Search

This paper contains an account of various experiments associated with the propagation of a pressure pulse up a vertical column of liquid. When such a pulse reaches the upper free surface of the liquid it is reflected downwards as a pulse of tension. This method therefore provides a means of subjecting the liquid to tension under dynamic conditions of stressing. If the value of the tension at any depth exceeds a certain critical value the liquid will cavitate. Values of this critical tension T were measured for liquids of varying viscosities η and it was found that the empirical relation T=kη0.1 holds. Secondly, pulse propagation across the interface between two immiscible liquids was studied, and it was found that the maximum tension which could be sustained by an interface separating silicone oil and water is less than the tension which produces cavitation in either of these two liquids. Thirdly, it has been found that the cavitation produced shows several cycles of growth and collapse, a phenomenon which has been observed photographically by previous workers.

A theoretical treatment of pulsed nitrogen laser operation is presented. The properties of laser pulses were investigated as functions of various parameters (electric circuit parameters, laser length, gas pressure). Based on this model some conditions are obtained which are necessary for effective laser pulse emission, and the known nitrogen laser devices are discussed.

A numerical solution is provided that may be used to predict the electromagnetic field within a partially evacuated cylindrical cavity excited by a pulse of ionizing radiation. Several examples are given to illustrate the pressure dependence of the nonlinear response and to acquaint the reader with principal characteristics of this response.

The simplest way of testing flow systems for non-ideal flow behaviour is based on the axially dispersed plug-flow model. A very simple experimental technique involves manually injecting a dose of tracer into the system and following the resulting response(s) down-stream. A method is proposed using a general description fitting to such pulses in the form The solution of the basic partial differential equation for the axially dispersed plug-flow model (ADPF) with this relation for the input function is far more realistic than, for example, the assumption of a perfect step or δ pulse and, as is shown, gives better results than the method of moments. It is far simpler, however, than the frequency response method at a comparable accuracy, as all calculations are carried out in the time domain only. The advantages of the proposed method manifest themselves best in the case of curves having extended tail sections.

The effect of an inhomogeneity of population inversion at an initial Q -switched time on the stability of the giant pulse from of a laser in an axial multimode oscillation was analysed numerically for the laser equation with an unrealistic assumption that the ratio of a cavity relaxation constant to a frequency difference between neighbouring modes is unity, principally Results indicate that for three mode oscillation there may be an initial spatial distribution of population which would uniform the giant pulse from irrespective of initial field value.

Reported herein are a theoretical treatment and an experimental investigation that deal with the interpretation of data from a pulse propagation test on a frequency‐dependent clay soil. A transfer function, which considers the superposition of an instantaneous response and the various modes of vibration, is obtained to relate the stress at the fixed end of a specimen to that at the input end, and the modulus of elasticity and viscosity are deduced from analyses of the fundamental resonant frequency of the specimen. Experimental data from shock tube tests on a clay soil provide a means for comparing the analytical predictions with the actual response. It is shown that use of the intuitively defined arrival time of a pulse yields values far too high for the modulus of elasticity, and higher values of damping and shorter lengths of specimen both contribute to making the results more unpredictable. Both the modulus of elasticity and the viscosity of the clay are found to be strongly dependent on frequency, the former increasing and the latter decreasing with increasing frequency.

When an ultrasonic pulse, containing, say, ten quasi-sinusoidal oscillations, is reflected in air from a rough surface, it is observed experimentally that the scattered wave train contains dislocations, which are closely analogous to those found in imperfect crystals. We show theoretically that such dislocations are to be expected whenever limited trains of waves, ultimately derived from the same oscillator, travel in different directions and interfere - for example in a scattering problem. Dispersion is not involved. Equations are given showing the detailed structure of edge, screw and mixed edge-screw dislocations, and also of parallel sets of such dislocations. Edge dislocations can glide relative to the wave train at any velocity; they can also climb, and screw dislocations can glide. Wavefront dislocations may be curved, and they may intersect; they may collide and rebound; they may annihilate each other or be created as loops or pairs. With dislocations in wave trains, unlike crystal dislocations, there is no breakdown of linearity near the centre. Mathematically they are lines along which the phase is indeterminate; this implies that the wave amplitude is zero.

Applying the parabolic approximation, the equations for two-frequency symmetric and antisymmetric mutual intensity functions for waves propagating through a random medium are derived, including the multiple scattering effects. These functions are applied to derive the general formulas for the covariance functions of narrowband pulses. They are used to compute the signal intensities for pulse trains passing through an ionospheric irregularity slab.

Pulse irrigation is suggested as an irrigation technique achieving a relatively low application rate while using an irrigation device with a higher application rate. A complete pulse irrigation is composed of a series of irrigation time cycles where each cycle includes two phases: the operating phase followed by the resting or nonoperative phase. The variables of the pulse pattern, the real irrigation time, the resting time, and the total time of a single pulse are defined as a function of the irrigation parameters and the number of cycles in the irrigation. A method is suggested to determine the number of cycles in one pulse irrigation which in general will be in the range of 5-10 cycles. According to the suggested principles and procedure, the required steps for pulse irrigation design are given. Numerical examples are included.

The formation of sonic pulses in the nearfield region of a pulsed piston radiator has been investigated by simulation on a digital computer. The results give insight into the sonic radiation process, showing the formation of pulses that replicate the piston motion, with trailing disturbances which originate from the rim. A comparison is made between pulsed and CW beam profiles, showing that there is little difference for moderate pulse lengths.

We consider a pair of differential equations whose solutions exhibit the qualitative properties of nerve conduction, yet which are simple enough to be solved exactly and explicitly. The equations are of the FitzHugh-Nagumo type, with a piecewise linear nonlinearity, and they contain two parameters. All the pulse and periodic solutions, and their propagation speeds, are found for these equations, and the stability of the solutions is analyzed. For certain parameter values, there are two different pulse-shaped waves with different propagation speeds. The slower pulse is shown to be unstable and the faster one to be stable, confirming conjectures which have been made before for other nerve conduction equations. Two periodic waves, representing trains of propagated impulses, are also found for each period greater than some minimum which depends on the parameters. The slower train is unstable and the faster one is usually stable, although in some cases both are unstable.

Except for exact numerical solutions to the point explosion problem[1], there is no simplified technique which is uniformly valid over the Mach number domain extending out to near sonic flows. Recently, however, a technique was proposed by Bach and Lee which has produced surprisingly accurate results for the entire regime of blast wave propagation[2]. The method is based on the assumption that the density profile behind the shock front may be described by a power law in the radius. This assumption, which is generally observed to be very good, enables one to integrate the continuity equation analytically to obtain the velocity which is the only other parameter which appears in that equation. Upon performing the integration, the momentum equation can then be integrated directly for the pressure profile. These analytic results are obtained in terms of the as yet unknown shock trajectory. The shock position-time relationship as expressed through the shock decay coefficient may be found, however, in terms of an integral energy conservation relation. The result is a coupled set of nonlinear ordinary differential equations which when solved in terms of appropriate boundary conditions yield the shock-wave decay coefficient. In the present work, we have extended this method to unsteady shock waves into which energy is deposited in a time-dependent fashion during propagation. The technique is applied to the case of energy addition by pulsed and cw laser radiation. Radiant energy absorption due to inverse bremsstrahlung is included and the nonequilibrium electron cascade process (breakdown) is accounted for in a phenomenological manner. A parametric study is conducted in which the effects of laser pulse shape, pulse duration and pulse power are determined. Laser pulse profiles typical of CO 2 TEA lasers are considered. Our results are compared to laser-driven detonation (LSD) waves observed experimentally in laser-target interaction experiments as described in the literature. In addition, the results are compared to exact numerical computations.

This paper describes a technique for measuring the speed of sound in molten salts employing a pulse method. The signal coming from the sample is made to coincide with that coming from a delay line of a variable length of water. The intervening parts between the emitting and receiving crystals are made of sintered alumina. The calculation of corrections due to the intervening parts and the calculation of error are given in detail. The technique is applied to measure the speed of sound in potassium bromide, alkali sulphates and the chromate, molybdate and tungsten of sodium. [Journal translation]

Pulse radiolysis of solutions of alkali metal cations in tetrahydrofuran (THF) demonstrates the formation of solvated electrons es−, alkali metal cation-ion pairs (M+, es−), and alkali metal anions M−. This paper describes the spectra, extinction coefficients, and radiolytic yields of es−, lithium, sodium, potassium, and cesium species in THF. The reaction kinetics are complex but largely involve reactions A and B[Formula: see text]with the concomitant disappearance of all three species by reaction with radiolytically produced radicals. Rate constants and ion-pair dissociation constants for es− and the sodium and potassium species are presented and compared with data established from studies of blue solutions of alkali metals dissolved in THF.

A p-n junction diode with an additional n+ island diffused into its anode and shortod to it is shown to exhibit a switching effect in its reverse characteristic if its geometry is chosen correctly. The effect is similar to that encountered in a PIN stop recovery diode and depends on the stored minority charge at the end of the forward conduction period and on the applied voltage frequency and waveform. The device is completely compatible with npn IC technology and can be used for pulse generation. A theoretical analysis of the device operation and the switching effect is made anil compares well with the experimental results.

Summary The composition of the reducible ammonia complex of cadmium and its reduction rate contant were determined. The calculation is based on the assumption that practically only one complex undergoes reduction at the electrode and that the equilibrium between Cd2+ ions, their ammonia complexes and ammonia is perfectly mobile. The form of the current-voltage curves at different rates of potential change confirms the plausibility of these assumptions.

A seismic trace after application of suitable amplitude recovery may be treated as a stationary time-series. Such a trace, or a portion of it, is modelled by the expression where j represents trace number on the record, t is time, αj is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and nj is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto-correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time-domain pulse itself is then reconstituted under the assumption of minimum-phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z-transform, (C) a fast method based on inverting the least-squares inverse of the wavelets, i.e. inverting the normal time-domain deconvolution operator. Problems associated with these three methods are most acute when the z-transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace-to-trace, from shot-to-shot, and from one shot-point medium to another. There is reasonable agreement between the minimum-phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge-factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.

A theory of ultrasonic spin echoes valid for arbitrary spin is presented. Semiclassical vector-model equations are constructed for components of the dipole and quadrupole moment tensors which are excited by ultrasonic pulses in analogy with the well-known Bloch equations. The echo amplitudes are found to depend on the wave number of the pulse, the crystal length, spin density, sound velocity, the density of the medium as well as the magnitude of the appropriate macroscopic dipole or quadrupole moment. Our numerical estimates for a number of physical systems indicate that ultrasonic-spin-echo experiments are feasible for a variety of nuclear and electronic spin systems.

A pulse-shape discrimination technique has been developed using a dual constant-fraction discriminator combination to analyze γ-ray pulses from a Ge(Li) coaxial detector, in order to obtain improved time resolution for this type of detector. A theoretical analysis of the pulse shapes from a coaxial detector as a function of the position of irradiation in the detector, and the synthesis of these pulses in a Constant-Fraction Pulse-Height Discriminator has been completed to form a theoretical base to the technique. Typical results for coincidence measurements with a 23 cm3 coaxial detector and a plastic scintillator are: 1.09 ns fwhm and 2.02 ns fw(0.1)m for a γ-ray energy range of 1.10 ≤ E ≤ 1.35 MeV and 650 ps fwhm for a 3.16 MeV γ-ray.

Discussed are the main aspects of operation, physics, design, and application of toroidal cores as nondestructive read-out analog memory elements. The analog memory element and switch are the basic components of the analog memory device of the open-loop type (i.e., without negative feedback). The toroidal core has been shown, both theoretically and experimentally, to exhibit linear read-write characteristics in pulse remagnetization. Diode switches are the most preferable for writing analog information. Analysis of the output and read circuits required to determine the optimal value for the read circuit resistance is given. The complex studies carried out resulted in a simple analog memory device with ± 3 percent error and the write time of 0.3μs. Ways to improve these parameters are described.

After an introductory description of the foundations the review outlines recent advances in the understanding and technology of transferred electron devices. Development of numerical techniques for calculating averages of the electron momentum distribution and its response rate to time varying electric fields have clarified limitations of device performance. High pulse powers are generated by overlength relaxation devices but the low power CW transit time oscillators have had the greatest application. Advances in material technology are removing some limitations of early diodes. Considerable interest is being shown in the amplification properties of supercritical transferred electron devices and in the potentialities of indium phosphide as a transferred electron material.

Voltage pulses of amplitude from 0 to 10 V, width 1 μs to 10 ms and with a wide range of repetition frequencies have been applied to electroformed Al-SiO x -Au devices and the pulsed current-voltage characteristics have been examined. The peak currents observed were up to 28 times larger than those obtained under d.c. bias conditions. It is argued that these results can be understood in terms of the filamentary model of conduction in electroformed devices but are in quantitative disagreement with the theory in its present form. Attempts to estimate the energy required for switching a device into a high impedance state were made using single 1 μs voltage pulses. These are compared with similar experiments reported in the literature. It is suggested that the present experiments yield the only unequivocal upper limit for the energy required to switch a device into a high impedance state.

Asymptotic transient field solutions of the form A(r,t) exp [iS (r, t)], where S is a rapidly and A a slowly varying function of space and time, may be analyzed in terms of wave packets with central frequency ω =-∂S/∂t and central wavenumber k = ∇S. When the (dispersive) medium is lossless, stationary, and homogeneous, wave packets with constant real ω and k move along straightline trajectories called space-time rays. In the presence of dissipation and (or) when the input signal has an exponential amplitude dependence, S is complex. The corresponding wave packets with constant complex ω and k move along complex space-time rays, i.e., along trajectories defined in a complex (r, t) coordinate space. The properties of complex space-time rays and of the fields propagating along them, and their relation to physical fields observed on real (r, t) coordinates, are illustrated for a plane pulse with Gaussian envelope and frequency swept carrier, launched into a lossy environment. Tracking of spatial and temporal maxima is performed by ray techniques, and a paraxial ray regime is defined that permits discussion of a signal velocity. Special attention is given to ray focusing and the associated phenomena of pulse compression. It is shown how a complex input frequency profile can be synthesized so as to achieve optimum compression at a real space-time observation point in a lossy medium. The general results are applied in detail to a cold dissipative plasma, and a representative set of numerical calculations is included.

Modern narrow-band pulse-amplitude modulation (PAM) and pulse-code modulation (PCM) systems require the generation of precisely shaped pulses in order to avoid intersymbol interference. It is not a simple matter to design analog filters having pulse responses with the requisite carefully positioned zeros, and this has led researchers to study other approaches. It is shown that the use of a binary transversal filter (BTF) coupled with a simple low-pass filter can generate extremely good pulses with small bandwidths. A BTF consists of a digital shift register and weighting resistor network to construct a staircase approximation to the desired pulse. The attendant circuitry is very simple, such that a highquality pulse generator can be built and adjusted with remarkable ease. The problem of pulse design using BTF's is considered in some generality, and a computational procedure is developed for adjusting the weighting network in the BTF to generate optimum pulse shapes. This method is then applied to several practical cases, and the circuitry required to generate excellent pulses is discussed. Test results on an implementation of such a generator using only five taps are presented, revealing the inherent simplicity and quality of the approach.

A theory of the pulse self-steepening in nonlinear difference-frequency and sum-frequency interactions is presented. The corresponding mathematical problem, consisting of the solution of a set of nonlinear partial-derivative differential equations, is solved exactly. The physical conditions under which the theory applies are considered.

Several properties of solitary waves that were measured on an easily constructed transmission line of very modest size (50 sections ∼1-m length) are described. Among the properties observed are their generation by a pulse or a sine wave, the recurrence phenomena, and the collision of two solitary waves.

A pulse of radiation from a circularly polarized 3 cm maser can be reflected with dramatic changes in intensity and frequency by electrons in a magnetostatic field of the order of 04 T.

This paper presents two new mechanical methods in the stroboscopic holographic vibration analysis. In one of the two, the oscillating mirror of the electromagnetic oscillograph is used, and in another, the pulse-motor is used. The mirror oscillating sinusoidally reflects the laser beam and the vibrated laser beam is strobed by the slit. The pulse-motor rotates by the constant angle when one pulse is given and the laser beam is strobed by the slits attached to the motor. As the oscillating mirror and the pulse-motor are driven by the signal that is the input to the vibrator of the subject, or the transformed one, it is easy to synchronize the strobing to the vibration of the subject and the strobing can be synchronized to the signal detected from the vibration of the subject. Particularly, the method using the oscillating mirror is easy, cheap and one of the mechanical methods that can be used in the highest frequency. The vibration patterns of the circular plate clamped at the center and the loudspeaker are got by those methods.

Experimental techniques for the generation of frequency-tunable picosecond pulses from passively mode-locked dye lasers are reviewed. Direct photoelectric measurements of pulse durations with a streak-camera of time resolution

A fully dynamic, self-consistent computer code has been developed to solve internal electromagnetic pulse (IEMP) problems in cylindrical geometries excited by a pulse of ionizing radiation. Comparisons between the fully dynamic and previous quasi-static solutions are made, and the range of validity of the quasi-static approximation is defined. Results show that non-linear effects arising from field-perturbed electron motion significantly affect the range of validity of the quasi-static approximation.

Many authors have reported disparate characteristics of pulses from Nd:glass mode-locked lasers. From these it has become clear that the well-developed pulse has a frequency sweep or subpicosecond structure and yields a contrast ratio less than the ideal 3 in the two-photon-fluorescence measurement. On the other hand, the early pulse is well behaved, has simple temporal and spectral structure, and yields a contrast ratio of 3 in TPF. The measurements are almost all indirect. Theories explaining the early pulse have appeared, but these fail for the fully developed pulse.

We have developed a dual-photocell, light-difference detector, easily attached to a comparator screen, which provides rapid and direct location of fringe centers from Rayleigh interferograms without the need for digital micrometers or measurement of optical densities. The device provides a pulse for digital micrometers which triggers the printing of fringe centers during manual movement of the stage, providing a two-thirds saving in time. From evaluation of sedimentation equilibrium patterns it was found that the precision of (1) concentration measurement is 0.003 fringes and (2) molecular weight determinations is several parts per thousand.

The paper is concerned with the measurement by an ultrasonic pulse technique (Markham 1970) of the elastic stiffness constants of oriented polyvinyl chloride sheet over a range of degrees of orientation produced by drawing. The technique involved immersing the sample in a tank of water containing an ultrasonic transmitter and receiver, and measuring the difference in transit time between the two, with and without the sample. In general, two types of wave were propagated through the sample, and their velocities were determined, from which the stiffness constants were deduced. The frequency was 5 MHz. Measurements of the optical birefringence were also made. The effect of drawing the initially elastically isotropic sheet was most marked in the case of c33 (axis 3 being the draw direction) which increased from 63 to 118 GN m−2, and least marked in the case of c44 which decreased from 18 to 16 GN m−2. The material was found to have transverse elastic isotropy about the draw direction, and the other three stiffness constants changed by intermediate percentages. The variation of stiffness constants with draw ratio was fitted quite well by a theory of Ward (1962), except for a discrepancy in the case of the unoriented material.

The back scattered light from a laser-produced plasma has been investigated. The laser consisted of a ruby oscillator and one amplifier producing a 10-nsec pulse of 10 joules. Observations of a Doppler-shifted component and of satellite lines are reported.

A study is made of the equations describing the propagation of a monochromatic pulse of radiation of arbitrary shape in absorbing media — a plasma and an absorbing two-level photodissociable medium. Exact analytic solutions are found for a wide variety of boundary conditions. The discussion is carried through for problems with plane, cylindrical, and spherical symmetry. The formulas obtained can be used directly to compare calculation and experiment.

Numerical procedures of the method of characteristics is presented to treat the problems of multilayered structures under impulsive load. A set of eight algebraic equations which are readily to be programmed into computer are derived. Stress analysis of a typical dynamic layered structure is given to illustrate the effectiveness of the method. Results of the example problem reveal the fact that pulse shape is very sensitive to transient stress wave propagation.

Experimental results on the operation of a Laflamme double‐discharge laser structure up to pressures of several atmospheres are presented. With an electrical energy input of 30 J/liter atm, a multimode pulse output of 1 J is obtained at 6 atm from a 1/3‐liter active volume, containing 7.5% CO2, 7.5% N2, and 85% He. It is found that a high level of energy deposition into the CO2 gas can be achieved, provided that the plasma E/p is optimized in both the main discharge and the preionizing discharge. On the basis of the understanding gained during this investigation, a ruggedized Laflamme structure capable of withstanding prolonged arcing conditions has been developed.

A density matrix analysis of the effects of phase modification in the “nonideal” inversion-recovery pulse sequence upon the apparent magnetization recovery is presented. The apparent magnetization recovery is, in general, nonexponential, depending on the ratio T1T2∗, the relative pulse phases in the inversion-recovery sequence, the off-resonance frequency, the observation direction, the radiofrequency field inhomogeneity, phase-glitch effect, and/or inaccurate settings of the pulse lengths. The interference effects produced by transverse magnetization in the case of T1 measurements by the inversion-recovery pulse sequence or saturation recovery pulse sequence in the high-resolution NMR spectra can be eliminated successively using the coincident phase and antiphase pulse sequences. This technique has the advantage of simplicity and allows the maximum resolution in the partly relaxed spectrum.

Summary State-space approach is used to obtain the steady state characteristics of SCR circuits. The method is applicable for both pulse gated and continuously gated thyristors. Even though the method is general, the application in mind was a continuously gated power regulator.

The conditions for a detailed experimental investigation of Dicke superradiance in the microwave region are presented. It is proposed to observe superradiant pulses from inverted populations in the Zeeman levels of atomic hydrogen in an external magnetic field. The small sample volume would be housed in a low- Q microwave cavity. Using a well-known self-consistency argument, the superradiant decay rates, pulse delay times, and average power per pulse as a function of the number density are estimated for such a system. A particular experimental arrangement is presented and discussed. The essential differences and main advantages of our proposed method over work recently reported in the literature are cited and discussed.

This paper is a complete report on both the experimental and theoretical aspects of the recently discovered self-phase modulation in laser-breakdown plasmas. Mainly responsible for these effects is the sudden index change which accompanies the ionization of the gaseous medium. Two theoretical models are introduced for the phase and amplitude modulation induced by the plasma. These effects are applied to the problem of short-optical-pulse generation, with emphasis on the prospects for producing a pulse consisting of only a few optical cycles. The techniques described here have the unique advantage that the generation mechanism is linear, resulting in particularly clean, reproducible and predictable optical transients. Methods are suggested for raising the plasma nucleation intensity by further cleaning up the gas. It is shown that index dispersion of the optical components may place a lower limit on pulse duration.

To reduce the gas flow from the ion source to accelerating tube, rotating disk pulsed gas shutter mounted on test vacuum chamber has been constructed and tested. The timig of periodic opening is synchronized to an external 20 Hz master pulse. Gas flow into the ion source is continuous and the outflow from the source to accelerating tube is pulsed. Average flow has been reduced from 2.7×10-2Torr.l/sec to 2.7×10-3Torr.. l/sec for operation, it is possible to eliminate the use of a conventional high speed, large capacity pump.

This paper presents results on mass‐resolved and time‐resolved energy spectra of the ions produced by the interaction of a laser pulse with an absorbing surface. A Q‐switched CO2 laser with a pulse width of 775 nsec and a power density at the target of approximately 7 × 106 W/cm2 was used to produce the ion emission inside a time‐of‐flight mass spectrometer. A method of data reduction was developed that yields the time development of the energy spectrum during each laser pulse with a resolution of approximately 100 nsec. The energy distribution of ions changes from one containing mostly low‐energy species during the early part of the laser pulse to a spectrum peaked at its high‐energy end near 200 eV later in the laser pulse.

The dynamics of the mode‐locking process for homogeneously broadened lasers are investigated. The investigation focuses attention primarily on the temporal development of the pulse width. However, the other parameters characterizing the mode‐locked laser pulse can also be determined in a similar manner. The temporal development of the pulse width is determined for amplitude‐modulated and frequency‐modulated mode‐locked lasers both without and with finite detuning. An important result of this investigation is the determination of the threshold for the mode‐locking process. An estimate of the modulation index required to achieve mode locking is given for amplitude and frequency mode‐locking processes. The effect of detuning on the required modulation index is also determined for both cases.