Frequency Comb from Femtosecond Laser Pulses

2 Frequency Comb from Femtosecond Laser Pulses 

Recently, a new technique has been developed [14.156] that allows the direct comparison of widely different reference frequencies and thus considerably simplifies the frequency chain from the cesium clock to optical frequencies by reducing it to a single step. Its basic principle can be understood as follows (Fig. 14.60)  

The frequency spectrum of a mode-locked continuous laser emitting a regular train of short pulses consists of a comb of equally spaced frequency components (the modes of the laser resonator). The spectral width of this comb spectrum depends on the temporal width of the laser pulses (Fourier theorem). With femtosecond pulses the comb spectrum extends over more than 30 THz. The spectral width can be further increased by focusing the laser pulses into an optical fiber, where by self-phase modulation the spectrum is considerably broadened and extends over one decade (e.g., from 1064nm to 532nm). This corresponds to a frequency span of 300THz [14.157]  

It turns out that the spectral modes of the comb are precisely equidistant, even in the far wings of the comb. This is also true when the spectrum is broadened by self-phase modulation. One example of frequency comparison over a broad spectral range is provided by the experimental setup in Fig. 14.60. 

The mode spacing Avm is locked to the cesium clock frequency vcs in such a way that vcs = m - Avm- Therefore the frequency difference N Ay between N comb modes is precisely known. The fourth harmonics of a stabilized HeNe laser at k = 3.39p m is now compared with the frequency of a mode of the frequency comb. The beat frequency fc between 4/HeNe nd the mode frequency f is measured by a frequency counter. A dye laser at 486 nm is frequency doubled and excites the two-photon transition 15-25 of the hydrogen atom. Its frequency is locked to the doubled frequency of a diode laser, which is in turn locked to a mode of the frequency comb. The dye laser frequency is not exactly 7 times the HeNe laser frequency /, but differs from 7/ by —2A/. A frequency divider chain (see Fig. 14.59) generates from / and 1 f — lAf the frequency 4/—A/, which is just half of the sum /-f7/ —2A/. This frequency, which corresponds to a wavelength of 851 nm, is compared with that of a mode of the frequency comb. The difference frequency fc2 is measured by a counter. 

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The frequency chain works as follows to the second harmonic of the He-Ne laser at 3.39 jum a NaCl OH color center laser at 1.70 pm is phase locked. To the second harmonic of the color center laser a laser diode at 848 nm is then phase locked. This is accomplished by first locking the laser diode to a selected mode of the frequency comb of a Kerr-lens mode-locked Ti sapphire femtosecond laser (Coherent model Mira 900), frequency-broadened in a standard single-mode silica fiber (Newport FS-F), and then controlling the position of the comb in frequency space [21,11]. At the same time the combs mode separation of 76 MHz is controlled by a local cesium atomic clock [22]. With one mode locked to the 4th harmonic of the CH4 standard and at the same time the pulse repetition rate (i.e. the mode separation) fixed [22], the femtosecond frequency comb provides a dense grid of reference frequencies known with the same fractional precision as the He-Ne S tandard [23,21,11]. With this tool a frequency interval of about 37 THz is bridged to lock a laser diode at 946 nm to the frequency comb, positioned n = 482 285 modes to lower frequencies from the initial mode at 848 nm. 

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