Linewidths of Single-Mode Lasers

This controllable shift of a laser frequency V] against a reference frequency yR can be also realized by electronic elements in the stabilization feedback circuit. This omits the Pockels cell of the previous method. A tunable laser is frequency-offset locked to a stable reference laser in such a way that the difference frequency / = vl — can be controlled electronically. This technique has been described by Hall [5.98b] and is used in many laboratories. 

In the previous sections we have seen that the frequency fluctuations of singlemode lasers caused by fluctuations of the product nd of the refractive index n and the resonator length d can be greatly reduced by appropriate stabilization techniques. The output beam of such a single-mode laser can be regarded for most applications as a monochromatic wave with a radial Gaussian amplitude profile, see (5.32). 

For some tasks in ultrahigh-resolution spectroscopy, the residual finite linewidth AyL, which may be small but nonzero, still plays an important role and must therefore be known. Furthermore, the question why there is an ultimate lower limit for the linewidth of a laser is of fundamental interest, since this leads to basic problems of the nature of electromagnetic waves. Any fluctuation of amplitude, phase, or frequency of our monochromatic wave results in a finite linewidth, as can be seen from a Fourier analysis of such a wave (see the analogous discussion in Sects. 3.1,3.2). Besides the technical noise caused by fluctuations of the product nd, there are essentially three noise sources of a fundamental nature, which cannot be eliminated, even by an ideal stabilization system. These noise sources are, to a different degree, responsible for the residual linewidth of a single-mode laser. 

The first contribution to the noise results from the spontaneous emission of excited atoms in the upper laser level Ei. The total power of the fluorescence spontaneously emitted on the transition / Ek is, according to Sect. 2.3, proportional to the population density A/, the active mode volume Vm, and the transition probability Aik, i.e.. 

This fluorescence is emitted into all modes of the EM field within the spectral width of the fluorescence line. According to Example 2.1 in Sect. 2.1, there are about 3 x 10 modes/cm within the Doppler-broadened linewidth Ayo = 10 Hz at A = 500 nm. The mean number of fluorescence photons per mode is therefore small. 

In a HeNe laser the stationary population density of the upper laser level is Ni 10 cm . With A/k = 10 s , the number of fluorescence photons per second is 10 s cm , which are emitted into 3 xlO modes. Into each mode a photon flux 0 = 3x10 photons/s is emitted, which corresponds to a mean photon density of (nph) = (p/c 10 in one mode. This has to be compared with 10 photons per mode due to induced emission inside the resonator at a laser output power of 1 mW through a mirror with E = 0.99. 

For some tasks in ultrahigh-resolution spectroscopy, the residual finite line width which may be small but nonzero, still plays an important 

For some problems in ultrahigh-resolution spectroscopy, the residual finite linewidth Av, which may be small but nonzero, still plays an important role and has therefore to be known. Furthermore the question why there is an ultimate lower limit for the linewidth of a laser is of fundamental interest, since this leads to basic problems of the nature of electromagnetic waves. 

This fluorescence is emitted into all modes of the EM field within the spectral width of the fluorescence line. According to the example in Sect.2.2, 

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In this section we will describe a number of high-resolution methods, in which the extremely narrow linewidth of single-mode lasers is utilized. Various ways of eliminating Doppler broadening have been investigated during recent years, leading to the development of Doppler-free laser spectroscopic techniques. The effective linewidth that is experimentally obtained is determinated by a number of effects ... 

Usually, mainly Doppler broadening determines the gain profile of a particular laser transition. Indeed, due to the different configurations achievable with gas lasers (namely, a large cavity length), the laser line can be narrower than the Doppler linewidth. Different experimental realizations of single-mode lasers are detailed elsewhere (Demtroder, 2(X)3). 

We shall describe the experimental techniques that are necessary for achieving optimal results in spectroscopic applications. These techniques comprise mode selection in lasers, wavelength and intensity stabilization of single-mode lasers, and experimental realizations of controlled wavele7 gth tuning. Furthermore we briefly discuss the interesting question of why a lower limit exists for the laser linewidth. At the end of this chapter some methods of relative and absolute frequency measurements in the optical region will be presented. 

The linewidth Afl of such a single mode laser is determined by the bandwidth A of the laser cavity (which is inversely proportional to its g-factor), the laser frequency v and the output power P at this frequency. 

The single-mode laser naturally gives less output power than a multimode laser with the same active volume since its induced emission is concentrated into a smaller frequency range. This loss in intensity, however, is much less than one would expect from the ratio of linewidths or from the reduction in oscillating mode number 3i. 32,41) jbis is due to the fact, that not only atoms with the exact transition frequency can contribute to the induced emission, but also those inside the homogeneous linewidth which is determined by collision processes in the case of gas lasers or by crystal line broadening in solid lasers... 

Using continuous wave (cw) laser excitation it is possible to excite atoms with substantially higher efficiency than using pulsed lasers. For example a single mode laser of 1 MHz linewidth has a resolution 3 x 104 better than the pulsed laser... 

Single-molecule spectra as a function of laser intensity provided details of the incoherent saturation behavior and the influence of the dark triplet state dynamics [33]. Clear heterogeneity in the observed saturation intensity was observed indicating that the individual molecules experience modihcations in photophysical parameters due to differences in local environments. It was also possible to measure the linewidth of single pentacene molecules as a function of temperature in order to probe dephasing effects produced by coupling to a local phonon mode [33]. 

Fig. 26.7. Sequence of fluorescence-excitation spectra of the narrow spectral feature recorded with the single-mode laser, (a) Stack of 23 fluorescence-excitation spectra recorded at a scan speed of 0.2cm /s (5GHz/s) and an excitation intensity of 0.5 W/cm. The fluorescence intensity is indicated by the gray scale. The averaged spectrum is shown in the lower panel and features a linewidth of 1.8cm (FWHM). (b) Individual fluorescence-excitation spectra together with Lorentzian fits (solid line). Prom top to bottom the linewidths (FWHM) are 1.8cm , 0.7cm , 0.9cm and 1.1 cm , respectively. Adapted from [61]...

Note the presence of only one spot revealing the absence of parasitic reflections between parallel faces of the Nd YAG ceramic sample. The spectral distribution of the laser radiation was also measured. From the laser spectrum (not shown in this work for the sake of brevity) we have corroborated single mode laser oscillation with a linewidth of 0.25 nm., centered around 1064.4 nm peak. And, in this way, we have experimental proofs about spectral and spatial quality of continuous wave laser emission from Nd YAG ceramic waveguide structure. 

When the beam of a single-mode laser passes in the z-direction through a molecular absorption cell, only molecules with velocity components Vz = 0 y are excited if the laser is tuned to the center frequency of an absorption line with the homogeneous width y. The fluorescence collected within a narrow cone around the z-axis then shows sub-Doppler linewidths, which may be resolved with Fourier transform spectroscopy (Fig. 1.54) [163]. 

A high spectral resolution can be achieved without using a monochromator. The Doppler width A >d, which represents a principal limitation in 90° spontaneous Raman scattering, is reduced to [(pulsed lasers, even linewidths down to 0.001 cm have been achieved with single-mode lasers. 

The situation is different when narrow-band lasers are used as pumping sources If the beam of a single-mode laser with the frequency co is sent in the z-direction through an absorption cell, only molecules within the velocity group = (co — (oo t y)/k can absorb the laser photons hco (Sect. 2.2) on the transition /) k) with Ek — Ei = hcoQ and homogeneous linewidth y. Therefore only molecules within this velocity group are excited. This implies that the absorption of a tunable narrow-band probe laser by these excited molecules yields a Doppler-free double-resonance signal. 

A single-mode laser beam with a Gaussian profile (w = 1 mm) and a power of 10 mW, tuned to the center coq of the sodium line (3 5 i/2 3 Pi/2) passes through a cell containing sodium vapor at p = 10" mbar at a temperature of 450 K. The absorption cross section is o-abs = 5 x 10" cm, the natural linewidth... 

The linewidth of the single-mode laser is determined by fluctuations in the optical path length of the resonator. These fluctuations are caused primarily by mechanieal instabilities of the optical moimts, and by temperatiue variations of the color center crystal. The mechanical structirre of the laser cavity is perturbed by floor vibrations and acoustics, both of which can be minimized with proper... 

Jitter Average residual frequency excursion or linewidth of a single-mode laser, due to residual envirorunental perturbations of the cavity length. 

Schawlow-Townes equation The equation which predicts theoretically the linewidth of the lasing transition of a single-mode laser. The linewidth predicted from this equation is inversely proportional to the output power and the cavity quality factor (Q-factor). 

Figure 5 shows three data points for the linewidths measured for a single mode PhSi-xSe diode laser (indicated by circles) in addition to the linewidth of the laser illustrated in Figure it (indicated by a square). Figure 5 shows the linewidths plotted as a function of the inverse of the single-ended laser power output. A linear extrapolation of the three data points of the single mode laser to zero inverse power indicated negligible linewidth intercept. Hence, the power-independent... 

The linewidth of the unstabilized single-mode laser has been measured to be smaller than 260 kHz, which was the resolution limit of the measuring system [5.144]. An estimated value for the overall linewidth Av is 25 kHz [5.146]. This extremely small linewidth is ideally suited to perform high-resolution Doppler-free spectroscopy (Chaps. 7-10). 

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