Spectro-Temporal Imaging of Optical Pulses With a Single Time Lens

Azaña, José; Berger, N.K.; Levit, Boris; Fischer, Baruch

doi:10.1109/lpt.2004.823702

Cited by 47 publications

(28 citation statements)

References 9 publications

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“…For the special choice β = 1/α the combined transformation applied to the photon is actually the Fourier transform, transforming time to frequency (the mathematics involved is exactly analogous to that describing spatial light propagation through a cylindrical lens, hence the name: "time lens"). The time resolution thus obtainable extends down to hundreds of femtoseconds [20,22].…”

Section: Measuring the Time-dependent Spectrummentioning

confidence: 99%

Time-dependent spectrum of a single photon and its positive-operator-valued measure

Enk

2017

Phys. Rev. A

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Suppose we measure the time-dependent spectrum of a single photon. That is, we first send the photon through a set of frequency filters (which we assume to have different filter frequencies but the same finite bandwidth Γ), and then record at what time (with some finite precision ∆t, and with some finite efficiency η) and after passing what filter the photon is detected. What is the POVM (PositiveOperator Valued Measure, the most general description of a quantum measurement) corresponding to such a measurement? We show how to construct the POVM in various cases, with special interest in the case Γ∆t 1 (time-frequency uncertainty still holds, even in that limit). One application of the formalism is to heralding single photons. We also find a Hong-Ou-Mandel type of interference effect with two photons entering a frequency filter.

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Section: Measuring the Time-dependent Spectrummentioning

confidence: 99%

Time-dependent spectrum of a single photon and its positive-operator-valued measure

Enk

2017

Phys. Rev. A

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“…The proposal of this real-time Fourier transformer, also known as frequency-to-time converter, was made by Muriel et al [21,22] who were the first to use a chirped Fiber Bragg Grating as the dispersive device. The realization of the Fourier transform by means of a dispersive medium in the optical domain has found several applications, such as the realization of temporal magnification systems, causing the waveform to be stretched in time and allowing thus the single-shot characterization of ultrafast waveforms [23][24][25][26]. In combination with electro-optic modulation, this setup can also perform the temporal and spectral shaping of optical pulses [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Temporal self-imaging effect for periodically modulated trains of pulses

Pérez-Herrera¹,

Erro²,

Garde³

et al. 2014

Opt. Express

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Abstract:In this paper, the mathematical description of the temporal selfimaging effect is studied, focusing on the situation in which the train of pulses to be dispersed has been previously periodically modulated in phase and amplitude. It is demonstrated that, for each input pulse and for some specific values of the chromatic dispersion, a subtrain of optical pulses is generated whose envelope is determined by the Discrete Fourier Transform of the modulating coefficients. The mathematical results are confirmed by simulations of various examples and some limits on the realization of the theory are commented. 161-237 (1995). 8. A. M. Weiner and A. M. Kan'an, "Femtosecond pulse shaping for synthesis, processing, and time-to-space conversion of ultrafast optical waveforms," IEEE J. Sel. Top. Quantum Electron. 4(2), 317-331 (1998). 9. B. H. Kolner, "Space-time duality and the theory of temporal imaging," IEEE J. Quantum Electron. 30(8), 1951Electron. 30(8), -1963Electron. 30(8), (1994. (McGraw-Hill, 1968). 11. S. A. Akhmanov, A. P. Sukhoruk, and A. S. Chirkin, "Nonstationary phenomena and space-time analogy in nonlinear optics," Sov. Phys. JETP-USSR28, 748 (1969). 12. E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum Electron. 5(9), 454^158 (1969). 13. B. H. Kolner and M. Nazarathy, "Temporal imaging with a time lens," Opt. Lett. 14(12), 630-632 (1989). References and links A. Papoulis, Systems and Transforms With Applications in Optics

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“…This situation corresponds to the dual situation, in the spectral domain, of the Fraunhofer far-field effect [10]. In other words, large temporal modulation on a pulse also induces TTF conversion.…”

mentioning

confidence: 96%

“…The scaling factor is just given by the chirping rate of the time lens. For the purposes of this Letter, it is important to recognize that a simplified configuration of this setup has been recently reported by Azaña et al, where the dispersive element can be dropped [10]. Following their work, since the action of a time lens can be mathematically described as a multiplicative element impressing parabolic phase modulation in the time domain, exp(iKt 2 /2), where K denotes the chirping rate, TTF conversion is achieved whenever the following inequality is satisfied…”

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confidence: 99%

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Lossless equalization of frequency combs

2008

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Frequency combs obtained by sinusoidal phase modulation of narrow-band continuous-wave lasers are widely used in the field of optical communications. However, the resulting spectral envelope of the comb is not flat. In this Letter, we propose a general and efficient approach to achieve flat frequency combs with tunable bandwidth. The idea is based on a two-step process. First, efficient generation of a train with temporal flat-top-pulse profile is required. Second, we use large parabolic phase modulation in every train period in order to map the temporal intensity shape into the spectral domain. In this way, the resulting spectral envelope is flat and the size is tunable with the chirping rate. Two different schemes are proposed and verified through numerical simulations.

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Spectro-Temporal Imaging of Optical Pulses With a Single Time Lens

Cited by 47 publications

References 9 publications

Time-dependent spectrum of a single photon and its positive-operator-valued measure

Time-dependent spectrum of a single photon and its positive-operator-valued measure

Temporal self-imaging effect for periodically modulated trains of pulses

Lossless equalization of frequency combs

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