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Abstract
A dual frequency Ti: sapphire laser is presented in which two lines operate simultaneously with the same intensity on two TM00 longitudinal modes. This operation is obtained by means of the 127I2 molecules contained in an intra-cavity cell, pumped by a low-power laser. Its properties are interesting: the two lines lase simultaneously, they overlap spatially, their spectral width could be very narrow, their frequency is automatically locked to molecular frequencies and can serve as a frequency reference, the frequency difference is adjustable over the thousands of rotational or vibrational molecular energy gaps in the 0.1-0.9 THz and 3-6 THz domains, and it is computable with high precision. THz wave production is demonstrated as a first application.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Many applications use dual-frequency lasers: THz wave generation, spectroscopy, lidar-radar Doppler, telemetry, underwater detection, very high speed network ... A dual-frequency laser system running on two longitudinal modes of a single cavity is an elegant solution for various reasons. Firstly it requires only one laser and is therefore technologically simpler and more reliable. Moreover, the two modes are spatially overlapped, which is essential for two-photon applications. But an even more important reason is the stability of the frequency difference of two longitudinal modes of the same cavity, which is intrinsically very robust. Indeed, unlike solutions that consist in using two different lasers, the frequency difference of the longitudinal modes of the same cavity is much more stable than the absolute frequency of a single mode because thermal, mechanical, acoustic or atmospheric disturbances are compensated up to a certain order [1].
However, there is a fundamental difficulty related to mode competition in laser cavities [2]: relative intensities of two modes can fluctuate temporally by 100%. This is a major problem for any application using two simultaneous photons. Different solutions have been proposed in the literature in order to force two modes to emit simultaneously with the same intensity. A recent solution is to use the frequency comb of a mode-locked laser [3] which could have very low relative intensity noise [4]. But, mode locking is a collective non-linear effect of a set of a large number of modes that are simultaneously lasing, so it is not possible to lock only two longitudinal laser modes. It is therefore necessary to develop methods outside the laser cavity to use only two selected modes. This significantly restricts applications and is at the expense of useful intensity. Another elegant solution [5] consists in introducing a phase anisotropy into a laser cavity that causes the laser to oscillate along two spatially separated orthogonal polarization eigenstates in the cavity, and then to recombine them. However, since the optical paths of the two intra-cavity modes are different, the frequencies of the two modes are not subject to the same disturbances and their difference can therefore fluctuate. Finally, let us quote a solution that consists in favoring two modes by means of a Fabry-Pérot étalon of well-chosen free spectral range. To avoid mode competition the output mirror is tilted with a critical angle [6]. The two modes are then no longer coupled because their paths no longer coincide in the amplifying medium. But then we have the previous problem of uncompensated fluctuations due to different optical paths. Furthermore the output mirror tilt induces critical instabilities and the two output lines are not collinear.
In this paper, we propose a solution [7] that does not reduce adjacent modes intensity by introducing losses but rather by favoring two selected modes by generating enough intra-cavity additional photons at the two corresponding frequencies simultaneously. Here we present experimental results and an application to THz wave production. A numerical model will be presented in a forthcoming paper.
2. Iodine-gain-filter
The method (Fig. 1 and Fig. 2) consists in exciting, with a “pump” laser, iodine 127I2 molecules contained in an intra-cavity cell which then emits photons in the form of rotational PR doublets (dump) in the gain curve of the laser amplifying medium (here Ti: sapphire). Other molecules could be used, but the iodine molecule has many advantages. At room temperature, a very large number of transitions are easily accessible in the visible and near infra-red. The spectrum is sufficiently resolved to allow selection of a single rotational PR doublet. In addition, the spectroscopy of the homo-nuclear isotope 127I2 is well documented and its transitions are calculable with very high precision [8–10]. Finally a low power “pump” laser can saturate the transitions of the iodine molecules, which is a fundamental point, as will be seen later.
Fig. 1 Iodine potential energy U versus inter nuclear distance R of I2 molecule and pump-dump transitions (see text).
Figure 1 shows a typical pump-dump cycle. From a rovibrational level (v”, J) of the fundamental electronic state, a rovibrational level (v’, J-1) of the electronic state is excited through a P transition. This excited level then emits PR doublets with the respective selection rules ΔJ = −1 and + 1. Several PR doublets are emitted on all vibrational states v of the fundamental electronic state. A broad band intra-cavity tuneable filter selects a single PR doublet. The pump and dump transitions are chosen to have a good vibrational wave function overlap (Franck-Condon factor). It is also necessary to take into account the thermal population of the starting level (v”, J) (Fig. 1); then for the excitation transition only the first vibrational levels of the electronic state X will be sufficiently populated at room temperature. Optimization of the rotational population for large values of J is performed by heating the cell. The frequency difference ν2-ν1 is adjusted with the rotational quantum number J during the excitation. The calculation of the frequencies ν1 and ν2 is done using Dunham’s parameters [10]. The frequency difference ν2-ν1 can be finely adjusted in the THz domain by a judicious choice of the vibrational quantum number v as the Dunham parameters depend on the anharmonicity of the molecular potential.
3. Experimental set-up
The experimental setup is shown in Fig. 2. A Z-shaped cavity contains a Ti:Sa (Ti: sapphire) laser medium which is optically pumped by a pulsed 532 nm Nd:YAG laser through a fold cavity mirror. In the absence of selective intra-cavity filter, the Ti:Sa laser emits over a wide spectral band and therefore over a large number of longitudinal modes of the cavity whose free spectral range is 250 MHz (cavity length of about 1.2 m). Only the optical properties of the mirrors and the amplifying medium limit the spectral band. We then use a Lyot filter with a single quartz plate to limit the spectral band to about 1 THz. A Brewster angle window iodine cell is then aligned in the cavity. Iodine molecules are excited by a 580 nm low power external “pump” laser, which is injected through the output mirror via a dichroic mirror. The spatial mode of the injected laser is adapted to that of the Ti:Sa cavity. An optical diode blocks reverse feedback in the “pump” laser. A spectral width of the “pump” laser of about 10 GHz is sufficient to select only one PR doublet. We use the laser described in [11, 12]. When the quartz plate is properly oriented and from a given intensity of the “pump” laser, the Ti:Sa laser emits only two longitudinal modes (Fig. 3). Below a threshold power that we estimate at a few mW, the laser works on many adjacent modes. The Ti:Sa laser works well with a 532 nm YAG laser power of one watt, which gives an output power at about 800 nm of the order of 100 mW.The gain of the transitions of the iodine molecules medium being proportional to the length of the cell, its length is chosen to be equal to 20 cm to fill one of the arms of the Z-shaped laser cavity. The pressure and temperature of the iodine vapor are adjusted with the temperature of the exhaust tube and the body of the cell in the range of 20 ° C to 150 ° C in order to optimize the gain for different values of the selected quantum numbers of vibration and rotation.
Fig. 3 Spectrum of the dual-frequency laser beam as a function of the rotational quantum number J of 127I2 molecule excitation.
The output beam passes through a BBO crystal to double and add the two frequencies, and then it is directed into a two-metre focal length high resolution monochromator. One can observe the spectrum of ν1 and ν2 in the near infra-red (~800 nm) and the spectrum of 2ν1, 2ν2 and ν1 + ν2 in the blue. At the monochromator output the lines ν1 and ν2 are spatially separated and the corresponding beams can be directed on two independent fast photodiodes (PD1, PD2). It is then possible to analyse with precision the intensity fluctuations of the two modes from pulse to pulse, a fast scope records a thousand consecutive pulse intensities. The spectral profile of a given mode (PD3) is controlled with a confocal Fabry-Pérot of 1 GHz free spectral range.
This system is actually relatively simple. Introducing an iodine cell at room temperature into a laser cavity is trivial. In addition, to pump I2 molecules, many all compact solid state lasers of a few mW power are now available. Finally, unlike with a Fabry-Pérot étalon, the frequency difference between the two lines may be adjusted by tuning the wavelength of the “pump” laser and can be calculated with precision [8, 9].
The experimental THz setup will be described below.
4. Properties of the dual-frequency laser
In this section, we discuss the spectral, temporal and intensity properties of the two modes. First of all it is important to emphasize that it is the Ti:Sa amplifying medium that lases and not the iodine molecules. Thus, when the Nd:YAG pumping of the Ti:Sa crystal is turned off, while the pumping of the iodine molecules with the “pump” laser is maintained, the whole system stops lasing. This means that, under the experimental constraints of this work, iodine molecules cannot lase alone, as has also been observed with other devices in the literature [13]. Here the iodine molecules are used as a kind of spectral gain-filter. The additional gain provided by the emission of the PR doublet is sufficient to force the Ti:Sa laser to operate exclusively on two of its modes in coincidence with the PR lines. Under these conditions, the properties of the system are interesting.
4.1 Spectral analysis
When the “pump” laser is blocked thousands of modes lase over a spectral width of about 1 THz. We discuss here the spectrum obtained when the “pump” laser is on and under the conditions described above. To demonstrate the spectral possibilities of the system we chose to excite the P(J)16-1 (v' = 16, v” = 1) transitions of iodine molecule at about 580 nm (see section 5 for precise calculated wavelengths). All transitions for J ranging from 10 to 150 are experimentally accessible thanks to the precise calculation of the corresponding frequencies of reference [8, 9] and the use of a lambda-meter (Fig. 2). Here, we only present the spectra of the laser beam when J varies from 10 to 10 (Fig. 3). As mentioned above, by means of the spectral selection of the “pump” laser, the quartz plate and the iodine molecule, a line-width of 10 GHz for the “pump” laser is sufficient to force the Ti:Sa laser to emit on a single PR doublet. The adjustment of the intensity of the two modes is obtained by rotation of the quartz plate around an axis perpendicular to its surface. In addition, tilting this quartz plate optimizes the coincidence of the frequencies of the lines PR with that of the two modes. Adjustment of the cavity length has the same effect. Finally the temperature of the iodine cell can also be adjusted to increase the thermal population and the molecular density for a more effective excitation. A “pump” laser operating in the mW range is sufficient to obtain the dual-frequency regime easily.
The calculation of the frequency difference ν2-ν1 depends only on the energy difference of the levels (v, J-2) and (v, J) of the fundamental electronic state (Fig. 1). It is calculated from the very precise data of [9] and [10]. Using the same notation we have:
where Ev(J) is the energy of the rovibrational level (v, J). Bv, Dv, Hv and Lv are the Dunham coefficients. It should be noted that these coefficients depend on the vibrational quantum number v of the ground electronic state. As a first approximation, the difference frequency ν2-ν1 varies linearly with J as can be seen in Fig. 3.The measurements made with our high resolution monochromator confirm this relationship. The confocal Fabry-Pérot of free spectral range 1 GHz used at the monochromator output analyses the spectral purity of each of these two lines ν1 or ν2. With a Fabry-Pérot finesse of about 100 and a free spectral range of the Ti:Sa cavity of 250 MHz, we observed that the two lines are separately single-mode and have a spectral width of a few tens of MHz. Our cavity length is free. In these conditions the stability is reduced by vibrations, temperature, as well as the pulse duration affects the linewidth. All these effects mean that the observed linewidth in these conditions could not be less than a few tens of MHz. But the cavity length could be locked by conventional methods and the pulse duration could be increased and even be cw.
4.2 Pulse characteristics
In the pulsed regime we use the same Nd: YAG laser to pump the Ti:Sa crystal and the dye of the “pump” laser. The duration of the pulse of the Nd:YAG laser is 50 ns, the lifetime of the excited state of Ti: Sa is 7 μs, the lifetime of the dye excited state of the order of ns and the lifetime of the iodine molecule excited state of about 1 μs. Considering these characteristic times, we set up a delay line to optimize the pumping conditions. Experimentally we found that the best condition in terms of intensity was that shown in Fig. 4: the “pump” laser pulse must be synchronized in the build-up of the Ti:Sa amplifying medium, a hundred ns before the rise of the intensity of the Ti:Sa laser. This result is in good agreement with numerical simulations. However the value of this delay is not very critical. As the lifetime of the excited states of Ti:Sa and I2 are in the µs range, a more detailed study with longer pulse durations remains to be done.
Fig. 4 “pump” laser pulse in blue and Ti:Sa dual-frequency laser pulse in red. The “pump” pulse starts in the Ti:Sa built-up.
4.3 Intensity fluctuations
The non-linear BBO crystal generates the frequencies 2ν2, ν1 + ν2 and 2ν1. Observation of the spectral component ν1 + ν2 shows that photons at the frequencies ν1 and ν2 are emitted simultaneously but does not measure correctly the relative fluctuations of the two frequencies. Then we spatially separated the two frequencies ν1 and ν2 using the monochromator. The corresponding two pulses are then detected on two fast photodiodes, and their intensities are recorded pulse by pulse for a large number of successive pulses. Their statistics are analysed using the following quantity:
where I1 and I2 represent the integrated pulse intensity of modes ν1 and ν2.Initially, to test the systems using the intra-cavity Fabry-Pérot described in the introduction [6], we replaced the iodine cell with an etalon of free spectral range 0.4 THz. The time-integrated output spectrum over several pulses is similar to those in Fig. 3. In this situation, the blue curve in Fig. 5 represents β. It clearly shows that the intensity fluctuations vary by 100%, which means that the laser operates most of its time on one line. This phenomenon is well understood and is described in the literature: it is due to competition of the intra-cavity longitudinal modes. This is a major drawback for two-photon applications, but this mode competition has been cleverly exploited for very high sensitivity spectroscopy [2, 14-15].
Fig. 5 Intensity fluctuation β: comparison of a Fabry-Pérot (blue) and an “iodine-gain-filter” (red) dual-frequency laser.
In view of the difficulties mentioned in the literature, to force the two frequencies to be emitted simultaneously with equal intensity, we inserted into the cavity, instead of a Fabry-Pérot, our “iodine-gain-filter” system described in paragraph 2. Beyond a certain “pump” laser intensity, which we believe to correspond to the saturation of the I2 transition, the spectacular result is shown in red in Fig. 5: the two lines are always emitted simultaneously with the same intensity and with very small relative intensity fluctuations. We estimate that these residual fluctuations correspond to instrumental disturbances.
5. THz generation
The above findings and the high peak power of our pulsed dual-frequency laser are well suited for generating THz radiation outside the Ti:Sa laser cavity. Figure 6 shows the corresponding arrangement. The laser beam is split into two arms for homodyne detection. For the emitter and the receiver we used two array iPCA antennas produced by BATOP. By using an array of 1000 micro-lens with a filling factor of 73.5% only every second gap between the finger structures is excited by the laser beam with photon energy larger than the energy gap. The gap size is 5 µm and the chip is made of a GaAs fast absorbing layer. The coherent excitation of the single emitters, located at every micro-lens spot results in a constructive interference of the radiated THz waves in the far field. Silicon lenses directly bonded to the substrates allow the THz radiation to be focused on the receiver. But we have observed that a modulation of the power supply of the emitter causes intense parasites. Then, to extract the THz signal from the receiver using a synchronous detection, we apply a stable DC voltage to the emitter and use a beam chopper on the laser beam of the transmitting arm. Optimally, the laser operates at 3 kHz and the chopper at 80 Hz. As the active GaAs gap array is of millimetre size, it is then relatively easy to obtain a signal.
Fig. 6 THz setup. The Ti:Sa dual-frequency beam is split: 10% in the receiver arm and 90% in the emitter arm. The laser repetition rate is 3 kHz and the chopper rate 80 Hz. The Lock-in amplifier output is averaged over several seconds for each delay line position.
A micrometric optical delay line is placed on the laser beam of the receiver arm. The THz photo-current detected in the homodyne assembly is proportional to the THz electric field generated by the emitter and oscillates at the THz beat frequency. It is proportional to [16,17]:
Λ is the THz wavelength and dz the optical path difference of the two arms of the homodyne setup. dz is adjusted with the micrometric delay line to measure the THz wavelength.Figure 7 shows the signal for two excitations of the iodine molecule: P(101)16-1 (17182.7712 cm−1, 581.9783 nm) and P(25)16-1 (17293.8638 cm−1, 578.2398 nm). The PR doublets (P(J)16-25-R(J-2)16-25) are centred at 800.62928 nm and 795.68157 nm respectively for J = 101 and 25. The calculated frequencies ν2-ν1 with Eq. (1) are respectively 0.41243 THz and 0.10054 THz, they are absolute molecular values. Figure 7 shows that the experimental points as well as the corresponding fit are in good agreement with the calculated values. Note that the calculated values are much more accurate (a few MHz) and reliable than our measured values. This experimental setup was only intended to verify the consistency of the THz waves and not to measure the wavelength of the THz waves accurately. It should be noted that an experimental accuracy of 1 MHz would require control of the delay line to within 3 nm.
Fig. 7 Homodyne signal for two excitations of the iodine molecule: red curve P(101)16-1 (17182.7712 cm−1) and black curve P(25)16-1 (17293.8638 cm−1). The repetition rate of the Ti: Sa laser is 3 kHz and the chopper frequency is 80 Hz. To improve the signal to noise ratio, each point is an integral of 6000 pulses. Points correspond to the experiment and full-lines to the fit. The black dots are the excitation of the transition P(25)16-1 of I2 and the red dots that of the transition P(101)16-1. The PR doublet corresponds to the vibrational numbers v ' = 16 and v = 25 (see Fig. 1 and 3).
6. Conclusion
We have demonstrated that an intra-cavity gain filter, such as our iodine-gain-filter, enables the construction of stable and high resolution dual-frequency lasers. The two modes are spatially overlapped inside and outside the cavity, and emit simultaneously. The iodine molecule provides more than 6000 different absolute dual-frequencies not only in the 0.1-0.9 THz band by the generation of rotational PR doublets but also in the 3-6 THz band by the generation of vibrational doublets. These molecular-dual-frequencies can serve as frequency-references. As the spectroscopy of the fundamental electronic state of the 127I2 molecule has been widely studied, their calculation with accuracy of a few MHz is already available, but higher accuracy could be obtained by very high resolution spectroscopy techniques [9]. Another advantage of the system presented in this paper is the possibility of concentrating high power (continuous or pulsed) on two laser lines emitted in the same beam simultaneously. This could be done by adding an amplifier to the system described here. The system is generalizable to other all-solid state laser media and could possibly be miniaturized. Finally, note that our system also works in CW regime and as Dual Frequency Shifted Feed Back laser using an intra-cavity acousto-optical shifter [18]. This could lead to new and interesting applications.
Funding
Centre National de la Recherche Scientifique (CNRS); Université Grenoble Alpes (UGA).
Acknowledgments
I thank Doctor Marie Plazanet for lending me her high-speed LeCroy 3.5 GHz oscilloscope. I also thank the members of Jean-Louis Coutaz's group for their valuable advice in the field of THz and Erik Geissler for the proofreading of this manuscript.
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