Babol Noshirvani University of Technology 5 Babol Noshirvani

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tp=0. 1[ps]; f 0=5[THz] Babol Noshirvani University of Technology tp=1[ps]; f 0=5[THz] 8

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ﺍﺻﻮﻝ پﺎیﻪ ﺍی ﻟیﺰﺭ Absorption spontaneous emission stimulated emission Absorption, stimulated emission, and spontaneous emission are the fundamental phenomena near the resonance. Babol Noshirvani University of Technology

The key process governing radiation from these different types of lasers is stimulated emission. The elemental parts of a laser system include 1) a gain medium, 2) a laser cavity, and 3) a pump. The gain medium is a material system in which stimulated emission takes place. Population inversion, which means that more atoms or molecules in the gain medium are in the excited states than the lower energy states, is a prerequisite of stimulated emission. Babol Noshirvani University of Technology

Population inversion cannot be attained in a two-level system by any pumping schemes because, for an external perturbation, the rate of the transition from the lower to the higher level is exactly the same as the one from the higher to the lower level. In order to achieve a population inversion, most lasers adopt either a three level or a four-level system. Light is confined within the laser cavity by high reflectors. One of the reflectors is partially transmissive so that its transmitted radiation can be used as the laser output. Babol Noshirvani University of Technology

Femtosecond Lasers Ultrashort optical pulses are produced by femtosecond lasers. The predominant gain medium of femtosecond laser systems is titaniumdoped aluminium oxide (Ti: sapphire), in which Ti 3+ ions (∼ 0. 1%) substitute Al 3+ ions in a sapphire matrix. Ti: sapphire has several outstanding properties to produce ultrashort laser pulses: ü the gain spectrum is extremely broad (650 to 1100 nm) ü the crystal can take high optical pumping power (∼ 20 W) due to its high thermal conductivity Babol Noshirvani University of Technology

Ti: Sapphire Lasing Mechanism Babol Noshirvani University of Technology

Gain Materials for femtosecond Lasers Babol Noshirvani University of Technology

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Mode Locking Mode-locking is a technique by which a laser can be made to produce pulses of extremely short duration, on the order of picoseconds (10 − 12 s) or femtoseconds (10− 15 s). The basis of the technique is to induce a fixed phase relationship between the modes of the laser's resonant cavity. The laser is then said to be phase-locked or mode-locked. Interference between these modes causes the laser light to be produced as a train of pulses. Babol Noshirvani University of Technology

A laser's bandwidth of operation is determined primarily by the gain medium (known as the gain bandwidth. ) For example, a typical helium-neon (He. Ne) laser has a gain bandwidth of about 1. 5 GHz (about 0. 002 nm wavelength range at a central wavelength of 633 nm), whereas a (Ti: sapphire) solid-state laser has a bandwidth of about 128 THz (a 300 -nm wavelength range centered at 800 nm). The second factor to determine a laser's emission frequencies is the optical cavity (or resonant cavity) of the laser. Babol Noshirvani University of Technology

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the 128 THz bandwidth of the Ti: sapphire laser could support approximately 250, 000 modes. m When more than one longitudinal mode is excited, the laser is said to be in "multimode" operation. When only one longitudinal mode is excited, the laser is said to be in "single-mode" operation. Babol Noshirvani University of Technology

Laser Fabry-Perot Cavity: The resonant modes Babol Noshirvani University of Technology

Producing Short Pulses by Mode Locking The gain medium compensates for losses, and the saturable absorber mirror (SA) enforces pulse generation. Each time the circulating pulse hits the output coupler mirror (OC), a pulse is emitted in the output. Babol Noshirvani University of Technology

Mode Locking Babol Noshirvani University of Technology

Mode-Locked Ti: Sapphire Laser ﺷکﻞ ﺯیﺮ یک ﺳیﺴﺘﻢ ﻟیﺰﺭ ﻓﻤﺘﻮﺛﺎﻧیﻪ ﻣﺒﺘﻨی ﺑﺮ ﺑﻠﻮﺭ یﺎﻗﻮﺕ کﺒﻮﺩ v. )آﻠﻮﻣیﻨیﻮﻡ ﺍکﺴیﺪ آﻼییﺪﻩ ﺑﺎ ﺗیﺘﺎﻧیﻮﻡ( ﺭﺍ ﻧﺸﺎﻥ ﻣی ﺩﻫﺪ A typical mode-locked Ti: sapphire oscillator is characterized by ∼ 10 n. J pulse energy, ∼ 80 MHz repetition rate, and 10 -100 fs pulse duration. Babol Noshirvani University of Technology 34

Group Velocity Dispersion Compensation Babol Noshirvani University of Technology

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The PC Antenna Babol Noshirvani University of Technology 41

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Carrier Mobility Drift current is the movement of charge carriers due to an external electric field. Drift velocity is the speed of the charge carriers in the drift current: Babol Noshirvani University of Technology 51

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Zn. Te ﺩﺭ q ﺷﺪﺕ ﺗﺎﺑﺶ ﺗﺮﺍﻫﺮﺗﺰ ﺑﺮ ﺣﺴﺐ Babol Noshirvani University of Technology 79

Velocity Matching in Optical Rectification The optical field amplitude The dipole radiation field from the thin layer is proportional to the second-order time derivative of the polarization waveform. Babol Noshirvani University of Technology

ﺷﺮﻁ ﺗﻄﺒیﻖ ﺳﺮﻋﺖ ﻓﺎﺯ ﺩﺭ یکﺴﻮﺳﺎﺯی ﺍﺗیکی In general, the velocity matching condition is difficult to satisfy. When the optical wave is faster than the THz wave (n. T > n. O), the optical pulse leads the THz pulse by the optical pulse duration, τp, after a walk-off length of: Babol Noshirvani University of Technology 85

Velocity Matching in Optical Rectification For Efficient THz generation requires that the nonlinear medium must have a long walk-off length and that its thickness must be shorter than the walk-off length. Babol Noshirvani University of Technology

Velocity Matching in Optical Rectification exit surface entrance surface Temporal waveform of the subpicosecond THz radiation from a 0. 5 -mmthick Li. Nb. O 3 crystal by optical rectification of femtosecond pulses with a 620 nm wavelength. The optical pulse is faster than the THz pulse in Li. Nb. O 3: n. O=2. 3 and n. T = 5. 2 Babol Noshirvani University of Technology

Dispersion at Optical and Terahertz Frequencies In practice, nonlinear crystals are dispersive both at optical and THz frequencies: the refractive index n(ω) varies with frequency. Consequently, velocity matching in a dispersive medium can be achieved only for a certain THz frequency when the optical pulse envelope travels at the phase velocity of the monochromatic THz wave. The optimal velocity-matching condition for a broadband THz pulse is that the optical group velocity is the same as the phase velocity of the central frequency of the THz spectrum. Zn. Te is the most widely used nonlinear crystal for THz generation because the group refractive index near the optical wavelength λ=0. 8 μm (the operational wavelength of Ti: sapphire femtosecond lasers) matches well with the THz refractive index. Babol Noshirvani University of Technology 88

Dispersion at Optical and Terahertz Frequencies For Zn. Te: Babol Noshirvani University of Technology

THz Pulse Generated by Optical Rectification in Zn. Te 1. 0 -mm thick <110> Zn. Te crystal using 100 fs optical pulses at 0. 8 μm Babol Noshirvani University of Technology 91

Dispersion at Optical and Terahertz Frequencies The degree of velocity-matching is measured by the interaction length of optical rectification. For example, the interaction length is infinitely long for perfect velocity-matching. The effective interaction length is expressed as the coherence length: The coherence length is the distance over which the optical pulse propagates before leading or lagging the THz wave by a pi/2 phase shift. Babol Noshirvani University of Technology

Coherence length for different crystals@2 THz Babol Noshirvani University of Technology

Absorption of Electro-Optic Crystals at the Terahertz Frequencies Absorption coefficient of Zn. Te from 0 to 5 THz at room temperature. Babol Noshirvani University of Technology

Other EO Crystals The spectral bandwidth of THz generation in a nonlinear crystal is limited by absorption in the THz frequency region. Most of the crystals have strong phonon absorption peaks between 5 and 10 THz. Babol Noshirvani University of Technology 95

A Typical Setup for Free-Space EO Sampling Babol Noshirvani University of Technology 97

Free-Space EO Sampling Using Zn. Te Babol Noshirvani University of Technology 99

Free-Space EO Sampling Using Zn. Te Babol Noshirvani University of Technology 100

Free-Space EO Sampling Using Zn. Te Babol Noshirvani University of Technology 101

2 nd-Order NL Susceptibility of Zn. Te Babol Noshirvani University of Technology 103

Zn. Te Response Function: The optical Pulse duration is 100 fs at λ=800 nm : Babol Noshirvani University of Technology 104

ﺗﺸﻌﺸﻊ ﺗﺮﺍﻫﺮﺗﺰ ﺍﺯ ﺷﺘﺎﺏ ﺩﻫﻨﺪﻩ ﻫﺎی ﺍﻟکﺘﺮﻭﻧی A relativistic electron subject to accelerations emits radiation beamed in a narrow cone in the direction of its velocity. The power radiated per unit solid angle is given as One method to generate radiation using high speed electrons is to shoot the electron beam at a metal target, which rapidly decelerates the electrons which is called bremsstrahlung, meaning “breaking radiation”. The radiation from relativistic electrons undergoing circular magnetic field is called motion due to a synchrotron radiation. Babol Noshirvani University of Technology 106

ﺗﺸﻌﺸﻊ ﺗﺮﺍﻫﺮﺗﺰ ﺍﺯ یک ﺷﺘﺎﺏ ﺩﻫﻨﺪﻩ ﻫﺎی ﺍﻟکﺘﺮﻭﻧی ﺧﻄی Femtosecond laser pulses trigger an electron source (photocathode electron guns or semiconductor surfaces have been used) produce ultrashort electron bunches. Babol Noshirvani University of Technology 107

ﺗﺸﻌﺸﻊ ﺗﺮﺍﻫﺮﺗﺰ ﺍﺯ یک ﺷﺘﺎﺏ ﺩﻫﻨﺪﻩ ﻫﺎی ﺍﻟکﺘﺮﻭﻧی ﺧﻄی The total radiation power: Babol Noshirvani University of Technology 108

Synchrotron Radiation The cutoff frequency νc, beyond which the radiation power is negligible has the relation Given that R ≈100 m, the electron energy E should be 10 -100 Me. V for n to c be in the THz region. For the generation of pulsed radiation, many electrons are bunched together and move in packets. When the size of the electron bunch is comparable to the radiation wavelength, emissions from individual electrons superimpose in phase, and the total radiation power is proportional to the square of the number of electrons. Babol Noshirvani University of Technology 109

Synchrotron Radiation Radiated power in unit solid angle: The total radiation power: The angle of radiation cone: Babol Noshirvani University of Technology 110