Coherent Multiheterodyne Spectroscopy Using Stabilized Optical Frequency Combs

The broadband, coherent nature of narrow-linewidth fiber frequency combs is exploited to measure the full complex spectrum of a molecular gas through multiheterodyne spectroscopy. We measure the absorption and phase shift experienced by each of 155 000 individual frequency-comb lines, spaced by 100 MHz and spanning from 1495 to 1620 nm, after passing through hydrogen cyanide gas. The measured phase spectrum agrees with the Kramers-Kronig transformation of the absorption spectrum. This technique can provide a full complex spectrum rapidly, over wide bandwidths, and with hertz-level accuracy.

Figure 1

Simplified schematic of the setup. Signal and LO frequency combs having slightly different tooth spacing are tightly phase locked to two narrow-linewidth laser sources. The signal comb is transmitted through the cell and heterodyned against the LO comb, yielding a rf comb containing information on the amplitude and phase of each tooth in the signal comb. (The laser and rf comb structures are not to scale.) Fiber optics transmitted the comb light to two interferometers. A signal interferometer contained a hydrogen cyanide (HCN) gas while a second reference interferometer provided a normalization signal.

Figure 2

(a) Example rf heterodyne power spectrum for 1 sec of data at a filter setting of 1536 nm and $\sim 200\mathrm{pW}$ per comb tooth. The $-25\mathrm{dB}$ width of the spectrum spans 10 MHz in the rf, covering 9000 resolved rf heterodyne beat signals between pairs of optical frequency-comb lines and 1 THz in the optical domain. The dips are molecular absorption lines. On this scale, the comb modes are too dense to resolve visually. (b) A $100\times$ expanded view near an absorption peak. (c) A $1000\times$ expanded view showing the resolved rf beats, each with a transform-limited 1 Hz FWHM and separated by $\Delta f_r=1.1\mathrm{kHz}$. These real data compare strikingly well with the schematic of Fig. 1.

Figure 3

(a) Measured transmission (black) and phase [gray (green)] spectrum for HCN spanning 15.5 THz of optical spectrum (from 1495 to 1620 nm). There are $\sim 155000$ individual points each corresponding to a single heterodyne beat, such as those shown in Fig. 2. The power per comb tooth varied from 2 nW in the center of the spectrum to 20 pW on the edges of the spectrum. (b) Expanded view covering the 4.5 THz containing the HCN absorption lines. (c) Further expanded view covering 0.3 THz. The measured phase agrees well with the calculated phase (dotted blue line, offset by 0.1 rad) from the Kramers-Kronig transformation of the absorption data. The standard deviation of the phase measurement is 1.6 mrad. The measured absorption agrees well with previous published data [22] (dashed blue line, offset by 0.2).