Multimode Beam Research Articles

Experimental evidence of multimode non‐classical light emission using OPOs

AbstractAny spatial measurement below the quantum standard limit requires multitransverse non‐classical light beams which can be produced by a transverse degenerate OPO. A multimode beam is characterized by a non uniform transverse repartition of noise. Using this criterion, we prove experimentally that a confocal Optical Parametric Oscillator emits a multimode non‐classical field.

Multimode combined intense laser-induced electron acceleration and violent bunch compression

The ponderomotive potential structure of a multimode combined intense laser beam is studied. Using a three-dimensional test particle simulation, the interaction of slow electrons with the combined laser beam in vacuum is investigated. The calculation shows that electrons distributed on a large scale can be accelerated to relativistic energy in vacuum. A violent longitudinal bunch compression phenomenon is also presented and discussed.

Incoherent superposition of off-axis polychromatic Hermite-Gaussian modes.

We study a statistical ensemble of multimode laser beams. Each beam is made up of an incoherent superposition of off-axis polychromatic Hermite-Gaussian modes. We obtain analytic expressions for the squared beam radius, the waist position, the Rayleigh range, the skewness parameter, the kurtosis parameter, and the squared beam-propagation factor. We demonstrate that the squared beam radius has a quadratic dependence on the distance from the waist plane. The skewness parameter may be different from zero in the near-field zone, but it tends to zero in the far-field zone. The kurtosis parameter in the far-field zone coincides with the kurtosis parameter of the incoherent superposition of on-axis modes.

Phase correction of radiation emitted by a powerful industrial laser with higher mode selection

Special features of operation of a high-power industrial CO2 laser with selection and correction of the phases of higher transverse modes are investigated theoretically and experimentally. An effective conversion of the higher-mode oscillation field into a narrow beam with inphase optical oscillations with an output power up to 1 kW with the help of a phase corrector is reported for the first time. The angular divergence is reduced to one-third of the value typical of a multimode beam. The physical origin of intracavity aberrations, which deteriorate the beam quality, is analysed. It is shown that the most significant effect is produced by an optical wedge-type aberration emerging due to transverse circulation of the active medium and transverse discharge. The prospects of application of this method for obtaining more powerful narrow laser beams are discussed.

Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays.

We investigate the design of free-space optical interconnects (FSOIs) based on arrays of vertical-cavity surface-emitting lasers (VCSELs), microlenses, and photodetectors. We explain the effect of the modal structure of a multimode VCSEL beam on the performance of a FSOI with microchannel architecture. A Gaussian-beam diffraction model is used in combination with the experimentally obtained spectrally resolved VCSEL beam profiles to determine the optical channel crosstalk and the signal-to-noise ratio (SNR) in the system. The dependence of the SNR on the feature parameters of a FSOI is investigated. We found that the presence of higher-order modes reduces the SNR and the maximum feasible interconnect distance. We also found that the positioning of a VCSEL array relative to the transmitter microlens has a significant impact on the SNR and the maximum feasible interconnect distance. Our analysis shows that the departure from the traditional confocal system yields several advantages including the extended interconnect distance and/or improved SNR. The results show that FSOIs based on multimode VCSELs can be efficiently utilized in both chip-level and board-level interconnects.

Thermal lens determination of LD end-pumped solid-state laser with stable resonator by slit scanning method

A simple method to determine the thermal focal length of LD end-pumped solid-state laser with stable resonator is presented. The M 2 factor describing the quality of the beam can be obtained by scanning a slit through the multi-mode Gaussian beam field. The waist width of the beam and the corresponding TEM 00 under the same parameters of laser are then deduced through the law of multi-mode Gaussian beam propagation. Based on the standard matrix theory of stable resonator, the thermal focal length of the gain medium can be easily achieved. To show the application of this approach, the thermal focal length of an LD pumped Nd:YVO 4 laser is measured and the experimental results are in agreement with the theoretical prediction.

A multimode-fibre laser-Doppler anemometer for highly spatiallyresolved velocity measurements using low-coherence light

The advantageous employment of multimode fibres for beam delivery inlaser-Doppler anemometers (LDAs) is presented. Multimode fibres allow thetransfer of significantly higher power into the LDA measurement volume andneed less alignment effort than do the single-mode fibres which are usuallyemployed. Powerful laser diodes can now be applied for LDA set-ups, allowingsensitive velocity measurements of fluid flows. It is demonstrated for thefirst time that the length of the measurement volume is less than that of thevolume of intersection of the two laser beams because of the low spatialcoherence of the multimode light. Highly spatially resolved measurements ofvariations in velocity in flows can be achieved. As a first result, ameasurement volume with a diameter of 584 µm, length 40 µm and280 fringes is presented. This allows precise frequency measurements and thedetermination of movements of accelerated particles. The speckle pattern ofthe multimode beam is sufficiently suppressed by choosing high-aperture fibreswith high intermodal dispersion and by the use of laser diode arrays withlow coherence lengths. A high accuracy in the determination of velocitygradients in laminar or turbulent boundary layers can be achieved with themultimode-fibre LDA.

Use of biorthogonal functions for the modal decomposition of multimode beams

From a recently proposed technique, used to determine the modal weights of beams made up of incoherent superpositions of Hermite–Gaussian (HG) modes, we derive the analytical expression of a family of functions which are biorthogonal to the squared HG functions. The knowledge of such functions enables the reconstruction of the modal content of these beams by means of the scalar-product with the intensity profile across a transverse plane.

Spatial output field for arbitrary input light field in a thermally self-induced inhomogeneous medium

Light propagation in a thermally self-induced inhomogeneous medium is investigated to find the transient spatial output field for an arbitrary incident field. The paraxial wave equation is coupled with the thermal diffusion equation to predict the output field as the index of refraction transiently changes due to absorption of light by the medium. The coupled equations are non-dimensionalized and are explicitly expressed in full non-linear form. A coupling parameter is derived to scale the degree of non-linearity. Limits for the validity of using the coupled wave-diffusion approach are given, with respect to bulk fluid motion and the transverse wave assumption. An additional constraint is given on the paraxial wave equation that arises due to the coupling with the diffusion equation. Numerical results are compared to exact solutions and experiments for Gaussian and multi-mode laser beams, which verify that this approach is accurate in the range of validity, and describes local, transient self-focusing in multi-mode beams.

Stimulated Brillouin scattering of CO2 radiation in compressed xenon

Stimulated Brillouin scattering (STBS) and phase conjugation of CO2 laser radiation have been demonstrated experimentally for the first time in compressed xenon (59 atm at 21°C) located inside the low-Q cavity of this laser. The nonlinear medium was exposed to the action of counterpropagating focused multimode radiation beams. The difference between the frequencies of the longitudinal cavity modes was set at the frequency of the acoustic wave (vs=32.2±0.3 MHz) excited as a result of STBS by 9.584 μm radiation. The duration of the radiation pulse τL was close to the acoustic phonon lifetime (τL<τph≈3× 10−6s). The excitation of STBS was manifested experimentally as the locking of longitudinal modes, an increase in power and energy, and also an increase in the duration of the lasing pulse and a reduction in the divergence to the diffraction limit.

Beam width measurements of asymmetric multi-mode laser beams

Beam width measurements of multi-mode asymmetric laser beams delivered by a XeCl laser, have been carried out in the focal plane of a lens, by the knife-edge and the variable rectangular aperture technique, respectively to determine beam divergence. It is shown that both methods provide beam width measurements in satisfactory agreement within experimental errors by properly choosing the clip levels. The analytical treatment for the clip level selection is also reported.

An alternative approach to determine the spot-size of a multi-mode laser beam and its application to diode laser beams

An alternative approach is suggested to determine the spot-size of a multi-mode laser beam. It has been shown by simulations that the suggested approach can give the beam quality factor and characteristic radius with less than 5% error. Unlike the power content method, the proposed method is applicable to the beams even with diameter one tenth of the CCD size. The new approach has been applied to a multi-mode diode laser output and it is shown that the ABCD matrix analysis can be used for beam propagation, with the measured parameters of the laser.

Numerical analysis for smoothing of CW multimode beam transformed by time-varying random phase plate

The numerical analysis of CW multimode laser beam transformed by time-varying random phase plate is presented in this paper. The method is based on diffraction integral formula. The dependence of the intensity distribution on the element size, changing frequency and duty ratio is discussed in detail. The numerical results account for the experimental results satisfactorily.

Self-reproduction of multimode hermite-gaussian beams

The condition for the self-reproduction of multimode Hermite-Gaussian beams is obtained and analyzed. Partial self-reproduction planes are also considered. A numerical example is presented.

Effects of laser mode and scanning direction on melt pool shape

A three-dimensional quasi-steady-state mathematical model is presented for laser heating with a multimode beam. The effects of laser beam scanning direction on the melt pool shape are investigated through the conduction analysis without phase change. The maximum temperature is found to be behind the center of the focal spot due to advection. The isotherms ahead of the focal spot bunch together and spread apart behind the focal spot on the surface of the workpiece due to the same effect. The temperature profile shows four distinct peaks as a result of four intensity peaks. Scanning direction affects the melt pool shape which needs to be considered for high precision cutting applications such as integrated circuit cutting. The melt pool shape is found to be symmetric about the x axis in the x-y plane and z axis in the y-z plane for the scanning angles φs=0° and −90°, however it is asymmetric for other scanning angles.

Tolerance of optical interconnections to misalignment

The fundamental reasons that determine the tolerance of free-space optical interconnect systems to misalignment are considered. By evaluation of the overlap of single-mode optical beams in the presence of misalignment it possible to determine an optimum beam configuration. It is shown that for any level of misalignment there is an optimum beam diameter that maximizes the coupling of light through the system. Many interconnect systems are not single mode throughout, so the analysis is extended to cover multimode systems. It is shown that, in principle, any level of misalignment can be accommodated by use of multimode beams, although at the cost of reduced channel density. It is shown that the presence of misalignment will mean that the number of channels that can be supported by an interconnect reduces with the length of the interconnect. As possible candidates for passively aligned systems, three example optical systems are analyzed by use of the methods developed.

Optical parametric oscillator with non-ideal mirrors and single- and multi-mode pump beams

Residual re ections of the idler wave in nominally singly resonant optical parametric oscillators can lead to uctuations in the output because the parametric conversion process is sensitive to the phases of the re ected waves. The energy fluctuations in a pulsed optical parametric oscillator are studied experimentally and numerically for single- or multi-longitudinal mode pump beams. We find that the fluctuations are reduced by a multi-mode pump so this may be preferable when unwanted re ections are present. We also observe that the parametric conversion process leads to serious self-focusing of the pump beam, and this limits the maximum safe pump energy.

MODE CORRELATION AND COHERENT-MODE REPRESEN-TATION OF MULTI-MODE LASER BEAMS

A detailed theoretical study on the mode correlation and coherent-mode representation of multi-mode laser beams has been performed.By using the theory of partially coherent light,the multi-mode laser beams behaving like Gaussian Schell-model(GSM) beams have been represented by the superposition of spatially coherent modes,which may be mutually correlated.The analytical expressions for the mode coherence cofficients have been given in the rectangular coordinate system.Furthermore,based on the M2-factor concept,the theory of the mode decomposition of multi-mode laser beams has been built up for the general case,where the mode correlation is considered.

Minimum averaged area of asymmetric multimode pumping beam

Formulae for the averaged area of a generally astigmatic multimode beam focused in an absorbing medium are derived. Criteria of the minimum pump area of an end-pumped solid state laser in the case of a multimode, asymmetrical pump beam are formulated. The role of asymmetry parameter M 2 of the pumping beam, absorption coefficient and the length of the active medium are investigated.

Channel Capacity for Optical Space Communication Systems

In this paper, discrete and continuous channel models of free-space optical channel have been described. The discrete channel model is used to determine the channel capacity with photon counter for single-mode and multimode laser beams. The channel capacities with preamplified PIN photodiode direct detection receiver, heterodyne receiver, homodyne receiver and preamplified threshold detection receiver for m-PPM signalling scheme are determined from the continuous channel model.