FM and AM mode locking of the homogeneous laser--Part I: Theory

A new general analysis for mode-locked operation of a homogeneously broadened laser with either internal phase (FM) or amplitude (AM) modulation is presented in this paper. In this analysis, a complex Gaussian pulse is followed through one pass around the laser cavity. Approximations are made to the line shape and modulation characteristics to keep the pulse Gaussian. After one round trip, a self-consistent solution is required. This yields simple analytic expressions for the pulse length, frequency chirp, and bandwidth of the mode-locked pulses. The analysis is further extended to include effects of detuning of the modulator, in which case analytical expressions are obtained for the phase shift of the pulse within the modulation cycle, the shift of the pulse spectrum off line center, the change in pulse length, and the change in power output. Numerical results for a typical Nd:YAG laser are given. In the case of the FM mode-locked laser it is found that there is a frequency chirp on the pulse and that this causes pulse compression and stretching when the modulator is detuned. Etalon effects and dispersion effects are also considered.     

FM-laser operation of the Nd:YAG laser

The FM-laser or frequency-sweeping mode of laser oscillation has been demonstrated in a Nd :YAG 1.06-μ laser with an intracavity LiNbO3phase modulator. The experimental results are in excellent agreement with the theoretical expressionDelta= (DeltaOmega/Deltanu) (delta/pi)where δ= peak single-pass phase retardation in the modulator,DeltaOmega= axial mode spacing,Deltanu=modulator detuning, and Δ=resulting FM index of the laser output. Modulation indices as large asDelta approx 230rad have been obtained, in which case the instantaneous laser frequency is sweeping over a full spectral range of2Delta cdot f_{m} approx 120GHz (≈ 4 cm^-1) at a repetition frequencyf_{m} approx 260MHz, with a time-bandwidth product per periodapprox 2Delta approx 460. The coherently mode-locked spectral bandwidth thus obtained in the FM-laser case is very much wider than can be achieved in the pulsed mode-locked case with the same Nd:YAG laser. Some possible ways of using this broad-band coherent FM spectrum are suggested.     

Short-pulse oscillator development for the Nd:glass laser-fusion systems

This paper describes the development of an actively mode-locked andQ-switched (AMQ) Nd:YAG oscillator system that generates a single pulse at 1.06 μm in the range of 100 ps to 1 ns, with energy ofsim 250 muJ, and with good stability and reliability. A stable single axial modeQ-switched oscillator is also described that generates a long smooth pulse out of which pulses in the ns range are sliced. Synchronization of these two oscillators is also discussed.     

Modulator frequency detuning effects in the FM mode-locked laser

The mode-locking behavior of a homogeneous laser with an intracavity FM modulator changes rapidly and asymmetrically when the modulation frequency is detuned by small amounts from its optimum value. We develop here a simple analysis of these detuning effects. The analysis gives explicit expressions for all aspects of the mode-locking behavior as functions of detuning. A physical interpretation of the analysis also makes clear which physical mechanisms are responsible for the detuning behavior.     

Controlled bistable operation of an FM mode-locked Nd:YAG laser

It is well known that there are two possible phase positions for the pulse in a mode-locked laser with an internal phase modulator. By using a modulator cut in the form of a Brewster angle prism, it becomes possible to operate an Nd:YAG laser stably in either position at will. The angular beam deflection is slightly different for the two modes and, hence, by mirror adjustment one mode or the other can be selected. A simple analysis is presented to estimate the magnitude of this effect in rough agreement with experimental observations.     

Proposed method for measuring picosecond pulsewidths and pulse shapes in CW mode-locked lasers

A new method is proposed for measuring the widths, and possibly even the detailed shapes, of picosecond pulses in CW mode-locked lasers. The pulses are passed through an electro-optic modulator, which is biased for zero transmission with zero applied voltage, and which is driven at a harmonic of the pulse-repetition frequency. The variation in average light transmission through the modulator is monitored while the relative phase between the light pulses and the modulator drive is varied. The pulsewidth may be deduced from one such measurement made at a microwave light-modulation frequency sufficiently high that the pulsewidth is a finite fraction of a period at the modulation frequency. By making such measurements at a number of harmonics, the complete Fourier expansion (including both amplitudes and phases) of the picosecond pulse envelope can, at least in principle, be determined without ambiguity.     

FM and AM mode locking of the homogeneous laser--Part II: Experimental results in a Nd:YAG laser with internal FM modulation

In Part I of this paper [1], a theoretical analysis of the mode-locked homogeneous laser was given. In this part we present experimental results for the Nd:YAG laser with internal phase modulation. LiNbO3was used as the modulator crystal, and a method to measure the single-pass phase retardation of the modulator accurately at 1.06 μ is described in detail. The pulsewidth and spectral width of the mode-locked laser were measured as a function of depth of modulation, and good agreement with theory was obtained. Etalon effects in the laser were observed, and the results agreed very well with the theory. Mode-locked spectral bandwidths of up to 16 GHz, implying mode-locked pulses as short as 40 ps, were obtained.     

Harmonic mode locking of the Nd:YAG laser

We present experimental and theoretical results forNth harmonic mode locking of a Nd:YAG laser with an intracavity phase modulator operating atN = 2, 3, 4,and 5 times the fundamentalc/2Lfrequency. The bandwidths of the resulting mode-locked spectra depend upon modulation frequency, modulation depth, and laser cavity losses in good agreement with the Gaussian-pulse analysis of Kuizenga and Siegman [5]. For modulation atN(c/2L)the resulting pulse-repetition frequency is alsoN(c/2L)in all cases. However, in theN = 2case, for example, the mode-locked optical spectrum includes every adjacent axial mode component if the laser rod is located near the center of the laser cavity, but only every other axial mode when the rod is located at the end of the laser cavity. This behavior is explained by a Lamb-type theoretical analysis taking into account the competition between the two "hypermodes," or sets of interleaved next-adjacent axial modes, that can oscillate separately or simultaneously in theN = 2case.     

Forced and self-mode-locking of the krypton ion laser

Mode-locking of a krypton ion laser has been studied using a graphite-bore plasma tube and acoustooptic modulator In forced mode locking, 0.2-ns pulses were achieved with the principal laser lines. In contrast with the argon laser, there is a marked tendency for self-locking in krypton.