z. Alam, and R. W. Boyd, “Nonlinear optical effects in epsilon-near-zero media,” Nat. Rev. Mater. 4, 535 (2019).
[Crossref]

M. Z. Alam, S. A. Schulz, J. Upham, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material,” Nat. Photonics 12, 79–83 (2018).
[Crossref]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352, 795–797 (2016).
[Crossref]

DeVault, C.

N. Kinsey, C. DeVault, A. Boltasseva, and V. M. Shalaev, “Near-zero-index materials for photonics,” Nat. Rev. Mater. 4, 742–760 (2019).
[Crossref]

S. Vezzoli, V. Bruno, C. DeVault, T. Roger, V. M. Shalaev, A. Boltasseva, M. Ferrera, M. Clerici, A. Dubietis, and D. Faccio, “Optical time reversal from time-dependent epsilon-near-zero media,” Phys. Rev. Lett. 120, 043902 (2018).
[Crossref]

E. G. Carnemolla, L. Caspani, C. DeVault, M. Clerici, S. Vezzoli, V. Bruno, V. M. Shalaev, D. Faccio, A. Boltasseva, and M. Ferrera, “Degenerate optical nonlinear enhancement in epsilon-near-zero transparent conducting oxides,” Opt. Mater. Express 8, 3392–3400 (2018).
[Crossref]

M. Clerici, N. Kinsey, C. DeVault, J. Kim, E. G. Carnemolla, L. Caspani, A. Shaltout, D. Faccio, V. M. Shalaev, A. Boltasseva, and M. Ferrera, “Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation,” Nat. Commun. 8, 1 (2017).
[Crossref]

N. Kinsey, C. DeVault, J. Kim, M. Ferrera, V. M. Shalaev, and A. Boltasseva, “Epsilon-near-zero Al-doped ZnO for ultrafast switching at telecom wavelengths,” Optica 2, 616–622 (2015).
[Crossref]

Di Falco, A.

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced Nonlinear Refractive Index in ε-Near-Zero Materials,” Phys. Rev. Lett. 116, 233901 (2016).
[Crossref]

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Supplementary Material (1)

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» Supplement 1       Supplementary Document

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Figures (4)

Fig. 1.
Fig. 1. Adiabatic frequency shift in (a) microcavity (or a photonic crystal) and (b) unconstrained epsilon-near-zero medium in which a rapid change of refractive index $\delta {n}$ (and permittivity $\delta \varepsilon $) causes a frequency shift $\delta \omega $.
Fig. 2.
Fig. 2. Adiabatic frequency shift in the material with Drude-like dispersion. As the permittivity changes, the dispersion curve shifts from 1 to 2. If the change of permittivity is very slow, the frequency ${\omega _1}$ stays unchanged while the wave vector shifts rightward from ${\textbf{k}_1}$ to ${\textbf{k}_2}$. If the change in permittivity is sufficiently fast, then the wave vector ${\textbf{k}_1}$ remains unchanged while the frequency shifts downward from ${\omega _1}$ to ${\omega _2}$. Also shown are imaginary parts of wave vector (dashed lines), and the tinted regions show the high reflectivity (or “metallic”) region with a negative real part of permittivity.
Fig. 3.
Fig. 3. (a) Shows a sketch of the experimental setup. A 785 nm laser pulse train of $\sim{115}\;{\rm fs}$ duration and intensity up to ${1}.{3}\;{{\rm TW/cm}^2}$ excites a 900 nm thick AZO film at 100 Hz repetition rate. The reflection and transmission signals are recorded with calibrated photodiodes for a probe pulse with a wavelength that is tuned between $\sim{1250}\;{\rm nm}$ and $\sim{1500}\;{\rm nm}$. The spectrum of the transmitted pulse is recorded with a spectrometer. (b) Linear index and (c) group index of the AZO sample as a function of wavelength. (d) shows the measured values for the real part of the permittivity (crosses) at different pump intensities (green, no pump; blue, $\sim{440}\;{{\rm GW/cm}^2}$; orange, $\sim{870}\;{{\rm GW/cm}^2}$; red, $\sim{1304}\;{{\rm GW/cm}^2}$). The solid lines of corresponding colors are obtained from a fit with a Drude model.
Fig. 4.
Fig. 4. (a), (c), and (e) show the spectrum (power spectral density, PSD) of a probe pulse as a function of the pump–probe delay $\tau $ for three different input central wavelengths (1155 nm, 1285 nm, 1455 nm, respectively) for a pump pulse of ${I_p}$ $\sim{870}\;{{\rm GW/cm}^2}$ peak intensity. (b), (d), and (f) show the probe carrier wavelength in function of the pump–probe delay for the three input wavelengths mentioned above, and for three different pump peak intensities (blue, ${440}\;{{\rm GW/cm}^2}$; orange, ${650}\;{{\rm GW/cm}^2}$; yellow, ${870}\;{{\rm GW/cm}^2}$). The dashed lines are the wavelength shifts predicted by the model, based on the measured $\delta n$ shown in Fig. S2 of Supplement 1).

Equations (18)

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ω n ( ω ) = k ( ω ) c ,
δ ( n ω ) = ω δ n + n δ ω = 0 ,
δ ω = δ n n ω .
ε r ( ω ) = ε ( 1 ω p 2 ω 2 + i ω γ ) ,
δ n ( ω ) = δ ε ( ω ) / 2 n ( ω ) ,
δ ω = δ ε r 2 n 2 ω = δ ε r ( ω ) 2 ε r ( ω ) ω .
n ( ω + δ ω ) n ( ω ) δ n ( ω ) + δ ω d n ( ω ) d ω .
ω n ( ω ) ( ω + δ ω ) [ n ( ω ) + δ n ( ω ) + δ ω d n ( ω ) d ω ] .
δ ω = δ n ( ω ) n g ( ω ) ω ,
n g ( ω ) = n ( ω ) + ω d n d ω .
δ ω ( t ) = t δ Φ ( t ) = ω c t 0 z ( t ) δ n ( z ) d z = ω c t 0 t v g δ n ( t ) d t = ω n g δ n ( t ) .
n ( ω ) n g ( ω ) = ε r ( ω ) + 1 2 ω d ε r ( ω ) d ω = ε .
δ ω δ ε r ( ω ) 2 ε ω ,
δ ε r ( ω ) = 2 ε ω p δ ω p / ω 2 .
δ ω δ ω p ω p ω δ ω p .
k ( ω ) = ω c n ( ω ) = ω c 1 ω p 2 ω 2 = c 1 ε 1 / 2 ω 2 ω p 2 .
F O M = δ ω ω I p u m p L = χ ( 3 ) Δ t c h a n g e 2 η 0 n g I p u m p / ε 2 ε I p u m p L = n g 2 χ ( 3 ) μ 0 ε 2 χ ( 3 ) μ 0 n 2 = χ ( 3 ) ε 0 η 2 .
δ ω ω L δ n / ( c Δ t c h a n g e ) .