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The quantum cascade laser
Quantum Cascade Lasers (QCLs) are mostly aimed to replace frequency multiplier chains as LOs at frequencies higher than 3 THz. Figure 2.10 shows a zoomed picture of a QCL made by the MPQ (Materials and Quantum Phenomena) laboratory.
THz QCLs need to operate at cryogenic temperatures, usually between 10 K and 70 K (cf. Ren et al. ) which is less convenient than frequency multiplier chains. Moreover, QCL are not very frequency stable, are difficult to phase lock and are usually not continuously tunable (cf. Ren et al. ). As QCLs’ beam is not very Gaussian, the coupling with the mixer is not perfect and has losses. Figure 2.11 shows the output power of QCL and frequency multiplier chains as a function of frequency.
FIGURE 2.11: Output power of different kinds of LOs as a function of frequency (Picture from Hesler et al. ) Today, QCLs are only used as LOs for frequencies above 2.5 THz, where frequency multiplier chains do not emit enough power to pump the mixer. However, as the technology of QCLs evolve, it should be possible, in a near future, to have more stable QCLs with an operating temperature above 77 K, which would make them more convenient to use as LOs.
Most SIS and HEB mixers have only one input antenna for both LO and RF signals In this case, a diplexer is used to superimpose the RF and LO signals before they reach the mixer. This element is very important because its losses have a direct impact on the sensitivity of the whole receiver. It must efficiently superimpose the two signals and lose as little RF power as possible, while the LO power transmitted to the mixer must still be high enough to pump it. Two major diplexers are used in THz heterodyne receivers, the beam splitter and the Martin Puplett interferometer (MPI). The beam splitter is more convenient to use, but it loses a lot of LO power, while the MPI is more complicated to align but has less LO losses. These two diplexers are presented below, and the MPI is described in detail in Chapter 4, as it is an important part of our 2.6 THz heterodyne receiver.
The beam splitter
The most commonly used diplexer in heterodyne receivers is a beam splitter. It can split an incoming beam into a reflected beam and a transmitted beam. In the case of a heterodyne receiver, it receives both LO and RF beams, and reflects the LO beam while it transmits the RF beam. Beam splitters for THz frequencies are often made of Mylar. Depending on the thick-ness of the Mylar, the power reflection and transmission coefficients vary with frequency. Usually, the beam splitter is chosen to have a power reflection of the LO beam around 5 % or 10 %, while the RF beam is transmitted at 90 % or 95 %. This method is very convenient because the beam splitter is easy to align, and transmits most of the RF signal, which is what we are interested in for astronomical observations. However, at high frequencies, multiplier chain LOs do not emit a lot of power and it is difficult to pump the mixer. So, losing 90 % or 95 % of the LO power becomes a problem. Other more complex diplexers with a better efficiency exist, like the Martin Puplett interferometer (MPI), presented below.
The Martin Puplett Interferometer
The Martin Puplett interferometer (MPI) is a diplexer which can superimpose the LO and RF signals with very little losses, for both signals. The functioning of the MPI is extensively described in chapter 4, because it is an important part of our 2.6 THz heterodyne receiver. The MPI is composed of two wire grids, G1 and G2, and two roof-top mirrors T1 and T2, as shown in figure 2.12. An ellipsoidal mirror (MLO) is added to focus the LO signal.
The MPI has already been used as diplexer in several major heterodyne receivers, such as GREAT  and CONDOR . However, as it is a lot more difficult to align than a simple beam splitter, it is only used in THz heterodyne receivers for high frequencies, where there is little LO power available.
The IF chain and the spectrometer
At the output of the mixer, the intermediate frequency (IF) signal needs to be amplified and filtered before being processed by a spectrometer. The first amplifier, just after the mixer, is usually a low noise cryogenic amplifier because it is important to add as little noise to the IF signal as possible. Then, ambient temperature low noise amplifiers (LNA) and a bandpass filter are often used to amplify further the IF signal and filter it. Finally, a spectrometer is used to analyze the down-converted spectrum of the IF signal. Because of recent technological developments, digital Fourier transform spectrometers (DFTS) have become the standard spectrometers for heterodyne receivers. A DFTS uses an analog to digital converter (ADC) card to digitize the input signal, and a FPGA to perform a fast Fourier transform (FFT) of the data, in real time. The spectral data can be directly transmitted to a computer. With the increasing speed of the FPGAs and ADC cards, DFTS are improving fast and some 5 GHz bandwidth DFTS are currently available (ie. the second generation of DFTS from Omnisys company).
Our 2.6 THz heterodyne receiver
Description of our 2.6 THz heterodyne receiver
During this PhD, I built, tested and improved a 2.6 THz heterodyne prototype receiver (fig-ure 2.14), whose elements are described below.
• The LO: I use a 2.6 THz frequency multiplier chain from VDI (Virginia diodes Inc.) which emits a maximum of 2 µW.
• The mixer: For our tests, we used a HEB using a log spiral antenna which was designed and produced at LERMA and LPN laboratories and works well for frequencies up to several THz (cf. Delorme et al.  and Lefèvre et al. ). It uses a NbN (niobium nitride) bridge on a silicon substrate and is phonon cooled. However, the final mixer will be a HEB with a twin-slot antenna optimized for 2.5 to 2.7 THz. In both cases, we add a silicon lens in front of the HEB to focus the signal.
• The mixer bias supply: The bias supply for the HEB has been manufactured at LERMA, according to the plans elaborated at SRON to build the bias supply for the HIFI instru-ment of the Herschel satellite.
• The diplexer: A Martin Puplett interferometer (MPI) is used as diplexer. I have specif-ically designed it for our 2.6 THz receiver and it is extensively described in chapter 4.
• The intermediate frequency (IF) chain: The IF chain is composed of a cryogenic am-plifier, two warm amplifiers a bandpass filter and some attenuators to avoid saturating the last amplifier and reduce possible standing waves. The low noise cryogenic am-plifier was bought from Caltech university. Between 300 MHz and 4 GHz, and at a temperature of 21K, it has a gain of 35 dB to 43 dB and a noise temperature below 4 K. The warm amplifiers were bought from Miteq (model: AFS3-00100600 13-10P-4) and have a gain of 33dB to 33.5dB in our frequency range at ambient temperature. The [0.5 – 1.5] GHz bandpass filter selects the range where our receiver is the most sensitive.
• The spectrometer: I use a DFTS bought from RPG which has 8192 channels and a bandwidth of 1.5 GHz.
• The cryostat: I use a wet cryostat filled with liquid Helium.
• Windows and IR filters: I use a 1mm thick HDPE (High density polyethylene) win-dow for the cryostat followed by two sheets of Zitex® G104 as infra-red filter (The transmission properties of Zitex® were studied by Benford et al. ).
This configuration has been used for most of the experiments described in this thesis, with two occasional changes: The 2.6 THz LO has been sometimes replaced by a 1.4 THz or a 600 GHz LO, and a beam splitter diplexer was used with these lower frequency LO.
Table of contents :
2 Terahertz heterodyne receivers
2.2 THz heterodyne receivers in astronomy
2.2.1 Main characteristics of heterodyne receivers
2.2.2 Overview of existing THz heterodyne receivers
2.3 General principle of heterodyne receivers
2.3.1 The heterodyne principle
2.3.2 Sensitivity of heterodyne receivers
2.4 Description of the different elements of a THz heterodyne receiver
2.4.1 The mixer
2.4.2 The local oscillator
2.4.3 The diplexer
2.4.4 The IF chain and the spectrometer
2.5 Our 2.6 THz heterodyne receiver
2.5.1 Description of our 2.6 THz heterodyne receiver
2.5.2 Main aspects of this PhD
3 Stability of the heterodyne receiver
3.1.2 Influence of the noise on the optimal integration time
3.2 The Allan variance
3.2.1 Background and theory
3.2.2 Allan variance theory
3.2.3 Total power and spectral Allan variance
3.2.4 The calculation algorithm
3.3 Stability of our heterodyne receiver
3.3.1 Warm intermediate frequency chain and DFTS
3.3.2 Stability of the bias circuit and the cryogenic amplifier
3.3.3 Stability of the local oscillator and the HEB mixer
4 The Martin Puplett Interferometer (MPI)
4.2 Gaussian beam optics
4.2.1 Context and motivation
4.2.2 Electric field distribution of a Gaussian beam
4.2.3 Gaussian beam characteristics
4.3 Description of the MPI
4.3.1 Input of the MPI
4.3.2 Detailed description of the elements of the MPI
4.3.3 The rotation of the polarization in the MPI
4.3.4 The bandwidth of the MPI
4.4 Design of our MPI
4.4.1 Calculation of the ellipsoidal mirror (MLO)
4.4.2 Calculation of the grids’ required characteristics
4.5 Test and evaluation of each individual component of the MPI
4.5.1 The ellipsoidal mirror (MLO)
4.5.2 The polarizing grids
4.5.3 Efficiency of the roof-top mirrors
4.5.4 Air absorbance
4.6 Efficiency of the whole MPI
4.6.1 Presentation of the experiment
4.6.2 Different steps of the experiment
5 Phase gratings
5.1 Background and theory
5.1.2 Presentation of the phase gratings
5.2 The stepped phase gratings
5.2.1 Overview of the stepped phase gratings
5.2.2 Theory of Dammann gratings
5.2.3 Test of a transmissive Dammann grating
5.3 The Fourier grating
5.4 The Global phase grating
5.4.1 General presentation
5.4.2 Numerical calculation
5.4.3 Conversion of a phase profile into a grating’s surface
5.4.4 Electromagnetic simulations
5.5 Reflective and transmissive phase grating prototypes
5.5.1 Design considerations for the two prototypes
5.5.2 Numerical calculation
5.5.3 Design of the transmissive and reflective phase gratings
5.5.4 Electromagnetic simulations
5.5.5 Mechanical design
5.5.6 Geometrical measurements of the 2 prototypes
5.5.7 Electromagnetic simulation of the manufactured reflective grating
5.5.8 Test of the 2 prototypes
5.5.9 Noise temperature measurement of the receiver with a phase grating