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arXiv:1609.06872 · Physical Review A

Transformation of the frequency-modulated continuous-wave field into a train of short pulses by resonant filters

R. N. Shakhmuratov

Published Mar 8, 2017• 7 citations
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Abstract

The resonant filtering method transforming the frequency-modulated radiation field into a train of short pulses is proposed to be applied in the optical domain. Effective frequency modulation can be achieved by using an electro-optic modulator. Due to frequency modulation, a narrow-spectrum cw radiation field is seen by the resonant filter as a comb of equidistant spectral components separated by the modulation frequency. Tuning a narrow-bandwidth filter in resonance with the $n\mathrm{th}$ spectral component of the comb transforms the radiation field into bunches of pulses, with $n$ pulses in each bunch. The transformation is explained by the interference of the coherently scattered resonant component of the field with the whole comb. Constructive interference results in the formation of pulses, while destructive interference is seen as dark windows between pulses. It is indicated that the optimal thickness of the resonant filter is several orders of magnitude smaller than the necessary thickness of the dispersive filters used before in the optical domain to produce short pulses from the frequency-modulated field.

DOI
10.1103/physreva.95.033805

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The resonant filtering method transforming the frequency-modulated radiation field into a train of short pulses is proposed to be applied in the optical domain. Effective frequency modulation can be achieved by using an electro-optic modulator. Due to frequency modulation, a narrow-spectrum cw radiation field is seen by the resonant filter as a comb of equidistant spectral components separated by the modulation frequency. Tuning a narrow-bandwidth filter in resonance with the nthn\mathrm{th}nth spectral component of the comb transforms the radiation field into bunches of pulses, with nnn pulses in each bunch. The transformation is explained by the interference of the coherently scattered resonant component of the field with the whole comb. Constructive interference results in the formation of pulses, while destructive interference is seen as dark windows between pulses. It is indicated that the optimal thickness of the resonant filter is several orders of magnitude smaller than the necessary thickness of the dispersive filters used before in the optical domain to produce short pulses from the frequency-modulated field.
A method for generating short pulses with a high repetition rate is proposed. It is based on periodic modulation of the radiation phase of a CW laser and subsequent filtering through a narrow-band frequency filter. At the output of the filter, a sequence of short pulses is generated with a period equal to half the modulation period. In the case of a resonant filter using atoms, ions or molecules with a narrow absorption line, the appearance of pulses can be explained by constructive interference of the incident radiation with radiation coherently scattered by resonant particles. An alternative explanation of the pulse generation in the general case, when frequency filters operating on other principles are used, is based on the interference of the spectral components remaining after filtering. The method can be applied for time division multiplexing to transmit digital information through a single channel at high speed. The advantage of the proposed method is the use of phase modulation (not strictly periodic), integrated with frequency filtering to generate pulses and encode information simultaneously in one circuit, while in other known methods, information is introduced into a sequence of regularly generated pulses using additional amplitude modulation.
A method for generating short pulses with a high repetition rate is proposed. It is based on periodic modulation of the radiation phase of a CW laser and subsequent filtering through a narrow-band frequency filter. At the output of the filter, a sequence of short pulses is generated with a period equal to half the modulation period. In the case of a resonant filter using atoms, ions or molecules with a narrow absorption line, the appearance of pulses can be explained by constructive interference of the incident radiation with radiation coherently scattered by resonant particles. An alternative explanation of the pulse generation in the general case, when frequency filters operating on other principles are used, is based on the interference of the spectral components remaining after filtering. The method can be applied for time division multiplexing to transmit digital information through a single channel at high speed. The advantage of the proposed method is the use of phase modulation (not strictly periodic), integrated with frequency filtering to generate pulses and encode information simultaneously in one circuit, while in other known methods, information is introduced into a sequence of regularly generated pulses using additional amplitude modulation.
We propose a method to transform a single-photon field into bunches of pulses with controllable timing and number of pulses in a bunch. The method is based on transmission of a photon through an optically thick single-line absorber vibrated with a frequency appreciably exceeding the width of the absorption line. The narrow spectrum of the incoming photon is ``seen'' by the vibrated absorber as a comb of equidistant spectral components separated by the vibration frequency. Tuning the absorber in resonance with mthm\mathrm{th}mth spectral component transforms the output radiation into bunches of pulses with mmm pulses in each bunch. We provide a simple analytical solution clearly describing this effect and experimentally demonstrate the proposed technique with a single 14.4-keV photon and an ensemble of vibrated 57Fe^{57}\mathrm{Fe}57Fe nuclei. This method opens an alternate way to the production of time-bin qubits.
We show that both the power and repetition rate of a frequency comb generated in a nonlinear ring resonator, pumped with continuous-wave (cw) coherent light, are modulated. The modulation is brought about by the interaction of the cw background with optical pulses excited in the resonator, and occurs in resonators with nonzero high-order chromatic dispersion and wavelength-dependent quality factor. The modulation frequency corresponds to the detuning of the pump frequency from the eigenfrequency of the pumped mode in the resonator.
Pulse filtering through a medium with infinite periodic structure in transmission spectrum is analyzed. Two types of filters are considered. The first, named harmonic frequency crystal (HFC), is the filter whose widths of transmitting and absorbing windows are equal. The second, named anharmonic frequency crystal (AHFC), has narrow absorption peaks separated by wide transmission windows. AHFC of moderate optical thickness demonstrates properties quite similar to those of high finesse atomic frequency comb (AFC) with limited number of the absorption peaks, which produce a few pulses from a short input pulse. On the contrary, HFC transforms the input pulse into a train of pulses whose maximum amplitudes follow a wide bell-shaped envelope. HFC allows to find an exact universal analytical solution, which describes transformation of a broadband pulse into a train of short pulses, slow light propagation for a pulse whose spectral width fits one of the transparency windows of the crystal, and absorption typical for a single line absorber if the pulse spectrum falls into one of the absorption peaks. Potential applications of HFC are discussed.
A simple analytical solution for the propagation of a weak Gaussian pulse in a dense absorptive medium with electromagnetically induced transparency is found. This solution is applied to the analysis of three regimes: (1) and (2) the pulse spectrum is narrower than the transparency window [which is narrow (1) or wide (2) with respect to the width of the absorption line] and (3) the pulse spectrum is broader than the transparency window. It is shown that the pulse maintains its area in all three regimes and maintains its Gaussian shape but narrows in spectrum in regime 1. In regime 2, the pulse begins to distort after a certain distance. In regime 3, the pulse is split into two parts. One part is an adiabatic part with a spectrum defined by the effective width of the transparency window for a thick medium and the other is an oscillating nonadiabatic part of short duration. The adiabatic part propagates slowly and the nonadiabatic part propagates with a velocity close to the speed of light. Thus in regime 3, the medium acts as a time-frequency filter, separating the narrow and wide spectrum components of the pulse in time at the output of the absorber.