VCSELs for Cesium-Based Miniaturized Atomic Clocks E-Book

Ahmed Al-Samaneh

• Herausgeber: Books on Demand
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 320

Veröffentlichungsjahr: 2015

Beschreibung

Frequency standards or clocks provide time references for a wide range of applications such as synchronization of communication networks, remote sensing and global positioning. Over the last couple of decades, demands on the data rates of many communication systems have substantially increased, imposing more restricted requirements on the stability of their timing devices. At the same time applications have become more mobile, increasing the demand for small and low-power clocks. Atomic clocks have provided the most stable frequency references for more than 50 years. However, the size and power requirements of microwave-cavity-based atomic clocks prohibit them from being portable and battery-operated. Hence, research on miniaturized atomic clocks (MACs) has been initiated by various research groups. A European research project on MACs, funded by the European commission started in 2008. This dissertation reports on the achievements within the European research project in the development of suitable lasers for such atomic clocks. Vertical-cavity surface-emitting lasers (VCSELs) are compelling light sources for MACs because of their low power consumption, high modulation bandwidth, and favorable beam characteristics. VCSELs must feature polarization-stable single-mode emission. Additionally, they must provide narrow linewidth emission at a center wavelength of about 894.6nm and be well suited for harmonic modulation at about 4.6GHz in order to employ coherent population trapping effect at the cesium D1 line. The polarization orientation of the emitted light of a standard VCSEL is a priori unknown. Polarization control is achieved by etching a shallow surface grating in the top Bragg mirror. For the purpose of integration with the clock microsystem, flip-chip-bondable VCSEL designs are realized. Such designs facilitate a straightforward mounting and make the electrical contacts high-frequency compatible.

Leseprobe

“Whoever treads a path seeking knowledge,

Allah will make easy for him the path to Paradise”,

The Prophet Muhammad (PBUH).

Acknowledgement

This dissertation would not have been possible without the help of many people. Firstly. I would like to express my sincere gratitude to my supervisor apl. Prof. Dr.-Ing. Rainer Michalzik, who gave me this great opportunity to do this work and to participate in a European collaborative research project involving several academic partners, international research institutes and many industrial enterprises with the target to realize the first European miniaturized atomic clock demonstrators. He was always a source of support and new ideas that have had a profound effect on this dissertation.

Special thanks go to all people at the Institute of Optoelectronics which I have gladly worked with during this dissertation, particularly, Wolfgang Schwarz who taught me how to process VCSELs, and always supported me with his vast expertise in microwave measurements, Dietmar Wahl who put much effort in growing many VCSEL wafers where reaching the Cs D1 wavelength was always challenging, my friend and office-mate Alexander Kern for his valuable advices to improve measurement setups, helping with SEM pictures and of course the very enjoyable time we spent together during our PhDs, Rudolf Rösch for his continuous support in dry etching, contact metallization and substrate thinning, Susanne Menzel for her great help in dealing with different chemicals in the cleanroom, Dr.-Ing. Jürgen Mähnß for reading and correcting the first draft of this dissertation, Alexander Hein for assistance with lifetime measurements and Anna Bergmann for her kind help with contact metallization.

I also thank very much all students who worked with me during the years of this PhD work and contributed strongly with their diploma, master and bachelor theses to the success of the atomic clock VCSELs. Namely, my thanks go to Simeon Renz, Andreas Strodl, Md. Jarez Miah and Mustafa Kazu. I would also like to thank Md. Tanvir Haidar, Sujoy Paul and Niazul Islam Khan for their great help in characterizing atomic clock VCSELs through their student jobs at the Institute of Optoelectronics.

I am very grateful to all people at the Institute of Electron Devices and Circuits at Ulm University for their support and assistance, particularly, Yakiv Men for performing the electron-beam lithography steps for all the grating VCSEL wafers and Tatyana Purtova and Gang Liu for their continuous assistance with microwave reflection measurements.

Many thanks go to all the project partners of MAC-TFC, especially Dr. Christoph Affolderbach from UniNE-LTF and Dr. Vincent Giordano from FEMTO-ST, who answered all the questions on the physics of miniaturized atomic clocks, enhancing greatly my understanding of the subject and Dr. Rahel Strässle and Dr. Yves Pétremand from SAMLAB at EPFL for providing me with microfabricated Cs vapor cells for the measurement of the absorption spectra presented in App. G.

I am very grateful to Dr.-Ing. Dieter Wiedenmann from Philips U-L-M Photonics and his team for their support especially with mounting VCSEL chips in TO cans. Acknowledgements also go to Dr. Pierluigi Debernardi from IEIIT-CNR Torino for performing simulations of grating VCSELs using his excellent model, Dr.-Ing. Marwan Bou Sanayeh from Notre Dame University who helped very much by processing VCSELs during his frequent visits as a guest scientist at the Institute of Optoelectronics.

My gratitude is also extended to the members of the PhD commission, apl. Prof. Dr.-Ing. Rainer Michalzik, Prof. Dr. Martin Hofmann from Ruhr-Universität Bochum, Prof. Dr. Ulrich Herr and Prof. Dr.-Ing. Albrecht Rothermel for all the efforts they exerted.

Finally, special thanks and appreciation to my beloved parents, my dear brother Samer and my dear sister Soha for their unconditional support and encouragement despite the long distance.

This dissertation was first published by Ulm University, Ulm in 2014.

Contents

Introduction and Motivation

Clocks and Frequency Standards: Concept, History, Miniaturization, and Applications

2.1 Key Aspects of Clocks

2.1.1 Accuracy

2.1.2 Stability

2.1.3 Quality Factor

2.2 Historical Prospective of Clocks

2.2.1 Mechanical Clocks

2.2.2 Quartz-Based Clocks

2.2.3 Microwave Atomic Clocks

2.3 Miniaturization of Atomic Clocks

2.3.1 Three-Level System and CPT Spectroscopy

2.3.2 Microfabricated Alkali Vapor Cells

2.3.3 Frequency Stability of MACs

2.3.4 Requirements on the Laser Source

2.4 Applications of MACs

Fundamentals of VCSELs

3.1 Device Structure and Properties

3.2 Threshold Conditions

3.3 Operation Characteristics

3.4 Temperature Behavior

3.4.1 Red-Shift Effect

3.4.2 Thermal Resistance

3.5 Dynamic and Noise Behavior

3.5.1 Rate Equations

3.5.2 Small-Signal Modulation Response

3.5.3 Intensity Modulation and Frequency Modulation

3.5.4 RIN

3.5.5 Emission Linewidth

3.6 Polarization Properties

3.7 VCSEL Applications

Design and Fabrication of VCSELs for Miniaturized Atomic Clocks

4.1 Adjustment of Layer Thicknesses

4.2 Design of the Active Region

4.2.1 Bandgap Energy of Bulk AlGaAs and InGaAs

4.2.2 Mechanical Strain Effect

4.2.3 Bandgap Renormalization

4.2.4 Relative Band Offset

4.2.5 Quantum Effect

4.2.6 Experimental Verification

4.3 Single-Mode Emission

4.4 Polarization Control

4.4.1 Concept of Surface Gratings for Polarization Control

4.4.2 Design of Surface Gratings

4.4.3 Simulations of Surface Grating VCSELs

4.5 Layer Structure

4.6 VCSEL Chip Design and Processing

4.6.1 Flip-Chip-Bondable Design

4.6.2 VCSEL Processing

Experimental Characterization of Atomic Clock VCSELs

5.1 Static Characteristics

5.1.1 Operation Characteristics and Emission Spectra

5.1.2 Polarization Control

5.1.3 Far-Field Properties

5.2 Dynamic Characteristics

5.2.1 Small-Signal Modulation Response

5.2.2 Intrinsic Modulation Behavior

Improved and Alternative Atomic Clock VCSELs

6.1 Modification of the Top Bragg Mirrors

6.2 Alternative Surface Grating Approaches

6.2.1 Regular Grating VCSELs

6.2.2 Inverted Grating Relief VCSELs

6.3 Reduction of Processing Complexity

6.4 Reliability Tests

Experimental Cesium-Based Atomic Clock Demonstrator

7.1 VCSEL Description and Packaging

7.1.1 Standard VCSELs

7.1.2 Inverted Grating Relief VCSELs

7.2 Laser Noise and Dynamics

7.2.1 Emission Linewidth

7.2.2 Relative Intensity and Frequency Noise

7.2.3 Modulation Sideband Characteristics

7.3 CPT Resonance Signal Measurement

Conclusion

Cesium Properties

A.1 Fine and Hyperfine Structure

A.2 Zeeman Splitting

MAC-TFC Consortium

Mask Layouts

VCSEL Processing

D.1 Flip-Chip-Bondable VCSELs with Thick Planarization Layers

D.2 Flip-Chip-Bondable VCSELs with Thin Planarization Layer (Simpler Processing)

VCSEL Epitaxial Structure

Experimental Measurement Setups

F.1 Polarization-Resolved Operation Characteristics and Emission Spectra

F.2 Far-Field Measurements

F.3 Small-Signal Modulation Response Measurements

F.4 RIN Measurements

Cesium Absorption Spectra

H List of Acronyms

List of Symbols

I.1 Mathematical Operators, Special Functions and Constants

I.2 Mathematical Symbols

I.3 Greek Symbols

Bibliography

Chapter 1

Introduction and Motivation

Frequency standards or clocks provide time references for a wide range of systems and applications such as synchronization of communication networks, remote sensing and global positioning. Over the last couple of decades, demands on the data rates of many communication systems have substantially increased, imposing more restricted requirements on the stability and accuracy of their timing devices. At the same time applications have become more mobile, increasing the demand for small frequency references with low power consumption.

Atomic clocks have provided the most stable frequency references for more than 50 years [1, 2]. However, the size and power requirements of microwave-cavity-based atomic clocks prohibit them from being portable and battery-operated. Hence, research on miniaturized atomic clocks (MACs) has been carried out by various research groups. The first demonstrations of MACs were done in 2004 separately by two research groups in the United States of America, led by the National Institute of Standards and Technology (NIST) [3] and Symmetricom [4]. A Joint European research project on MACs, funded by the European commission started in 2008 [5, 6]. This dissertation reports on the achievements within the European research project in the design, fabrication and characterization of suitable laser sources for such atomic clocks. MACs use the principle of all-optical coherent population trapping (CPT) excitation which does not require a microwave cavity [7, 8]. Owing to their enhanced stability and low power consumption compared to thermally stabilized quartz-based oscillators, MACs are becoming key elements for the above-stated applications and systems. The CPT excitation is obtained in an extremely compact cesium-based vapor cell of a few cubic millimeters volume which is illuminated by an intensity-modulated laser source at a GHz-range modulation frequency.

Vertical-cavity surface-emitting lasers (VCSELs) are compelling light sources for MACs because of their low power consumption, high modulation bandwidth, and favorable beam characteristics. Similar to their use in tunable diode laser absorption spectroscopy (TD-LAS) for regular gas sensing, VCSELs must feature strictly polarization-stable singlemode emission. Additionally, they must provide narrow linewidth emission at a center wavelength of about 894.6nm and be well suited for harmonic modulation at about 4.6GHz in order to employ the CPT effect at the cesium D1 line. VCSELs emitting at 894.6nm have been developed and employed in prototype atomic clocks [9, 10]. Those standard VCSELs with circularly symmetric resonators are often found to be polarizationstable. However, the stability cannot be guaranteed, especially after handling steps like soldering or bonding, which are necessary for microsystem integration and which might cause internal strain. Such unpredictable behavior can considerably reduce the yield of suitable devices from a fabricated wafer. In fact, owing to the cylindrical symmetry of the VCSEL resonator and the isotropic gain and reflectivity provided by the quantum wells and the Bragg mirrors, respectively, the polarization orientation of the emitted light of a standard VCSEL is a priori unknown. In the worst case, the orientation of the polarization can change during operation [11]. Therefore, several attempts have been undertaken in the past to lift the symmetry of the VCSEL structure and the isotropic property of the gain and reflectivity in the device in order to stabilize the polarization in a fixed direction [12]. Among all of these, the incorporation of a linear semiconductor surface grating at the outcoupling facet was found to be the most advantageous. The polarizing effect is induced by the difference in optical losses and thus threshold gains of modes polarized parallel or orthogonal to the grating lines.

The VCSELs for cesium-based MACs, designed and fabricated during the research performed for this dissertation, employ such pure semiconductor–air surface gratings as will be discussed thoroughly in the upcoming chapters. For the purpose of integration with the clock microsystem, flip-chip-bondable VCSEL chip designs are realized and developed. Such chip designs facilitate not only a straightforward mounting but also make the electrical contacts high-frequency compatible. Extensive static and dynamic VCSEL characterization has been performed along with several optimization cycles, supported by numerical simulations of the laser resonator.

The dissertation is organized as follows: first, general key concepts of clocks and frequency standards along with a brief historical overview on their development are introduced. Subsequently, the concept of atomic clocks, their performance, the necessity of their miniaturization, the essentiality of VCSELs as their laser sources and their main applications are discussed. The fundamentals of VCSEL design, operation and applications are presented in Chap. 3. The design of single-mode polarization-stable VCSELs emitting at 894.6nm wavelength suitable for cesium-based MACs is outlined in Chap. 4. The concept of surface gratings for polarization control is presented in the same chapter, where the design of the gratings is based on advanced electromagnetic simulations using a fully-vectorial three-dimensional model [13]. At the end of the chapter, the layer structure of atomic clock VCSELs, the chip design and the fabrication process are discussed. Static and dynamic characteristics of initial generations of atomic clock VCSELs are discussed in Chap. 5, before further improvements and alternatives of such VCSELs are presented in Chap. 6. In the same chapter, preliminary reliability tests of some VCSELs are reported. Investigations on some atomic clock VCSELs, proving their high-level performance and their validity as laser sources for MACs, are discussed in Chap. 7. Such investigations include characterizations of noise and harmonic modulation properties of individual stand-alone VCSELs as well as delineation of the CPT signal of a prototype atomic clock employing such VCSELs. Finally, a conclusion is given in Chap. 8.

Chapter 2

Clocks and Frequency Standards: Concept, History, Miniaturization, and Applications

In this chapter, some key concepts characterizing clock performance are discussed. A brief historical overview on the development of clocks and frequency standards is given. Atomic clocks show best performance in terms of accuracy and stability. However, portable battery-operated applications require miniaturization of the atomic clock to reduce its power and size requirements, as will be explained. Finally, some applications of miniaturized atomic clocks are presented.

2.1 Key Aspects of Clocks

Clocks or frequency standards are devices which are capable of producing stable and well known frequencies with a given accuracy. They can provide necessary timing references and signals covering a wide range of frequencies which are of a great concern for vast fields in sciences and technologies [2]. A clock consists of two parts, an oscillator which produces stable periodic events and a counter which counts these events and displays the time or frequency. The oscillator itself consists of two components, in particular, a resonator which generates the periodic events and an energy source which provides energy to sustain the stability of the periodic events [14,15]. Commonly, the performance of clocks is evaluated by three figures of merit, namely accuracy, stability and the quality factor of the employed resonator.

2.1.1 Accuracy

Accuracy is the degree of closeness of a measured value to its definition or its ideal value. Conversely, inaccuracy of a measured value is its offset from the ideal value. Practically, the clock accuracy is measured by determining the frequency offset of the periodic events generated by the oscillator from its ideal value known as nominal frequency fnom. The frequency offset can be measured in either the frequency or the time domain. A simple measurement in the frequency domain involves a frequency counter to count and display the frequency output of the clock under test. The relative frequency offset can be given by [15]

where fmeas is the reading from the frequency counter and fnom is the frequency labeled on the clock oscillator. is known also as the relative inaccuracy. Frequency offset measurements in the time domain involve phase comparison between the outputs of the clock under test and a reference clock which has to be highly accurate, e.g., the microwave atomic clocks which will be introduced in Sec. 2.2.3. The relative frequency offset in the time domain can be given by [15]

where Δt is the amount of the time deviation and τ is the measurement period. Assuming a clock accumulates 1 μs of time deviation with respect to a reference clock over a measurement period of 24 hours (i.e., 86,400,000,000 μs), the relative frequency offset or the relative inaccuracy has thus a value of .

2.1.2 Stability

Different from accuracy, which indicates how well a clock is set on its nominal frequency, stability indicates how well a clock can produce the same frequency offset over a given interval of time. In practice, clock stability is estimated by measuring frequency offsets over a given interval of time with respect to the mean frequency. In the simplest method, stability can be determined by estimating the standard deviation of a data set of measured frequency offsets. However, frequency offsets are usually a non-stationary data set, since they are time dependent. Thus the mean and the standard deviation often do not converge to particular values. Instead, the mean is alternating each time a new measured data point is added. For these reasons, a non-classical statistic method called Allan deviation is often utilized to estimate the fractional frequency stability as a function of averaging time τ. The Allan deviation [15]

is based on differences of the adjacent values rather than on the differences from the mean value (as is the case for a “true” standard deviation), where is a set of relative frequency offsets containing , and is their number. From (2.2), and (2.3) can be thus rewritten as [15]

where ti is a set of time measurements in the time domain containing , and is the number of data points in the ti set which are equally spaced by τ.

2.1.3 Quality Factor

The quality or Q factor of a resonator is defined as the ratio of the resonance frequency over the linewidth of the resonance. Resonators with high resonance frequency and narrow linewidth exhibit high Q factors. Clock accuracy and stability are closely related to the quality factor of the employed resonator. Today, the unit of “second” is defined in terms of a particular resonant frequency in the cesium (Cs) atom. Therefore, if a high-Q resonator has a resonance frequency of the Cs atom, then the clock employing such a resonator will accurately generate a “second” according to its definition. A high-Q resonator has a narrow resonance linewidth which constrains the oscillator to run always at a frequency near its resonance, i.e., higher Q factor leads to better stability. However, a clock with a high-Q resonator would show good stability but poor accuracy, if the resonance frequency of its resonator is not according to the definition of “second” [14]. Another definition of the Q factor is the ratio of the stored energy in the resonator to the energy loss per each oscillation cycle. Therefore, an ideal resonator with infinity Q factor would run for ever, given a single initial push [14].

2.2 Historical Prospective of Clocks

Sundial clocks or shadow clocks are considered to be the most ancient clocks mankind got to know in the past [14]. Such clocks count and keep the track of the axial spin of the earth around its polar axis and of its rotation around the sun. Both motions were employed as oscillators for this type of clocks. As early as 3500 B.C., ancient Egyptians had built obelisks that could be used to divide the day into several divisions [16]. Obelisks also showed the longest and shortest days of the year when the shadow at noon was the shortest and longest, respectively [16]. In addition to sundial clocks, Egyptians constructed water clocks that in their simplest form consisted of a bowl which is wide at the top and narrow at the bottom, and marked from inside with horizontal “hour” ticks. The bowl was filled with water that leaks out through a small hole in the bottom [14]. Until the 14th century, Chinese, Greeks and Romans continued to rely on water and even sand clocks [14].

2.2.1 Mechanical Clocks

Water and sand clocks suffered from many problems such as ability to freeze, poor accuracy, and limitation to measure only short time intervals. By the start of the 15th century, the focus was shifted to mechanical clocks. Among the different types of mechanical clocks, the pendulum clock was considered to be the most accurate and popular at that time. The pendulum was first realized as a device by the Italian researcher Galileo Galilei who credited that it could be used as a clock resonator. However, he did not construct a workable clock before his death in the year 1642 [14]. The first working pendulum clock was acknowledged to the Dutch physicist Christian Huygens, who built it in the year 1656. The advanced models of his clock were reported to have inaccuracies smaller than 10 s per day corresponding to a relative inaccuracy of using (2.2) [2, 14]. This was a dramatic improvement over the other clocks from the past. The accuracy and stability of such clocks is mainly limited by the thermal expansion of the mechanical parts including the pendulum length and the losses in the pendulum energy due to the air resistance and the clockwork. In 1721 the English inventor George Graham improved the pendulum clock by inventing a temperature-compensated pendulum known as the mercury pendulum, which compensates for changes in the pendulum length due to temperature variations. This has further enhanced the relative inaccuracy of the clock to be one second per day [2]. Over the century after, continuous improvements and refinements had culminated in very stable pendulum clocks like the ones manufactured by Siegmund Riefler in Germany at the end of the 19th century. His clocks achieved inaccuracies as low as 10 ms per day and became a timing standard in many astronomical observatories until the twenties of the previous century before being replaced by the Shortt clock [2]. In 1920 William H. Shortt constructed a clock with two synchronized pendulums, one of which is a master pendulum that swings as unperturbed as possible in a vacuum housing. The second is a slave pendulum which gives the master pendulum gentle pushes to maintain its motion, and also drives the hands of the clock. This allows the master pendulum to remain free from mechanical tasks that would disturb its regularity. The inaccuracies of the Shortt clocks were lower than 2 ms per day and lower than a second per year [2].

2.2.2 Quartz-Based Clocks

Quartz crystals were first employed in oscillators and clocks in the 1920s. Typical Q factors of quartz resonators show values between 105 and 106 [14]. The resonance of the quartz crystal is caused by the piezoelectric effect which is a mutual effect between the mechanical stress and the electric field produced by the crystal [14]. Specifically, the quartz crystal vibrates when applying an alternating electric field. At the same time, it generates an oscillating electric field because of its vibration. By employing suitable electronic circuitries, the piezoelectric effect causes crystal vibration and generates an electric signal of relatively constant frequency that can operate an electronic clock display. The first quartz-based clock was developed by the American scientist Warren A. Marrison in the year 1929, which was enclosed in a cabinet having a volume of 7.5m3 [14]. For several decades quartz wrist watches are available commercially. This gives an indication of the great breakthroughs done during the last century to miniaturize the electronic circuitries.

The frequency stability of a quartz-based oscillator in the short term is influenced by fluctuations of several ambient parameters, such as temperature, humidity, pressure, external magnetic fields, external vibrations, shocks, and noise in the electronic circuitries [2,14,15]. On the other hand, the frequency stability in the long term is influenced by crystal aging [14].

2.2.3 Microwave Atomic Clocks

2.3 Miniaturization of Atomic Clocks

Research on MACs has been carried out by various research groups. The first demonstrations of MACs based on CPT spectroscopy and MEMS fabrication techniques were done in 2004 collaboratively by two research groups in the United States of America, led by NIST [3] and Symmetricom [4]. Such frequency sources have recently become commercially available [32,33]. In 2008, the European commission started to fund a collaborative research project within its seventh framework programme (FP7) for research and technological development to realize the first European MAC. It was called MEMS atomic clocks for timing, frequency control & communications (MAC-TFC) [5, 6]. The objective of MAC-TFC was to develop and demonstrate all necessary technology to achieve a miniaturized battery-operated atomic clock having a volume less than 10 cm3, a power consumption not exceeding 155mW, and a short-term instability of over one hour averaging time [5,6]. In general, MACs can utilize the same vapors as microwave atomic clocks, namely rubidium (Rb) or cesium (Cs). They require laser wavelengths of 780.2nm (Rb D2 transition line), 795.0nm (Rb D1), 852.4nm (Cs D2), or 894.6nm (Cs D1) [9]. It has been shown that excitation on the D1 line results in higher contrast and narrower CPT resonance signals12 compared to the D2 line, for both Rb [34] and Cs [35]. For MAC-TFC, the Cs D1 line was employed.

Figure 2.1: Simplified Cs energy level diagram showing the D1 optical transition and the hyperfine splitting of the ground state 62S1/2 and the excited state 62P1/2 (a). Illustration of the optical spectra of a CW-operated VCSEL (b) and of an intensitymodulated VCSEL (c).

The MAC-TFC consortium, including 10 partners from academic, research and industrial sectors, possessed all required knowledge and technologies in order to achieve the MAC-TFC objectives. Names and locations of the consortium partners can be found in App. B.

2.3.1 Three-Level System and CPT Spectroscopy

CPT excitation is based on the quantum mechanical phenomenon that the population probability of the highest energy level in a three-level system (also known as a Λ system) can be drastically reduced via illumination by two coherent light sources whose emission wavelengths match the transition energies between the two lower energy levels and the upper level [7, 36]. Figure 2.1 (a) depicts a simplified Cs energy level diagram showing the D1 line. Due to the interaction between the total angular momentum of the electrons and total angular momentum of the nuclear spin, the ground level 62S1/2 and the excited level 62P1/2 are split into two hyperfine levels separated by about 9.192GHz and 1.167 GHz frequency differences, respectively. The hyperfine levels are identified by the quantum number F associated with the total atomic angular momentum F. As explained in App. A.1, to distinguish between the hyperfine structures of 62S1/2 and 62P1/2 levels, they are assigned quantum numbers F and F′, respectively, and take values of 3 and 4, as depicted in Fig. 2.1 (a). More information on the fine and hyperfine structure of the Cs energy system can be found in App. A.1. Two separate lasers can be used to achieve the CPT effect. However, since the two ground energy levels are very close, it is also possible to produce light with the two required wavelengths by modulating a single laser source with a radio frequency (RF) signal at a frequency that is equal to half of the Cs hyperfine ground splitting frequency. One then makes use of the modulation sidebands.

Figure 2.2: Typical CPT curve showing the transmitted optical power through a Cs vapor cell as a function of the VCSEL modulation frequency, where the VCSEL wavelength is 894.6nm.

VCSELs are ideal laser sources for this purpose owing to high-speed, high-efficiency modulation capability and low power consumption. Figures 2.1 (b) and (c) show schematic emission spectra of a VCSEL operating in continuous-wave (CW) mode and of an intensitymodulated VCSEL at 4.596GHz modulation frequency, respectively. The RF power is distributed over several modulation sidebands which are equally separated by the modulation frequency. The first-order sidebands at ±4.596 GHz can be employed for the operation of the atomic clock. Vapor of Cs atoms in the CPT condition shows reduced absorption or increased transparency at 4.596 GHz modulation frequency, as depicted in Fig. 2.2. Therefore this phenomenon is also called electromagnetically induced transparency (EIT) [37]. The contrast of the CPT signal is defined by the ratio of the signal amplitude and the direct current (DC) background noise as [9]

where the background noise arises from the photodetector noise and the laser intensity and frequency noise. CPT signals with high contrast and narrow linewidth13 ΔfCPT are highly desirable to achieve reduced short-term instabilities for CPT-based atomic clocks [29].

Figure 2.3: Simplified block diagram of a Cs-based MAC.

2.3.2 Microfabricated Alkali Vapor Cells

The heart component of a MAC is a microfabricated cell containing alkali vapor and a buffer gas atmosphere. Recently, FEMTO-ST15 has successfully microfabricated alkali vapor cells based on an extremely compact sealed cavity. The cell is formed by etching a silicon wafer and sealing it between two borosilicate glass wafers using anodic bonding in an atmosphere of a buffer gas (or gases) [38,39]. The cell vapor cavity has an optical window with 2mm diameter and 1.4mm length, as depicted in Fig. 2.4. After fully fabricating the cell, Cs vapor is generated by local heating of a side-cavity (of 1.65mm×1.65mm size) containing Cs metallic dispenser using a high-power infrared laser source [38, 39]. Reliability tests of the microfabricated cells have demonstrated excellent long-term stability. A major contribution of the CPT linewidth are the collisions of the alkali atoms with the cell walls [29]. To reduce such an effect, the vapor cell is filled with an inert buffer gas (e.g., Ne or Ar) or molecules (e.g., N2), thus the time between wall collisions can be prolonged and the residual Doppler broadening of the CPT signal can be reduced [40,41].

Figure 2.4: Microfabricated alkali vapor cells on a one-cent Euro coin [6].

2.3.3 Frequency Stability of MACs

For most applications of MACs the absolute clock frequency is of minor interest, since it can be calibrated. However, it is of great importance that the frequency does not change over time, i.e., it needs to have good stability, but not necessarily good accuracy [29]. Over short averaging times τ, the stability of many atomic clocks including MACs is characterized by white frequency noise, where can be expressed as [35]

with being the overall noise of the MAC at the RF modulation signal. There are many contributions of including shot and thermal noise of the photodetector, laser frequency and intensity noise, phase noise of the tunable oscillator and noise of the electronics. The proportionality of is commonly found in practice for short averaging times τ and is almost a standard way to represent , as mentioned at the end of Sect. 2.2.3. According to (2.6), it is desirable to have a high signal-to-noise ratio and a narrow linewidth ΔfCPT