Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Express

Mutually modulated cross-gain modulation with a considerable modulation wavenumber-interaction length product

Ligang Huang, Weihua Peng, Feng Gao, Fang Bo, Guoquan Zhang, Jingjun Xu

Published Apr 28, 2015• 1 citation
Publisher

Abstract

An extended theory of the mutually modulated cross-gain modulation was developed to make it valid under considerable modulated wavenumber-interaction length product. Parametric analysis of the extended theory shows that, in the modulated probe beam out of the gain medium, the spectral sensitivity of the first harmonic wave is associated with its amplitude. The larger the sensitivity is, the smaller the amplitude will be. An effective method was provided to monitor and achieve high spectral sensitivity at a pre-selected frequency detuning in practice. The validity of the extended theory was confirmed by a sensing experiment in a piece of ∼10-km fiber with 10 kHz modulation frequency, in which a fast light propagation with a sensitivity of 0.592 mrad/kHz was achieved.

DOI
10.1364/oe.23.012004

Related papers

Kilohertz laser frequency sensing with Brillouin mutually modulated cross-gain modulation

Shmuel Sternklar, Maxim Wart, Alexander Lifshitz +2 more

Using mutually modulated cross-gain modulation, Stokes optical frequency changes are converted into modulation phase changes with high sensitivity. In the slow-light transition regime, we demonstrate kilohertz sensitivity to the Stokes optical carrier frequency. The sensitivity is inversely proportional to the modulation frequency of the pump and Stokes beams.

Optics Letters•Oct 18, 2011•11 citations

Mutually-modulated cross-gain modulation and slow light

Shmuel Sternklar, Eyal Sarid, Maxim Wart +1 more

The interaction of pump and Stokes light in a Brillouin medium, where both beams are modulated, can be utilized for controlling the group velocity of the amplified Stokes (or depleted pump). The dependence of the group velocity for this mutually-modulated cross-gain modulation (MMXGM) technique on the Brillouin gain parameter is studied. A sharp transition to slow light occurs in the G1α/β≈1 regime, where G1 is the Brillouin gain parameter, and α and β are the pump and Stokes modulation indices, respectively. A comparison of MMXGM slow light to the Brillouin dispersion-based slow-light technique reveals the fundamental differences between them. The formation of higher harmonics of the modulation frequency is also discussed. The theoretical predictions are experimentally corroborated and potential applications in fiber-based sensing and interferometry are discussed.

Journal of Optics•Sep 24, 2010•10 citations

Wavelength monitoring with mutually modulated cross-gain modulation in a semiconductor optical amplifier and Brillouin amplifier

Shalom Bloch, Alexander Lifshitz, Er’el Granot +1 more

We analyze and implement mutually modulated cross-gain modulation (MMXGM) in a semiconductor optical amplifier (SOA). In this effect, optical wavelength changes are converted into modulation phase changes with high sensitivity and resolution. In the slow-light transition regime, we demonstrate picometer sensitivity to the optical wavelength. We analyze the spectroscopic performance of the SOA-based MMXGM and the previously developed Brillouin-based MMXGM techniques, and compare them to that of material-dispersion-enhanced, slow-light spectroscopy in a Brillouin amplifier.

Journal of the Optical Society of America B•Mar 20, 2013•6 citations

Group velocity manipulation in active fibers using mutually modulated cross-gain modulation: from ultraslow to superluminal propagation

Kai Qian, Li Zhan, Liqun Zhang +6 more

We propose and experimentally demonstrate the propagation of slow/fast light in an erbium-doped fiber (EDF) using mutually modulated cross-gain modulation. The group velocity of the light signal can be manipulated by the effect of gain cross-saturation modulation by a saturating light at an arbitrary wavelength in the gain bandwidth of the EDF. The ultraslow propagation with a small group velocity of 5.6 × 10⁻³c (c is the light speed in free space) and superluminal propagation with a negative group velocity of -1.1 × 10⁻³c has been observed under different modulation phases.

Optics Letters•Jun 6, 2011•43 citations

Slow-light sensors in optical gain media based on mutually-modulated cross-gain modulation

Shmuel Sternklar, Shalom Bloch, Alexander Lifshitz

We review the theory and applications of mutually-modulated cross-gain modulation (MMXGM) in optical gain media. MMXGM transforms changes in various physical parameters, such as optical wavelength, into modulation-phase changes with high sensitivity.

Nonlinear Optics•Jan 1, 2013•0 citations

Propagation of modulated optical fields through saturable-absorbing media: a general theory of modulation spectroscopy

Mark A. Kramer, Robert W. Boyd, Lloyd W. Hillman +1 more

The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.

Journal of the Optical Society of America B•Sep 1, 1985•22 citations
An extended theory of the mutually modulated cross-gain modulation was developed to make it valid under considerable modulated wavenumber-interaction length product. Parametric analysis of the extended theory shows that, in the modulated probe beam out of the gain medium, the spectral sensitivity of the first harmonic wave is associated with its amplitude. The larger the sensitivity is, the smaller the amplitude will be. An effective method was provided to monitor and achieve high spectral sensitivity at a pre-selected frequency detuning in practice. The validity of the extended theory was confirmed by a sensing experiment in a piece of ∼10-km fiber with 10 kHz modulation frequency, in which a fast light propagation with a sensitivity of 0.592 mrad/kHz was achieved.
The interaction of pump and Stokes light in a Brillouin medium, where both beams are modulated, can be utilized for controlling the group velocity of the amplified Stokes (or depleted pump). The dependence of the group velocity for this mutually-modulated cross-gain modulation (MMXGM) technique on the Brillouin gain parameter is studied. A sharp transition to slow light occurs in the G1α/β≈1 regime, where G1 is the Brillouin gain parameter, and α and β are the pump and Stokes modulation indices, respectively. A comparison of MMXGM slow light to the Brillouin dispersion-based slow-light technique reveals the fundamental differences between them. The formation of higher harmonics of the modulation frequency is also discussed. The theoretical predictions are experimentally corroborated and potential applications in fiber-based sensing and interferometry are discussed.
We analyze and implement mutually modulated cross-gain modulation (MMXGM) in a semiconductor optical amplifier (SOA). In this effect, optical wavelength changes are converted into modulation phase changes with high sensitivity and resolution. In the slow-light transition regime, we demonstrate picometer sensitivity to the optical wavelength. We analyze the spectroscopic performance of the SOA-based MMXGM and the previously developed Brillouin-based MMXGM techniques, and compare them to that of material-dispersion-enhanced, slow-light spectroscopy in a Brillouin amplifier.
We propose and experimentally demonstrate the propagation of slow/fast light in an erbium-doped fiber (EDF) using mutually modulated cross-gain modulation. The group velocity of the light signal can be manipulated by the effect of gain cross-saturation modulation by a saturating light at an arbitrary wavelength in the gain bandwidth of the EDF. The ultraslow propagation with a small group velocity of 5.6 × 10⁻³c (c is the light speed in free space) and superluminal propagation with a negative group velocity of -1.1 × 10⁻³c has been observed under different modulation phases.
The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.