Bolometer

Bolometric detectors have been used for far-infrared (FIR), submillimeter- (submm) and millimeter-wave (mm) astronomy for the past 40 years. A hot electron bolometer is a device, of which the resistance responds to the change of the electron's temperature when it absorbs incident radiation. A traditional bolometer consists of a heat-sensitive detection element mounted inside a heat sink and

physically supported by a thermally conductive physical supporter. The most common systems are helium-cooled Si, Germanium and InSb bolometer. It can measure the power of nW grade, but it losses all the information of phase and frequency. The usual method to get the power of THz radiation is to use Martin-Puplett interferometer, we will introduce the details later.

1.3.2 Photoconductive antenna detection

Since early 80’s, photoconductive (PC) sampling has been widely used to detect THz radiation[1]. Although its high signal to noise ratio, its speed is limited by the resonant character of the antenna structure and the finite carrier lifetime of the photocarriers[2]. Typically, the laser source is divided into two beams (pump and probe beam). When the pump beam illuminates the emitter, THz radiation is generated, then, THz and the synchronous probe beam illuminate the PC-antenna. THz radiation introduce the transient current and probe beam accelerate

1.3.3 Electro-Optic sampling

Recently, since Electro-Optic sampling has high bandwidth and is easy to implement, technique of Electro-Optic sampling became an alternative to PC detection.[9] Here, the Zinc-blende crystal was used to measure THz radiation based on the Pockels effect.[9] When we vary the temporal delay between pump and probe beam , the synchronous probe beam will probe the transient change of refractive index result from THz changing the refractive index. There is a trade-off in this method , thickness plays an important role in it, thick crystal will introduce longer interaction length but reduce the frequency response.

1.4 Objective

Due to the advantages of CW THz system, we want to build a continuous-wave THz system including CW THz source and the detection system. Otherwise, we try to understand the relationship between carry lifetime of the photoconductive antennas and the coherence length of CW THz radiation emitted from the photoconductive antenna. First of all, we use two laser diodes to be the beating source and to illuminate the THz emitter (photoconductive antenna) to generate CW THz. In order to measure the coherence length of the CW THz, we need to use Martin-Puplett interferometer and bolometer for detection. We also want to understand the mechanism of the saturation effect of the Large-Aperture photoconductive antenna

1.5 Organization of this thesis

There are four chapters in this thesis. We introduce the general conception of THz wave in Chap.1,then we give the basic theory of generation THz and the relationship between carry lifefime of the photoconductive antenna and coherence length of CW THz wave in Chap.2. At Chap.3 we give the experiment setup, results and analyses.

Finally, we make some conclusions and the future work.

ChapterⅡ Basic theory of THz wave

In this chapter, we will introduce the basic theory of generation CW THz using photoconductive antenna as the emitter. We also introduce the coherent characteristics of CW THz radiation and the detection system (Martin-Puplett polarization interferometer).

2.1THz wave generated by photoconductive antennas (current surge model)

Photodetectors generally consist of a semiconductor material which has a bandgap energy such that it is sensitive to light in a certain wavelength range.When the photoconductive antenna is illuminated by optical source, where the photon energy is greater than the bandgap of the semiconductor (substrate of the photoconductive antenna). The photon of light can cause the generation of an electron-hole pair which under an applied electric field causes a current to flow. And the expression can be described from the current-surge model.

Initially [12], the radiating source is defined as time-varying parameters, including charge densityρ

(

x,y,z,t

)

, current densityJv

(

x,y,z,t

)

, electric field^Er

(

^x,^y,^z,^t

)

, and magnetic flux ^Bv

(

^x,^y,^z,^t

)

. And then, it is necessary to construct Maxwell’s equation before deducing current-surge model.

Maxwell’s equation:

t

And then, some non-vector value, V, is induced in the equation.

From (2.6), set Next, the two inhomogeneous wave equations written in terms of A and V could also be deduced from the inhomogeneous Maxwell equations:

From (2.3)

E So that, (2.12) becomes as

J Finally, the two inhomogeneous wave equations expressed in (2.15) and (2.16) are demonstrated. The two equations are used to determine a functional, time dependent form of the radiated electric field in the far

field.

From (2.3), the continuity equation of the free carriers is obtained.

( )

⁼⁰ Actually, the current density in the bias photoconductor is strictly a transverse current (parallel to the surface of the photoconductor and perpendicular to the direction of propagation), so that

=0

•

∇ Jr

(2.18) Equation (2.17) and (2.18) imply that the charge density dose not vary in time and not contribute to the time-dependent radiated electric field. As a result, from (2.9) the electric field is

( )

A

( )

t The solution to the wave equation (2.15) and hence for the vector potential Av leads to the expression for the time-dependent radiated electric field Ev_rad =( trv, ) at a displacement rv from the center of the vacuum, Jv_s is the surface current in the photoconductor evaluated at the retarded time, and d ′a is the increment of surface area at a displacement

r r At the same time, the gap between the electrodes of the photoconductor is assumed to be uniformly illuminated by the laser.

Therefore, the surface current Jv_s can be assumed to be constant at all points on the surface of the emitter. And then, the radiated electric field can be written as Where A is the illuminated area of the emitter. It is considered that the radiation emitted (and detect) on axis (i.e. x=y=0), and let ⎟

⎠ An expression for the surface current

If we want to know the radiation power of the antenna, we can use a simpler equivalent circuit of the antenna shown in figure 2-1.

(a) (b)

Fig. 2-1 The structure of antenna (a), and the equivalent circuit (b).

Z

C G(t)

V

_b

The equivalent circuit equation can be written as: where G(t) is the conductance, C is the capacitance, Z is the radiation impedance.

Solve the equation (2.24), we can get:

] the respective pump powers, h₁ and h₂ are the external quantum efficiencies, W is the difference frequency, t is the photocarrier lifetime, R is the resistance of the THz load circuit, C is the photomixer capacitance, and e, h, and c are well-known physical constants. Using this CW photomixing equation, we can estimate THz power for the case of shaped pulses. Due to the high peak power of femtosecond pulses, THz intensity generated by the femtosecond pulses can easily exceed that generated by two single mode CW lasers. Another advantage is that the two frequency parts that are to be photomixed are inherently coherent, so that we can bypass the difficulty of phase-locking two ultranarrow band CW lasers.

The current surge model is widely accepted as a model describing the process of THz radiation generation in biased photoconductors.[1] In this method, the surface current density Js(t) of the photoconductive

Here,

σ

_s

( ) t

is the time-dependent surface conductivity,

E

_bias^and

E

_surf

( ) t

are the static bias field applied to the emitter and the waveform of generated THz radiation field observed on the surface of the emitter, respectively. From the boundary condition of Maxwell’s equations,

surf

( )

E t

is related to Js(t) as

( )

0

( )

surf

1

s

E t η J t

= − ε

+

(2.27) where

η

₀ is the impedance of vacuum and

ε

is the dielectric constant of the emitter medium. Combine (2.26) and (2.27), an expression for

surf

( )

E t

is obtained as

0 0

( ) ( )

( ) (1 )

s

surf bias

s

E t t E

t

σ η

σ η ε

= − + +

(2.28)

According to the relation between

σ

_s

( ) t

and the carrier density N(t), we can rewrite the surface field after illumination of the pump pulse is expressed as (assuming that decay of the carrier density due to recombination or trapping is slow and can be neglected in the time window of interest)

surf

( )

bias

sat

E t F E

F F

= − +

(2.29)

where

( ) F

^∞

I t dt

= ∫

−∞ (2.30)

is the pump fluence and the saturation fluence ,F_sat(t), is defined as Where R is the reflectance of the emitter and I(t) is the pump intensity.

The electric field of the focused THz pulse,

E

_focus

( ) t

, has been shown to be proportional to the time derivative of the surface. By assuming the pump light to be Gaussian as

It can be shown that the focused field is proportional to the normalized focused field,

E %

_focus

( ) t

Finally, the expression for the normalized surface field is obtained as

( )

2.2 Photomixing

The basic technique of generation CW THz wave is through photomixing which produces optical intensity beats at THz frequencies by mixing two single-mode lasers or mode beating within a single laser.

The combination of two waves with slightly different frequencies is equivalent to a wave which envelope is modulated by the difference frequency. The intensity-modulated beam will excite the electron-hole pairs in PC antennas then accelerated by the bias voltage applied to the PC antennas. The generated THz frequency is as the same as the optical beating frequency.

When two electric fields with slightly different frequencies propagate collinearly into biased PC antennas, beating signal will be radiated. Set two parallel, scalar electric fields as:

) (

)

( _{10 1 1}

1 t =E Cos wt+φ E

E₂(t)=E₂₀Cos(w₂t+φ₂) (2.36) Where E₁₀, E₂₀, w₁, w₂, f₁ and f₂ are the amplitudes, angular frequencies and constant phases of wave 1 and wave 2, respectively. And the total electric filed is the superposition of the two waves:

) (

) (

) ( ) ( )

(t =E₁ t +E₂ t =E₁Cos w₁t+φ₁ +E₂Cos w₂t+φ₂

E (2.37)

From the simulated curves of figure 2-2, we can see that the total electric field has the waveform with a slowly various envelope and a fast carrier frequency inside.

-400 -200 0 200 400

Fig. 2-2 The simulated curves of two wave with slightly different

frequencies. The thin curve is the sum of the two waves. The thick curve

is the plot of the wave with frequency of (w₁- w₂)/2

Because the PC antenna has photocarrier lifetime about 1 ps, so it can’t response the faster frequencies. The beating intensity needs to be time averaged:

space, T is the detector response time.

Substituting (2.39) into (2.38), the formula will become simpler:

2 ]} values will decrease rapidly.

Fig. 2-3 The plot of Sinc-function.

When x values larger then p (3.1415), the y values are small enough to ignore it. The laser frequency is about 10¹⁵ Hz, but the fast detector response time T is just about 10^-12 s. We can ignore these faster terms in equation (2.40), so the equation can be written as:

2 ] The first two terms are the average intensities of wave 1 and wave 2, respectively. W is the difference of angular frequency between two waves.

f is the phase difference of the two waves (figure 2-4).

Fig. 2-4 The beating intensity with an angular frequency of W. In the

simulation, we set I1 equals I2.

2.3 Coherence and Martin-puplett interferometor

2.3.1 Carry lifetime and Coherence length

0 5 10 15 20 25

lifetime of photoconductive antenna’s substrate and the coherence length of CW THz wave. First, we assume that the spectrum of the light sources are Gaussian shape. Assume that the line width of the LD (source) are the

same,δw.

Then, we can get the Fourier transform of Ei(ω). We only need the envelope decay term, so the E_i(t) become the last formula of equation (2.32).

Finally, follow the formula below, we can get the intensity beating signal of the CW source.

and the signal in frequency domain I(ω),

1

2 ( 1 2 )2 2 2( 1 2 )2 ( 1 2 )2 ( 1 2 )2

From the rate equation of carrier in the substrate of the photoconductive antennas

R is the reflectivity of the sample. From eq (2.23), we know that radiated THz field is proportional to the derivation of photocurrent with respect to the time Then we take the Fourier transform of the recombination of (2.46), (2.23) and (2.47)

Finally, we find the THz field like this formula

2 2

3.00E+011

Fig. 2-5 CW THz field at frequency domain (a) waveform with different carrier lifetime (b) saturation effect as increasing carrier lifetime(c) waveform with different line-width of the dual-wavelength

Simulation with different carrier lifetime (1, 10 and 100 picosecond), the central frequency of the dual-wavelength system were 3.606*10¹⁴ and 3.603*10¹⁴ Hz, the corresponding wavelength were about 830nm, and the line width of each laser diode was δw=30MHz. We find that the central frequency of the simulated CW THz radiation field was 0.3 THz, which was equal to the frequency difference of the dual-wavelength system.

Form Fig.2-5(a), we find that the line-width of the radiation with different carrier lifetime were about 84.68MHz, the corresponding

coherence length was above 350cm. As we increase the carrier lifetime of the PC antenna, the calculated amplitude of CW THz radiation waveform increases, but shows the saturation effect. We plot the peak amplitude of the CW THz radiation with carrier lifetime in Fig.2-5(b). It shows much clearer that the peak amplitude of the CW THz radiation saturated when the carrier lifetime is longer than 10picosecond. It also demonstrates that the substrate of the PC antenna with carrier lifetime below 10picosecond performed as the LT-GaAs PC antenna. We changed the linewidth of the dual-wavelength system and the THz waveform was shown in Fig.2-5(c).

The linewidth of the dual-wavelength system was from 30 to 50MHz, and the peak amplitude of the THz radiation was decreasing. From these mathematical analyses, we conclude that the carrier lifetime doesn’t relate to the line-width of the CW THz field, it means that carrier lifetime and the coherence length of the CW THz wave are almost independent.

2.4 Martin-Puplett polarization interferometer

The design of most interferometers used for infrared spectrometry today is based on the two-beam interferometer originally designed by Michelson in 1891. For the electromagnetic field of THz frequency range, Martin-Puplett polarization interferometer is the most usual ones, which is based on a concept originally produced by Martin and Puplett in 1969.

Historically, the Martin-Puplett1 polarizing interferometer has been the

particular importance in astronomical spectroscopy. For example, the modulation efficiency of a polarizing beamsplitter is both high and uniform over a wide spectral range. Martin-puplett interferometer mainly measures the Degree of Coherence function γ(

τ

), the following we will describe the details. The interferometer consisted of a wire grid polarizing beam-splitter rotated 45± relative to the polarization of the incident light wave. The reflected and transmitted light waves are of equal intensity and orthogonally polarized. Retro-reflectors in each arm rotate the polarization of the incident light 180±. The orthogonal transmitted and reflected light waves are recombined at the beamsplitter.

A final wire grid polarizer (analyzer) transmits components of the combined outgoing beams with the same polarization. The interferometer structure shows as figure 2-5

Beam divider

Polarizer Time delay

PM

PM

Fig. 2-6 The setup structure of Martin-puplett interferometer

The total field at the detector is composed of the two beams :

from ep (2.40) and ep (2.41), we computer the intensity at the detector

0 * The function I(t) stands for the intensity of one of the beams arriving at the detector while the opposite path of the interferometer is blocked.

For short laser pulses (sub-nanosecond), the detector automatically integrates the entire energy (per area) of the pulse since the detector cannot keep up with the detailed temporal variations of the pulse envelope. When the integration of (2.42) over time yields

0 *

( , ) 2 ( ) 2Re ( )

(2.55) describes the accumulated energy arriving to the detector after the Martin-puplett interferometer, and the

τ

dependence (path delay) is entirely contained in the function

γ τ ( )

.

Finally, we consider the continuous light source case (CW laser source)

2

The duration T must be large enough to average over any fluctuations present in the light source. So (2.56) can be rewritten

( , ) 2 ( ) [1 Re ( )] continuous source

d t t

I t τ I t γ τ

〈 〉 = 〈 〉 +

(2.58)

The degree of coherence function

γ τ ( )

is responsible for oscillations in intensity at the detector as the mirror in one of the arms is moved. The real part of

γ τ ( )

is analogous to cosω

τ

in (2-41).. For large delays, the oscillations tend to vanish as different frequencies individually interfere.

We define the coherence time to be the function of

γ τ ( )

and means the necessary amount of delay to cause

γ τ ( )

to quit oscillating, so the usual definition for the coherence time is

2 2

0

( ) ( )

c

d d

τ

^∞

γ τ τ

^∞

γ τ τ

−∞

≡ ∫ = ∫

(2.59)

and we can find the coherence length which is the distance that light travels duration the coherence time.

c

*

c

l ≡ c τ

(2.60)

Chapter.Ⅲ experiment setup and result

3.1 Dual-wavelength laser diodes system

3.1.1 Laser diodes performance

Our CW THz source are formed by two independent circular laser diodes (bluesky research PS025-00) with maximum output power 40mW and wavelength at 830nm. Our normal operation current is 110mA at 20 ^o

C

with the output power 40mW. The L-I curve of the laser diodes are showing in Fig.3-1 and Fig.3-2

0 20 40 60 80 100 120

0 5 10 15 20 25 30 35 40

Power (mW)

Current (mA) LD1 PS025-00

I_th=31.62mA

Fig.3-1 L-I curve of laser diode 1 (LD1), Ith=31.62mA

0 20 40 60 80 100 120 -5

0 5 10 15 20 25 30 35

Power (mW)

Current (mA) LD2 PS025-00

I_TH=32.04mA

Fig.3-2 L-I curve of laser diode 2 (LD2), Ith=32.04mA

The linewidth of LD1 and LD2 measured by Fabry-Perot interferometer are showing in Fig.3-3 and Fig.3-4, where their linewidth are 50 and 44MHz, respectively.

0 2 4

Amplitude (a.u.)

LD1 linewidth is about 29.3MHz FSR=2GHz

-0.015 -0.010 -0.005 0.000 0.005 0.010 0

2 4 6

Amplitude (a.u.)

Scan time (s)

LD2 linewidth is about 31.11MHz FSR=2GHz

Fig.3-4 Linewidth of LD2 measured by Fabry-Perot

In our experiment, we can get CW THz radiation with different central frequency by turning the wavelength of each LD. Therefore, by controlling the operation current and temperature, we can turn the wavelength difference between the two laser diodes. The accuracy of the LD driver and the Temperature controller are 0.1mA and 0.1 ^o

C

85 90 95 100 105 110

835.96 835.98 836.00 836.02 836.04

Wavelength (nm)

Current (mA) LD1

T=19^?C 0.00395nm/mA

19.0 19.5 20.0 20.5 21.0

836.06 836.08 836.10 836.12 836.14 836.16 836.18

Wavelength (nm)

T(^?C)

LD1 I=106.6mA 0.0525nm/^?C

(a) Temperature control (b) Current control Fig.3-5 LD1 wavelength shift (a) controlling current at 19^o

C

(b) controlling the temperature at operation current=106.6mA

85 90 95 100 105 110

835.38 835.40 835.42 835.44 835.46 835.48

Wavelength (nm)

Current (mA) LD2

T=19^?C 0.00381nm/mA

19.0 19.5 20.0 20.5 21.0

835.48 835.50 835.52 835.54 835.56 835.58

Wavelength (nm)

T(^?C) LD2

I=108.6mA 0.048nm/^?C

(a) Temperature control (b) Current control

Fig.3-6 LD2 wavelength shift (a) controlling current at 19^o

C

(b) controlling the temperature at operation current=108.6mA

Form Fig.3-5 and Fig.3-6, the wavelength shift caused by changing current are 0.00395nm/mA and 0.00381 nm/mA, respectively; the shift caused by shifting temperature are 0.0525nm/ ^o

C

and 0.048/ ^o

C

, respectively. Table 3-1 show the summary of the two LD

LD 1 LD 2

wavelength ~830nm ~830 nm

power 40mW @110mA 40mW @110mA

Line width 29.3 MHz 31.11MHz

Current vs. f 1.71 GHz/mA 1.65 GHz/mA T vs. f 22.75 GHz/∞C 20.8 GHz/∞C

Table 3-1 The characteristics of the two laser diodes

3.1.2 Dual-wavelength laser diodes (LD) system

Our dual-wavelength light source system is presented in Fig.3-7. It is composed by two frequency-independent laser diodes (bluesky research PS025-00) and some proper optics. The polarization of the LD is S polarization. The 40X objective lens are used to focus the spot size of the two LD, when light passed through the isolator, the polarization of the incident light will be rotated to 45

° C

to prevent the optical feedback from other optics, when the light passed through the half-wave plate, the polarization will be changed from linear polarization to elliptical polarization.

LD2 LD1

isolator

isolator PBS

PBS

λ/2 λ/2/2 λ/2 λ/2 λ

λ/2

(a) (b)

Fig.3-7 Dual-wavelength system (a) diagram of the system (b) the actual system

3.2 Photoconductive Antennas

Due to our purpose, we need to have two kinds of antennas (Low-Temperature grown GaAs and Semi-Insulating GaAs) with different carrier lifetime and the same structure. Carrier lifetime of Low-Temperature grown GaAs and Semi-Insulating GaAs are few and hundreds of pico-seconds and the structure are bow-tie structure.

1mm/θ =90^o θ

0.0 0.2 0.4 0.6 0.8 0.1

1

Intensity (a.u.)

Frequency (THz)

(c) (d)

Fig.3-8 (a) the actual structure of the antenna (b) the diagram of the antennas (c) frequency response of SI GaAs antenna (d) frequency response of SI GaAs antenna

3.3 Martin-Puplett Polarizing interferometer

In order to get the power spectrum of the CW THz radiation, we set up a Martin-Puplett interferometer, the whole setup is in Fig.3-9 (a). When the CW light source illuminates the photoconductive antenna, we use the method showing in Fig.3-9, the radiation from the bow-tie antennas is linearly polarized in the bow-tie direction, and its polarization is oriented so as to pass through the wire-grid polarizers at the input port of a Martin-Puplett interferometer. The interferometer consisted of two wire-grid polarizers with 45^°

C

polarization with respect to each other in order to divide the THz radiation into two parts, one of which was reflected by a fixed mirror and the other is reflected by a scanning mirror.

The interferometer signal at the output port is measured with a Silicon hot-electron bolometer cooled to 4.2 K. The laser beam is chopped at 187Hz and the modulated signal voltage from the bolometer is detected with a lock-in amplifier

Beam

divider Antenna

Si-lens

Time delay

Polarizer

Lock-in Amplifier

PM

PM

Bolometer

Fig.3-8 (a) diagram of Martin-Puplett interferometer

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