Frequency Spacing Of Modes Research Articles

Tunable frequency comb from echo-enabled harmonic generation free electron laser

We propose a novel scheme for the generation of a tunable soft x-ray frequency comb in a seeded free-electron laser (FEL) via the chirped pulse beating technology. Our research shows that harnessing the chirped pulse laser to imprint a submillimeter-scale energy modulation in the phase space of the relativistic electron beam together with the process of echo-enabled effect, multichromatic output soft x-ray radiation with a series of longitudinal modes can be amplified in an echo-enabled harmonic generation (EEHG) free electron laser, which finally forms a comb-liked shape in the frequency spectrum with the mode spacing frequency at terahertz (THz) band. Based on the theoretical and numerical analyses of the modulation process, the electron beam maintains a nanometer-scale microstructures due to the echo effect, while the beam obtains an energy modulation at submillimeter-scale from the chirped pulse beating laser. This leads to a series of longitudinal modes in the downstream radiator. Three-dimension time-dependent simulation results show that a frequency comb with a central wavelength of 8.9 nm can be generated directly with the help of chirped beating laser. The frequency spacing between the frequency lines on the radiation spectrum can be tuned easily by changing the parameters of chirped beating laser.

InAs/InP Quantum Dash Semiconductor Coherent Comb Lasers and their Applications in Optical Networks

We report on the design, growth, and fabrication of InAs/InP quantum dash (QD) gain materials and their use in lasers for optical network applications. A noise performance comparison between QD and quantum well (QW) Fabry–Perot (F-P) lasers has been made. By using the QD gain material we have successfully developed and assembled C-band coherent comb laser (CCL) modules with an electrical fast feedback loop control system to ensure a targeted mode frequency spacing. The frequency spacing was maintained within ±100 ppm and the operation wavelengths locked on the desired ITU grid within 0.01 nm over a period of several months. We also investigated a 25-GHz C-band QD CCL with an external cavity self-injection feedback locking (SIFL) system to reduce the optical linewidth of each individual channel to below 200 kHz in the wavelength range from 1537.55 nm to 1545.14 nm. The RF mode beating signal 3-dB bandwidth was also reduced from 9 kHz to approximately 500 Hz with this SIFL system. These QD CCLs with ultra-low relative intensity noise (RIN), ultra-narrow optical linewidth, and ultra-low timing jitter are excellent laser sources for multi-terabit optical networks. Using a 34.2 GHz QD CCL we demonstrate 10.8 Tbit/s (16QAM 48 × 28 GBaud PDM) coherent data transmission over 100 km of standard single mode fiber (SSMF) and 5.4 Tbit/s (PAM-4 48 × 28 GBaud PDM) aggregate data transmission capacity over 25 km of SSMF with error-free operation.

Generation of broadband frequency-variable laser comb allowing full-frequency sweep in the near-infrared region

We succeeded in developing a broadband-frequency-variable laser comb with a mode spacing of 12.5 GHz in the near-infrared region. We found that the spectrum of optical pump pulses can be frequency shifted over the mode spacing frequency by a single-sideband (SSB) optical modulator involving the amplitude and phase. Optical heterodyne measurement showed that the frequency shift of the optical pump pulses was precisely consistent with the modulation frequency applied to the SSB modulator with an accuracy of 20 kHz. The pump pulses were amplified and compressed to enhance the peak intensity. Finally, the frequency-shifted pump pulses launched into highly nonlinear fibers and generated a frequency-shifted laser comb. The precise frequency shift of pump pulses induced a simultaneous frequency shift of all modes of the laser comb. As a result, we succeeded in fast frequency sweeping of the laser comb over a full spectral range of 1080 to 1750 nm. This full-wavelength tuning implies that laser light of arbitrary and accurate wavelength can be obtained over the comb bandwidth.

Size Effects in Quasi-Static Energy Transport for Microscopic Quantum Systems

ABSTRACTWe consider finite size effects on energy transfer between nanoparticles mediated by quantum systems. The nanoparticles are considered as heat reservoirs with a finite number of modes. An expression for the quasi-static energy transport between the heat reservoirs having a finite mode frequency spacing Δ is derived. The resulting equations describing long-term (t ≥1/Δ) relaxation for the mode temperatures and the average temperatures of the nanoparticles are solved. The solutions depend on small number of measurable parameters and show unusual peculiarities in their temporal variations. As is shown, Fourier’s law in a chain of identical subsystems (nanoparticles) can be validated only on a short time scale. For a larger times, when t ∼ 1/Δ, the temperatures of different modes deviate from each other, thus preventing thermal equilibrium in each subsystem, and the validity of Fourier’s law cannot be established.

Perpendicular-field magnetoresistance and thermal-ferromagnetic resonance measurement of easy-plane anisotropy in nanostructured magnetic tunnel junctions

We report on measurements of the easy-plane anisotropy field of MgO-based magnetic tunnel junctions. The free layer easy-plane anisotropy field was measured by perpendicular field thermal noise-based ferromagnetic resonance spectroscopy (T-FMR) and by tunneling magnetoresistance (TMR). A model was derived to extract the saturation field of the free layer from perpendicular TMR-based resistance-field data. Both measurements confirm that for 20 Å CoFeB free layers, the measured effective easy-plane anisotropy field of 4πMeff equal to (5.3±0.6) kOe is well below the bulk value based on demagnetization. T-FMR measurements show a base resonant mode with a linear field dependence in accordance with the Kittel formula. Higher-order modes are also observed, suggesting the presence of confined spin-wave excitations. The mode frequency spacing, however, shows significant device-to-device variations whose origin is not yet uniquely determined.

Frequency splitting phenomenon of dual transverse modes in a Nd:YAG laser

We observed frequency splitting phenomenon of dual transverse modes (TEM 00q and TEM 01q) in a Nd:YAG microchip standing wave laser utilizing intracavity stress birefringence effects. Four resonance frequencies ( ν 00qe, ν 00qo, ν 01qe, and ν 01qo, respectively) were produced and tuned by changing the diametral compression force applied on the laser crystal. The transverse mode frequency spacing for the same longitudinal mode number (Δ ν trans) was 1.16 GHz, and the magnitude of frequency splitting (Δ ν) ranged from 0 MHz to 1.16 GHz. Based on this phenomenon, a four-mode differential standing wave laser, whose signal characteristics were a little like those of a four-mode differential travelling wave laser gyro however with a much larger frequency splitting range, was produced. The theoretical analysis is in good agreement with the experimental results. This phenomenon not only can be used to make lasers with two or more frequency differences, but also can be used to make high-resolution self-sensing laser sensors (e.g. laser force sensors and laser accelerometers).

Towards mode selection in δ Scuti stars: regularities in observed and theoretical frequency spectra

Only a fraction of the theoretically predicted nonradial pulsation modes have so far been observed in Delta Scuti stars. Nevertheless, the large number of frequencies detected in recent photometric studies of selected Delta Scuti stars allow us to look for regularities in the frequency spacing of modes. Mode identifications are used to interpret these results. Statistical analyses of several Delta Scuti stars (FG Vir, 44 Tau, BL Cam and others) show that the photometrically observed frequencies are not distributed at random, but that the excited nonradial modes cluster around the frequencies of the radial modes over many radial orders. The observed regularities can be partly explained by modes trapped in the stellar envelope. This mode selection mechanism was proposed by Dziembowski & Krolikowska (1990) and shown to be efficient for l = 1 modes. New pulsation model calculations confirm the observed regularities. We present the s-f diagram, which compares the average separation of the radial frequencies (s) with the frequency of the lowest-frequency unstable radial mode (f). This provides an estimate for the log g value of the observed star, if we assume that the centers of the observed frequency clusters correspond to the radial mode frequencies. This assumption is confirmed by examples of well-studied Delta Scuti variables in which radial modes were definitely identified.

Full Stabilization of a Microresonator-Based Optical Frequency Comb

We demonstrate control and stabilization of an optical frequency comb generated by four-wave mixing in a monolithic microresonator with a mode spacing in the microwave regime (86 GHz). The comb parameters (mode spacing and offset frequency) are controlled via the power and the frequency of the pump laser, which constitutes one of the comb modes. Furthermore, generation of a microwave beat note at the comb's mode spacing frequency is demonstrated, enabling direct stabilization to a microwave frequency standard.

Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback

We investigate a versatile vertical cavity surface-emitting laser (VCSEL) with a slight optical feedback from a simple wedge positioned at a well determined distance from the VCSEL. We use such a laser in conjunction with a miniature Rb atomic cell to detect coherent population trapping (CPT) when the external cavity mode spacing frequency corresponds to half the hyperfine frequency of Rb. The feedback greatly enhances the rf modulation efficiency of the VCSEL and as a result we obtain high contrast CPT signals at an input of −16dBm of rf modulation power compared to +1.25dBm needed in the absence of the external cavity.

Mode Locking in a Free-Electron Laser Amplifier

A technique is proposed to generate attosecond pulse trains of radiation from a free-electron laser amplifier. The optics-free technique synthesizes a comb of longitudinal modes by applying a series of spatiotemporal shifts between the copropagating radiation and electron bunch in the free-electron laser. The modes may be phase locked by modulating the electron beam energy at the mode spacing frequency. Three-dimensional simulations demonstrate the generation of a train of 400 as pulses at gigawatt power levels evenly spaced by 2.5 fs at a wavelength of 124 angstroms. In the x-ray at wavelength 1.5 angstroms, trains of 23 as pulses evenly spaced by 150 as and of peak power up to 6 GW are predicted.

Spectrum-based analysis and synthesis of percussion sounds

From the standpoint of the listener, convenient ways to catagorize percussion sounds are in terms of mode frequency positions, mode frequency spacing, and decay rates. Some sounds, like those of bells, chimes, and other struck bars, have modes which are widely spaced. Other sounds, such as those of timpani, tam-tam, and cymbals, have many more closely spaced modes. Measurements of average modal spacing, time-varying spectral shift, spectral incoherence, attack time, and decay rate are presented for a variety of percussion instrument sounds. Examples of percussion synthesis using this information will be presented.

Mode behavior in ultralarge ring lasers.

Contrary to expectations based on mode spacing, single-mode operation in very large He-Ne ring lasers may be achieved at intracavity power levels up to approximately0.15 times the saturation intensity for the He-Ne transition. Homogeneous line broadening at a high total gas pressure of 4-6 Torr allows a single-peaked gain profile that suppresses closely spaced multiple modes. At startup, decay of initial multiple modes may take tens of seconds. The single remaining mode in each direction persists metastably as the cavity is detuned by many times the mode frequency spacing. A theoretical explanation requires the gain profile to be concave down and to satisfy an inequality related to slope and saturation at the operating frequency. Calculated metastable frequency ranges are > 150 MHz at 6 Torr and depend strongly on pressure. Examples of unusual stable mode configurations are shown, with differently numbered modes in the two directions and with multiple modes at a spacing of approximately 100 MHz.

Longitudinal mode noise conversion by atomic vapour

An external cavity diode laser with very low levels of amplitude noise is shown to have considerable amounts of frequency noise at the longitudinal mode spacing frequency. This noise is observed by tuning the laser near to resonance with an atomic vapour and measuring the transmission of the vapour with a photodiode. The measured noise is enhanced by more than two orders of magnitude at the longitudinal modespacing frequency by conversion of frequency noise to amplitude noise by the vapour. The frequency noise was also simulated using intracavity electro optic modulation.

Synchronous mode locking in a closed cavity electron cyclotron maser

It is theoretically demonstrated that mode locked operation can be achieved in a closed cavity electron cyclotron maser (gyrotron). This work is unique in two respects. First, the cavity provides a highly dispersive guiding structure for the electromagnetic wave, hence, the mode frequency spacing varies by an amount comparable to the average spacing between modes. The dispersive properties of the electron beam are used to compensate that of the cavity to allow eight longitudinal TE11n modes to lock together. Second, the locking is obtained by rf modulation of the axial velocity of the electron beam. A numerical example shows that subnanosecond radiation pulses can be generated at 16 GHz with an order of magnitude increase in power level over the free-running maser.

Active mode-locked operation of a diode pumped colour-centre laser

The cw laser diode pumping of an (F + 2) ∗ colour centre laser has been recently demonstrated in our laboratory. The intensity of the pumping diode can easily be hf modulated. We present here the first experiments in which the colour centre laser is synchronously pumped at the mode spacing frequency, resulting in the emission of clean, regularly spaced pulses. The opto-electronic feedback is a very promising method of obtaining such a pulsed operation of a diode pumped colour centre laser without the use of an external hf oscillator.

Single-mode laser frequency modulation

This paper presents an analysis of the frequency response of single-mode laser frequency modulation. The method employed is based on the combined concepts of an active Fabry-Perot interferometer and of internal phase modulation, and is very transparent. The calculation of the sideband amplitudes and phases of the laser output reveals two main regions of the frequency response: for modulating frequencies lower than the cavity mode spacing the laser generates an ideally frequency-modulated signal. At higher frequencies the sideband amplitude versus modulating frequency shows an oscillatory behavior. Here, the response is mainly determined by the cavity mode spacing frequency and by the position of the modulator within the cavity. Comparing the theoretical results with previously reported experiments, very good agreement was found.

Passive mode locking of a ruby laser using a birefringent crystal and a fractional-commensurate cavity length

Mode-locked operation has been observed in a Q-switched, ruby laser using a quartz crystal as the passvie mode-locking element and a laser cavity length which is a whole fraction of that which is commensurate in mode-frequency spacing with the lowfrequency stimulated Brillouin scattering (lf S BS) in the crystal element. In addition, high-bit-rate operation has been observed, suggesting that the passive modulation of the lf S BS process is sufficiently strong to maintain a fixed-phase relation between several neighboring oscillating modes of the laser.